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                                HANDBOOK
                                   OF

                         RAILROAD CONSTRUCTION;

                             FOR THE USE OF

                          AMERICAN ENGINEERS.

                             CONTAINING THE

                  NECESSARY RULES, TABLES, AND FORMULÆ

                                FOR THE

LOCATION, CONSTRUCTION, EQUIPMENT, AND MANAGEMENT OF RAILROADS, AS BUILT
                         IN THE UNITED STATES.

                         With 158 Illustrations


                                    BY
                             GEORGE L. VOSE,
                              CIVIL ENGINEER

 “RULES THEMSELVES OBLIGE US TO REFLECT, THAT WE MAY SEE WHETHER WE HAVE
                    NOT DEPARTED FROM THEM.”—NAPOLEON.

                          BOSTON AND CAMBRIDGE:
                        JAMES MUNROE AND COMPANY.
                                  1857.




       Entered according to Act of Congress, in the year 1857, by
                       JAMES MUNROE AND COMPANY,
     In the Clerk’s Office of the District Court of the District of
                             Massachusetts.


                               CAMBRIDGE:
                      ALLEN AND FARNHAM, PRINTERS.

------------------------------------------------------------------------




                                PREFACE.


The object of this work is to give in the plainest possible manner all
instructions, rules, and tables necessary for the location,
construction, equipment, and management of railroads.

As a general thing, American engineers are not educated for their
business; and when they do possess a knowledge of pure science, they are
at a loss how to apply it.

The reader is presumed acquainted with the elements of arithmetic,
geometry, algebra, and mechanics: being thus provided, he will, by a
perusal of what follows, be enabled to correctly proportion bridges, of
wood, stone, and iron: abutments, piers, retaining walls,
superstructure, and locomotive engines; and to plan and lay out,
execute, and estimate any description of work occurring upon railroads.

As the object has been more to be useful than original, the best
engineering writers and experimenters have been consulted; among whom
are,—Gauthey, Navier, Vieat, Tredgold, Barlow, Totten, Fairbairn,
Hodgkinson, Clark, and Lardner. Also a great number of reports by
American civil engineers upon railroad matters.

If assumptions take the place of demonstration, it will be on good
authority. Readers will bear in mind that the work is a “handbook,” and
not a “treatise.” It is intended more as an office companion than as a
text-book for students. It will give in all cases the actual numerical
result needed, whether it be the scantling of a bridge chord, the
thickness of a wall, or the dimensions of a locomotive boiler.

In connection, it will be found convenient to use the works of Trautwine
and Henck, on Field Work: of Lieutenant Smith, on Topography; Davies, on
Surveying; and Gurley, on the Use of Instruments.

Any one wishing a complete treatise on the principles of bridge
construction is referred to the excellent work of Hermann Haupt.

I take this opportunity of heartily thanking the engineers who in many
ways have aided in making the work, as it is believed, of some worth.

                                                                G. L. V.




                       GENERAL TABLE OF CONTENTS.


                                                    Page

                INTRODUCTION                           1

                 CHAPTER I.— RECONNOISSANCE           12

                        II.— SURVEY                   24

                       III.— LOCATION                 41

                        IV.— PRELIMINARY OPERATIONS   55

                         V.— LAYING OUT WORK          89

                        VI.— EARTHWORK                97

                       VII.— ROCKWORK                115

                      VIII.— WOODEN BRIDGING         122

                        IX.— IRON BRIDGING           192

                         X.— STONE BRIDGING          233

                        XI.— MASONRY                 248

                       XII.— FOUNDATIONS             261

                      XIII.— SUPERSTRUCTURE          272

                       XIV.— EQUIPMENT               302

                        XV.— STATIONS                403

                       XVI.— MANAGEMENT              413

                    APPENDIX                         459




                           ANALYTICAL INDEX.


                             INTRODUCTION.

                                                               PAGE

     Rise and progress of railroads                               1
     Influence of railroads                                       3
     Safety of railroad travelling                                5
     Preliminary operations                                       5
     Mechanical principles of locomotion                          6
     Determination of character of road                           7
     Gauge                                                        8
     General establishment of route                              10


                               CHAPTER I.

                            RECONNOISSANCE.
     General topography                                          12
     Barometrical levelling                                      18


                              CHAPTER II.

                                SURVEY.

     Topographical sketching                                     24
     General establishment of grades                             32
     Equating for grades                                         34
     Comparison of surveyed lines                                39


                              CHAPTER III.

                               LOCATION.

     Alignment                                                   41
     Final adjustment of grades                                  46
     Comparison of located lines                                 47


                              CHAPTER IV.

                        PRELIMINARY OPERATIONS.

     Specification                                               55
     Contract                                                    81
     Solicit                                                     84
     Bid                                                         85
     Comparison of bids                                          87


                               CHAPTER V.

                            LAYING OUT WORK.

     Slopes                                                      89
     Culverts                                                    90
     Masonry                                                     91
     Tunnels                                                     95


                              CHAPTER VI.

                               EARTHWORK.

     Form of railroad sections                                   97
     Excavation and embankment                                  104
     Transport of material                                      106
     Average haul                                               106
     Drainage                                                   109
     Method of conducting construction operations               111


                              CHAPTER VII.

                               ROCKWORK.

     Rock excavation                                            115
     Blasting and quarrying                                 115–117
     Tunnelling                                                 118


                             CHAPTER VIII.

                            WOODEN BRIDGING.

     Of the forces at work in bridges                           122
     Extension                                                  123
     Compression                                                123
     Cross strain                                               124
     Detrusion                                                  126
     Strength of materials                                      126
     Rules for practice                                         131
     Of the truss                                               139
     Of the arch                                                169
     Of the road-way                                            174
     Lateral bracing                                            175
     Pile bridging                                              178
     Trestling                                                  180
     Draw bridges                                               181
     Centres                                                    182


                              CHAPTER IX.

                             IRON BRIDGES.

     Nature and strength of iron                                192
     Classification of iron bridges                             194
     Iron truss frames                                          195
     Suspension bridges                                         203
     Boiler plate bridges                                       223


                               CHAPTER X.

                            STONE BRIDGING.

     Of the water-way                                           233
     Form of the arch                                           236
     Thickness of voussoirs                                     238
     Form and thickness of abutments                            239
     Form and dimensions of piers                               245


                              CHAPTER XI.

                                MASONRY.

     Stone                                                      248
     Cements, mortars, and concretes                            249
     Construction of arches, wings, and parapet                 253
     Culverts and drains                                        255
     Retaining walls                                            256


                              CHAPTER XII.

                              FOUNDATIONS.

     Pile driving, common system                                262
     Mitchell’s screw pile                                      266
     Potts’s atmospheric system                                 266
     Coffer-dam                                                 267
     Caisson                                                    269


                             CHAPTER XIII.

                            SUPERSTRUCTURE.

     Timber work                                                273
     Rail section                                               276
     Chairs and joints                                          282
     Frogs                                                      290
     Switches                                                   294
     Sidings and crossings                                      298
     Elevation of exterior rail                                 298


                              CHAPTER XIV.

                               EQUIPMENT.

                          PART I. LOCOMOTIVES.

     Introduction                                               302
     Birth and growth of the locomotive                         302
     The English locomotive of 1850                             304
     The American locomotive of 1855                            305
     General description                                        306
     Mechanical and physical principles                         312
     Resistance to the motion of trains                         312
     Traction and adhesion                                      316
     Fuel                                                       317
     Generation of steam                                        330
     Application of steam                                       336
     Boiler proportions and dimensions                          340
     Rules and tables for practice                              354
     Adaptation of locomotives to the movement of trains        360
     Classification of engines                                  371


                              PART SECOND.

                                 CARS.

     Wheels and axles                                           396
     Classification of cars                                     400
     Retarding of trains                                        401


                              CHAPTER XV.

                               STATIONS.

     Classification of buildings                                403
     Location of buildings                                      403
     Terminal passenger house                                   403
     Terminal freight house                                     405
     Engine house and appurtenances                             405
     Way passenger and freight house                            407
     Wood shed and tank                                         407


                              CHAPTER XVI.

                              MANAGEMENT.

     Organization of employees                                  413
     Duties of employees                                        415
     Number of trains to be used                                418
     Amount of service of engines                               418
     Expenses, receipts, profits                                420
     Express trains                                             428
     Comparative cost of working heavy and light trains         434
     Branch roads                                               436
     Reproduction of road and of stock                          437
     Working railroads by contract                              439
     Classification of freight                                  439
     Time tables                                                443
     Locomotive registers                                       444
     Electric telegraph                                         454
     New York and Erie Railroad                                 456

                               APPENDIX.

     A.—Decimal Arithmetic                                      459
     B.—Algebraic formulæ                                       461
     C.—Weights and measures                                    464
     D.—Value of the Birmingham gauges                          465
     E.—Locomotive boilers                                      466
     F.—Effect of grades on the cost of working                 468
     G.—Form for a locomotive specification                     471
     H.—Relative cost of transport by railroad and by stage     476
     I.—Form for experimental trips with locomotives            478
     K.—Proper weight for locomotives                           479




                ADDITIONS, ALTERATIONS, AND CORRECTIONS.


The reader is particularly requested to apply the following errata
before perusing the work. They are partly mistakes in printing, and
partly errors in the original MS. The only excuse the writer can offer
for the number is, that, being engaged in Missouri, while his publishers
were in Boston, he has been prevented from seeing a single proof-sheet
in time for its correction.

  Page 5, line 7, for “499.999,” read “499,999.”

  — 5, l. 9, for “49.999,” read “49,999.”

  — 10, l. 1, for “can be,” read “can never be.”

  — 12 to 23, headings, for “reconnoitre,” read “reconnoissance.”

  — 18, l. 24, for “36.9,” read “36.8.”

  — 19, l. 6, for “table B,” read “table D.”

  — 24, l. 1, for “any thing,” read “every thing.”

  — 25, l. 17, for “horizontal line m m m,” read “line 1, 2, 3,” etc.

  — 26, l. 2, for “land,” read “level.”

  — 27, l. 1, for “at the place,” read “at the right place.”

  — 28, l. 29, for “reconnoitre,” read “reconnoissance.”

  — 30, l. 3, for “A _c d_ B,” read “A C D B.”

  — 32, l. 2, the point _m_ in the cut, is one whole division above C;
        it should be only three fourths of a division.

  — 38, l. 10 from bottom, for “276,” read “268.”

  — 39, l. 10 from bottom, for “142.13,” read “143.13”; and last line,
        for “58.46,” read “48.46.”

  — 40, l. 7, for “10310,667,” read “10,277,333.”

  — 42, l. 9, for “Thus,” read “These.”

  — 42, l. 8 from bottom, for “2°.81 or 2° 48′.6” read “2°.86 or
        2°.51.6.”

  — 43, l. 27, for “Hencke,” read “Henck.”

  — 47, 48, 49, for “McCullum,” read “McCallum.”

  — 47, l. 18, for “distance,” read “resistance.”

  — 48, l. 6, for “infringing,” read “impinging”; line 9, for
        “slacking,” read “shackling”; l. 8 from bottom, for
        “increased,” read “increases.”

  — 50, l. 17, for “110 + 15.60,” read “110 + 15.62.”

  — 52, l. 15, for “45.59,” read “45.49”; also l. 17, for “1132,” read
        “11.32.”

  — 58, l. 10, for “of size,” read “and size.”

  — 58, l. 5 from bottom, for “one cent,” read “/100 of a cent.”

  — 61, l. 3, for “are necessary,” read “are not necessary.”

  — 63, l. 28, for “stretches,” read “stretchers.”

  — 65, l. 15, for “spanded,” read “spandrel.”

  — 71, l. 6 from bottom, for “left,” read “let.”

  — 73, l. 19, for “chains,” read “chairs.”

  — 74, l. 5, for “across ties,” read “on cross-ties.”

  — 74, l. 12, for “28 inches,” read “27 inches.”

  — 75, l. 18, for “land,” read “haul.”

  — 76, l. 8, for “top,” read “bottom,” and for “charred when,” read
        “charred where.”

  — 76, l. 11, for “twopenny,” read “tenpenny.”

  — 78, l. 1 and 2, for “base,” read “basis.”

  — 84, l. 13, for “as,” read “or.”

  — 89, l. 6, for “Whenever,” read “Wherever”; l. 12, for “Letting,”
        read “Setting.”

  — 90, l. 4, for “cost,” read “cut.”

  — 93, l. 6, for “37 and 38,” read “36 and 37.”

  — 95, l. 1, for “beach,” read “bench”; l. 3, for “to so,” read “so
        to”; l. 13, for “b being 10 ft. back of 2 is ... 100.00,” read
        “b being 10 ft. back of 2 is 0.1 ft. higher than 2, or ...
        100.10.”

  — 102, l. 1, head of middle col., for “Slopes 1¼,” read “Slopes 1½.”

  — 103, l. 4 from bottom, for “and ten feet,” read “and one end ten
        feet.”

  — 104, l. 9, for “any,” read “very.”

  — 108, l. 9, for “Elwood,” read “Ellwood.”

  — 115, l. 5, for “a loam,” read “a berm”; l. 16, for “a rent,” read
        “a vent.”

  — 117, l. 7, for “volcanic,” read “voltaic.”

  — 117, l. 9, for “Round Drum,” read “Round Down.”

  — 117, l. 18, for “Col. Puseling,” read “Col. Pasley.”

  — 118, l. 2, for “Maillefaut,” read “Maillefert.”

  — 118, l. 16, for “insert,” read “invert.”

  — 118, l. 25, for “quointed,” read “grouted.”

  — 119, l. 30, for “furnished,” read “finished.”

  — 120, Table, for “Nochistingo,” read “Nochistongo”; for
        “Supperton,” read “Sapperton”; and for “Black Rock, W. S.”
        read “Black Rock, U. S.”

  — 121, l. 19, for “Belchingly,” read “Blechingly.”

  — 125, in table at bottom, for “90/69,” read “90/66,” and for “140,
        20/140, 20/160 or 0.13,” read “111, 20/111, 20/131, or 0.15.”

  — 126, l. 1, for “extensive,” read “extensile.”

  — 127, l. 10, for “67,200,” read “65,251.”

  — 127, l. 26, for “Hodgekinson,” read “Hodgkinson.”

  — 128, l. 4, for “12000,” read “11000.”

  — 128, l. 15 and 22, for “Hodgekinson,” read “Hodgkinson.”

  — 129, l. 5, for “12000,” read “11000.”

  — 129, l. 2 from bottom, for “Sun Wood,” read “Ironwood.”

  — 130, l. 7, for “_WL^2_ = 4_Sbd^2_,” read “_WL_ = 4_Sbd^2_.”

  — 131, l. 9, for “wood 143,” read “wood 133.”

  — 134, in art. 164, for “700,” read “952.”

  — 136, for example there given, place the following:—

      Span   30 feet,           Whence—
      Length 34 feet,           Length       34 feet,
      Load   10 tons at centre. Span         30 feet,
                                Depth        25½ inches,
                                Lower flange 32.58 square inches,
                                Upper flange 5.34 square inches,

             _a_ = (6 × 10 × 12 × 30)/(26 × (34 × 12)/16) = 32.58

        and 32.58/6.1 = 5.34.

  — 141, last line, Fig. 63 A was omitted; it is the same as fig. 102,
        page 200, inverted.

  — 142, last line, for “span,” read “spans.”

  — 146, head of col. 7, for “Top Washer,” read “Thickness of Washer.”

  — 150, after line 9, Figs. 67 D and 67 E (page 153) should be
        inserted.

  — 151, l. 3, for “_W_ = 2249,” etc., read “_W_ = 2240,” etc.

  — 151, l. 18, for “opposite to 31,416, is the diam. 1⅝,” read
        “opposite to 41,415, is the diam. 1⅞.”

  — 151, l. 19, for “1⅝,” read “1⅞.”

  — 154, last line, for “tubular,” read “tabular.”

  — 156, l. 4 from bottom, for “washer band,” read “washer used.”

  — 164, l. 10 to 14, inclusive. The first number of ratios should be
        20 instead of 15.

  — 166, l. 11, for “69 B,” read “69 A.”

  — 171, head of col. 5 of table, for “Rod of Arch,” read “Rad. of
        Arch.”

  — 173, l. 25, for “ability,” read “stability.”

  — 173, l. 32, for “Whence,” read “Where.”

  — 175, l. 8, for “triangular,” read “diagonal.”

  — 178, l. 3, for “article,” read “outside.”

  — 184, l. 4 from bottom, for “barriers,” read “voussoirs.”

  — 187, fig. 96 is upside down; also, fig. 97, page 188, and fig. 98,
        page 189.

  — 193, l. 4, col. 3 of table, for “.00000675,” read “.00000685”;
        also, l. 16, col. 5, for “straining,” read “shearing”; l. 7
        from bottom, for “15,000,” read “18,000;” and l. 6 from
        bottom, for “75,000,” read “105,000.”

  — 199, l. 7 from bottom, for “20,132,” read “20,312.”

  — 200, l. 4, for “A C,” read “A G”; and l. 6, for “that on A R,”
        read “that on A K.”

  — 202, l. 7, for “on page 193,” read “on page 138.”

  — 204, l. 5 from bottom, for “varied line,” read “versed sine.”

  — 207, l. 5 and 6, for “F G, G E, in place of E F, E C,” read “G L,
        G E, in place of F L, F C.”

  — 210, in place of “_f′_ = (π_F_)/(4_ph_),” put “_D_ = √(¾[_V^2_ –
        _d^2_]) – √(¾[_l^2_ – _d^2_]).

        where _D_ = depression,
              _l_ = half length of curve before elongation,
              _V_ = half length of curve after elongation,
              _d_ = half distance between points of suspension.” Omit
                 the remainder of the paragraph.

  — 211, omit the 6th and 7th lines, and in place of formula there
        given, use that on page 210, (as corrected,) _V_ being the
        length of semi-curve as elongated by heat instead of by
        tension; the elongations, both by heat and tension, being
        found by table on page 193.

  — 212, l. 2, for “510.69,” read “510.80,” which result, of course,
        runs through the whole example.

  — 213 and 214. The remarks under “Anchoring Masonry,” are evidently
        wrong throughout: 1st, the whole tension should be divided by
        _two_, instead of _four_, as half of the whole tension acts at
        each point of suspension; 2d, no reduction should be made for
        the direction of the pulling force. One half of the tension is
        3,321,250 lbs.; which is resisted by a column of masonry of
        3,321,250/160 = 20,758 cubic feet, or 20 × 20 × 52 feet, or by
        a mass 15 × 15 × 91 feet.

  — 214, l. 6, for “561,527,” read “562,542.”

  — 215, l. 14 from bottom, for “STIFFENING TOWERS,” read “STIFFENING
        TRUSSES.”

  — 225, l. 14, for “194,” read “193.”

  — 226, l. 3, for “see page 128,” read “see page 193.”

  — 227, l. 4, for “detensional,” read “detrusional.”

  — 228, in place of equations at l. 16, put “_R_ × _a_ = _R′_ × (2
        _d_ × _t_)”,

                   whence _d_ = (_R_ × _a_)/(2_R′_ × _t_);
                    where _a_ = area of rivet,
                          _d_ = distance,
                          _t_ = plate thickness.

  — 229, in art. 242, the strengths of “wrought iron,” have been taken
        for those of “boiler plate”; that is, 11,000 for 7,500, and
        15,000 for 12,740, which is wrong.

  — 231, l. 21, for “chopped,” read “dropped.”

  — 234, l. 4, for “joint,” read “just.”

  — 235, l. 14, for “0.016 feet,” read “0.047 feet.”

  — 236, l. 9, for “care,” read “ease.”

  — 237, l. 3 from bottom, for “representing,” read “separating.”

  — 241, l. 2, for “localities,” read “locality.”

  — 242, l. 7, omit “and _c_ _e_, the parapets.”

  — 243, l. 9, for “embankment,” read “abutment.”

  — 244, l. 9, for “is thus,” read “is found thus.”

  — 245, l. 17, for “latter,” read “batter.”

  — 249, l. 23, for “common hydraulic,” read “common mortar,
        hydraulic.”

  — 249, l. 27, for “argyle magnesia,” read “argil, magnesia.”

  — 251, l. 16, for “7½ to 2,” read “1½ to 2.”

  — 254, last l., for “corners,” read “courses.”

  — 256, l. 13, for “formed,” read “found.”

  — 258, art. 276, in place of “20/2 × 15 × 1 × 100 × 20/3,” put “20 ×
        15 × 1 × 100 × 2 × 20/3,” where 2 represents the ratio between
        C^{_a_} 6, and 6–2; thus, 20 × 15 × 1 × 100 × 6.6/12 × 20/3 =
        111,111, for the overthrowing force in place of 100,000. The
        overthrowing force is thus large, because the maximum weight
        of earth has been assumed to press against the wall with its
        whole force, no allowance being made for friction. In
        practice, 4/10 of the height has been found amply thick for
        walls retaining ordinary earth.

  — 262, last l. but one, for “superstratum,” read “substratum.”

  — 264, in example, l. 5, for “26,667,” read “48,000.”

  — 266, l. 25, for “Godwin,” read “Goodwin.”

  — 266, l. 26, for “There, sands,” read “These sands.”

  — 267, l. 22, for “bottom,” read “proper level.”

  — 281, l. 4 from bottom, for “curve,” read “cone.”

  — 282, l. 20, for “Daniel,” read “David.”

  — 282, l. 4 from bottom, for “cup,” read “cap.”

  — 284, l. 10, and 285, l. 8, for “compressed rails,” read “compound
        rails.”

  — 285, l. 5, for “extension,” read “extensile.”

  — 289, invert col. 1 of table, so that it shall read—

                At 100° place the rails in contact.
                At 90° at a distance of .00136 feet, or 0.016 inches.
                At 80° at a distance of .00272 feet, or 0.032 inches
                   Etc.

  — 289, last l., for “levelled,” read “bevelled.”

  — 291, last l., for “_a c_, 4.8,” read “_a c_, L 8.”

  — 292, l. 9, for “_e h_ and _d k_,” read “_e L_ and _d k_”; same p.
        l. 6 from bottom, for “_a_, 9 is three, etc.” read “_a b_ is
        three,” etc.

  — 293, l. 6 and 7, for “_i g_, _e h_, _b b_, 8, 9, _A s_ 79,” read
        “_i g_, _e h_, _a c_, _b c_.”

  — 296, l. 14, for “_R^2_ – (_R_ – 8)^2,” read “_R^2_ – (_R_ –
        _g_)^2.”

  — 303, art. 299, for “M. Leguire,” read “M. Seguin.”

  — 306, l. 2, for “R. R. & G.,” read “R. K. and G.”

  — 314, l. 2, for “D. R. Clark,” read “D. K. Clark.”

  — 320, l. 1, for “Railroad, three pounds (Pennsylvania),” read
        “Railroad (Pennsylvania), three pounds.”

  — 320, l. 7, for “coal,” read “coke.”

  — 331, near bottom, for “The area is, therefore,

 Sides, twice length, etc., read “Sides, twice length by height, etc.,
 Back, twice height, etc.,       Back, height by width, etc.,
 Front, twice height, etc.,      Front, height by width, etc.,
 Top, twice length, etc.,”       Top, length by width, etc.”

  — 334, l. 15, for “44.7 lbs.,” read “14.7 lbs.”

  — 335, l. 7, for “Railway Mechanics,” read “Railway Machinery.”

  — 335, l. 10, for “two velocities,” read “low velocities.”

  — 336, last l., for “entering part,” read “entering port.”

  — 341, l. 11, for “properties,” read “proportions.”

  — 341, last l., for “Nollan,” read “Nollau.”

  — 346, l. 17, for “part,” read “port,” and for “construction,” read
        “contraction.”

  — 355, l. 7, for “6300,” read “5170”; and l. 9, for “16,905,” read
        “15,775.”

  — 363, l. 17, for “44 × 2 = 80,” read “44 × 2 = 88.”

  — 363, l. 18, for “54½ × 3 = 103½,” read “54½ × 3 = 163½.”

  — 367, l. 16, for “15.0/10,” read “15.0/16,”

  — 368, l. 15, for “_u_ = 135,” read “_n_ = 135,” etc.

  — 370, l. 7, for “feet,” read “per cent.”

  — 376, for “19090,” read “19050.”

  — 384, in last part of example, for “5280/(4½ × 3.1416) × 4 =
        37300,” read “25 × 5280/(4 × 3.1416) × 4 = 37348.”

  — 421, bottom line, for “decision,” read “division.”

  — 423 and 424, in table, for “count,” read “cost.”

  — 427, l. 32, for “which,” read “we.”

  — 428, l. 4, transpose “Dr. Lardner, (1850,)” to the end of line 3.

  — 443, l. 28, for “valuation,” read “solution.”

  — 446, l. 11, for “attained,” read “obtained.”

  — 459, l. 20, for “Hectametre,” read “Hectometre.”

  — 459, l. 21, for “Ridometre,” read “Kilometre.”

  — 461, l. 7, for “less than _a_, or _o_,” read “less _a_, or 0.”

  — 468, l. 30, for “fractions,” read “functions.”

  — 474, l. 18, for “Balbett,” read “Babbitt.”

  — 479, l. 10, for “one sixth, with much less,” read “one sixth; with
        sand, much less.”




                                HANDBOOK

                                   OF

                         RAILROAD CONSTRUCTION.




                             INTRODUCTION.


  “They build not merely roads of earth and stone, as of old, but they
  build iron roads: and not content with horses of flesh, they are
  building horses of iron, such as never faint nor lose their
  breath.”—DR. BUSHNELL.


                    RISE AND PROGRESS OF RAILROADS.

1. In 1825, the Stockton and Darlington Railroad (England), was opened.

In 1827, the Quincy (of Massachusetts), and Mauch-Chunk (Pennsylvania),
were completed.

In 1829, the Liverpool and Manchester road, (England), was finished.

In 1833, a road was opened from Charleston, (South Carolina), to Augusta
(Georgia).

In 1840, Belgium opened 190 miles of railroad.

In 1843, the railroad from Paris to Rouen (France), was completed.

In 1844, Belgium finished her system of 347 miles.

In 1846, Russia opened a railroad from the Wolga to the Don.

In 1847, Germany had in operation 2,828 miles.

In 1852, the Moscow and St. Petersburg road was finished.

2. In 1856, the United States of America had in operation 23,000 miles,
and in progress 17,000 miles; employing 6,000 locomotive engines, 10,000
passenger and 70,000 freight cars; costing in all about 750,000,000 of
dollars; running annually 114,000,000 miles, and transporting 123½
millions of passengers, and 30 millions of tons of freight per annum;
performing a passenger mileage of 4,750,000,000, and a freight mileage
of 3,000,000,000.

  3. By mileage is meant the product of miles run, by tons or by
  passengers carried. Thus, 500 persons carried 100 miles, and 750
  persons carried 75 miles, give a passenger mileage of

                    500 × 100 + 750 × 75 = 106,250.

4. The rate of progress in the United States has been as follows:—

                      In 1828, there were 3 miles.
                      In 1830,           41 miles.
                      In 1840,        2,167 miles.
                      In 1850,        7,355 miles.
                      In 1856,       23,242 miles.

At the present time, January 1, 1857, there is probably, in round
numbers, 25,000 miles of completed road, or enough to extend entirely
around the world. As regards the ratio of completed road to population,
and as regards the actual length of railroad in operation, the United
States stand before any other country.


                        INFLUENCE OF RAILROADS.

5. The effect of a judicious system of railroads upon any community is
to increase consumption and to stimulate the production of agricultural
products; to distribute more generally the population, to cause a
balance between supply and demand, and to increase both the amount and
safety of travelling. It is stated that within two years after the
opening of the New York and Erie Railroad, it was carrying more
agricultural produce than the entire quantity which had been raised
throughout the tributary country before the road was built.

  6. The following table, cut from a Chicago paper, shows the effect
  of railroad transport upon the cost of grain in that market:—

                     │      WHEAT.       │       CORN.
                     │By R. R.  By Wagon.│By R. R.  By Wagon.
           At market,│   $49.50    $49.50│   $25.60    $25.60
            10 miles,│    49.25     48.00│    24.25     23.26
            50 miles,│    48.75     42.00│    24.00     17.25
           100 miles,│    48.00     34.50│    23.25      9.75
           150 miles,│    47.25     27.00│    22.50      2.25
           200 miles,│    46.50     19.50│    21.75      0.00
           250 miles,│    45.75     12.00│    21.00      0.00
           300 miles,│    45.00      4.50│    20.25      0.00
           330 miles,│    44.55      0.00│    19.80      0.00

Thus a ton of corn carried two hundred miles, costs, per wagon
transport, more than it brings at market; while moved by railroad, it is
worth $21.75 per ton. Also wheat will not bear wagon transport of three
hundred and thirty miles; while moved that distance by railroad it is
worth $44.55 per ton.

7. By railroads, large cities are supplied with fresh meats and
vegetables, butter, eggs, and milk. An unhealthy increase of density of
population is prevented, by enabling business men to live five, ten, or
fifteen miles away from the city and yet do business therein. The amount
of this diffusion is as the square of the speed of transport. If a
person walks four miles per hour, and supposing one hour allowed for
passing from the house to the place of business, he cannot live at a
greater distance than four miles from his work. The area, therefore,
which may be lived in, is the circle of which the radius is four, the
diameter eight, and the area fifty and one quarter square miles. If by
horse one can go eight miles per hour, the diameter becomes sixteen
miles, and area two hundred and one square miles; and, if by railroad he
moves thirty miles per hour, the diameter becomes sixty miles, and the
area 2,827 square miles. The effect of such diffusion is plainly seen
about Boston, (Massachusetts). People who in 1830 were mostly confined
to the city, now live in Dorchester, Milton, Dedham, Roxbury, Brookline,
Brighton, Cambridge, Charlestown, Somerville, Chelsea, Lynn, and Salem;
places distant from two to thirteen miles.

8. In railroads, as in other labor saving (and labor producing)
machines, the innovation has been loudly decried. But though it does
render some classes of labor useless, and throw out of employment some
persons, it creates new labor far more than the old, and gives much more
than it takes away. Twenty years of experience shows that the diminished
cost of transport by railroad invariably augments the amount of commerce
transacted, and in a much larger ratio than the reduction of cost. It is
estimated by Dr. Lardner, that 300,000 horses working daily in stages
would be required to perform the passenger traffic alone, which took
place in England during the year 1848. It is concluded, also, from
reliable returns, that could the whole number of passengers carried by
railroad, have been transported by stage, the excess of cost by that
method above that by railroad would have been $40,000,000.


                     SAFETY OF RAILROAD TRAVELLING.

9. If we know that in a given time the whole distance travelled by
passengers was 500,000 miles, and that in such time there occurred one
fatal accident, it follows that when a person travels one mile, the
chances are 499,999 against one of losing life. If he travel ten miles,
the chances are 49,999 against one, or ten times as many of meeting with
loss of life; and generally the chances of accident are as the distance
travelled. In 1855, the whole number of miles run by passengers in the
United States was, in round numbers, 4,750,000,000, while there were
killed one hundred and sixteen; or one in every 41,000,000, very nearly.
(The ratio in England is one in every 65,000,000.) Now if for each
400,000 miles travelled by stage passengers, (a distance equal to
sixteen times round the world,) one passenger was killed, and if the
whole railroad mileage could be worked by stages, there would be
annually 11,875 lives lost; or one hundred times the number annually
lost by railroad. Thus it would be one hundred times safer to travel by
railroad than by stage. The danger of steamboat travelling is far
greater than by stage.


                        PRELIMINARY OPERATIONS.

10. The first step to be taken in starting a railroad enterprise, is the
choice of a board of directors (provisional), whose duty is to find all
that can be known of the commercial, financial, and agricultural nature
of the country to be traversed. To determine as near as possible its
ability to build and support a road; and to obtain the necessary
legislative enactments.

11. The determination of the increase of traffic which the road may be
expected to excite, is a difficult matter. There can be few rules given
for proceeding in such an inquiry. It seems very easy to prove by what
roads have done, that any project will be profitable.

  An abstract of a report lately published, tries to prove that a road
  will pay forty-five and one half per cent. net; the working expenses
  being assumed at only thirteen and one half per cent. of the gross
  receipts. The error here lies in assuming the working expenses too
  low, as few roads in the country have been worked for less than
  forty per cent.; a more common ratio being fifty one-hundredths of
  the gross receipts.

Not one half of railroads are built for the original estimate. In few
cases has sufficient allowance been made for the sacrifice undergone in
negotiating the companies’ securities. All general instructions that can
be given relating to the determination of prospective profits, are, to
keep the estimate of constructing and working expenses high, and that of
the assumed traffic low; not so low, however, as to require a too
lightly built road.


                  MECHANICAL PRINCIPLES OF LOCOMOTION.

12. The superiority which the modern railroad possesses over the common,
McAdam, plank, or turnpike-road, consists, first, in the reduction of
the resistance to motion, and second, in the application of the
locomotive steam-engine.

13. The effect of grades of a given incline upon a railroad is
_relatively_ more than upon common roads; for as the _absolute_
resistance on a level decreases, the _relative_ resistance of grades
augments: whence to obtain the full benefit of the system, we must
reduce much more the grades and curvature upon a railroad, than on a
common road. For example, if the resistance to moving one ton upon a
level upon a railroad was ten pounds, and upon a common road forty
pounds, where a twenty-three feet grade would be admissible upon the
former, we might use an incline of ninety-three feet per mile upon the
latter.

14. The resistance to the motion of railroad trains increases rapidly
with the speed;[1] whence the grades of a passenger road where a high
average speed is used, may be steeper than those of a road doing a
freight business chiefly.

Footnote 1:

  See chapter XIV.


                  DETERMINATION OF CHARACTER OF ROAD.

15. Upon a correct idea of what the road ought to be, depends in a great
degree its success. The amount of capital expended upon the reduction of
the natural surface, depends upon the expected amount of traffic. The
traffic remaining the same, the greater the capital expended in reducing
grades and curvature, the less will be the working expense; and the less
the construction capital, the greater that for maintenance. The limit of
expenditure must be such as to render the sum of construction and
maintaining capital a minimum.

The bad effect of grades upon the cost of maintaining and of working
railroads, is not so great as many suppose. Of the whole cost of
working, only about forty per cent. can be charged to locomotive power;
and of this, not more than sixty-two per cent. is effected by grades.[2]

Footnote 2:

  See appendix F.

16. The degree of curvature to be admitted upon any road depends
somewhat upon the speeds at which trains are to be run. The larger the
radius of curvature, the greater may be the speed; at the same time the
elevation of the exterior rail upon curves may be less, and therefore
more adapted to freight trains. High rates of speed are considered upon
some competing roads necessary; but are, even in such cases, necessary
evils. The wear of cars and of engines, of permanent way and of bridges,
increase in a rapid ratio with the velocity. The maximum speed for
freight trains should never exceed fifteen miles per hour, or for
passenger trains from twenty to twenty-five miles per hour.[3]

Footnote 3:

  See chapter XVI.

17. The agricultural nature of the country and its commercial position,
will determine the nature of the traffic, whether passenger or freight,
and also the amount. The amount and nature of the traffic will limit the
curvature, and will partially determine the arrangement of grades.


                                 GAUGE.

18. The question of broad and narrow gauge has led to much discussion,
and both plans claim among their advocates some of the best engineers.
The narrow gauge (American and English,) is four feet eight and one half
inches (from inside to inside of rail). The maximum adopted, is (the
Great Western of England) seven feet. The American maximum (New York and
Erie, and Ohio and Mississippi) is six feet. There is also in America
four feet ten inches, five feet, and five feet six inches. The advantage
of the broad gauge for a road doing an extensive business, is the
increased stowage room in freight cars, thus rendering admissible
shorter trains; by which the locomotive power is more directly applied
on curves. More comfortable passenger cars, (the same length of car of
course accommodates the same number of passengers). The disadvantages of
a wide gauge are, increased expense of cutting, embanking, bridging, and
masonry; increased expense of engines, cars, rails, sleepers, and all
machinery; more wear and tear upon curves, by reason of greater
difference between the lengths of inner and outer rails, and increased
atmospheric resistance to fast trains, from increased bulk.

19. The general conclusion arrived at by a commission appointed by the
Great Western Railway Company, (England,) consisting of Messrs. Nicholas
Wood, J. K. Brunel, and John Hawkshaw, was, that four feet, eight and
one half inches was rather narrow, but still enough for a certain class
of roads; that two or three inches made no material difference; that
seven feet was too wide for any road; that the weight of the broad gauge
engine, compared with the small increase of power, was a serious evil;
that engines could be run with perfect safety upon the narrow gauge at
any speed from thirty to sixty miles per hour, and that no more had been
attained upon the broad; that rolling friction was less upon the broad,
owing to the increased diameter of wheels, but that friction from curves
and atmospheric resistance was greater.

20. D. K. Clark, in “Railway Machinery,” p. 300, 301, makes the
resistance as deduced from experiments made upon both the four feet,
eight and one half inches, and the seven feet gauge, considerably
greater upon the former than on the latter; but as the narrow gauge
trials were made upon a curved road, with rails in a bad state, in
average weather, while those upon the broad were made in good weather,
upon a good and straight line, he leaves the gauge question open, and
uses the same formula for all widths.

21. Want of increased power, can be an apology for increased gauge,
until the capacity of the narrow gauge has been filled. The strongest
engines in the world are upon the four feet, eight and one half inch
gauge. No engines in America surpass or compare for absolute strength,
with those upon the Baltimore and Ohio Railroad. The most powerful
passenger engine ever built for high speeds, is Crampton’s engine
“Liverpool,” (London and North-western Railroad, England,) gauge four
feet, eight and one half inches.


                    GENERAL ESTABLISHMENT OF ROUTE.

22. The straight and level line connecting any two points, is of course
the best for the completed road; but this is seldom practicable. Way
towns must be accommodated to a certain extent; but the main line should
not be lengthened on that account, unless the traffic and capital
furnished by such town is not only sufficient to pay for the
construction and maintenance of the extra length, but also to carry the
entire through traffic over such increased distance. If the town is
unable to support such a burden, it may be able to build and maintain a
branch.

23. Routes placed upon the immediate bank of a large stream, are
generally crossed by a great number of deep gorges, which serve to drain
the side lands.

24. Routes placed upon sloping land, when the axis of the road and the
natural descent are at right angles to each other, are more subject to
slides than when placed upon plateaus or “bottoms.”

25. Lines crossing the dividing ridges of separate waters, rise and fall
a great deal; thus rendering necessary a strong motive power to work the
road. Such roads are the Western of Massachusetts, passing from the
valley of the Connecticut at Springfield, to the Hudson River valley at
Greenbush. Also those roads crossing the Alleghanies. And such will be
the Pacific road, crossing first the Rocky Mountains to the Great Basin,
and second, the Sierra Nevada into the Sacramento valley.




                               CHAPTER I.
                            RECONNOISSANCE.


26. The object of the reconnoitre is to find approximately the place for
the road, (i. e. within half of a mile,) to find the general form of the
country, and to choose that part which with reference to the expected
traffic, shall give the best gradients; to determine the elevations of
summits upon competing routes; and, in fine, to prepare the way for the
survey.


                          GENERAL TOPOGRAPHY.

27. The general topography of a country may be ascertained by reference
to State maps, where such exist, and when not, by riding over the
district. The direction and size of watercourses, will show at once the
position of summits.

[Illustration: Fig. 1.]

28. Water flowing as in fig. 1, indicates a fall from B to E; and also
traverse slopes from _a a_ and _c c_ to _d d_.

[Illustration: Fig. 2.]

29. Fig. 2 shows a broken ridge _a a a_ from which the water flows in
both directions; and in general, the sources of streams point towards
the higher lands.

[Illustration: Fig. 3.]

30. If it be required to join the points A and D by railroad, (fig. 3.)
it may be better to pass at once from A through B and C, than to go by
the streams F E, F′ E′. By the latter route the road would _ascend_ all
of the way from A to E; and descend from E′ to D. By the first if it
requires steep gradients to rise from A to B, and to fall from C to D,
still if the section B C is a plateau, and if the rise between A and B
and A and E is the same, by grouping the grades at B and C we may so
adapt the motive power, as to take the same train from A to D without
breaking. The general arrangement of grades by the line A B C D is then
as fig. 4; and A F E E′ F′ D, as in fig. 5. The saving in this case is
by length, as the same amount of power is required to overcome a given
ascent.

[Illustration: Fig. 4.]

[Illustration: Fig. 5.]

31. Valleys generally rise much faster near their source, than at any
point lower down; also the width increases as we approach the debouch.
Fig. 6 shows the cross sections of a valley from its source to the
mouth.

[Illustration: Fig. 6.]

32. In the case of parallel valleys running in the same direction, the
form will be as in fig 7. Let 1 2, 1 2, etc., represent a datum level,
or a horizontal plane passing through the lowest point. The line _a b_,
shows the height of the bottom at B; _c d_ that at D, _e f_ that at E,
and _g h_ that at C. The broken lines _i, k, l, m, n_, show the general
form of the land. Now by the route _m m m m_, from A to F, we have the
profile _m m m m_, fig. 8, by _n n n n_, the profile _n n n n_, and by
_o o o_, the profile _o o o_.

[Illustration: Fig. 7.]

[Illustration: Fig. 8.]

[Illustration: Fig. 9.]

33. In the case of parallel valleys running in opposite directions, as
in fig. 9, we have the form there shown; and the profiles corresponding
to the several lines are shown in fig. 10. As we should always adopt the
line giving the least rise and fall, other things being equal, it is
plain which line on the plan we must follow.

[Illustration: Fig. 10.]

34. In passing from A to B, figs. 11 and 12, by the several lines _c, d,
e, f_, we have the profiles shown at _c, d, e, f_, from which it
appears, that the nearer we cross to the heads of streams, the less is
the difference of heights.

[Illustration: Fig. 11.]

[Illustration: Fig. 12.]

[Illustration: Fig. 12 (_a_).]

35. If we wish to go from A to B, fig. 12 (_a_), we should of course
take first the straight line; but being obliged to avoid the hill C, on
arriving at _d_, we should not try to recover that line at _e_, but
proceed at once to B. Also as we are obliged to pass through _d_, we
ought to go _directly_ to _d_ and not by the way of _c_; and the same
idea is repeated between A and _d_; the last line being A _b d_ B. Few
rules can be given in the choice of routes. Practice only will enable
the engineer to find the best location for a railroad.


                        BAROMETRICAL LEVELLING.

36. The relative height of summits, the rate of fall of streams, and
absolute elevation, within a few feet, may be easily, rapidly, and
cheaply found by the barometer. This also affords an excellent check
upon subsequent levelling operations. The results thus obtained depend
upon the physical property, that the density of the air decreases as the
square of the height.

37. The barometer is a glass tube, partly filled with mercury, having a
vacuum in the upper part. By it the exact density of the air at any
point is determined. Accompanying are two thermometers; one _attached_,
showing the temperature of the _barometer_; the other _detached_,
showing the _atmospheric_ temperature.

38. Knowing now the manner of finding the density of the air at any two
points, and also the relation between density and height, the operation
of levelling by the barometer is very simple.

The _modus operandi_ is as follows, (see tables A, B, C, and D):—

Let us have the notes.

                        Barom.      Attached Therm. Detached Therm.
     Upper Station,      29.75           28.5            27.9
     Lower Station,      26.80           36.8            36.3
                                    Latitude 46° N.

 We have by table A, against the bar. point,              29.75,  6108.6
 also by table A, against the bar. point,                 26.80,  5276.6
                                                                  ——————
                                                  The difference   832.0
 Diff. of attached therm. 36.8°- 28.5° = 8.3°          (table B)   -12.2
                                                                  ——————
                                                                   819.8

 Double the sum of detached thermometers multiplied by 1/1000 of
   819.8 is
                    2(27.9 + 36.3) × .8198 =                     + 105.3
                                                                  ——————
                                                                   925.1
 Correction (see table C) for lat. 46° N. and approximate height
   925.1                                                           + 3.1
                                                                  ——————
                                                                   928.2

  Final correction by table D. The barometer at the lower station
  being 26.80, and the tabular number against 27.56 being 0.22, that
  for 26.80 will be 0.31, and we have

                 1000 to .31 as 928.2 to 0.287, or 0.3,

  which add to 928.2 and we have as the final height

             928.5 metres, or 928.5 × 3.28 = 3045.48 feet.

The tables above referred to, are those of Mr. Oltman, and are
considered as the most convenient and reliable of any published.

                               TABLE A.

                   ┌───────────────┬───────────────┐
                   │English Inches.│    Metres.    │
                   ├───────────────┼───────────────┤
                   │          14.56│          418.5│
                   │          14.61│          440.0│
                   │          14.65│          461.5│
                   │          14.68│          482.9│
                   │          14.72│          504.2│
                   │          14.76│          525.4│
                   │          14.80│          546.6│
                   │          14.84│          567.8│
                   │          14.88│          588.9│
                   │          14.92│          609.9│
                   │          14.96│          630.9│
                   │          15.00│          651.8│
                   │          15.04│          672.7│
                   │          15.08│          693.5│
                   │          15.12│          714.3│
                   │          15.16│          735.0│
                   │          15.20│          755.6│
                   │          15.24│          776.2│
                   │          15.28│          796.8│
                   │          15.31│          817.3│
                   │          15.35│          837.8│
                   │          15.39│          858.2│
                   │          15.43│          878.5│
                   │          15.47│          898.8│
                   │          15.51│          919.0│
                   │          15.55│          939.2│
                   │          15.59│          959.3│
                   │          15.63│          979.4│
                   │          15.67│          999.5│
                   │          15.71│         1019.5│
                   │          15.75│         1039.4│
                   │          15.79│         1059.3│
                   │          15.83│         1079.1│
                   │          15.87│         1098.9│
                   │          15.91│         1118.6│
                   │          15.95│         1138.3│
                   │          15.98│         1157.9│
                   │          16.02│         1177.5│
                   │          16.06│         1197.1│
                   │          16.10│         1216.6│
                   │          16.14│         1236.0│
                   │          16.18│         1255.4│
                   │          16.22│         1274.8│
                   │          16.26│         1294.1│
                   │          16.30│         1313.3│
                   │          16.34│         1332.5│
                   │          16.38│         1351.7│
                   │          16.42│         1370.8│
                   │          16.46│         1389.9│
                   │          16.50│         1408.9│
                   │          16.54│         1427.9│
                   │          16.57│         1446.8│
                   │          16.61│         1465.7│
                   │          16.65│         1484.7│
                   │          16.69│         1503.4│
                   │          16.73│         1522.2│
                   │          16.77│         1540.8│
                   │          16.81│         1559.5│
                   │          16.85│         1578.2│
                   │          16.89│         1596.8│
                   │          16.93│         1615.3│
                   │          16.97│         1633.8│
                   │          17.01│         1652.2│
                   │          17.05│         1670.6│
                   │          17.09│         1689.0│
                   │          17.13│         1707.3│
                   │          17.17│         1725.6│
                   │          17.20│         1743.8│
                   │          17.24│         1762.1│
                   │          17.28│         1780.3│
                   │          17.32│         1798.4│
                   │          17.36│         1816.5│
                   │          17.40│         1834.5│
                   │          17.44│         1852.5│
                   │          17.48│         1870.4│
                   │          17.52│         1888.3│
                   │          17.56│         1906.2│
                   │          17.60│         1924.0│
                   │          17.64│         1941.8│
                   │          17.68│         1959.6│
                   │          17.72│         1977.3│
                   │          17.76│         1994.9│
                   │          17.79│         2012.6│
                   │          17.83│         2030.2│
                   │          17.87│         2047.8│
                   │          17.91│         2065.3│
                   │          17.95│         2082.8│
                   │          17.99│         2100.2│
                   │          18.03│         2117.6│
                   │          18.07│         2135.0│
                   │          18.11│         2152.3│
                   │          18.15│         2169.6│
                   │          18.19│         2186.9│
                   │          18.23│         2204.1│
                   │          18.27│         2221.3│
                   │          18.31│         2238.4│
                   │          18.35│         2255.5│
                   │          18.39│         2272.6│
                   │          18.42│         2289.6│
                   │          18.46│         2306.6│
                   │          18.50│         2323.6│
                   │          18.54│         2340.5│
                   │          18.58│         2357.4│
                   │          18.62│         2374.2│
                   │          18.66│         2391.1│
                   │          18.70│         2407.9│
                   │          18.74│         2424.6│
                   │          18.78│         2441.3│
                   │          18.82│         2458.0│
                   │          18.86│         2474.6│
                   │          18.90│         2491.3│
                   │          18.94│         2507.9│
                   │          18.98│         2524.3│
                   │          19.02│         2540.8│
                   │          19.05│         2557.3│
                   │          19.09│         2573.7│
                   │          19.13│         2590.2│
                   │          19.17│         2506.6│
                   │          19.21│         2622.9│
                   │          19.25│         2639.2│
                   │          19.29│         2655.4│
                   │          19.33│         2671.6│
                   │          19.37│         2687.9│
                   │          19.41│         2704.1│
                   │          19.45│         2720.2│
                   │          19.49│         2736.3│
                   │          19.53│         2752.3│
                   │          19.57│         2768.3│
                   │          19.61│         2784.4│
                   │          19.65│         2800.4│
                   │          19.68│         2816.3│
                   │          19.72│         2832.2│
                   │          19.76│         2848.1│
                   │          19.80│         2864.0│
                   │          19.84│         2879.8│
                   │          19.88│         2895.6│
                   │          19.92│         2911.3│
                   │          19.96│         2927.0│
                   │          20.00│         2942.7│
                   │          20.04│         2958.4│
                   │          20.08│         2974.0│
                   │          20.12│         2989.6│
                   │          20.16│         3005.2│
                   │          20.20│         3020.7│
                   │          20.24│         3036.2│
                   │          20.28│         3051.7│
                   │          20.31│         3067.2│
                   │          20.35│         3082.6│
                   │          20.39│         3097.9│
                   │          20.43│         3113.3│
                   │          20.47│         3128.6│
                   │          20.51│         3143.9│
                   │          20.55│         3159.2│
                   │          20.59│         3174.4│
                   │          20.63│         3189.7│
                   │          20.67│         3204.9│
                   │          20.71│         3220.0│
                   │          20.75│         3235.1│
                   │          20.79│         3250.2│
                   │          20.83│         3265.3│
                   │          20.87│         3280.3│
                   │          20.90│         3295.3│
                   │          20.94│         3310.3│
                   │          20.98│         3325.3│
                   │          21.02│         3340.2│
                   │          21.06│         3355.1│
                   │          21.10│         3370.0│
                   │          21.14│         3384.8│
                   │          21.18│         3399.6│
                   │          21.22│         3414.4│
                   │          21.26│         3429.2│
                   │          21.30│         3443.9│
                   │          21.34│         3458.6│
                   │          21.38│         3473.3│
                   │          21.42│         3487.9│
                   │          21.46│         3502.5│
                   │          21.50│         3517.2│
                   │          21.54│         3531.8│
                   │          21.57│         3546.3│
                   │          21.61│         3560.8│
                   │          21.65│         3575.3│
                   │          21.69│         3589.8│
                   │          21.73│         3604.2│
                   │          21.77│         3618.6│
                   │          21.81│         3633.0│
                   │          21.85│         3647.4│
                   │          21.89│         3661.7│
                   │          21.93│         3676.0│
                   │          21.97│         3690.3│
                   │          22.01│         3704.6│
                   │          22.05│         3718.8│
                   │          22.09│         3733.0│
                   │          22.13│         3747.2│
                   │          22.17│         3761.3│
                   │          22.20│         3775.4│
                   │          22.24│         3789.5│
                   │          22.28│         3803.6│
                   │          22.32│         3817.7│
                   │          22.36│         3831.7│
                   │          22.40│         3845.7│
                   │          22.44│         3859.7│
                   │          22.48│         3873.7│
                   │          22.52│         3887.6│
                   │          22.56│         3901.5│
                   │          22.60│         3915.4│
                   │          22.64│         3929.3│
                   │          22.68│         3943.1│
                   │          22.72│         3956.9│
                   │          22.76│         3970.7│
                   │          22.80│         3984.5│
                   │          22.83│         3998.2│
                   │          22.87│         4011.9│
                   │          22.91│         4025.6│
                   │          22.95│         4039.3│
                   │          22.99│         4052.9│
                   │          23.03│         4066.6│
                   │          23.07│         4080.2│
                   │          23.11│         4093.8│
                   │          23.15│         4107.3│
                   │          23.19│         4120.8│
                   │          23.23│         4134.3│
                   │          23.27│         4147.8│
                   │          23.31│         4161.3│
                   │          23.35│         4174.7│
                   │          23.39│         4188.1│
                   │          23.43│         4201.5│
                   │          23.46│         4214.9│
                   │          23.50│         4228.2│
                   │          23.54│         4241.6│
                   │          23.58│         4254.9│
                   │          23.62│         4268.2│
                   │          23.66│         4281.4│
                   │          23.70│         4294.7│
                   │          23.74│         4307.9│
                   │          23.78│         4321.1│
                   │          23.82│         4334.3│
                   │          23.86│         4347.4│
                   │          23.90│         4360.5│
                   │          23.94│         4373.7│
                   │          23.98│         4386.7│
                   │          24.02│         4399.8│
                   │          24.06│         4412.8│
                   │          24.09│         4425.9│
                   │          24.13│         4438.9│
                   │          24.17│         4451.9│
                   │          24.21│         4464.8│
                   │          24.25│         4477.7│
                   │          24.29│         4490.7│
                   │          24.33│         4503.6│
                   │          24.37│         4516.4│
                   │          24.41│         4529.3│
                   │          24.45│         4542.1│
                   │          24.49│         4554.9│
                   │          24.53│         4567.7│
                   │          24.57│         4580.5│
                   │          24.61│         4593.2│
                   │          24.65│         4606.0│
                   │          24.68│         4618.7│
                   │          24.72│         4631.4│
                   │          24.76│         4644.0│
                   │          24.80│         4656.7│
                   │          24.84│         4669.3│
                   │          24.88│         4682.0│
                   │          24.92│         4694.5│
                   │          24.96│         4707.1│
                   │          25.00│         4719.7│
                   │          25.04│         4732.2│
                   │          25.08│         4744.7│
                   │          25.12│         4757.2│
                   │          25.16│         4769.7│
                   │          25.20│         4782.1│
                   │          25.24│         4794.6│
                   │          25.28│         4807.0│
                   │          25.31│         4819.4│
                   │          25.35│         4831.7│
                   │          25.39│         4844.1│
                   │          25.43│         4856.4│
                   │          25.47│         4868.7│
                   │          25.51│         4881.0│
                   │          25.55│         4893.3│
                   │          25.59│         4905.6│
                   │          25.63│         4917.8│
                   │          25.67│         4930.0│
                   │          25.71│         4942.2│
                   │          25.75│         4954.4│
                   │          25.79│         4966.6│
                   │          25.83│         4978.7│
                   │          25.87│         4990.9│
                   │          25.91│         5003.0│
                   │          25.94│         5015.1│
                   │          25.98│         5027.2│
                   │          26.02│         5039.3│
                   │          26.06│         5051.2│
                   │          26.10│         5063.2│
                   │          26.14│         5075.3│
                   │          26.18│         5087.2│
                   │          26.22│         5099.2│
                   │          26.26│         5111.2│
                   │          26.30│         5123.1│
                   │          26.34│         5135.0│
                   │          26.38│         5146.9│
                   │          26.42│         5158.8│
                   │          26.46│         5170.6│
                   │          26.50│         5182.5│
                   │          26.54│         5194.3│
                   │          26.57│         5206.1│
                   │          26.61│         5217.9│
                   │          26.65│         5229.7│
                   │          26.69│         5241.4│
                   │          26.73│         5253.2│
                   │          26.77│         5264.9│
                   │          26.81│         5276.6│
                   │          26.85│         5288.3│
                   │          26.89│         5300.0│
                   │          26.93│         5311.6│
                   │          26.97│         5323.2│
                   │          27.01│         5334.8│
                   │          27.05│         5346.4│
                   │          27.09│         5358.0│
                   │          27.13│         5369.6│
                   │          27.17│         5381.1│
                   │          27.21│         5392.7│
                   │          27.25│         5404.2│
                   │          27.28│         5415.6│
                   │          27.32│         5427.2│
                   │          27.36│         5438.7│
                   │          27.40│         5450.1│
                   │          27.44│         5461.5│
                   │          27.48│         5472.9│
                   │          27.52│         5484.3│
                   │          27.56│         5495.7│
                   │          27.60│         5507.1│
                   │          27.64│         5518.4│
                   │          27.68│         5529.8│
                   │          27.72│         5541.1│
                   │          27.76│         5552.4│
                   │          27.80│         5563.7│
                   │          27.84│         5575.0│
                   │          27.87│         5586.2│
                   │          27.91│         5597.5│
                   │          27.95│         5608.7│
                   │          27.99│         5619.6│
                   │          28.03│         5631.1│
                   │          28.07│         5642.2│
                   │          28.11│         5653.4│
                   │          28.15│         5664.6│
                   │          28.19│         5675.7│
                   │          28.23│         5686.8│
                   │          28.27│         5697.9│
                   │          28.31│         5709.0│
                   │          28.35│         5720.1│
                   │          28.39│         5731.1│
                   │          28.43│         5742.1│
                   │          28.46│         5753.1│
                   │          28.50│         5764.2│
                   │          28.54│         5775.1│
                   │          28.58│         5786.1│
                   │          28.62│         5797.1│
                   │          28.66│         5808.0│
                   │          28.70│         5819.0│
                   │          28.74│         5829.9│
                   │          28.78│         5840.8│
                   │          28.82│         5851.7│
                   │          28.86│         5862.5│
                   │          28.90│         5873.4│
                   │          28.94│         5884.2│
                   │          28.98│         5894.9│
                   │          29.02│         5905.8│
                   │          29.06│         5916.7│
                   │          29.09│         5927.5│
                   │          29.13│         5938.2│
                   │          29.17│         5949.0│
                   │          29.21│         5959.7│
                   │          29.25│         5970.4│
                   │          29.29│         5981.2│
                   │          29.33│         5991.9│
                   │          29.37│         6002.5│
                   │          29.41│         6013.2│
                   │          29.45│         6023.8│
                   │          29.49│         6034.4│
                   │          29.53│         6045.1│
                   │          29.57│         6055.7│
                   │          29.61│         6066.3│
                   │          29.65│         6076.9│
                   │          29.69│         6087.5│
                   │          29.72│         6098.0│
                   │          29.76│         6108.6│
                   │          29.80│         6119.1│
                   │          29.84│         6129.6│
                   │          29.88│         6140.1│
                   │          29.92│         6150.6│
                   │          29.96│         6161.1│
                   │          30.00│         6171.5│
                   │          30.04│         6182.0│
                   │          30.08│         6192.4│
                   │          30.12│         6202.8│
                   │          30.16│         6213.2│
                   │          30.20│         6223.6│
                   │          30.24│         6234.0│
                   │          30.28│         6244.4│
                   │          30.32│         6254.7│
                   │          30.35│         6265.0│
                   │          30.39│         6275.4│
                   │          30.43│         6285.7│
                   │          30.47│         6296.0│
                   │          30.51│         6306.2│
                   │          30.55│         6316.5│
                   │          30.59│         6326.7│
                   │          30.63│         6337.0│
                   │          30.67│         6347.2│
                   │          30.71│         6357.4│
                   │          30.75│         6367.6│
                   │          30.79│         6377.8│
                   │          30.83│         6388.0│
                   │          30.87│         6398.2│
                   │          30.91│         6408.3│
                   │          30.94│         6418.5│
                   │          30.98│         6428.6│
                   │          31.02│         6438.7│
                   │          31.06│         6448.8│
                   └───────────────┴───────────────┘

                               TABLE B.

                   ┌───────────────┬───────────────┐
                   │    Deg.[4]    │     Met.      │
                   ├───────────────┼───────────────┤
                   │            0.2│            0.3│
                   │            0.4│            0.6│
                   │            0.6│            0.9│
                   │            0.8│            1.2│
                   │            1.0│            1.5│
                   │            1.2│            1.8│
                   │            1.4│            2.1│
                   │            1.6│            2.3│
                   │            1.8│            2.6│
                   │            2.0│            2.9│
                   │            2.2│            3.2│
                   │            2.4│            3.5│
                   │            2.6│            3.8│
                   │            2.8│            4.1│
                   │            3.0│            4.4│
                   │            3.2│            4.7│
                   │            3.4│            5.0│
                   │            3.6│            5.3│
                   │            3.8│            5.6│
                   │            4.0│            5.9│
                   │            4.2│            6.2│
                   │            4.4│            6.5│
                   │            4.6│            6.8│
                   │            4.8│            7.1│
                   │            5.0│            7.4│
                   │            5.2│            7.6│
                   │            5.4│            7.9│
                   │            5.6│            8.2│
                   │            5.8│            8.5│
                   │            6.0│            8.8│
                   │            6.2│            9.1│
                   │            6.4│            9.4│
                   │            6.6│            9.7│
                   │            6.8│           10.0│
                   │            7.0│           10.3│
                   │            7.2│           10.6│
                   │            7.4│           10.9│
                   │            7.6│           11.2│
                   │            7.8│           11.5│
                   │            8.0│           11.8│
                   │            8.2│           12.1│
                   │            8.4│           12.4│
                   │            8.6│           12.6│
                   │            8.8│           12.9│
                   │            9.0│           13.2│
                   │            9.2│           13.5│
                   │            9.4│           13.8│
                   │            9.6│           14.1│
                   │            9.8│           14.4│
                   │           10.0│           14.7│
                   │           10.2│           15.0│
                   │           10.4│           15.3│
                   │           10.6│           15.6│
                   │           10.8│           15.9│
                   │           11.0│           16.2│
                   │           11.2│           16.5│
                   │           11.4│           16.8│
                   │           11.6│           17.1│
                   │           11.8│           17.4│
                   │           12.0│           17.6│
                   │           12.2│           17.9│
                   │           12.4│           18.2│
                   │           12.6│           18.5│
                   │           12.8│           18.8│
                   │           13.0│           19.1│
                   │           13.2│           19.4│
                   │           13.4│           19.7│
                   │           13.6│           20.0│
                   │           13.8│           20.3│
                   │           14.0│           20.6│
                   │           14.2│           20.9│
                   │           14.4│           21.2│
                   │           14.6│           21.5│
                   │           14.8│           21.8│
                   │           15.0│           22.1│
                   │           15.2│           22.4│
                   │           15.4│           22.7│
                   │           15.6│           22.9│
                   │           15.8│           23.2│
                   │           16.0│           23.5│
                   │           16.2│           23.8│
                   │           16.4│           24.1│
                   │           16.6│           24.4│
                   │           16.8│           24.7│
                   │           17.0│           25.0│
                   │           17.2│           25.3│
                   │           17.4│           25.6│
                   │           17.6│           25.9│
                   │           17.8│           26.2│
                   │           18.0│           26.5│
                   │           18.2│           26.8│
                   │           18.4│           27.1│
                   │           18.6│           27.4│
                   │           18.8│           27.7│
                   │           19.0│           28.0│
                   │           19.2│           28.2│
                   │           19.4│           28.5│
                   │           19.6│           28.8│
                   │           19.8│           29.1│
                   │           20.0│           29.4│
                   └───────────────┴───────────────┘

Footnote 4:

  The degrees refer to the centigrade thermometer.

                                TABLE C.

 ┌─────────────┬─────────────┬─────────────┬─────────────┬─────────────┐
 │ Approximate │     0°      │     15°     │     40°     │     55°     │
 │   Height.   │             │             │             │             │
 ├─────────────┼─────────────┼─────────────┼─────────────┼─────────────┤
 │          200│          1.2│          1.0│          0.6│          0.4│
 │          400│          2.4│          2.2│          1.4│          0.8│
 │          600│          3.4│          3.2│          2.0│          1.2│
 │          800│          4.5│          4.3│          2.8│          1.7│
 │         1000│          5.7│          5.3│          3.4│          2.2│
 │         1200│          7.0│          6.4│          4.2│          2.6│
 │         1400│          8.2│          7.6│          4.8│          3.0│
 │         1600│          9.2│          8.8│          5.6│          3.4│
 │         1800│         10.4│          9.8│          6.3│          3.8│
 │         2000│         11.6│         11.0│          7.0│          4.2│
 │         2200│         12.8│         12.1│          7.6│          4.6│
 │         2400│         14.0│         13.3│          8.4│          5.1│
 │         2600│         15.2│         14.4│          9.2│          5.6│
 │         2800│         16.5│         15.6│         10.0│          6.2│
 │         3000│         17.7│         16.8│         10.8│          6.6│
 │         3200│         10.1│         18.0│         11.5│          7.0│
 │         3400│         20.5│         19.3│         12.4│          7.7│
 │         3600│         21.8│         20.4│         13.4│          8.2│
 │         3800│         23.1│         21.6│         14.3│          8.7│
 │         4000│         24.6│         22.9│         15.1│          9.4│
 │         4200│         25.9│         24.3│         15.9│         10.1│
 │         4400│         27.5│         25.8│         16.9│         10.8│
 │         4600│         28.9│         27.1│         18.0│         11.5│
 │         4800│         30.4│         28.4│         19.0│         12.1│
 │         5000│         31.8│         29.8│         19.9│         12.7│
 │         5200│         33.0│         31.0│         20.8│         13.3│
 │         5400│         34.3│         32.4│         21.7│         13.9│
 │         5600│         35.7│         33.7│         22.6│         14.5│
 │         5800│         37.1│         35.0│         23.6│         15.1│
 │         6000│         38.5│         36.3│         24.6│         15.7│
 └─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘

                               TABLE D.

                   ┌───────────────┬───────────────┐
                   │ Barometrical  │    Metres     │
                   │    Height     │               │
                   ├───────────────┼───────────────┤
                   │     15.75     │     1.71      │
                   │     17.72     │     1.39      │
                   │     19.68     │     1.11      │
                   │     21.65     │     0.86      │
                   │     23.62     │     0.63      │
                   │     25.59     │     0.42      │
                   │     27.56     │     0.22      │
                   │     29.53     │     0.03      │
                   └───────────────┴───────────────┘




                              CHAPTER II.
                                SURVEY.


                        TOPOGRAPHICAL SKETCHING.

39. Topographical drawing includes every thing relating to an accurate
representation upon paper, of any piece of ground. The state of
cultivation, roads, town, county, and state boundaries, and all else
that occurs in nature. The sketching necessary in railroad surveying,
however, does not embrace all of this, but only the delineation of
streams and the undulations of ground within that limit which affects
the road, perhaps 500 feet on each side of the line. The making of such
sketches consists in tracing the irregular lines formed by the
intersection of the natural surface, by a system of horizontal planes,
at a vertical distance of five, ten, fifteen, or twenty feet, according
to the accuracy required.

[Illustration: Fig. 13.]

40. Suppose that we wish to represent upon a horizontal surface a right
cone. The base _m m_, fig. 13, is shown by the circle of which the
diameter is _m, m_. If the elevation is cut by the horizontal planes _a
a_, _b b_, _c c_, the intersection of these planes with the conical
surface is shown by the circles _a_, _b_, _c_, in plan. The less we make
the horizontal distances, on plan, between the circles, the less also
will be the vertical distance between the planes.

Wishing to find the elevation of any line which exists on plan, as 1, 2,
3, 3, 2, 1, we have only to find the intersection of the verticals drawn
through the points 1, 2, 3, 3, 2, 1, and the elevation lines _a a_, _b
b_, _c c_; this gives us the curve 4, 5, 6, 7, 6, 5, 4.

[Illustration: Fig. 14.]

41. Again, in fig. 14, the cone is oblique, which causes the circles on
plan to become eccentric and elliptic. Having given the line 1, 2, 3, as
before, we find it upon the elevation in the same manner.

42. In the section of regular and full lined figures, the horizontal and
vertical projections are also regular and full lined; but in a broken
surface like the ground, the lines become quite irregular.

Suppose we wish to show on plan the hill of which we have the plan, fig.
15, and the sections figs. 16, 17, and 18. Let AD be the profile (made
with the level) of the line AD on plan, fig. 15. B E that of B E, and C
F that of CF.

[Illustration: Fig. 15.]

[Illustration: Fig. 16.]

[Illustration: Fig. 17.]

[Illustration: Fig. 18.]

To form the plan from the profiles proceed as follows:—

Intersect each of the profiles by the horizontal planes _a a_, _b b_, _c
c_, _d d_, equidistant vertically. In the profile A D, fig. 18, drop a
vertical on to the base line from each of the intersections _a_, _b_,
_c_, _d_, _d_, _c_, _b_, _a_. Make now A 1,1 2, 2 3, 3 4, etc., on the
plan equal to the same on the profile. Next draw, on the plan, the line
B E, at the right place and at the proper angle with A D; and having
found the distances B 1, 1 2, 2 3, etc., as before, transfer them to the
line B E on plan. Proceed in the same manner with the line C F.

The points _a a a_, _b b b_, _c c c_, are evidently at the same height
above the base upon the profiles, whence the intersections of these
lines with the surface line or 1 1 1, 2 2 2, 3 3 3, etc., on the plan,
are also at the same height above the base; and an irregular line traced
through the points 1 1 1, or 2 2 2, will show the intersection of a
horizontal plane, with the natural surface.

When as at A we observe the contour lines near to each other, we
conclude that the ground is steep. And when the distances are large, as
at 6, 7, 8, we know that the ground falls gently. This is plainly seen
both on plan and profile.

[Illustration: Fig. 15.]

Having now the topographical sketch, fig. 15, we may easily deduce
therefrom at any point a profile. If we would have a profile of G E, on
plan, upon an indefinite line G E, fig. 19, we set off G 1, 1 2, 2 3, 3
4, etc., equal to the same distances on the plan. From these points draw
verticals intersecting the horizontals _a a_, _b b_, _c c_; and lastly,
through the intersections draw the broken line (surface line or profile)
_a_, _b_, _c_, _d_, _d_, _c_, _b_, _a_. Thus we see how complete a
knowledge of the ground a correct topographical sketch gives.

[Illustration: Fig. 19.]

43. Field sketches for railroad work are generally made by the eye. The
field book being ruled in squares representing one hundred feet each.
When we need a more accurate sketch than this method gives, we may cross
section the ground either by rods or with the level.

By making a very detailed map of a survey, and filling in with sketches
of this kind, the location may be made upon paper and afterwards
transferred to the ground.

So far we have dealt with but one summit; but the mode of proceeding is
precisely the same when applied to a group or range of hills, or indeed
to any piece of ground.

44. As a general thing, the intersection of the horizontal planes with
the natural surface (contour lines) are concave to the lower land in
depressions, and convex to the lower land on spurs and elevations. Thus
at B B B _b b_, fig. 20, upon the spurs, we have the lines convex to the
stream; and in the hollows _c c c_, the lines are concave to the bottom.

45. Having by reconnoissance found approximately the place for the road,
we proceed to run a trial line by compass. In doing this we choose the
apparent best place, stake out the centre line, make a profile of it,
and sketch in the topography right and left.

[Illustration: Fig. 20.]

[Illustration: Fig. 21.]

[Illustration: Fig. 22.]

Suppose that by doing so we have obtained the plan and profile shown in
figs. 21 and 22, where A _a a_ B is the profile of A C D B, on the plan.
The lowest line of the valley though quite moderately inclined at first,
from A to C, rises quite fast from C to the summit; and as the
inclination becomes greater, the contour lines become nearer to each
other.

Now that the line may ascend uniformly from A to the summit, the
horizontal distances between the contour lines must be equal; this
equality is effected by causing the surveyed line to cut the contours
_square_ at 1, 2, 3, 4, and _obliquely_ at 5, 8, 10. Thus we obtain the
profile A 5 5 B.

[Illustration: Figs. 23 and 24.]

46. Having given the plan and profile, figs. 23 and 24, where A C D B
represents the bed of the stream, in profile, if it were required to put
the uniformly inclined line A _m m_ B, upon the plan, we should proceed
as follows. Take the horizontal distance A _m_ from the profile, and
with A (on plan) as a centre, describe the arc 1, 3. The point _m_ on
the profile is evidently three fourths of a division above the bed of
the stream. So on the plan we must trace the arc 1, 3, until we come to
_a_, which is three fourths of _b c_, from _b_. Again, _m′_ is nine and
one half divisions above _m_. From _a_, with a radius _m n_ on profile,
describe the arc 4, 5, 6. Now, as on the profile, in going from _m_ to
_m′_, we cross nine contour lines, and come upon the tenth at _m′_, so
on the plan we must cross nine contour lines and come upon the tenth,
and at the same time upon the arc 4, 5, 6.

Proceeding in this way, we find A, _a_, _b_, B, on the plan, as
corresponding to A _m m′_ B on the profile.

To establish in this manner any particular grade, we have first to place
it upon the profile, and next to transfer it to the plan.

47. It may be remembered as a general thing, that the steepest line is
that which cuts the contour line at right angles; the contour line
itself is level, and as we vary between these limits we vary the
incline.


                    GENERAL ESTABLISHMENT OF GRADES.

48. Considerable has been written upon the relation which ought to exist
between the maximum grade, and the direction of the traffic. Some have
given formulæ for obtaining the rate and direction of inclines as
depending upon the capacity of power. This seems going quite too far, as
the nature of the ground and of the traffic generally fix these in
advance.

49. Between two places which are at the same absolute elevation, there
should be as little rise and fall as possible.

50. Between points at different elevations, we should if possible have
no rise while descending, and consequently no fall while on the ascent.

51. Some engineers express themselves very much in favor of long levels
and short but steep inclines. There are cases where the momentum
acquired upon one grade, or upon a level, assists the train up the next
incline. The distance on the rise during which momentum lasts, is not
very great. A train in descending a plane does not receive a constant
increase of _available_ momentum, but arrives at a certain speed, where
by increased resistance and by added effect of gravity, the motion
becomes nearly regular. Up to this point the momentum acquired is
useful, but not beyond.

Any road being divided into _locomotive sections_, the section given to
any one engine should be such as to require a constant expenditure of
power as nearly as possible; i. e., one section, or the run of one
engine, should not embrace long levels and steep grades. If an engine
can carry a load over a sixty feet grade, it will be too heavy to work
the same load upon a level economically. It is best to group all of the
necessarily steep grades in one place, and also the easy portions of the
road; then by properly adapting the locomotives the cost of power may be
reduced to a minimum.

As to long levels and short inclines the same power is required to
overcome a given rise, but quite a difference may be made in the means
used to surmount that ascent.

[Illustration: Fig. 25.]

52. Suppose we have the profiles A E D and A B D, fig. 25. The
resistance from A to D by the continuous twenty feet grade is the same
as the whole resistance from A to B and from B to D. The reason for
preferring A E D is, that an engine to take a given load from B to D
would be unnecessarily heavy for the section A B; while the same power
must be exerted at each point, of A E D. Also the return by A E D is
made by a small and constant expenditure of power, being all of the way
aided by gravity; while in descending by B, we have more aid from
gravity than we require from D to B, after which we have none.

When the distances A B, B C, are sixty and twenty miles in place of six
and two, we may consider the grades grouped at B D, and use a heavier
engine at that point, as we should hardly find eighty miles admitting of
a continuous and uniform grade.


                          EQUATING FOR GRADES.

53. In comparing the relative advantages of several lines having
different systems of grades, it is customary to reduce them all to the
level line involving an equal expenditure of power.

The question is to find the vertical rise, consuming an amount of power
equal to that expended upon the horizontal unit of length. This has been
estimated by engineers all the way from twenty to seventy feet. For
simple comparison it does not matter much what number is used if it is
the same in all cases; but to find the equivalent horizontal length to
any location, regard must be had to the nature of the expected traffic.

The elements of the problem are, the length, the inclination or the
total rise and fall, and the resistance to the motion of the train upon
a level, which latter depends upon the speed and the state of the rails
and machinery.

From chapter XIV. we have the following resistances to the motion of
trains upon a level:—

       Velocity, in miles, per hour. Resistance, in lbs. per ton.
                                  10                          8.6
                                  15                          9.3
                                  20                         10.3
                                  25                         11.6
                                  30                         13.3
                                  40                         17.3
                                  50                         22.6
                                  60                         27.1
                                 100                         66.5

The power expended upon any road is of course the product of the
resistance per unit of length, by the number of units. Calling _R_ the
resistance per unit upon a level, and _R′_ the resistance per unit on
any grade, and designating the lengths by _L_ and _L′_, that there shall
be in both cases an equal expenditure of power, we must have

                             _RL_ = _R′L′_,

whence the level length must be

                          _L_ = (_L′R′_)/_R_.

Thus assuming the resistance on a level as twenty lbs. per ton, that on
a fifty feet grade is

              20 + 50/5280 of 2240, or 20 + 21.2 or 41.2,

and if the length of the inclined line is ten miles, the equivalent
level length is

         _L_ = (41.2 × 52800)/20 = 108768 feet, or 20.6 miles.

                    Also 10 miles × 41.2 lbs. = 412,
                    and 20.6 miles × 20 lbs. = 412.

54. The above may be somewhat abridged as follows: Let _R_ be the
resistance on a level. The resistance due to any grade is expressed by

                              _W_ × 1/_a_,

where 1/_a_ is the fraction showing the grade, and _W_ the weight of the
load.

The vertical height in feet, to overcome which we must expend an amount
of power sufficient to move the train one mile on a level, must be such
that

                           _W_ × 1/_a_ = _R_,

or

                            1/_a_ = _R_/_W_;

and to find the number by which to equate, we have only to place the
values of _R_ and _W_ in the formula. For example, let the speed be
twenty miles per hour, the corresponding resistance is 10.3 lbs. per
ton. _W_ being one ton, or 2240 lbs., we have

 1/_a_ = _R_/_W_ = 10.3/2240 = 1/218 of 5280, (the number of feet in one
                                  mile,)

                         1/218 of 5280 = 24 feet.

In the same manner we have

              Speed, in miles, per hour. Equating number.
                                      15               22
                                      20               24
                                      30               32
                                      40               41
                                      50               53
                                      60               67
                                     100              155

Thus when we take the speed as thirty miles per hour, for each
thirty-two feet rise we shall consume an amount of power sufficient to
move the train one mile on a level. In descending, the grade instead of
being an obstacle, becomes an aid; indeed the incline may be such as to
move the trains independently of the steam power. Thus if on account of
ascending grades we increase the equated length, so also in descending
we must reduce the length. The amount of reduction is not, however, the
reverse of the increase in ascending, as after thirty or forty feet any
additional fall per mile instead of being an advantage is an evil; as
too much gravity obliges us to run down grades with brakes on.
Twenty-five feet per mile is sufficient to allow the train to roll down,
and any more than this is of very little use. Therefore for every mile
of grade descending at the rate of twenty-five feet per mile we may
deduct one mile in equating, and for every mile of grade descending
twelve and one half feet per mile deduct a proportional amount; but for
any _more_ fall per mile than twenty-five feet, no allowance should be
made; i. e., if we descend at the rate of forty feet per mile, we may
deduct one mile in equating for the twenty-five feet of fall, and throw
aside the remaining fifteen feet.

55. This is a common method of equating for grades, and represents a
length which is proportional to the power expended, but not proportional
to the cost of working, as the ratios of power expended and cost of
working under different conditions are very different, double power
requiring only twenty per cent. more working capital. The above rules,
therefore, require a correction.

 The cost of working a power represented by unity being expressed by 100;
 That of working a power 2 is expressed by                           125;
 That of working a power 3 is expressed by                           150;
 That of working a power 4 is expressed by                           175;
 That of working a power 5 is expressed by                           200.

                            (See Appendix F.)

Now the resistance on a level being at a velocity of twenty miles per
hour, 10.3 lbs. per ton by the formula

                            1/_a_ = _R_/_W_,

the vertical height in feet causing a double expenditure of power is
twenty-four; but as above, the whole expense of a double power is
increased by only twenty-five per cent.; we should not add one mile for
twenty-four feet rise, but one fourth of a mile only, or one mile for
each ninety-six feet; and by correcting our former table in this manner,
we have the following table:—

              Speed, in miles, per hour. Equating number.
                                      15               88
                                      20               96
                                      25              110
                                      30              128
                                      40              164
                                      50              212
                                      60              268
                                     100              620

So much for equating for the ascents. In descending, we have allowed one
mile reduction for each mile of twenty-five feet of descending grade;
but as in ascending we correct the first made table, so in descending we
must also correct as follows. If we needed no steam power either while
descending or afterwards, we should only save wood and water; as a
general thing the fire must be kept up while descending, and the only
gain is a small part of the expense of fuel; so small, in fine, that
with the exception of roads which incline for the whole or a great part
of their length, no reduction should be made.


                     COMPARISON OF SURVEYED LINES.

56. The requisite data for an approximate comparison of lines are, the
measured length, total rise, total fall.

                Let the length of line A be  100 miles,
                Let the length of line B be   90 miles,
                Whole rise on A             2000 feet,
                Whole rise on B             5100 feet,
                Whole fall on A             1200 feet,
                Whole fall on B             4300 feet.

Assume the number by which to equate, as ninety-six, and we shall have

                                Line A.
                 Ascending,  100 + 2000/96 =     120.83
                 Descending, 100 + 1200/96 =     112.50
                                                 ——————
                                             Sum 233.33
                                            Mean 116.66

                                Line B.
                 Ascending,   90 + 5100/96 =     143.13
                 Descending,  90 + 4300/96 =     134.80
                                                 ——————
                                             Sum 276.93
                                            Mean 138.46

                 The mean equated length of A is 116.66
                 The measured length of A is     100.00
                                                 ——————
                                  The difference  16.66

                 The mean equated length of B is 138.46
                 The measured length of B is      90.00
                                                 ——————
                                  The difference 48.46.

The cost of construction being assumed as the actual length, and that of
working as the equated length, we have the final approximate comparison
thus:—

Assume the construction cost as $25,000 per mile, and the cost of
maintenance $4,000 per mile, and we have

The line A to the line B as

       100 × 25000 + (116.66 × 4000) × 100/6 = 10,277,333, is to

        90 × 25000 + (138.46 × 4000) × 100/6 = 11,480,667;

or A is to B as 10.3 to 11.5 nearly, although the line A is ten miles
longer than B.




                              CHAPTER III.
                               LOCATION.


                               ALIGNMENT.

57. The broken line furnished by the survey is of course unfit for the
centre line of a railroad. The angles require to be rounded off to
render the passage from one straight portion to the other easy.

[Illustration: Fig. 26.]

58. Let A X B, fig. 26, represent the angle formed by any two tangents
which it is required to connect by a circular curve. It is plain that
knowing the angle of deflection of the lines A X, B X, we obtain also
the angles A C X, X C B. The manner of laying these curves upon the
ground is by placing an angular instrument at any point of the curve, as
at A, and laying off the partial angles E A _a_, E A M, E A G, etc.,
which combined with the corresponding distances A _a_, _a_ M, M G, fix
points in the curve.

These small chords are generally assumed at one hundred feet, except in
curves of small radius (five hundred feet) when they are taken less.

The only calculation necessary in laying out curves, is, knowing the
partial deflection to find the corresponding chord, or knowing the
chord, to get the partial angle.

As the radius of that curve of which the angle of deflection is 1° is
5730 feet, the degree of curvature for any other radius is easily found.
Thus the radius 2865 has a degree of curvature per one hundred feet of

                            5730/2865 = 2°;

again,

                     5730/2000 = 2°.86 or 2° 51.6.

The radius corresponding to any angle is found by reversing the
operation. If the angle is 3° 30′, or 210′, we have

                  (5730 × 60)/210 = 1637 feet radius.

The following figures show the angle of deflection for chords one
hundred feet long, corresponding to different radii:—

                 Angle of deflection.     Radius, in feet.
                       ¼°          or 15′          22920.0
                       ½°          or 30′          11460.0
                       ¾°          or 45′           7640.0
                       1°          or 60′           5730.0
                      1¼°                           4585.0
                      1½°                           3820.0
                      1¾°                           3274.0
                       2°                           2865.0
                      2½°                           2292.0
                       3°                           1910.0
                      3½°                           1637.0
                       4°                           1433.0
                      4½°                           1274.0
                       5°                           1146.0
                      5½°                           1042.0
                       6°                            955.4
                      6½°                            822.0
                       7°                            819.0
                      7½°                            764.5
                       8°                            716.8
                      10°                            573.7

Points in any curve may also be fixed by ordinates, as _a b_, M D′, G F,
or by E _a_, K M, etc.

For the details of locating, of running simple and compound curves, and
of the calculations therefor, the reader is referred to the works of
Trautwine, and of Henck.

[Illustration: Fig. 27.]

59. Suppose now that we have the surveyed lines _m m_, and _n n_, fig.
27, one of which is to be finally adjusted to the ground. The shortest
line is the straight one, which is generally impracticable. The most
level line is the contour line, which is also impracticable. Between
these two lies the right line, which is to be found by an instrumental
location. The line A _n n n n_ B, on the plan, gives the profile A _n n
n n_ B. The line A _m m m m_ B gives the profile A _m m m m_ B, while
the finally adjusted line A 1 2 3 4 5 6 gives the profile A 1 2 3 4 5 6
B.

[Illustration: Fig. 28.]

60. Again, in fig. 28, the straight line A _n n n_ B gives the profile A
_n n n_ B, requiring either steep grades or a great deal of work. By
fitting the line to the ground, as by the line A _a b c d_ ... _m n o_
B, we obtain the profile A _a b c_ ... _m n o_ B.


                       FINAL ADJUSTING OF GRADES.

[Illustration: Fig. 29.]

61. The general arrangement of inclines must not be interfered with to
save work, but a large part of the excavation and embankment may be
saved by breaking up long grades so as not to affect materially the
character of the road. Upon some lines the grades must necessarily
undulate, as in fig. 29. The difference in the amount of work is plainly
seen. The steepest grades thus applied must not be greater than the
ruling grade upon the travel of one engine.

62. In long and shallow cuts and fills, the best plan is to place the
grade line quite high, avoiding much cutting, and to make the
embankments from side cuttings, (ditching). Banks must at least be
placed two or three feet above the natural surface, first to prevent the
snow from lodging too much upon the rails, second, to insure draining.

63. Snow fences are much used in the northern parts of the United
States. These are high pieces of lattice-work, made roughly, but well
braced; from eight to twelve feet high, and standing from sixty to one
hundred feet from the road. The object of the fence is to break the
current of the wind, and cause it to precipitate its snow. Close fences
effect the object no better than the open ones, are more liable to blow
down, and cost more.

64. In locating a road which is to have a double track eventually,
regard must be paid to this fact in side-hill work. The first track
should, if possible, be so placed as not to require moving when the
double line is put on.


                      COMPARISON OF LOCATED LINES.

65. In this comparison there is an element which does not enter the
approximate comparison of surveyed lines, curvature. The resistance
arising from this cause has never been accurately determined. Mr.
McCallum estimates the resistance at one half pound per degree of
curvature per one hundred feet; i. e., the resistance due to curvature
on a 4° curve, would be two lbs. per ton, (see report of September 30,
1855). Mr. Clark estimates the resistance due to curves of one mile
radius and under, as 6.3 lbs. per ton, or twenty per cent. of the whole
resistance. The average radius encountered, therefore, by Mr. Clark,
would be, at Mr. McCallum’s estimate,

                  6.3/0.5 = 12° nearly, or 477.5 feet.

So small a radius is by no means allowable upon English roads; thus the
estimate of Mr. Clark and of Mr. McCallum differ considerably.
Experiments might easily be made with the dynamometer upon different
curves, by which we might find very nearly the correct resistance caused
by curves.

The curvature on any road cannot be adjusted to trains moving at
different speeds.

66. The tractive power acts always tangent to the curve at the point
where the engine is, and thus tends to pull the cars against the _inner_
rail. The tangential force, generated by the motion of the cars, tends
to keep the flanges of the wheels against the _outer_ rail; and only
when a just balance is made between the tractive and tangential forces,
the wheel will run without impinging on either rail, (the wheel being
properly coned). For these forces to balance, there must be a fixed
ratio between the weight of a _car_ and the speed, (not the weight of a
_train_, as the shackling allows the cars to act nearly independently,
some indeed rubbing hard for a moment against the rail, while the next
car is working at ease). Whenever the right proportion is departed from,
as it nearly always is, (and perhaps necessarily in some cases,) upon
railroads, the wheels will rub against one rail or the other. Thus on
any road where the speed on the same curve, or the radii of curvature
under the same speed, differ, there must be loss of power, and dragging
or pushing against the rails.

67. We are obliged to elevate the outer rail (see chapter XIII.), for
the fastest trains, and the slower trains on such roads will therefore
always drag against the inner rails. Thus in practice we generally find
the inside of the outer rail most worn on passenger roads, and the
inside of the inner rail upon chiefly freight roads.

68. It has been the practice of some engineers in equating for
curvature, to add one fourth of a mile to the measured length for each
360° of curvature, disregarding the radius, as the length of
circumference increases inversely as the degree of curvature.

69. Now in equating for grades, in doubling the power we do not double
the expense of working. We however increase it more by curvature than we
do by grades, because besides requiring double power, the wear and tear
of cars and rails and all machinery is increased upon curves, which is
not the case upon grades.

70. The analysis of expense (in Appendix F.) upon the New York system of
roads, gives the following:—

                      Locomotives,   40 per cent.
                      Cars,          20 per cent.
                      Way and works, 15 per cent.
                                     ——
                        or in all,   75 per cent.

Now each 360° will be equal to 75/100 of one quarter of a mile, or
75/400 of a mile; whence the number of degrees which shall cause an
expense equal to one straight and level mile, will be 1920°.

71. The number of degrees by Mr. McCallum’s estimate would be thus:—

The resistance upon a level being ten lbs. per ton, and that due to
curves one half pound per ton, per degree per one hundred feet; the
length of a 2° curve to equal one mile will be

                             10 lbs./1 lb.,

or ten miles. Also ten miles, or 530 hundred feet by 2° is 1060°.

72. Again, by Mr. Clark’s resistance of twenty per cent. of the level
resistance, upon curves averaging 2°, we have as the length of 2° curve

                            10/2 = 5 miles,

or 265 hundred feet, which by 2° gives 530°.

73. Averaging the first and last, we have as the number of degrees which
should be considered as causing an amount of expense equal to one
straight and level mile, 1225°, which averaging with the estimated
resistance by Mr. McCallum, gives finally 1142½° as causing an expense
equal to one straight and level mile, or, in round numbers, 1140°.

74. Suppose now that we would know which of the lines below to choose.

               Line A.    Line B.       Description.
              100 miles, 110 miles, Actual length,
              5000 feet, 3000 feet, Rise,
              3500 feet, 1500 feet, Fall,
                3600°      9000°    Degrees of curvature.

Assuming the speed as twenty miles per hour, the number by which to
equate for grades, see chapter II., is ninety-six, also the number of
degrees for curvature 1140, whence,

        Line A ascending  100 + 52.1  + 3.16 = 155.26  │147.46
        Line A descending 100 + 36.5  + 3.16 = 139.66  │

        Line B ascending  110 + 31.25 + 7.89 = 149.14  │141.31,
        Line B descending 110 + 15.62 + 7.89 = 133.49  │

and if the cost of construction is as the actual, and the cost of
maintaining and working as the mean equated length, we have, as a final
comparison,

                A to B as 100 + 147.46 to 110 + 141.31,

or as

                           247.46 to 251.31.

Here the extra grades on the one hand nearly equal the curvature and the
extra length on the other hand.

75. As a further example in the comparison of competing lines, let us
take the actual case of the location of the eastern part of the New York
and Erie Railroad.

It was questioned which of the two lines between Binghampton and Deposit
should be adopted, and also between the mouth of Callicoon Creek and
Port Jervis.

[Illustration: Fig. 30.]

Between A and _c_, fig. 30, were located the lines shown in the sketch,
one following the Susquehanna river from A to B, thence crossing the
dividing ridge between that river and the Delaware to Deposit (_c_). The
other passing up the Chenango river to _a_, thence crossing first the
summit M to the Susquehanna at L, and second the summit K, to Deposit
(_c_). The elements of the two lines are as follows:—

                           A route, A B _c_.    B route, A M K _c_.
   Length,                               39.29                 43.58
   Rise A to _c_,                       540.00               1087.00
   Rise _c_ to A,                       395.00                936.00
   Whole rise and fall,                 935.00               2023.00
   Degrees of curvature,              2371°.00              3253°.00
   Estimated cost,                 $746,900.00           $628,600.00

Assuming the number by which to equate for grades, as 96, and the
equating number of degrees of curvature as 1140°; equating for grades
and curvature in both directions, we have,

                     Route A. A to _c_.                    │Mean, 46.25.
 39.29 +  540/96 + 2371/1140 = 39.29 +  5.63 + 2.08 = 47.00│
                                                           │
                     Route A. _c_ to A.                    │
 39.29 +  395/96 + 2371/1140 = 39.29 +  4.12 + 2.08 = 45.49│

                     Route B. A to _c_.                    │Mean, 56.96.
 43.58 + 1087/96 + 3253/1140 = 43.58 + 11.32 + 2.85 = 57.75│
                                                           │
                     Route B. _c_ to A.                    │
 43.58 +  936/96 + 3253/1140 = 43.58 +  9.75 + 2.85 = 56.18│

Assuming the cost of working and of maintaining as $4,000 per mile, we
have

 The cost of building A to B as $746,900 to $628,600

 The cost of operating A to B as (46.25 × 4000) × 100/6 to (56.96 × 4000)
    × 100/6,

                or as          $3,083,334 to $3,797,334
                               ——————————    ——————————
                and the sum as $3,830,234    $4,425,934

giving the preference of $595,700 to the route A B _c_, notwithstanding
that the estimate thereon exceeds that on B by $118,300. The route A B
_c_ was adopted.

Again, it was doubtful whether to adopt the route E F, in going from D
to G, or the line I H. The following are the elements of the two lines:—

                                     I H.       E F.
                 Measured length,      61.14      58.53
                 Rise D to G,           1187        454
                 Rise G to D,           1049        316
                 Degrees curve,        7609°      4588°
                 Estimated cost,  $1,094,950 $1,496,430

The mean equated lengths are as follows:—

                     Line I H. D to G.                     │Mean, 79.46,
 61.14 + 1187/96 + 7609/1140 = 61.14 + 12.36 + 6.68 = 80.18│
                                                           │
                     Line I H. G to D.                     │
 61.14 + 1049/96 + 7609/1140 = 61.14 + 10.93 + 6.68 = 78.75│

                     Line E F. D to G.                     │Mean, 66.56.
 58.53 +  454/96 + 4588/1140 = 58.53 +  4.73 + 4.02 = 67.28│
                                                           │
                     Line E F. G to D.                     │
 58.53 +  316/96 + 4588/1140 = 58.53 +  3.29 + 4.02 = 65.84│

The comparison as to cost is

                I H to E F as $1,094,950 to $1,496,430,

and as to working,

    I H to E F as (79.46 × 4000) × 100/6 to (66.56 × 4000) × 100/6,

and the sum as

                          1,094,950 to   1,496,430
                        + 5,297,334    + 4,437,334
                         ——————————     ——————————
                     or  $6,392,284 to  $5,933,764

Although the cost of E F is $401,480 more than that of I H, the line E F
was adopted.




                              CHAPTER IV.
                        PRELIMINARY OPERATIONS.


                             SPECIFICATION.

76. The object of this paper is to define exactly the terms of the
contract as regards execution of work. Every thing therein should be
expressed in a manner so plain as to leave no room for misunderstanding.


                           A AND B RAILROAD.


                  77. _Specification for Graduation._


                                 LINE.

The centre of the road-bed to conform correctly to the centre line of
the railroad, as staked out or otherwise indicated on the ground, and to
its appropriate curvatures and grades as defined and described by the
engineer; and the contractor shall make such deviations from these lines
or grades at any time, as the said engineer may require. The road-bed to
conform to the cross section which shall be given or described, or to
such other instructions as may be given as hereinafter limited; and the
same of the ditches and slopes of the work, and of all operations
pertinent to the satisfactory performance of the graduation or masonry
on the part or parts of the line contracted for.


                               CLEARING.

The ground forming the base of all embankments, and five feet beyond the
foot of the slopes of all embankments, to be cleared as close to the
surface as practicable, of all timber, saplings, brush, logs, stumps, or
other perishable material. The valuable timber to be laid aside, beyond
the clearing as directed by the engineer, the rest to be burned, if this
can be done safely, otherwise to be moved beyond the limits of the
cleared ground. The ground for ten feet beyond the top lines of all
slopes of cuttings shall be cleared in like manner, of all timber and
saplings. Wherever additional ground has to be taken in widening
excavations to obtain materials, or in widening embankments to dispose
of surplus material, or in grading for turnouts or depot grounds, an
additional amount of ground shall be cleared in like manner; and when
directed by the engineer, wherever additional space is required for
outside ditching, or for alterations of roads or watercourses, or
otherwise.


                               GRUBBING.

All stumps and large roots within ten feet of the grade line shall be
grubbed out to the entire width of the work, and moved at least ten feet
beyond the slopes. The cost of all clearing and grubbing is included in
the price for earth work, which price is also understood to include all
clearing and grubbing necessary in borrowing pits, spoil banks, road
crossings, alterations of roads and watercourses, the formation of
ditches or otherwise. The necessary clearing and grubbing in all cases
to be kept completed five hundred feet in advance of any work in
progress.


                                MUCKING.

Wherever mud, muck, or similar soft material occurs in excavations or
embankments, within two feet of subgrade, it shall be removed and
replaced by compact earth or gravel.


                                 GRADE.

The grade lines on the profiles show the true grade, and correspond with
a line two inches below the bottom of the iron rail of the
superstructure. What is called subgrade corresponds with a line placed
eighteen inches below the grade.[5]

Footnote 5:

  The distance between grade and subgrade depends somewhat upon the
  climate, but is generally between one and two feet. See chap. XIII.


                       WIDTH OF ROAD, AND SLOPES.

The width of road-way, unless otherwise directed, shall be twenty-two
feet wide at grade in earth excavations, and eighteen feet wide in rock
excavations. Both rock and earth shall be taken out eighteen inches
below grade for the entire width of road-way. The bottoming to be
replaced by gravel, broken stone, or spawls, in such manner as shall be
directed by the engineer, leaving the necessary ditches of the width and
depth directed on either side. The contractor will not be paid for any
rock excavated beyond the slope lines of one to eight from the required
width, or for any earth excavated beyond slope lines of one and one half
horizontal to one vertical, unless directed by the engineer to move
additional rock or earth.


                               BLASTING.

All blasting shall be done at the risk of the first party, who shall be
liable to the second parties, or to the railroad company, for any
damages incurred in consequence, to dwelling-houses, individuals, or
otherwise.


                                DITCHES.

Whenever required, ditches shall be cut along the tops of the slopes, of
the form and size and in the position directed.


                           SURPLUS MATERIAL.

Whenever the earth or rock required for the adjoining embankments
exceeds the amount in the neighboring excavations, the contractor, when
required, shall increase the width of said excavations, as directed by
the engineer, to a sufficient width for a double track, provided that
this additional width shall not be extended so as to produce an average
haul of more than eight hundred lineal feet, on said borrowed stuff. And
whenever the earth or rock to be moved from any cut exceeds in amount
the adjoining embankments, (unless elsewhere wanted,) it shall be
applied to widening the embankment to a width for a double track, within
the same limits of haul; but for a greater haul than eight hundred feet,
the contractor shall be paid /100 of a cent per yard per hundred feet of
excess.


                              BORROW PITS.

Where the excavation does not furnish sufficient material to make the
adjoining embankments, borrow pits may be opened. But no earth shall be
deposited in spoil banks nor borrow pits opened without the knowledge
and consent of the superintending engineer, who shall take care that
such operations are arranged so as not to damage the road or its slopes,
nor interfere with the widening of the road-bed at a future time for
additional tracks.


                         MATERIAL TO BE SAVED.

If materials be found in the excavations applicable to useful purposes,
such as building stone, limestone, gravel, minerals, etc., they shall be
laid aside in such place as the engineer may direct, for use, to be
applied then or subsequently to the construction of the road under the
conditions of these specifications and of the contract.


                      CLASSIFICATION OF MATERIALS.

_Earth_—every thing except solid and loose rock. _Loose rock_—all
boulders and detached masses of rock measuring over one cubic foot in
bulk and less than five cubic yards. _Solid rock_, includes all work in
ledge, which requires drilling and splitting, and all _loose rocks_
containing more than five cubic yards.

The prices for excavation include all earth or rock excavated in
ditching, bottoming, borrowing, road crossings, alterations of road
crossings and water channels, and the construction of temporary roads,
provided the average distance hauled on each section, be the same as
stated on the schedule here annexed; but if the actual average haul on
any section is found, on completion, to have been greater or less than
the distance stated, a corresponding addition or deduction shall be
made, of one cent per cubic yard per hundred feet which the actual haul
exceeds or falls short of that stated.


                              EMBANKMENTS.

The embankments to be formed fifteen feet wide on the surface, unless
otherwise directed, with slopes of one and one half horizontal to one
vertical. Wherever the embankment is formed from ditching on either
side, such ditching, and the crest of the slopes thereof shall in no
case approach within six feet, nor within double the depth of ditch, of
the foot of the proper embankment slope, allowing always on one side for
a double track; and no soft mud or muck shall be allowed to enter the
bank. Wherever watercourses or new channels for rivers require to be
formed, they shall not approach within once and one half of the depth of
such stream, plus twenty-five feet. Care shall be taken in forming
embankments to exclude all perishable material.


                              SUBSIDENCE.

To allow for the after settlement of materials on embankments, they
shall, when delivered to and accepted by the second parties, be finished
to the full width to the following heights above subgrades, namely: all
banks below five feet in height to be finished three inches above
subgrade; at ten feet in depth, five inches; at twenty feet, six inches;
and twenty-eight feet, seven inches; at thirty-five feet, eight inches;
and at forty feet in depth, nine inches above grade; and intermediate
heights in proportion; the engineer having the power to change these
proportions at his discretion.


                    EXTRA EXCAVATION AND EMBANKMENT.

Whenever it is considered necessary to increase the width of the
road-way for turnouts, water stations, or depot grounds, whether in
excavation or embankment, such work shall be done at the contract
prices, as may be directed. The opening of foundation pits in simple
excavation, where coffer-dams or such like expedients are not necessary,
and in places where such expedients are necessary, all excavation above
the water line shall also be done at such increase or decrease of the
contract price as shall be deemed proper by the engineer.


                   EMBANKING AT BRIDGES AND CULVERTS.

The contractor for earthwork shall not carry forward in the usual way
any embankments within fifty feet of any piece of masonry, finished or
in progress, (counting from the bottom of the slopes,) but shall in
every such case have the earth wheeled to the walls or abutments, and
carefully rammed to such width and depth, and in such manner as may be
directed, when the embankment may be carried on as usual. The expense
attendant upon any damage or rebuilding of mason work, consequent on
neglect of these directions, shall be charged to the account of the
first party. In case the mason work shall not be finished when the
embankment approaches it, the contractor shall erect a temporary
structure to carry over the earth, and proceed with the embankment on
the opposite side; and the expense of said structure shall be paid by,
and charged to, the contractor for masonry, in case such contractor
shall have delayed beyond the proper or required time, the construction
of the mason work; but if the mason work could not have been ready in
season for the bank, then shall the expense belong to the contractor for
the earthwork, whose price for graduation is understood to comprehend
all such contingencies. For the above work of wheeling and ramming
efficiently the earth around any piece of masonry, the contractor shall
be paid —— cents per cubic yard, by the engineer’s measurement.


                        ROADS AND WATERCOURSES.

The first party is to make good and convenient road crossings wherever
directed, and shall also make such alterations of existing roads, or
watercourses, or river channels, or such new pieces of these pertinent
the section undertaken by him, as may be required, and shall be paid for
such work, whether earth, rock, or masonry, the prices, and no more,
applicable to this contract. And such road crossings or other
alterations referred to, he shall make at and within such times and in
such form and manner as the engineer shall direct; and whenever the
operations of the first party interfere with a travelled road, public or
private, either by crossing or by making required alterations on it, the
first party shall so operate as to afford at all times a safe and free
passage to the public travel; and the first party shall be liable for
any damage to which the second parties or the railroad company may
become lawfully liable by reason of his neglect to maintain a safe and
properly protected passage for the current travel.


                              BALLASTING.

Where gravel is used for the ballasting of the road-bed, it shall be of
a quality satisfactory to the engineer, and shall be spread upon the
road-bed to the width and depth required. When broken stone is used, it
shall be of durable quality, and shall be broken so as to pass through a
ring of three inches in diameter. The quantity will be measured in the
road-bed as finished, and the contractor will be required to keep the
ditches trimmed and clear.


                       RIP-RAP, OR RUBBLE SLOPES.

The first party shall distribute rubble stone over the slopes of earth
embankments, whenever required to do so, to protect said slopes from the
action of water. Such stone to be arranged by competent hands, and laid
to such thickness, and with stones of such size, as shall be directed.
Where the contractor has rock in the neighboring cuttings which is
available, it shall be reserved and applied to this purpose; and when
not, good rock shall be obtained where the contractor can conveniently
get it.


                             MEASUREMENTS.

All earth or rock necessarily moved to complete the grading of this
contract according to direction, will be measured in excavation only;
and if the contractor (with the consent of the engineer,) should find it
convenient to waste earth from an excavation, instead of carrying it to
its proper embankment, and to borrow at some nearer point earth for said
embankment to replace that which was wasted, he shall be paid for the
earth from the original excavation in the order of its most economical
arrangement for the second parties. All earth moved from borrowing pits
shall also be measured in excavation only.


                    78. _Specification for Masonry._


                          FIRST CLASS MASONRY.

First class masonry will apply to bridge abutments exceeding twenty-five
feet in height, to the ring stones of arches, and to the piers of
bridges in running water. The stone shall be laid at the rate of one
header to two stretchers, disposed so as to make efficient bond. No
header to be less than forty inches long, and no stretcher to be less
than eighteen inches in width. No stone less than twelve inches in
thickness, no stone to have a greater height than width, all stones to
be placed upon the natural bed. The masonry throughout to have hammer
dressed beds and joints. Vertical joints to be continued back at least
ten inches from the face of the wall. The mortar joints on the face not
to exceed one fourth of an inch in thickness. The stone to be laid with
regard to breaking joints in the adjoining courses. The stone must be
dressed complete before laying, and not be moved after being placed in
the mortar. The face will not be tooled, but only roughly hewed, except
for one half inch from the beds and joints, where it will be hammered.
The ring stones of arches shall have beds to conform to the radius of
the arch, with the end joints vertical, and be made to set smoothly on
the centering, with the beds with the proper inclination. Each stone
must extend through the whole thickness of the arch, and not be less
than eight inches thick on the intrados. No spawls or pinners will be
admitted. The ring stone shall be dimension work, according to the plans
furnished, the beds and joints being truly dressed, but the faces left
rough.

All first class work shall be carefully laid in good cement mortar, (see
Art. Cement). Each stone before being laid shall be carefully cleaned
and moistened; and masonry built in hot weather shall be protected from
the sun as fast as laid, by covering with boards. Copings shall be built
of stone of equal thickness, neatly dressed and laid.

All first class masonry shall be well pointed with cement pointing.


                         SECOND CLASS MASONRY.

To be applied to abutments less than twenty-five feet high, ring and
face walls of bridges and culverts, and to piers not in running water,
shall consist of stones cut in bed and build to a uniform thickness
throughout, before being laid, but not hammered; they shall be laid on a
level bed, and have vertical joints continued back at right angles at
least eight inches from the face of the wall. The work need not be
carried up in regular courses, but shall be well bonded, having one
header for every three stretchers, and not more than one third of the
stones shall contain less than two cubic feet, or be less than nine
inches thick; and none of that third shall contain less than one and one
half cubic feet, or be less than six inches thick. No more small stones
shall be used than necessary to make even beds, the whole to be laid in
cement mortar and pointed.


                          THIRD CLASS MASONRY.

Applicable to culverts, and to the spandrel backing of arches, shall
consist of strong and well built rubble masonry, laid dry for culverts,
but wet for backing. The culverts to be of such form and dimensions as
the engineer may direct. The foundation courses of the side walls to
consist of large flat stones, from eight to ten inches in thickness,
laid so as to give a solid and regular basis for the side walls. The
side walls to be laid with sound stone, and of sufficient size, and with
beds having a fair bearing surface and good bond. The covering stone for
culverts being not less than ten inches thick for two feet culverts,
twelve inches for three feet culverts, and fifteen inches for four feet
culverts; to be free from flaw or defect, and to have a well bedded rest
upon each side wall, of not less than twelve inches for two and three
feet culverts; and not less than fifteen inches for larger ones. In case
such stone cannot be obtained, a dry rubble arch may be thrown instead,
well pinned and backed; but the price for the arch shall not be more
than the general price for third class masonry, with an allowance for
the centering.


                         FOURTH CLASS MASONRY.

Applicable to cattle-guards, pavement of culverts, and slope and
protection walls, shall consist of stones of not less than one cubic
foot in contents, so laid and bonded as to give the greatest degree of
strength in preference to appearance; being laid when directed with beds
perpendicular to the inclined face. Pavements under culverts shall be
made by excavating one foot in depth of that part to be paved, which
space shall be filled with flat stones one foot wide, set on edge, close
together, and made to present an even upper face.


                     TIMBER AND PLANK FOUNDATIONS.

Timber and plank foundations require the beds to be perfectly well
levelled, and timber of such dimensions, and so laid, as shown by the
plans; to be well bedded and brought to an even and level top surface.
The spaces between them to be filled and well rammed with such material
as the engineer may direct. On these timbers planks shall be laid, and
trenailed or spiked if required. The materials shall be of quality and
shape approved by the engineer, and the price shall be in full for
material and labor in laying the whole in a thorough and workmanlike
manner.


                                PILING.

Piling may be used either as bearing piles for foundations, or for piled
bridges. In the former case they will be bid for by the running foot
driven, and in the latter by the stick of twenty-five feet in length.
The piles in either case must be straight round timber, of a quality
approved by the engineer, not less than ten inches in diameter at the
small end, barked, and properly banded and pointed for driving. They
shall be driven in such places, and to such depths as required, and the
heads cut off square, or finished with a tenon to receive caps, as may
be required. Bearing piles will be cut off so far below the lowest water
that any timber foundation laid thereon shall be at all times entirely
immersed.


                                CEMENT.

Cement when used shall be of the best quality, hydraulic, newly
manufactured, well housed and packed, and so preserved until required
for use. And none shall be used in the work until tested and approved by
the engineer.


                             CEMENT MORTAR.

The proportion of sand and cement for construction shall be one of
cement, to two of clean, sharp sand, unless in special cases the
engineer direct otherwise, for which due allowance shall be made. It
shall be used directly after mixing, and none remaining on hand over
night shall be remixed.


                              LIME MORTAR.

Lime mortar (which in all cases shall contain cement), will consist,
unless otherwise directed, of two parts of best quick lime, one of
cement, and five of sand; the ordinary mortar of lime and sand being
first properly made, and the cement thrown in and thoroughly mixed
immediately before using.


                               CONCRETE.

Whenever concrete is required to be used, it shall be formed of clean
broken stone, cement, and sharp, clean sand. The stone, which shall be
of satisfactory quality, shall be broken so as to pass through a ring
three inches in diameter. The cement and sand shall be thoroughly mixed
in the proportions already described for cement mortar. Thus prepared,
it shall be carefully mixed with the broken stone in the proportion of
one of mortar to two or two and one half of broken stone, as the
engineer upon experiment shall determine, and shall be immediately laid
carefully in its place, and well rammed. The concrete shall be protected
on the sides by boards, and be allowed to remain undisturbed after
laying until it is properly set; and in special cases the engineer shall
direct the mode of application. For the proper preparation and laying of
such concrete, there shall be paid the price applicable to second class
masonry. The contractor shall furnish all tools and plank necessary to
the operation.


                               POINTING.

All masonry in cement or lime will be finished with a good pointing of
cement, without extra charge.


                               BRICKWORK.

When bricks are required, or allowed to be used, they shall consist of
sound, hard-burned brick, laid in cement, or common mortar, as directed,
and no soft or salmon brick will be admitted; and none but regular
bricklayers must be employed.


                         CENTERING AND BACKING.

The whole top of all arches, whether brick or stone, shall be finished
by plastering with a good coat of cement, so as to prevent the
percolation of water, and turn it away from the arch. The centering
shall be such as the engineer approves of in every respect, and shall
not be removed until he directs. The cost of backing to be included in
the price bid. For arches of more than twenty-five feet span,
compensation shall be made, at the engineer’s estimate, for the extra
value and cost of the centering proper for large arches.


                           GENERAL PROVISION.

79. The engineer reserves the right to require the whole or any part of
the above described work of masonry to be laid in cement, lime, mortar,
or dry, at his discretion. First and second class masonry, and
brickwork, will be bid for at prices for laying in cement, from which
will be deducted fifty cents per yard if laid in lime mortar, and one
dollar if laid dry. Third and fourth class masonry at prices for laying
dry, to which will be added fifty cents per yard if laid in lime mortar,
and one dollar if laid in cement.


                              SCAFFOLDING.

80. Nothing shall be allowed for workmanship or timber of any
scaffolding used in the construction of timber bridges, or in carrying
up abutments, piers, coffer-dams, or otherwise. Should the timber used
in any coffer-dam be carried away by floods, the renewal of it shall
fall upon the first party.


                              FOUNDATIONS.

81. The foundations for all structures shall be executed by the
contractor for masonry in such manner and to such depth as to secure a
safe and secure foundation, of which the engineer will judge. If a
natural foundation cannot be procured at a reasonable depth, then the
contractor shall prepare such artificial foundation as the engineer may
direct. The stuff moved from the foundations, if of the proper quality,
shall be deposited in the adjoining embankment, provided the site for
said embankment has been cleared of all perishable material. So much of
the stuff as shall not be fit for the embankment, and all roots, stumps,
etc., shall be deposited beyond the limits of the clearing, so as not to
obstruct roads, watercourses, or ditches.

For the earth moved from such foundations, and for all earth used
according to direction, in the construction of coffer-dams, there shall
be paid —— cents per cubic yard.

Whenever it may be necessary to pump or bale water in the foundations,
the contractor shall furnish the pumps or buckets, and all scaffolding
and apparatus necessary to work them. He shall be allowed the net cost
of all labor employed in the operations of pumping or baling water, and
shall make a monthly return to the engineer of the value of such labor,
provided that these operations are conducted in an economical manner,
with efficient men, pumps, and tools, under the direction and to the
satisfaction of the engineer. He shall also be allowed such compensation
for the use of the pumps and apparatus, and for superintendence, as the
engineer shall judge to be fair and reasonable.


                             TRESTLE WORK.

82. Includes all wooden structures commonly used as substitutes for
abutments and piers, and for farm passes, etc., etc. These shall be
built according to the plans furnished, and directions given by the
engineer, of sound, durable material, to be approved by him. The price
bid shall be by the thousand feet board measure, and will be considered
as in full for all material except iron, and for the labor of building
and erecting complete. The iron used will be of the best American, and
the workmanship of approved quality. The bids will be by the pound, and
will cover all cost of material and the labor incident to its use.
Spikes and nails when used will be furnished by the contractor at cost.


                               BRIDGING.

83. Contractors may submit plans for bridging in connection with, or
separate from their bids; but the engineer of the company may reject
such plans if he choose, and substitute others, which if the contractor
decline building at the approved prices, may be let to other parties. In
every case, the exact manner of building, erecting, adjusting, and
finishing bridges, and the determination of the nature and amount of
material, will be specified by the engineer. The price bid must be by
the running foot of the whole _length_ of bridge, as erected and
finished complete.


                84. _Specifications for Superstructure._


                               SUBSILLS.

To maintain the track in good adjustment until embankments are settled,
subsills will be laid on certain banks, and likewise in cuts where the
imperfect nature of the bottoming may, in the opinion of the engineer,
render them expedient. These subsills to be fairly bedded in the earth
or ballasting, and carefully adjusted and rammed so as to correspond
with the grade lines given by the engineer. An additional piece of sill,
four feet long, shall be laid at each joint of the subsill, either under
the sill, or alongside, as may be directed. The sills will be of 3 × 9
plank, in length of twelve, fifteen, eighteen, and twenty-one feet; of
which one fourth may be below fifteen, one fourth below eighteen, and
one fourth below twenty-one feet. The plank must be square at the ends,
and of sound, durable material, and not have more than two inches wane
on one end only. There will be about 25,000 feet, board measure, laid
per mile where it may be required, and 660 joint sills, 3 × 9 inches,
and four feet long. When the depth of stuff to be moved to admit the
subsills exceeds six inches, an allowance shall be made for extra labor,
the amount of which shall be noted by the assistants on their receiving
notice of such extra labor from the contractor or his agent.


                              CROSS TIES.

The cross ties shall be of white, black, or yellow oak, burr oak,
chestnut, red elm, black walnut, or other sound timber of suitable
character in the opinion of the engineer. Eight feet long, and not more
than three inches out of straight, hewn to a smooth surface on two
parallel plane faces six inches apart, the faces being not less than
seven inches wide for at least half of the number, and the remainder not
less than six inches wide. The ties shall be carefully and solidly laid
on the subsills, or ballasting, or earth previously properly prepared,
so as to give the true planes required by the rails, whether on straight
or curved lines. They shall be laid at the rate of eight ties to each
eighteen feet rail. All imperfect ties shall be excluded by the
tracklaying party. The surface of the ties to be faithfully adjusted to
the grades given, and to the web of the rail; and the rail to be truly
laid and firmly spiked so as to correspond neatly to the alignment of
the road. There will be about 2,500 ties required per mile of road.


                           CHAIRS AND JOINTS.

When chairs are used, they shall be such as directed by the engineer,
and furnished by the company, and shall be well and accurately placed
and spiked in such manner and position as required. When chairs are
used, the largest ties shall be selected for the joints. When the joint
is made by fishing, there will be no tie directly under the joint.


                                 RAILS.

The rails will weigh about sixty pounds per lineal yard. No rail shall
be laid on the tangents which is in any way twisted or bent. It shall be
the duty of the first party to correct and make true any crooked rails
received by him, also to bend to the proper curve, and in such a manner
as not to affect the strength of the bar, all rails laid in curves.
Punching of rails, and cutting, will also be done by the contractor.


                             TRACK LAYING.

The materials composing the track will be furnished by the company, and
it will be laid in the best manner according to the conditions
following. The track will be laid on cross-ties, and the ties at the
proper places on subsills. Where the sills are used, they will be laid
with four feet blocks at the joints, and with six feet blocks at the
rail joints, the whole being set to their places by stakes, and by the
engineer’s directions, and mauled down to a perfect bearing, being
settled at least half an inch by mauling. The cross ties will be placed
uniformly distant, (twenty-eight inches from centre to centre). The iron
must be so cut or selected that the joints of the parallel rails shall
be within two inches of being opposite to each other; no joint tie being
allowed a greater amount of askew than this, whether on tangents or
curves. A slip of metal shall be inserted at the rail joints while
laying, to keep the rails apart sufficiently to allow for expansion,
which thickness, (depending upon the temperature,) shall be fixed by the
engineer. Notches to be cut at the centre of each bar, to correspond
with half a spike, to prevent longitudinal motion of the rails. Each
joint chair to be fastened with four spikes. Two spikes at each end of
each tie upon straight lines and upon curves of less than 1,500 feet
radius at the outer end of the tie two spikes outside and one inside,
and at the inner end two spikes outside and one inside of the rail. Upon
curves the outer rail to be raised by such an amount, depending on the
radius of curvature, as the engineer may direct.


                               TURNOUTS.

The contractor to put in such turnouts and sidings, with the necessary
frogs and switches, as may be required; the frogs and switches to be
firmly and truly placed in position so as to work easily.


                         FILLING AND DITCHING.

The stuff moved in bedding the sills and ties, to be placed between the
latter. The ditches to be properly cleaned out after the track is laid;
the filling never to rise higher than the top of the cross tie. Any
surplus stuff to be moved out of the cuts, or if on embankment, to be
thrown over the bank, leaving the track and road-bed in a neat and
workmanlike shape.


                         DELIVERY OF MATERIALS.

The ties and sills to be delivered at some point on the road as near as
possible to the places where they are to be used, in no case requiring
more than one thousand feet of haul; to be so piled as easily to be
counted and inspected. The bids for ties will be by the piece; the
proposal stating the number and conditions; the sills to be bid for by
the thousand, board measure. All material furnished in connection with
track laying to be delivered in such manner and time as to comply in
good season with the contract for laying the rails.


                         MEASUREMENT OF TRACK.

The measurement of track laid shall include the turnouts, measuring from
heel to heel of switch. No extra allowance being made for putting in
frogs or switch machinery.


                    85. _Specification for Fencing._

Bids for fencing will be by the running foot, or mile, including both
sides of the road. Where required, it will consist of posts placed eight
feet apart from centre to centre, set three feet into the ground, either
by digging or boring, and not by mauling. The posts shall be of oak,
elm, chestnut, or other durable wood, not less than eight inches in
diameter at the bottom, barked and charred where put into the ground.
The boards to be 6 × 1 inches, and to square sixteen feet long, to be
placed six inches apart vertically, and fastened to the posts with
tenpenny nails at each bearing, and breaking joint with each other.
There will be five bars in depth, the top of the uppermost being five
feet from the ground. In side hill and in ground liable to slide,
particular care shall be taken to place the posts firmly in the ground.
At cattle guards, the fence will be turned in to the proper distance,
and such arrangement made as to prevent the passage of animals.


                       86. _General Provisions._


                            CLASSIFICATION.

The classification of material excavated will be referred to the
engineer, in all cases where the nature of the material is questioned,
and his judgment taken thereon. Also all material used in structures
will be submitted to the inspection of the engineer or his assistants.


                 QUANTITIES AND QUALITIES APPROXIMATE.

The quantities and qualities of work presented in the schedule are
merely approximate, and the information given on the maps and profiles
in relation thereto is according to the best present knowledge. The
company retains the right to change at any time during the progress of
the work, the alignment, grades, and width of the road, or any part
thereof; and also the limits of the sections, or to alter the character,
vary the dimensions, or change the location of structures, or substitute
one kind of work or material for another, or to omit entirely, when
found necessary, or to require to be built where not now contemplated;
and the contractor shall carry into effect all such alterations when
required, without the contract prices being thereby affected, unless the
aggregate value of all work contemplated by the contract be changed full
twenty per cent., in which case a fair allowance, either for the company
or the contractor, shall be made by the engineer. In case, however, the
aggregate value of the work be changed by over twenty per cent. of the
original amount, and the contractor be not satisfied with the altered
compensation, then said contractor may throw up said contract, on
condition, that within ten days after receiving notice from the engineer
of such alteration, he give written notice to the engineer or the
company of his desire to do so. In which case, as in other cases of
throwing up the contract, he shall as soon as desired, give peaceable
possession to the company or their agents; leaving also in their
possession any tools or machinery upon which they have advanced any
thing; and the company may then settle with the contractor on the
measure of damages which either shall suffer.


                BASIS FOR ESTIMATING EFFECT OF CHANGES.

The basis for estimating any changes as above mentioned is understood to
be the schedule exhibited at the letting.


                       NO LIQUOR, AND GOOD ORDER.

The contractor shall not sell, or allow to be sold or brought within the
limits of his work any spirituous liquors, and will in every way
discountenance their use by persons in his employ. He will do all in his
power by his own act, or by assisting the officers of the county, or of
the corporation, in maintaining the laws and such regulations as conduce
to good order and peaceable progress, and prevent encroachment on the
rights of persons or property; and he shall discharge from his service,
when required by the engineer, any disorderly, dangerous, insubordinate,
or incompetent person, and refuse to receive into his employ any who may
have been discharged for such cause from other parts of the work.


                           MONTHLY ESTIMATES.

Measurements and estimates shall be made by the engineer once in each
month, by means of which may be known approximately the amount of work
done, and the contractor shall be entitled to payment therefor at such
rates below his contract prices as the engineer or president of the
company deems expedient; it being understood that the contractor has no
claim on account of any material not laid in its place in the road-way,
or for labor bestowed thereon; and the quantities shall be estimated
from the dimensions when so laid, though on the advice of the engineer,
advances may be made on such material when delivered for use, in which
case it becomes the property of the company, in the contractor’s care
and keeping, and he becomes liable for its loss or injury.


                              EXTRA WORK.

No claim for extra work or for work not provided for in the contract
shall be allowed, unless a written order to perform such work shall have
been given by the engineer; or that the work be subsequently certified
by him, and the certificate produced at the time of demanding the
payment of the monthly estimate next after such work shall have been
performed.


                             SUB-CONTRACTS.

The contractor will be required to perform the work himself, and no
sub-contracts relieving him from the responsibility of a proper
performance of his contract will be permitted, unless by the written
consent of the president of the company. And no moneys shall be paid to
any such sub-contractor for work or materials, without sufficient
authority from the principal contractor.


                       WHEN WORK TO BE COMMENCED.

On the acceptance of a proposal, the chief engineer will give notice
thereof to the person proposing, by letter directed to his stated
address; and in twenty days from the date of such notice, provided there
be no impediment on the part of the company, or in twenty days after
such impediment is removed if there be, the work shall be begun with an
adequate force, and from that time be prosecuted vigorously until its
completion.


                            HOW TO PROGRESS.

It shall be understood that proper progress is not made, if the amount
of work done in each month is not in due proportion to the total amount
to be done up to the time fixed for completion by the contract; in which
case the engineer shall call the attention of the contractor (or whoever
may be in charge of the work if the contractor be absent,) to the fact,
and state to him what additional exertion is necessary to be made, and
what further force is required, in such reasonable time as may be
prescribed.


                         PUTTING ON MORE FORCE.

In default of the contractor’s making such additional exertion, and
supplying such force, the chief engineer, or president of the company
may have such force sent to the work, and the necessary buildings may be
erected to receive them at the contractor’s charge and expense, who
shall receive the said force in his employ, and work it at whatever
price it may have been found necessary to employ it, without diminishing
the previous force of the work, and regarding always such extra force as
if employed by himself.


                         CAUSES FOR DETENTION.

There shall be no claim for detention on account of work not being laid
out, unless a written notice three days in advance, that it is required,
shall have been given to the engineer; and the damage for such detention
shall be estimated by the engineer. The right of way shall be furnished
by the company, but if it fail to do so for any particular place,
damages for detention shall not be claimed unless the contractor be
detained full twenty days after he shall have given written notice to
the engineer of his wish to commence work at such place. Then the
engineer may either estimate to him the amount of damage which he shall
take as satisfactory, or he may extend the time of the completion of
such work by as many days beyond the contract time, as the contractor is
detained beyond the twenty days following his notice to the engineer.


                             THE ENGINEER.

In all cases where the word “engineer” is used, the engineer in charge
of construction is meant; but the directions of any subordinate engineer
shall be obeyed when given in regard to any of the ordinary operations,
or where they are evidently in accordance with the specifications, or
when transmitting the orders of his superiors. In other cases they may
be referred to the resident engineer, and finally to the chief engineer,
he being the authorized officer, at the time acting in that capacity.


                              CONTRACTOR.

The word “contractor” applies to and includes all persons contracting
jointly, any one of whom shall be considered the authorized agent for
and in behalf of his associates, and empowered to receipt payment of
moneys, receive and act upon orders.


                             THE CONTRACT.

87. This is the mutually binding legal article of agreement between the
contractor and the company, specifying the times of completing, manner
of payment, and describing the work which is to be done. Thus:—

                       A AND B RAILROAD COMPANY.

                              _Contract._

           Graduation on sections A C D,
           Masonry on sections A C D,
           Ballasting on sections A C D,
           Bridging on sections A X T,
           Fencing on sections O O O,
           Sills and ties on sections O O O,
           Track laying on sections O O O.

                               ____________ }
                               ____________ } _Contractors._

Articles of agreement made and concluded this first day of January, A.
D. 1857, between —— of the first part, and the A and B Railroad Company
of the second part, being a company duly incorporated by the State of ——
of the second part, whereby it is mutually agreed as follows, namely:
The said party/parties of the first part hereby agree to and with the
said party of the second part that he/they will perform in a substantial
and workmanlike manner the following work, namely:—

                      [_The work here described._]

The said work to be performed and completed agreeably to the directions
and to the approval of the chief engineer of said company for the time
being, and subject to all the general provisions of the specification
attached to and forming a part of this agreement, and also subject to
such of the special provisions of said specifications as are applicable
to the work hereby contracted for.

And in consideration of the full and faithful performance by the said
party/parties of the first part of this agreement on his/their part, the
said party of the second part hereby agrees to pay for the same in the
time and in the manner hereinafter mentioned, at the rates as follows,
namely:—

          [_Here insert the items and corresponding prices._]

It is mutually agreed that this contract applies only to those items to
which prices are attached, and that where it embraces both labor and
materials introduced in the work, such prices are in full compensation
therefor when introduced in the manner required. When it embraces
materials only, such prices are in full compensation for the materials
and the labor necessary to deliver the same to the company, and when it
embraces labor only, such prices are in full compensation for such
labor, and every incident to its complete and proper performance. In
every case the estimate for ascertaining the amount of compensation
shall be made by the engineer from the actual work, from the material
furnished, or from that on which the labor contracted for is bestowed.

It is also agreed that partial payments shall be made from time to time
during the progress of the work as follows:—

                    [_Times and manner of payment._]

And that in thirty days after the contract is fully completed to the
satisfaction of the chief engineer of the company for the time being,
and the work is surrendered to and accepted by the company, a final
measurement and estimate thereof shall be made under the direction of
the chief engineer, and be duly certified by him, on the return of which
to the president of the company the whole amount then found to be due to
the said party/parties of the first part shall be paid to him/them on
demand as follows:—

                      [_Insert mode of payment._]

And it is also hereby further agreed, that bank-bills current in the
State of —— shall be accepted for cash in payment for all claims under
this contract.

And the said party/parties of the first part further agree/agrees that
in twenty days after he/they shall be notified to do so, as provided for
in said specifications, he/they will begin the work hereby contracted to
be performed, with a force of all kinds sufficient for its completion in
the time herein prescribed, and that he/they will finish and deliver the
same to the company fully completed in all its parts as follows:—

                  *       *       *       *       *

And the said specifications hereunto annexed are hereby made a component
part of this contract and (except so far as any provision therein may
not be pertinent to the subject-matter of the contract or may be
specially modified herein,) shall be looked to in ascertaining the
meaning, extent, and purport of this agreement, and in determining the
rights, powers, duties, privileges, and obligations of the contracting
parties as to any particular embraced therein.

In virtue whereof the said party/parties of the first part has/have
hereunto set his/their hand and seal, and the said party of the second
part have caused their president to subscribe his name and affix the
corporate seal of the company hereto, all done in triplicate the day and
year first above written.

                                       _Contractor’s name_,      [SEAL.]
                                       _President’s name_,       [SEAL.]


                           SOLICIT FOR BIDS.

88. The approximate estimates, plans, and profiles being made, and other
preliminaries settled, proposals for executing work are solicited by the
public papers. Thus:—

                                    NEW YORK, January 1, 1857.         }
                               Office of the A and B Railroad Company. }

Proposals for executing the graduation, bridging, masonry, and track
laying, and for the supply of materials upon the A and B railroad will
be received at this office until the 31st day of January, 1857.

Plans, profiles, and schedules of amounts of work may be seen, and blank
bids obtained by application at this office.

All proposals must be directed to the chief engineer of the A and B
Railroad Company.

No bids will be received after January 31st, at 12, M.

                            Per order,
                                    C. D., _Secretary A and B R. R. Co._


                            FORM FOR A BID.

89. That proposers may make their bids in a convenient form for
comparison, a blank, somewhat like the following, is given them to fill
out.

 ┌─────────────────────────────────────────┬──────┬──────┬──────┬──────┐
 │           Number of Section.            │ Sec. │ Sec. │ Sec. │ Sec. │
 │                                         │  1.  │  2.  │  3.  │  4.  │
 ├─────────────────────────────────────────┼──────┼──────┼──────┼──────┤
 │            Length in miles.             │  1½  │  1¼  │  1¾  │  1½  │
 ├──────────────┬──────────────────────────┼──────┼──────┼──────┼──────┤
 │Graduation.   │Clearing and grubbing,    │      │      │      │      │
 │              │Price per acre,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Earth excavation,         │      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Loose rock excavation,    │      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Solid rock excavation,    │      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Average haul on section,  │      │      │      │      │
 │              │Ballasting,               │      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Whole cost of graduation, │      │      │      │      │
 ├──────────────┼──────────────────────────┼──────┼──────┼──────┼──────┤
 │Masonry.      │First class masonry,      │      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Second class masonry,     │      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Third class masonry,      │      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Foundation timber,        │      │      │      │      │
 │              │Cost per M., b’d measure, │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Excavation for foundation,│      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Rip rap,                  │      │      │      │      │
 │              │Price per yard,           │      │      │      │      │
 │              │Cost on the section,      │      │      │      │      │
 │              │Whole cost of masonry,    │      │      │      │      │
 ├──────────────┼──────────────────────────┼──────┼──────┼──────┼──────┤
 │Bridging.     │Detailed as above,        │      │      │      │      │
 ├──────────────┼──────────────────────────┼──────┼──────┼──────┼──────┤
 │Track laying. │                          │      │      │      │      │
 ├──────────────┼──────────────────────────┼──────┼──────┼──────┼──────┤
 │Fencing.      │                          │      │      │      │      │
 └──────────────┴──────────────────────────┴──────┴──────┴──────┴──────┘

This form being filled out, evidently gives the cost of each or all of
the items upon any one or all of the sections, the cost of all the items
upon any one section being at the foot of that section, and the whole
cost of any one item at the extreme right and on the line of that item.

On the bottom of the form is printed, “The undersigned having read the
specifications, and made due examination, hereby proposes to the A and B
Railroad Company, to perform the work in the above schedule, to which
he/they has/have set figures, at those prices and under the conditions
described, and upon acceptance of this proposal by the company,
binds/bind himself/themselves to enter into a written contract to that
effect, and to furnish the required security.

                                                          _Name_,
                                                              _Address_,

 _Name of Surety_,
     _Address of Surety_.”


                          COMPARISON OF BIDS.

90. The bids being received, are compared as follows:—

 ┌───────┬──────────────────────────────┬──────────────────────────────┐
 │Name of│         Graduation.          │           Masonry.           │
 │bidder.│                              │                              │
 ├───────┼─────┬─────┬─────┬─────┬──────┼─────┬─────┬─────┬─────┬──────┤
 │       │Sec. │Sec. │Sec. │Sec. │Total.│Sec. │Sec. │Sec. │Sec. │Total.│
 │       │ 1.  │ 2.  │ 3.  │ 4.  │      │ 1.  │ 2.  │ 3.  │ 4.  │      │
 ├───────┼─────┼─────┼─────┼─────┼──────┼─────┼─────┼─────┼─────┼──────┤
 │   A   │     │     │     │     │      │     │     │     │     │      │
 │   B   │     │     │     │     │      │     │     │     │     │      │
 │   C   │     │     │     │     │      │     │     │     │     │      │
 └───────┴─────┴─────┴─────┴─────┴──────┴─────┴─────┴─────┴─────┴──────┘

 ┌───────┬──────────────────────────────┬──────────────────────────────┐
 │Name of│          Bridging.           │       Superstructure.        │
 │bidder.│                              │                              │
 ├───────┼─────┬─────┬─────┬─────┬──────┼─────┬─────┬─────┬─────┬──────┤
 │       │Sec. │Sec. │Sec. │Sec. │Total.│Sec. │Sec. │Sec. │Sec. │Total.│
 │       │ 1.  │ 2.  │ 3.  │ 4.  │      │ 1.  │ 2.  │ 3.  │ 4.  │      │
 ├───────┼─────┼─────┼─────┼─────┼──────┼─────┼─────┼─────┼─────┼──────┤
 │   A   │     │     │     │     │      │     │     │     │     │      │
 │   B   │     │     │     │     │      │     │     │     │     │      │
 │   C   │     │     │     │     │      │     │     │     │     │      │
 └───────┴─────┴─────┴─────┴─────┴──────┴─────┴─────┴─────┴─────┴──────┘

            ┌───────┬──────────────────────────────┬──────┐
            │Name of│           Fencing.           │Grand │
            │bidder.│                              │Total.│
            ├───────┼─────┬─────┬─────┬─────┬──────┼──────┤
            │       │Sec. │Sec. │Sec. │Sec. │Total.│      │
            │       │ 1.  │ 2.  │ 3.  │ 4.  │      │      │
            ├───────┼─────┼─────┼─────┼─────┼──────┼──────┤
            │   A   │     │     │     │     │      │      │
            │   B   │     │     │     │     │      │      │
            │   C   │     │     │     │     │      │      │
            └───────┴─────┴─────┴─────┴─────┴──────┴──────┘

From which the names may be easily selected either for one or more
sections, for any or all of the items, that shall give the least cost.




                               CHAPTER V.
                            LAYING OUT WORK.


91. The running of the line consists in placing a stake at every one
hundred feet upon tangents, and at every fifty feet distance upon sharp
curves; also a permanent post at each tangent point, and at points of
compound and reversed curvature. This is the centre line, the axis of
the road, and the base of all field operations. Wherever the work is
going on, the centre pins should be referred to fixed points outside of
the ground occupied by the road.

92. The first operation in preparing for excavation is to place side
stakes at one half the width of road-bed plus the ditch, on each side of
the centre line.


                                SLOPES.

93. Setting out slopes is a term applied to laying off upon the ground,
on each side of the centre, the distance to which the slope, commencing
at the outer edge of the ditch, will extend, depending upon the angle of
slope, width of road-bed and ditch, and depth of cutting. There are here
five distinct cases which may occur:—

In embankment when the natural surface is horizontal. In embankment when
the natural surface is inclined. In excavation when the natural surface
is horizontal. In excavation when the natural surface is inclined.

In mixed work (side hill,) when the road-bed is partly in cut and partly
in fill. In both excavation and embankment, when the natural surface is
horizontal, we have only to add the cut, in feet and decimals,
multiplied by the slope, to one half the width of road-bed plus ditch.

            Thus suppose the cut is              20.55 feet,
              half the road-bed,                 10.25 feet,
              ditch,                              3.00 feet,
              slope 1½ horizontal to 1 vertical,

and we have

               (20.55 × 1½) + 10.25 + 3.0 = 44.075 feet.

When the ground is inclined transversely to the axis of the road, first
assume a point upon the ground, (apparently right) find its height above
grade with the level, multiply this by the slope and add one half the
distance between the outer edge of ditches, and see how near it comes to
the measured distance from the centre to the assumed point; if within a
foot, it will answer; if not, a second trial will fix the place.


                               CULVERTS.

94. The length of any structure passing under a railroad embankment is
_L_ – 2_Rh_, where _L_ is the distance between slope stakes, _R_
inclination of slopes, _h_ the height of structure from the natural
surface. Thus, suppose the distance between slope stakes to be 100 feet,
slope 1½ to 1, and _h_ 10 feet, we have

            _L_ = 100 – (10 × 1½ × 2) = 100 – 30 = 70 feet.

The length of an oblique structure will of course be greater than that
of one at right angles to the road; the length depending upon the
obliquity.


                                MASONRY.

95. There are eight general cases which may occur in laying out such
structures as bridge abutments with wings.

               1. A right bridge on a level tangent.
               2. A right bridge on a level curve.
               3. A skew bridge on a level tangent.
               4. A skew bridge on a level curve.
               5. A right bridge on an inclined tangent.
               6. A right bridge on an inclined curve.
               7. A skew bridge on an inclined tangent.
               8. A skew bridge on an inclined curve.

And these eight cases will vary again according to the natural surface
of the ground, whether horizontal, or inclined transversely.

96. The general position of wing walls and general form of the line
inclosing the base of the bridge, is shown from fig. 31 to fig. 38. Fig.
31 represents case one. The points A, B, C, D, are fixed by squares from
the centre line at E F, G H.

[Illustration: Fig. 31.]

Fig. 32 represents case two. The wings 3_c_, 4_d_, must evidently have a
different inclination from A1, B2. The points A, B, _c_, _d_, 1, 2, 3,
4, as before, are laid off by squares from a tangent to the curve.

[Illustration: Fig. 32.]

Fig. 33 explains itself.

[Illustration: Fig. 33.]

[Illustration: Fig. 34.]

Fig. 34, case five. Here the wings A1, C4, are the same, as also B2, D3,
the former being longer, on account of the greater depth of the fill.

[Illustration: Fig. 35.]

Fig. 35, case seven. Here each wing is peculiar; the figure being a
compound of figs. 33 and 34.

[Illustration: Figs. 36 and 37.]

Figs. 36 and 37, case 8. This is the most difficult of all. No two wings
have the same length or inclination on plan. The natural surface being
horizontal, the line inclosing the bridge is A″ B″ C″ D″. If the natural
surface descended from C″ to A, the position taken would be A, B, C, D.
Fig. 37 is the elevation of the position A B C D. The several points are
laid off from the line _n_, _n_.

The general manner of fixing the lines of figures 31 to 38, is to assume
the angle of some one wing, as A 1, in fig. 34, to draw A C parallel to
E F; and from C, the intersection of A C with the base of the
embankment, C 4 gives the other wing. Local circumstances will of course
often fix at once the length and angle of the wings. Upon simple curves,
as in fig. 32, the lines A _c_ and B _d_ are made radial.

97. In curving a viaduct, the axes of the piers are made radial to the
centre of the located curve, and the planes of the springing lines are
made parallel to the axes of the arches. The pier thus becomes a wedge,
and should be strengthened by a starling, upon the outside of the curve,
to resist the resultant of the thrusts of two adjoining arches.

98. We should never try to stake out the exact horizontal projection of
a complicated piece of work upon rough ground, but only the trenches,
which being cut, give a horizontal surface to work upon. In placing the
stakes, we must be careful to have them so far outside of the work that
they will remain undisturbed while operations are going on. The pegs for
cutting pits and trenches may be placed at the angles of the latter, but
the working pegs must be so placed that the lines stretched from one to
the other will define the masonry. All measurements made in laying out
work should be made by graduated rods, and carefully checked.

99. In founding piers, and in aquatic operations generally, two stakes
upon the shore, or a fixed transit, will define any line in the water.
Two transits will define points.

100. A permanent bench mark should be carefully fixed at each structure,
from which its levels may be obtained.

101. In adjusting oblique bridges, care must be taken so to place the
bridge seats that the floor beams shall lie in a correct plane, and not
be at all warped or winding.

[Illustration: Fig. 38.]

102. As an example of laying out work with regard to heights, take the
case of fig. 38. Let the grade of the centre line be one in 100, the
angle of obliquity 45°, the width of bridge twenty feet, and span on the
skew one hundred feet. Required the elevations of the points _a_, _b_,
_c_, _d_.

    Assume the height of (2) as                               100.00
      That of (3) will be                                      99.00
      _b_ being 10 ft. back of 2 is 0.1 ft. higher than 2, or 100.10
      and _d_ 0.1 feet less than (2) or                        99.90
      also _a_ = 99.00 + 0.10, or                              99.10
      and _c_ = 99.00 – 0.10, or                               98.90


                                TUNNELS.

103. The maintaining a correct centre line through tunnels is generally
considered difficult. The fixing of the line in deep shafts requires
great care, owing to the short distance between the only two fixed
points, that can be transferred from the surface to the bottom of the
pit. This is a matter of manual skill and of instrumental manipulation.
There is no difficulty in aligning the upper ends of two plumb-lines;
and the lower ones will certainly be governed by their position. The
following method has been found to answer every purpose.

Let the opening of the shaft be ten feet in diameter. Place two
horizontal bars at right angles to the road across the opening, upon
which slide blocks holding the upper end of the plumb-lines. Adjust
these lines, at the surface, with a transit; and when fixed, place iron
pins at the point marked by the plumbs at the bottom of the shaft. Upon
these pins fix the exact centres. For keeping the line in the shaft
headings, a straight rod, with steel points at each end, should be used,
which being placed upon the iron centre pins, fixes the centre line of
the tunnel. When the tunnel is curved, the line should be laid off by
offsets from the tangent to the curve at the shaft.

By this method points at ten feet distance may be fixed within 1/100 of
an inch, a difference of which would cause an error of ⅒ of an inch per
one hundred, or an inch per thousand feet.




                              CHAPTER VI.
                               EARTHWORK.


                       FORM OF RAILROAD SECTIONS.

104. The reader is presumed to be acquainted with the manner of finding
the areas and cubes of simple geometric figures and bodies. The
following fifteen figures show the forms which may be taken by the cross
section of a railroad in cutting; for embankment invert the same. They
are easily separable into simple figures.

[Illustration: Fig. 39.]

[Illustration: Fig. 40.]

[Illustration: Fig. 41.]

[Illustration: Fig. 42.]

[Illustration: Fig. 43.]

[Illustration: Fig. 44.]

[Illustration: Fig. 45.]

[Illustration: Fig. 46.]

[Illustration: Fig. 47.]

[Illustration: Fig. 48.]

[Illustration: Fig. 49.]

[Illustration: Fig. 50.]

[Illustration: Fig. 51.]

[Illustration: Fig. 52.]

[Illustration: Fig. 53.]

[Illustration: Fig. 54.]

105. The formation of tables for the amount of earth in level cutting is
very simple. The area of the following section, where B is the base, and
R the horizontal dimension of the slope, is

         (_B_ + _B_ + 2_R_)/2 × _h_, or (2_B_ + 2_R_)/2 × _h_,

or finally

                           (_B_ + _R_) × _h_,

i. e., the base of a rectangle by its height. Multiply this by 100 and
divide the product by 27; or divide by 27/100, and we have the cubic
amount in a prism one hundred feet long. The road-bed being nineteen
feet wide, and slopes one and a half to one, the formula for the amount
of a prism one hundred feet long is

                        ((19 + 1½_h_)_h_)/0.27,

and assuming the base of rock cutting as eighteen feet, and slope one
quarter to one, and embankment eighteen feet at subgrade, we have, rock,

                         ((72 + _h_)_h_)/1.08,

and embankment,

                        ((18 + 1½_h_)_h_)/0.27,

the figure being inverted for embankment. For a prism of ten or of one
thousand feet in length, we have only to move the decimal point. In
forming a table, proceed as follows:—

   _h_    _B_ + 1½_h_   (_B_ + 1½_h_) × _h_   ((_B_ + 1½_h_) × _h_)/0.27
   _a_        _b_               _c_                      _d_
  _a′_       _b′_              _c′_                      _d′_
  _a^n_      _b^n_             _c^n_                    _d^n_.

[Illustration: Fig. 55.]

It is evident from inspection of fig. 55, that _c_ exceeds _c_^o by _h_
× 2_r_; and that _c″_ exceeds _c′_ by _h′_ × 2_r′_; and so on as far as
we go; this increase being constant, we have then to find the area of
_c_, and for the area _c_ + _c′_ double _c_, and add the increment;
whence the rule:—

Having found the increase (which varies with the angle of the slope) for
the _second_ section, add the increase to twice the first. For the
_third_, add twice the increase to three times the first; and for the
_n_th, add _n_ – 1 times the increment to _n_ times the first area, or
algebraically calling _a_ the first area, _a′_ the second, _a″_ the
third, _a^n_ the _n_th area, and we have

              The first area                  _a_ = _a_;
              The second area          2_a_ + _i_ = _a′_;
              The third area          3_a_ + 2_i_ = _a″_;
              The _n_th area  _na_ + (_n_ – 1)_i_ = _a^n_.

We might operate at once upon the cubic contents, but for the length to
which some decimals run; some indeed circulating.

106. The table thus made may be of the following form:—

 Cut (or fill), in feet.   Cubic yards Earth.       Cubic yards Rock.
                             Slopes 1½ to 1.         Slopes ¼ to 1.
                       1                      76                      68
                       2                     163                     137
                       3                     261                     208
                       4                     371                     282
                       5                     491                     356
                       6                     622                     433
                       7                     802                     512
                       8                     919                     593
                       9                    1083                     675
                      10                    1260                     759

i. e., cut being eight feet, each one hundred feet length gives nine
hundred and nineteen cubic yards; one thousand feet, 9190 yards, and ten
feet of length 91.9 cubic yards.

107. The preceding system is intended only for approximate estimates.
Let one person read off the cuts or fills from the profile, a second
give the corresponding number of yards by the table made as above, while
a third sets the figures down; being careful to separate the cuts from
the fills.

For final measurements, none but the prismoidal formula should be used;
the length of the prismoids being taken at each one hundred feet, and
nearer when the ground is rough.

108. As an example of the comparative amounts given by the above
formula, and by the common method of averaging end areas, take the
following, the slopes being 1½ to 1.

         Base. Distance. Cut. End Area. Mean Area. Middle Area.
            20         0    0       000        000          000
            20        50    5       137        069          059
            20        50   10       350        244          236
            20        50   15       637        493          483
            20        50   00       000        318          236

By averaging end areas we have

                     50 ×  69 =  3,450
                     50 × 244 = 12,200
                     50 × 493 = 24,650
                     50 × 318 = 15,900 Sum, 56,200.

And by the prismoidal formula,

                  50 ×   305
                  50 × 1,257
                  50 × 2,669
                  50 × 1,755 Sum 299,300 ÷ 6 = 49,000,

                      and 56,200 – 49,000 = 7,200

cubic feet in favor of the method of end areas.

109. The prismoidal formula is algebraically

                   ((_a_ + _a′_ + 4_a″_)/6)_L_ = _c_,

                     when _L_ = length,
                          _c_ = cubic contents,
                          _a_ = area of one end,
                         _a′_ = area of other end,
                         _a″_ = middle area;

or, verbally, _to the sum of the end areas add four times the middle
area, and multiply the result by one sixth of the length_; the _middle_
area being the area made upon the mean height of the two ends. Thus if
the length is one hundred feet, and one end ten feet high, the other
twenty feet high, and slopes one and a half to one, the cubic amount is,
(the base being twenty-two feet,)

 [((22 + 22 + 30)/2 × 10) + ((22 + 22 + 60)/2 × 20) + ((22 + 22 + 45)/2 ×
                            15 × 4)] × 100./6


                       EXCAVATION AND EMBANKMENT.

110. Some writers have considered that the grades of a road should be so
adjusted as to equalize the cutting and the filling. The total rise and
fall might not be much affected by this, but the mechanical effect of
grades might. A perfect balance between the cuts and fills is not to be
desired. The whole cost of earthwork must be a minimum, and it is often
cheaper to waste and borrow, than to make very long hauls, and to form
the grade line by interchange of material on the profile only.

111. The transverse slopes depend upon the nature of the soil in which
the cut is made. Gravel will stand at a slope of one and a half
horizontal to one vertical, and in some cases one and a quarter, or even
one to one. Clay stands nearly vertical for some time, but finally
assumes a very flat slope, in some cases two, three, and even four
horizontal to one vertical. In places where a stratum of clay underlies
more reliable earth, to avoid a very long slope, it may be economical to
support the clay by a wall, and to slope the earth only.

112. Care should be taken in every case to secure good drainage and to
protect the slopes by surface drains at the top. The drains in long cuts
should be slightly inclined to insure the running off of the water. A
fall of ten feet per mile is enough; five will answer in many cases. On
side hill cuts a surface drain along the top of the upper slope will do
good service. On many high embankments, catchwater drains, commencing at
the road-bed and gradually sloping to the base, will prevent, in a great
degree, cutting of the bank.

113. Embankments, when made rapidly, should be finished to the full
width, somewhat above true grade, to allow for the after settlement.
(See specification.)

114. The following allowances have been made for the shrinkage of
material in some parts of America.

                        Light, sandy earth 0.12
                        Clayey earth       0.10
                        Gravelly earth     0.08
                        Gravel and sand    0.09
                        Loam               0.12
                        Clay               0.10
                        Clay puddled       0.25
                        Wet surface earth  0.15

The bulk of quarried rock on the contrary increases from twenty-five to
fifty per cent.

115. When embankments are carried up slowly, in layers of three or four
feet at a time, the after settling is very little; when carried up all
at once it will be more. The full width must be kept, even above the
required height. Fig. 56 shows the forms of a bank both before and after
settlement.

[Illustration: Fig. 56.]

The best method of forming a bank of bad material is to ram the layers
as in fig. 57; thus the tendency is to consolidate by settling, and not
to destroy the work by sliding.

[Illustration: Fig. 57.]


                         TRANSPORT OF MATERIAL.

116. In the formation of embankments it is not always advisable to make
the whole bank from an adjoining cut or cuts. The length of haul may be
too long. In this case it is customary to waste a part of the cut and to
borrow earth from some nearer point for the bank. That the transport
shall be effected in the most economical manner, the product of the cube
of earth, by the mean distance, (the distance between the centres of
gravity, of excavation and embankment) must be a minimum. To determine
the theoretical minimum expense, the problem becomes very complicated on
account of the great number of variable elements entering therein; and
the result obtained is applicable only to a particular case. Local
circumstances more than any other thing, determine the position of a
borrow pit, and the path over which the material is to be transported.


                          OF THE AVERAGE HAUL.

117. To find the cost of the movement of earth on any section, we must
have, the total amount of earth to be moved, and the _average haul_; the
latter being the distance through which, if the whole amount were moved,
the cost would be the same as the sum of the costs of moving the partial
amounts their respective distances. To find the average haul proceed as
follows: _First_, find the distance between the centres of gravity of
each mass both before and after moving, which may be done with
sufficient accuracy for practice by inspection of the profile. _Next_,

118. _Divide the sum of the products of the partial amounts by their
respective hauls, by the total amount_; the result is the average haul
in feet. Or algebraically, representing the partial amounts by _m_,
_m′_, _m″_, _m‴_, the respective hauls by _d_, _d′_, _d″_, _d‴_, the
total amount by _S_, and the average haul by _D_, we have

              (_md_ + _m′d′_ + _m″d″_ + _m‴d‴_)/_S_ = _D_.

_Example._—Let column 1 show the partial amounts in cubic yards. Column
2 the corresponding hauls.

                         1,000 × 200 =   200,000
                         2,000 × 300 =   600,000
                         5,000 × 400 = 2,000,000
                         8,000 × 600 = 4,800,000
                        ——————         —————————
                        16,000         7,600,000

            and 7,600,000/16,000 = 475 feet _average haul_.

_Proof._—Assume the cost of moving 1,000 yards one foot as ten cents,
the costs of the separate masses are

                    1,000 yards 200 feet is  $20.00
                    2,000 yards 300 feet is   60.00
                    5,000 yards 400 feet is  200.00
                    8,000 yards 600 feet is  480.00
                                            ———————
                                       Sum, $760.00

also the cost of moving 16,000 yards 475 feet is

                        16 × 475 × 10 = $760.00.

119. The movement of earth is effected by shovels, barrows, horses and
carts, or by cars. In round numbers we can move earth

                  By shovels alone  10 to    20 feet,
                  By barrows alone  20 to   100 feet,
                  By carts         100 to   500 feet,
                  By cars          500 to 5,000 feet,

As the haul increases, the number of vehicles of transport remaining the
same, the number of excavators must decrease. Earths easily removed do
not admit of so large a haul, with a given number of excavators, as hard
earths. The nature of the ground, form of carts, kind of horses, season
of the year, and price of labor are some of the elements entering the
problem of transport. The best illustration of the matter will be found
among the very able writings of Ellwood Morris, Esq., C. E., in the
Journal of the Franklin Institute. Knowing the value of wages, the
nature of the earth and length of haul, it is easy to see what mode of
transport must have the preference.


                       CONTRACTOR’S MEASUREMENTS.

120. The price of executing any piece of work is paid to the contractor
at stated intervals, generally once each month. The amount of work done
at these partial payments is obtained by instrumental reference to the
ground. Towards the completion of operations the most correct and
easiest method of finding the rate of progress is to deduct the amount
already done from the total as given by primary measurement. The full
price is not paid to the contractor, but a percentage is kept back,
which insures a faithful performance of work. It is impossible to
establish a _pro rata_ price at first, owing to the uncertain nature of
the work; what appears to be earth may be rock. By deducting a maximum
price estimate for all but one of the items, an approximate _pro rata_
value for that one may be determined. An analysis of cost will define
the minimum limit for advantage to the contractor; and the _pro rata_
value less the percentage, the maximum for the company’s benefit.


                               DRAINING.

121. When a level is to be drained, or the water carried off from the
surface of a swamp, the first point to be ascertained is the location of
the lowest outfall. The direction in which aquatic plants lie show the
natural fall of the water, these always pointing down stream. When the
most available outlet has been decided upon, a main drain should be set
out, from which oblique branches are to be cut, pointing in the
direction of the current; into these all minor cuts are to be collected
so that the whole district may be equally drained. The fall should be
greatest at the most remote points, decreasing as the amount of water
increases. Large and deep rivers run sufficiently fast when the fall is
one foot per mile. For small rivers, double that is necessary. Ditches
and ordinary drains require eight feet per mile. When the water is made
to pass away from the surface, it should flow very gradually, that the
sides and bottom of the ditches may not be worn away by friction; it
should be in constant motion that the channel may be kept clean and
increase in velocity as it proceeds. When the surface is a perfect
level, the drains should of course be made straight.

After the quantity of water has been determined by careful observation,
the section of the main and branches must be fixed, so that regarding
both their areas and velocities, the main drain will not be overcharged.

To facilitate the current, the sides should be inclined about one and a
quarter to one; and the breadth of base should be two thirds of the
depth of water. These results are obtained from the practice of English
engineers, who have given a great deal of attention to the subject.

Drains cut through bogs, may have sides nearly, if not quite vertical,
as the fibres of plants forming the soil resist the action of the water.


                           SUBSOIL DRAINING.

Geology has assisted this operation very materially by rendering us
acquainted with the quality and nature, as well as of the succession of
strata. The soils which are impervious are usually the heaviest, and the
porous are those of lighter quality. Clays, when they receive water,
will only part with it by evaporation, when left in a natural state; and
therefore to make such a surface fit for a useful end requires
considerable ingenuity, and often great expense. Such a soil is not
rendered unstable by underground springs, and may be effectually drained
by boring through, and letting the water off into an under stratum, when
this is of a porous nature.

When land abounds with springs, or is subject to the oozing out of
subterraneous water, draining is effected in a different manner. Springs
have their origin in the accumulation of rain water, which falling upon
the earth, after passing the porous strata, lodges upon the impervious,
and glides along the sloping surface until it crops out, generally in
some valley where it forms a watercourse.

Descending streams are easily taken care of by collecting them into a
body before they reach the low lands.

When a morass is to be drained, the strata upon which it reposes should
be examined, and if, as is often the case, a layer of clay intervenes
between the substratum and the mossy covering, which holds the water, by
tapping this in well chosen places, the whole will sink away.

A fine example of embankment upon a bad bottom was performed by Mr.
Stephenson, on the Great Western Railroad, England, at the crossing of
Chatmoss. This moss was so soft that cattle could not walk upon it, and
an iron bar sank into it by its own weight. The moss was first
thoroughly drained by a system of longitudinal and cross drains, and the
embankment made of the lightest material possible—the dried moss itself.
Without this treatment, the moss would have sank beneath the bank alone;
it now supports the passage of the heaviest railroad trains.


                    METHOD OF CONDUCTING OPERATIONS.

122. The organization of the engineer corps upon a railroad is as
follows, differing somewhat in different parts of the country.

_The Chief Engineer_ has entire charge of all the work, of all
assistants, appointing and dismissing members of the corps, designing of
all structures, making of specifications, and of all mechanical
operations incident to the thorough, correct, and timely construction of
the road; and should be able also to specify, generally, the amount and
character of the equipment needed.

_The Resident Engineer_ has charge of the detailed construction of from
twenty-five to fifty miles of road, according to the nature of the work,
being responsible to the chief engineer for the proper execution of the
orders from headquarters; he returns to the chief engineer a monthly
account of the exact condition of his work, both as to the amount
executed, and also that remaining to be done.

The assistants of the resident engineer are a leveller and transit man;
to whom, under his supervision, is the duty of laying out, measuring,
and estimating the work. The leveller has with him one or more rodmen.
The transit man, two chainmen, and one or more axemen.

In some cases, added to the above are inspectors of masonry, bridging,
and superstructure. These are necessary only when the road embraces a
great number of mechanical structures; too many to leave the proper time
to the resident engineer for his other duties. Once each month the exact
amount of graduation, bridging, and masonry _executed_ is obtained by
the resident and his assistants. The chief engineer applies the prices
to these amounts, and the percentage deduction being made, the estimate
is ready for the treasurer.

123. The abstract prepared from the monthly estimate should show
clearly, without unnecessary figures, the amount of work completed, and
also that remaining to be done.

For convenience, the various blanks used on railroads should fold to the
same form and size. The blanks are,

              The Contract,
              The Specification,
              The Resident Engineer’s Monthly Return,
              The Assistant’s Weekly and Monthly Returns,
              The Force Return,
              The Pay Roll,
              Vouchers.

The contract and specification are given in chapter IV. The resident’s
monthly return to the chief engineer is somewhat as follows:—

Monthly return of work done on the _first_ division of the A and B
Railroad, for the month ending ——, showing also the whole amount of work
up to ——; also the present estimate for completion.

                 ┌─────────────────┬─────────────────┐
                 │    Section.     │   Contractor.   │
                 ├─────────────────┼─────────────────┤
                 │        1        │                 │
                 └─────────────────┴─────────────────┘

 ┌──────────────────────────────────────────────────────────────────────┐
 │                             GRADUATION.                              │
 ├────────────────────────────────────┬─────────────────────────────────┤
 │       Clearing and Grubbing.       │           Excavation.           │
 ├───────────────────┬────────────────┼────────────────┬────────────────┤
 │     In July.      │ Total to date. │    In July.    │ Total to date. │
 ├──────┬──────┬─────┼──────┬───┬─────┼──────┬───┬─────┼──────┬───┬─────┤
 │Acres.│Price.│Am’t.│Acres.│Pr.│Am’t.│Yards.│Pr.│Am’t.│Yards.│Pr.│Am’t.│
 ├──────┼──────┼─────┼──────┼───┼─────┼──────┼───┼─────┼──────┼───┼─────┤
 │  15  │ 100  │1500 │ 300  │100│30000│44000 │10 │4400 │100000│10 │10000│
 └──────┴──────┴─────┴──────┴───┴─────┴──────┴───┴─────┴──────┴───┴─────┘

 ┌─────────────────────────────────────────────────────────────────────┐
 │                              MASONRY.                               │
 ├─────────────────────────────┬─────────┬─────────┬─────────┬─────────┤
 │                             │         │         │  Foun-  │  Foun-  │
 │        First Class.         │ Second  │  Third  │dation in│ dation  │
 │                             │ Class.  │ Class.  │ Excava- │ Timber. │
 │                             │         │         │  tion.  │         │
 ├──────────────┬──────────────┼───┬─────┼───┬─────┼───┬─────┼───┬─────┤
 │              │              │In │Tot. │In │Tot. │In │Tot. │In │Tot. │
 │   In July.   │Total to date.│Ju-│ to  │Ju-│ to  │Ju-│ to  │Ju-│ to  │
 │              │              │ly.│date.│ly.│date.│ly.│date.│ly.│date.│
 ├────┬───┬─────┼────┬───┬─────┼───┼─────┼───┼─────┼───┼─────┼───┼─────┤
 │Yds.│Pr.│Am’t.│Yds.│Pr.│Am’t.│   │     │   │     │   │     │   │     │
 │    │   │     │    │   │     │   │     │   │     │   │     │   │     │
 │    │   │     │    │   │     │   │     │   │     │   │     │   │     │
 │    │   │     │    │   │     │   │     │   │     │   │     │   │     │
 └────┴───┴─────┴────┴───┴─────┴───┴─────┴───┴─────┴───┴─────┴───┴─────┘

 ┌────────────────────────────────────────────────────────────────────┐
 │                      BRIDGING AND TIMBERWORK.                      │
 ├───────────────────────────────────┬──────────┬──────────┬──────────┤
 │          Truss Bridges.           │   Pile   │ Stringer │Trestling.│
 │                                   │ Bridges. │ Bridges. │          │
 ├─────────────────┬─────────────────┼──────────┼──────────┼──────────┤
 │    In July.     │ Total to date.  │          │          │          │
 ├─────┬─────┬─────┼─────┬─────┬─────┼──────────┼──────────┼──────────┤
 │Feet.│ C.  │Am’t.│Feet.│ C.  │Am’t.│          │          │          │
 │     │     │     │     │     │     │          │          │          │
 │     │     │     │     │     │     │          │          │          │
 │     │     │     │     │     │     │          │          │          │
 └─────┴─────┴─────┴─────┴─────┴─────┴──────────┴──────────┴──────────┘

 ┌─────────────────────────────────────────────────────────────────────┐
 │                     SUPERSTRUCTURE AND FENCING.                     │
 ├─────────────────────────────────────────────────────┬───────────────┤
 │                   Superstructure.                   │   Fencing.    │
 ├──────────────────────────┬──────────────────────────┼───────┬───────┤
 │                          │                          │  In   │ Total │
 │         In July.         │      Total to date.      │ July. │  to   │
 │                          │                          │       │ date. │
 ├────────┬────────┬────────┼────────┬────────┬────────┼───────┼───────┤
 │ Miles. │ Price. │ Am’t.  │ Miles. │ Price. │ Am’t.  │       │       │
 │        │        │        │        │        │        │       │       │
 │        │        │        │        │        │        │       │       │
 │        │        │        │        │        │        │       │       │
 └────────┴────────┴────────┴────────┴────────┴────────┴───────┴───────┘

 ┌─────────────────────────────────────────────────────────────────────┐
 │                  VALUE OF WORK AND PAYMENTS MADE.                   │
 ├─────────────┬─────────────┬─────────────┬─────────────┬─────────────┤
 │Value of Work│ Amount paid │ Whole value │Whole amount │ Amount left │
 │  in July.   │  in July.   │  to date.   │    paid.    │    due.     │
 ├─────────────┼─────────────┼─────────────┼─────────────┼─────────────┤
 │             │             │             │             │             │
 │             │             │             │             │             │
 │             │             │             │             │             │
 └─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘

 ┌─────────────────────────────────────────────────────────────────────┐
 │                           VALUE OF LABOR.                           │
 ├─────────────┬─────────────┬─────────────┬─────────────┬─────────────┤
 │ Foreman and │  Laborers.  │ Carts with  │ Carts with  │Whole value. │
 │ Mechanics.  │             │   Horses.   │    Oxen.    │             │
 ├─────────────┼─────────────┼─────────────┼─────────────┼─────────────┤
 │             │             │             │             │             │
 │             │             │             │             │             │
 │             │             │             │             │             │
 └─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘

 ┌────────────────────────────────────────────────────────────────────┐
 │                          RECAPITULATION.                           │
 ├──────────────────────┬──────────────────────┬──────────────────────┤
 │Value of work done in │ Value of work up to  │   Remaining Value.   │
 │        July.         │        date.         │                      │
 ├──────────────────────┼──────────────────────┼──────────────────────┤
 │                      │                      │                      │
 │                      │                      │                      │
 │                      │                      │                      │
 └──────────────────────┴──────────────────────┴──────────────────────┘

The resident engineer’s assistants return to him weekly a statement of
the amount and value of the force employed upon the several sections,
and monthly the exact amount of work done on the same, for each of which
there should be a blank. The above forms may be printed and folded in
8vo., or may be the continuous headings of a large sheet.




                              CHAPTER VII.
                               ROCKWORK.


                            ROCK EXCAVATION.

125. The sides of rock excavation are sometimes cut to a small slope, as
one fourth or one fifth horizontal to one vertical, and sometimes cut
quite perpendicularly. The earth, when it occurs, which covers the rock,
is first taken out at the proper slope; a berm of one or two feet being
left between the foot of the earth and the crest of the rock.

126. Rock is taken out one or two feet below grade, as well as earth, to
allow the introduction of the necessary ballast.


                        BLASTING AND QUARRYING.

127. The most common mode of removing rock is by blasting; for this
holes are drilled by steel-edged jumpers, worked either by hand or by
steam. The first object in cutting a passage through rock, is to open a
working face, so as to get the necessary lines of least resistance,
(this line is that by which the powder finds the least opposition to a
vent at right angles to the length of the drill); these lines should, if
possible, be at right angles to the beds of stratification; the holes
should be drilled parallel to the seams of the rock, as the powder will
then lift off the strata. In working a vertical face, it may be best to
blast out the lower part first, and so undermine the overhanging mass.

128. The amount of powder in different charges to produce proportional
results should be as the cube of the line of least resistance; for
example:—

                   2^3 is to 4 oz. as 3^3 is 13½ oz.,

or

                          8 to 4 as 27 to 13½;

and generally,

                     _L^3_ : _w_ :: _L′^3_ : _w′_;

whence

                        _w′_ = (_wL′^3_)/_L^3_.

129. The following charges corresponding to lines of least resistance
are from the works of Sir John Burgoyne.

           Line of least resistance.    Charge of powder.
                             2 feet,            0 lbs.  4 oz.
                             4 feet,            2 lbs.  0 oz.
                             6 feet,            6 lbs. 12 oz.
                             8 feet,           16 lbs.  0 oz.

130. After the powdered stone is removed, the powder is placed in the
lower part of the hole; after which a wad of turf, or some other light
material, follows; next the tamping of powdered brick, dried clay, or
something similar, and finally a stopper of wet clay, or some other firm
substance. A hole is left through all, communicating with the powder by
ramming the tamping around a wire; through this hole a fuse is inserted
by which to light the charge. The most perfect tamping would offer a
resistance as great as that by the natural rock. A great improvement
upon the above method is the sand blast; the powder is put in, and the
hole filled with loose, dry sand, simply poured in and settled by a
gentle stirring, but not at all rammed; the explosion of the powder
spreads the sand as a wedge, and causes the power of the blast to be
exerted sideways. In some cases a small cone of wood has been placed
(base down) in the hole with the sand, which aids very much in stopping
the exit of the blast through the drill.

131. Of late years an admirable method of lighting large charges
simultaneously has been employed, namely, voltaic electricity.

132. A gigantic example of the application of this method has been
furnished by the English engineers in overthrowing a portion of Round
Down Cliff, about two miles from Dover, (England). Two chambers, 13 × 5½
× 4½, and one 10 × 5½ × 4 feet were cut in the rock. Within these were
placed fifty bags of powder, amounting in all to eight and one half
tons. The charges were lighted by the voltaic system, by which operation
a mass of rock (chalk) 380 × 360 × 80 feet, amounting to 400,000 cubic
yards, was thrown into the sea, and by which there was estimated to have
been saved nearly $40,000.

133. The following table from Colonel Pasley’s memoranda on mining,
shows the capacity of different drills for powder, by weight, and also
the depth of holes of different diameters, to contain one pound of
powder.

 Diameter of hole  Ounces of powder    Powder in one   Depth of hole in
    in inches.        in one inch       foot deep.     inches to contain
                        depth.                            one pound.
                                             lbs.  oz.
 1                               0.4            0  5.0              38.2
 1½                              0.9            0 11.3              16.9
 2                               1.7            1  4.1               9.5
 2½                              2.6            1 15.4               6.1
 3                               3.7            2 13.2               4.2
 3½                              5.1            3 13.5               3.1
 4                               6.7            5  0.4               2.4
 4½                              8.4            6  5.7               1.9
 5                              10.5            7 13.6               1.5
 5½                             12.7            9  8.0               1.3
 6                              15.1           11  4.9               1.0

134. Blasting under water has been practised to some extent, and with
great success by Messrs. Maillefert and Raasloff, both in New York
harbor and in the St. Lawrence River. The method is merely to explode
bodies of powder _upon the surface of the rock_, the water itself being
a sufficient source of reaction to the blast.


                              TUNNELLING.

135. Tunnels are driven through hills to avoid very deep cutting. When
in rock of a solid nature, the roof supports itself; but when in earth
or in loose rock, an artificial arched lining becomes necessary. Figs.
58 and 59 show sections in both rock and earth; the invert _b b_ is
placed in a bed of concrete. In excavating earth, a temporary roof is
made use of while the work is in progress, which is afterwards replaced
by an arch of brick or stone. The back of the arch must be closely
wedged, grouted, and the earth well rammed in.

[Illustration: Fig. 58.]

[Illustration: Fig. 59.]

The great disadvantages attending the construction of tunnels are want
of air, light, room, and drainage. To facilitate the latter requirement,
a very light grade may be introduced; this may easily be done, as they
generally occur on summits, or on the approach to summits; 1/1000 or
five feet per mile is sufficient.

In working a tunnel which is upon a grade, one end naturally drains
itself if the approach is taken out; the other drains the wrong way, to
meet which obstacle we must resort to pumps which follow the work,
keeping always in the lowest place, or by sinking a well at the shaft
through which the water is raised to the surface.

The ventilation of tunnels is effected by drawing off the bad air when a
fresh supply must enter.

136. In taking out the rock, the expense will depend much upon the
nature and stratification of the rock encountered.


                                SHAFTS.

137. In tunnels of considerable length, a long time would be consumed in
working from the ends only. In such cases it is customary to sink shafts
at the most convenient places (the shallowest when at the proper
distance,) and to commence at the bottom of these to work both ways.
This operation involves considerable expense, as all draining,
ventilating, and removal of excavated materials must be effected through
the shaft.

In leaving openings for the exit of smoke and for admission of light in
artificial arches, regard must be had to their position. They should be
at the springing rather than at the crown of the arch, as they will thus
less affect the strength of the masonry.

The approaches of tunnels in cities and in other places where appearance
is of importance, are finished with face coping and wings.

138. Tunnels, when conducted in the most expeditious manner, require for
their completion a long time. The following table shows the rate of
progress upon some of the most important tunnels of America.

        Name of Tunnel.                                    Average daily
                                 Length in                  advance, in
                                   feet.     Time in days.     feet.
 *Penn Railroad,                       3,612           697          5.18
 *Kingwood B. & O. R. R.               4,100           750          5.47
 Board Tree B. & O. R. R.              2,250           675          3.32
 *Welling, B. & O. R. R.               1,240           524          2.37
 Pacific Railroad,                       700           210          3.33
 Pittsburgh and Connelsville,
   (estimated)                         4,500           810          5.56
                                                                   —————
          General average daily advance, in feet,                  4.205

 Those marked * being for a double track.

The following table also gives the time and cost of other tunnels in
different parts of the world.

 ┌────────────────┬──────────────┬──────┬─────┬───────┬─────────┬──────┐
 │    Name and    │  Material.   │      │     │ Daily │         │      │
 │  location of   │              │Length│Time │average│         │ Cost │
 │    tunnel.     │              │  in  │ in  │  in   │         │ per  │
 │                │              │feet. │days.│ feet. │Section. │foot. │
 ├────────────────┼──────────────┼──────┼─────┼───────┼─────────┼──────┤
 │                │              │      │     │       │         │  $   │
 │Nerthe, France, │Hard limestone│15,153│   ——│       │29½ × 26¼│      │
 │Riqueral,       │Chalk         │      │     │       │         │      │
 │  France,       │              │18,623│2,139│    8.7│26¼ × 26¼│ 39.89│
 │Pouilly, France,│Chalk & clay  │10,928│2,504│    4.4│20⅓ × 20⅓│113.96│
 │Arscherville,   │——            │      │     │       │         │      │
 │  France,       │              │ 7,348│1,878│    3.9│26¼ × 26¼│ 68.38│
 │Maurage, France,│——            │15,752│2,085│    7.5│25½ × 25½│ 94.43│
 │Rolleboise,     │Chalk         │      │     │       │         │      │
 │  France,       │              │ 8,670│  626│   13.9│25  × 25 │ 62.98│
 │Roule, France,  │——            │ 5,645│  522│   10.8│25  × 25 │ 62.98│
 │Lioran, France, │——            │ 4,548│2,087│    2.2│21⅓ × 21⅓│ 56.98│
 │Kilsby, England,│Clay and sand │ 7,233│1,252│    5.8│27  × 23½│194.31│
 │Belchingly,     │Blue clay     │      │     │       │         │      │
 │  England,      │              │ 3,972│  626│    6.3│24  × 25 │102.86│
 │Thames & Medway,│Chalk         │      │     │       │         │      │
 │  Eng’d,        │              │11,880│  939│   12.6│30  × 38⅔│ 45.59│
 │Box, England,   │Marble,       │      │     │       │         │      │
 │                │  freestone   │      │     │       │         │      │
 │                │  and marl    │ 9,680│1,252│    7.7│35  × 39 │148.15│
 │Harecastle,     │Rock and sand │      │     │       │         │      │
 │  England,      │              │ 8,778│  939│    9.3│14  × 16 │ 57.05│
 │Nochistongo,    │Clay and marl │      │     │       │         │      │
 │  Mexico,       │              │21,659│  287│   75.4│13¾ × 11½│    ——│
 │Blisworth,      │Rock and clay │      │     │       │         │      │
 │  England,      │              │ 9,240│2,191│    4.2│16½ × 18 │ 23.18│
 │Sapperton,      │Rock          │      │     │       │         │      │
 │  England,      │              │12,900│1,878│    6.9│15  × 15 │ 12.44│
 │Black Rock, U.  │Greywacke     │      │     │       │         │      │
 │  S.            │  slate       │ 1,932│   ——│     ——│19  × 17¼│ 77.18│
 │Blaisy, France, │Chalk and clay│13,455│1,043│   12.9│26¼ × 26¼│136.06│
 │Edge Hill,      │Clay &        │      │     │       │         │      │
 │  England,      │  freestone   │ 6,600│   ——│     ——│22  × 16 │ 30.15│
 │Littlebourg,    │——            │      │     │       │         │      │
 │  England,      │              │ 8,607│  590│   14.6│27½ × 24 │129.61│
 │Woodhead,       │Millstone     │      │     │       │         │      │
 │  England,      │              │15,840│1,800│    8.8│   ——    │    ——│
 └────────────────┴──────────────┴──────┴─────┴───────┴─────────┴──────┘

The cost per cubic yard for excavating tunnels in some places has been
as follows:—

            Name.             Material.       Cost per cubic yard.
      Blackrock, U. S.  hard greywacke slate,        $6.60
      Lehigh, U. S.     very hard granite,            4.36
      Schuylkill, U. S. slate,                        2.00
      Union, U. S.      slate,                       2.08½
      Blue Ridge, U. S. ——,                           4.00

The Blue Ridge tunnel on the Virginia Central Railroad is 4,280 feet
long, made for a single track, 21 × 15 feet. Lining about four feet
thick. Excavation where lining is used is 26 × 23.

The Hoosac tunnel (Massachusetts) is proposed to be four and one half
miles long, 23 × 22 feet section. To have two shafts eight hundred and
fifty and seven hundred and fifty feet deep, and ten feet in diameter.

Artificial ventilation becomes necessary in headings over four hundred
and fifty or five hundred feet in length.

The cost of the shafts of the Blechingly tunnel, (England,) ninety-seven
feet deep, and ten and one half feet in diameter, cut through blue clay,
and lined, was $68.44 per yard down.

The shafts of the Blaisy tunnel average five hundred feet deep, through
clay and chalk and loose earth, (being lined,) cost $139.11 per yard
down.

The shafts of the Black Rock tunnel, one hundred and thirty-nine feet
deep, in hard slate, cost $18.72 per cubic yard.




                             CHAPTER VIII.
                            WOODEN BRIDGES.


139. Wooden bridging, owing to its cheapness and fitness for universal
application, has been and is being adopted in all parts of the country.
Almost any variety of form may be seen upon our railroads, and though
less durable than stone or iron, it may with proper precaution be made
to last a long time.


                   OF THE FORCES AT WORK IN BRIDGES.

140. There are four distinct strains to which a piece of timber or a bar
of metal may be exposed, each of which tends to destroy the piece in a
different manner. The amount and character of these strains, depend upon
the position of the bar or beam, and upon the direction of the force.

A beam may be pulled apart by stretching,—_Tension_.

It may be destroyed by crushing,—_Compression_.

It may be broken transversely,—_Cross strain_.

It may be crushed across the grain,—_Detrusion_.


                                TENSION.

141. If one thousand pounds were hung from the end of a suspended
timber, so that the direction of the weight coincides with the axis of
the timber, then will the tension upon the beam be one thousand pounds.

If the direction of the force is vertical, and the beam is inclined,
then the strain is increased by as much as the diagonal of inclination
exceeds the vertical; for example, let one thousand pounds be suspended
from the lower end of a beam ten feet long, inclined at an angle of 45°.
The diagonal being ten, the vertical will be 7.07 feet, and the strain
is increased as follows:—

                   7.07 to 10 as 1,000 to 1,414 lbs.

As the angle of inclination, from the horizontal, increases, the strain
from a given load decreases, until the beam is vertical, when a weight
acts with its least power.


                              COMPRESSION.

142. If a vertical post is loaded with one thousand pounds, the
compressive strain upon that post will also be one thousand pounds. If a
post is inclined, the amount of strain is increased, as noticed in the
case of tension, and to the same amount, that is, depending upon the
inclination.

A piece of wood or metal acting as a post, or pillar, must not only be
able to resist crushing, but also bending or bulging laterally.

143. A cylinder of which the length is only seven or eight times the
diameter, will not bulge by any force that can be applied to it
longitudinally, but will split. When the length exceeds this, it will be
destroyed by a similar movement to that produced by a cross strain. When
the length of a cast-iron pillar is thirty diameters, the fracture is
produced by bending alone; when less, partly by bending and partly by
fracture. When the column is cast hollow, and enlarged towards the
middle, the strength is increased in a very great ratio.

144. The formula for finding the weight which any beam acting as a post,
will support before bending, is, according to Barlow, who considers the
weight as varying inversely as the length, as follows:—

                       (_WL^2_)/(80_E_) = _bd^3_,

and the value of _W_ is

                       (_bd^3_ × 80_E_)/(_L^2_),

and the weight being given, and the sectional dimensions assumed, we
have

                      _d_ = ∛((_WL^2_)/(80_Eb_)),

and

                       _b_ = (_WL^2_)/(80_Ed^3_),

              Where _W_ represents the weight in pounds,
                    _L_ represents the length in feet,
                    _E_ represents a constant,
                    _d_ represents the depth in inches,
                    _b_ represents the breadth in inches.


                             CROSS STRAIN.

145. The amount of strain caused by any weight applied in a transverse
direction, to a beam supported at both ends, is as the breadth, as the
length inversely, and as the square of the depth. Whatever depression
takes place, tends to shorten the upper, and to extend the under-side;
whence the fibres of the top part suffer compression, and those of the
bottom extension. The amounts of compression and extension must of
course be equal, and therefore if any material resists these two strains
in a different degree, the number of fibres opposing each will also be
different.

The top being compressed, while the bottom is extended, of course at
some point within the beam there exists a line which suffers neither
compression nor extension. The position of this line (the neutral axis)
depends upon the relative power of the material to oppose the strains,
upon its form and upon its position. Thus if wood resists two thousand
pounds per square inch of extension, and one thousand pounds of
compression, the axis will be twice as far from the top as from the
bottom.

In some materials the neutral axis changes its place while the bar is at
work; thus wrought iron, after being a little compressed, will bear a
great deal more compression than when in its original state; also the
lower fibres, after being extended, will resist less than at first; the
effect of which two actions is to move the neutral axis up.

146. The following table shows the relative resisting powers of wood,
wrought and cast-iron; with the corresponding positions of the axis,
with sufficient accuracy for practice.

                                                       Distance of axis
   Material.   Resistance to  Resistance to   Ratio.     from top, in
                extension.    compression.             fractions of the
                                                            depth.

 Wrought iron,            90              66   90/66    90/156   or 0.58
 Cast-iron,               20             111  20/111    20/131   or 0.15
 Wood,                     2               1    2/1        ⅔     or 0.66

Thus in beams subjected to a cross strain, as well as to a direct
extensile or compressive one, the resistance is effected by the
incompressibility and inextensibility of the material.

147. The formula for dimensioning any beam to support a given weight
transversely is

                          _S_ = (4_bd^2_)/_e_,

           Where _S_ represents the ultimate strength in lbs.
                 _b_ represents the breadth in inches,
                 _d_ represents the depth in inches,
                 _e_ represents the length in inches,


                               DETRUSION.

148. Detrusion, or crushing across a fixed point, is such as occurs
wherever a brace abuts against a chord, or where a bridge bears upon a
bolster or wall plate; also the shearing of bolts, pins, and rivets.


                    GENERAL RESISTANCE OF MATERIALS.

149. The resistance to extension, to compression, (as regards simple
crushing,) and to detrusion, is as the area of cross section; i. e., if
we double the area, we double the strength. The resistance to a cross
strain is _as the breadth_, _as the length inversely_, and _as the
square of the depth_; i. e. if we double the breadth we double the
strength; if we double the length, we divide the strength by two; and if
we double the depth, we multiply the strength by four.


                     ACTUAL STRENGTH OF MATERIALS.

150. Any material will bear a much larger load for a short time than for
a long one. The weight that does not so injure materials as to render
them unsafe, is from one third to one fourth only of the ultimate
strength. Throughout the present work one fourth will be the most that
will in any case be used.


                             WROUGHT IRON.

151. _Extension._

                                              lbs. per square inch.
    Mean of 17 experiments by Barlow (p. 270)                62,720
    Weisbach’s Mechanics (Vol. ii., p. 71)                   60,500
    Overman’s Mechanics, (p. 408, 409)                       61,333
    Brown, Rennie, and Telford, (mean)                       65,251
                                                             ——————
    The mean                                                 62,451
                                                             ——————
    Reducing by 4 for safety                                 15,613

Or in round numbers 15,000 lbs. per square inch, is the resistance of
wrought iron to extension, to be used in practice.

152. _Compression._—Great discrepancies appear among writers on the
strength of materials, as to the compressive strength of wrought iron.
Though all estimate the resistance to compression, as great as to
extension, yet no one in summing up the general result of experiment,
places the former at more than from 50 to 75 per cent. of the latter.
William Fairbairn gives, as the relative resistances to extension and
compression in bars applied as girders, 2 to 1.

           We have by Weisbach   56,000
           We have by Rondelet   70,000
           We have by Hodgkinson 65,000
                                 ——————
           The mean              63,667
                                 ——————
           Reducing by 4         15,917
                                 ——————
           In round numbers      16,000 lbs. per square inch.

As far as practice is any guide, from 8,000 to 12,000 pounds per inch is
the most to be used. The ratio of 90 to 66, seems to express very nearly
the action as in the most reliable structures; which will, therefore, be
adopted, or 11,000 pounds per square inch nearly. The resistance to
compression is very much greater after wrought iron has been somewhat
compressed.


                               CAST-IRON.

153. _Extension._—This material is seldom used to resist a tensile
force. That the tables may be complete, however, the following is
given:—

             By Weisbach                    20,000 pounds.
             By Barlow                      18,233 pounds.
             By Overman                     20,000 pounds.
             By Rennie                      18,000 pounds.
             By Hodgkinson                  16,577 pounds.
             By the British Iron Commission 15,711 pounds.
                                            ——————
             The mean                       18,087 pounds.
                                            ——————
             Reducing by 4                   4,522 pounds.
                                            ——————
             In round numbers                4,500 pounds.

154. _Compression._

         By Weisbach                           109,800 pounds.
         By Hodgkinson                         107,520 pounds.
         By Iron Commission                    100,000 pounds.
         Stirling’s toughened                  130,000 pounds.
                                               ———————
         Mean of Common                        105,773 pounds.
                                               ———————
         Mean of Stirling’s                    130,000 pounds.
                                               ———————
         Reducing by 4 for safety (Common)      26,443 pounds.
                                               ———————
         Reducing by 4 for safety (Stirling’s)  32,500 pounds.
                                               ———————
         In round numbers (Common)              25,000 pounds.
                                               ———————
         In round numbers (Stirling’s)          30,000 pounds.

155. Following are given the condensed results of the preceding figures,
which may be relied upon as giving perfectly safe dimensions in
practice.

             Wrought Iron. Cast-Iron.
                    15,000      4,500 Tensile strength,
                    11,000     25,000 Compressive strength.

For additional remarks on iron, see chap. IX.

156. _Nature and Strength of American Woods._

  Name of the  Weight per  Resistance  Resistance  Value of
     wood.     cubic foot.     to          to        _S_.    Elasticity.
                           Extension. Compression.

 White Pine             26     12,000        6,000     1,229          ——
 Yellow Pine            31     12,000        6,000     1,185          ——
 Pitch Pine             46     12,000        6,000     1,727       4,900
 Red Pine               35     12,000        6,000     1,527       7,359
 Virginia Pine          37     12,000        6,000     1,456          ——
 Spruce                 48     12,000        6,000     1,036          ——
 Larch                  33     12,000        6,000       907       2,465
 Tamarack               26     12,000        6,000       907          ——
 White Cedar            22      8,000        4,000       766          ——
 Canada Balsam          34     12,000        6,000     1,123          ——
 White Oak              48     15,000        7,500     1,743       8,595
 Red Oak                41     15,000        7,600     1,687          ——
 Live Oak               72     15,000        7,200     1,862          ——
 White Beech            44     18,000        9,100     1,380       5,417
 Red Beech              48     18,000        9,000     1,739          ——
 Birch                  44     15,000        7,000     1,928          ——
 Black Birch            41     15,000        7,200     2,061          ——
 Yellow Birch           36     15,000        7,200     1,335          ——
 Ash                    38     16,000        8,100     1,795       6,581
 Black Ash              35     16,000        8,000       861          ——
 Swamp Ash              57     16,000        8,000     1,165          ——
 Hickory                51     15,000        7,200     2,129          ——
 Butternut              54     15,000        7,600     1,465          ——
 Ironwood               54     16,000        8,100     1,800          ——
 Rock Elm               45     16,000        8,011     1,970       2,799

 The mean tensile strength of wood is                        14,080 lbs.
 Reducing by 4 for safety                                     3,520 lbs.
 Reducing for want of seasoning                               2,000 lbs.
 The reduced mean compressive strength                        1,000 lbs.
 Reduced resistance to detrusion                                150 lbs.
 Ratio of tensile to compressive strength                   2 to 1.
 Mean value of _S_ in formula (_WL_ = 4_Sbd^2_) for the
   woods most used in practice                               1,250.

157. The lateral adhesion of fir was found, by Barlow, to be six hundred
pounds per square inch. (Lateral adhesion is the resistance which the
fibres offer to sliding past each other in the direction of the grain;
as, in pulling off the top of a post where it is halved on to the
chord.)

158. As regards the nature of timber, seasoning, time of cutting, etc.,
although these are important items, still, generally, commercial
considerations outbalance all else. The most complete treatise on the
nature of woods, is “Du Hamel, _L′exploitation des bois_;” from which it
appears that the best oaks, elms, and other large trees, are the product
of good lands, rather dry than moist. They have a fine, clear bark, the
sap is thinner in proportion to the diameter of the trunk, the layers
are less thick, but more adherent the one to another; and more uniform
than those of trees growing on moist places. The grain of the latter may
look very fine and compact, but microscopic examination shows the pores
to be full of gluten.

The density of the same species of timber, in the same climate, but on
different soils, will vary as 7 to 5; and the strength, both before and
after seasoning, as 5 to 4.

In trees not beyond their prime, the density of the butt is to that of
the top, as 4 to 3; and of centre to circumference, as 7 to 5. After
maturity, the reverse occurs in both cases.

Oak, in seasoning, loses from ¼ to ⅓ of its weight; but its strength is
increased from 30 to 40 per cent.


               GENERAL TABLE OF THE NATURE OF MATERIALS.

159. _The tensile strength of wrought iron assumed as 1,000._

                                                     Weight Sum divided
  Material.   Tension. Compression.  Cross    Sum.    per    by weight
                                    Strain.          cubic   per cub.
                                                      ft.       ft.
 Cast-Iron         300        1,666   31.68 1,997.68    450         4.4
 Wrought Iron    1,000          733   55.40 1,788.40    480         3.7
 Wood              133           66    5.60   204.60     30         6.8

The advantage possessed by iron over wood, is in durability only. The
above figures show how much more of the strength of the material is
consumed by its own weight in iron than in wood. In actual practice,
however, the method of making joints and other details often render iron
the lightest material.


                          RULES FOR PRACTICE.


                                TENSION.

160. The tensile strength of any material, is expressed by the formula

                              _T_ = _Sa_,

          Where _T_ represents the whole strength,
                _S_ represents the strength per square inch,
                _a_ represents the area of section in inches.

whence the necessary area of section of any material to resist a tensile
strain, is found by the following rules:—

Wrought Iron

                           _a_ = _W_/15,000,

Cast-Iron

                            _a_ = _W_/4,500,

Wood

                            _a_ = _W_/2,000.


                              COMPRESSION.

161. Wrought Iron

                           _a_ = _W_/12,000,

Cast-Iron

                           _a_ = _W_/25,000,

Wood

                            _a_ = _W_/1,000.


                             CROSS STRAIN.

162. The power of any material to resist a cross strain, is shown by the
formula

                         _W_ = (4_sbd_^2)/_L_,

        Where _W_ represents the breaking weight in pounds,
              _s_ represents the constant in the table of woods,
              _b_ represents the breadth in inches,
              _d_ represents the depth in inches,
          and _L_ represents the length in inches,

and to reduce the load to one fourth of the breaking weight

                        _W_ = (4_sbd_^2)/(4_L_),

and finally, by substituting for 4_s_, 4 × 1,250, (1,250 of the table of
woods,) we have

                       _W_ = (5000_bd_^2)/(4_L_).

Also, knowing the weight to be supported, and requiring the dimensions,
we take out the values of _d_ and _b_, and have

              _d_ = √((_W_ × 4_L_)/(5000_b_)) = the depth,

             _b_ = (_W_ × 4_L_)/(5000_d_^2) = the breadth.

As an example of the use of the formula, take the following:—

                  Let the span, or length, be 20 feet,
                  The breadth 12 inches, and depth 18,

required the load.

The formula

                       _W_ = (5000_bd_^2)/(4_L_)

becomes

             _W_ = (5000 × 12 × 18^2)/4 × 240 = 20,250 lbs.

Again, the weight to be supported being 15,000 lbs., length 30 feet,
breadth 16 inches, the formula for the depth becomes

       _d_ = √((15000 × 1440)/(5000 × 16)) = √(270) = 16 inches,

also,

   _b_ = (15000 × 1440)/(5000 × 256) = 21600000/1280000 = 16 inches.


                               CAST-IRON.

163. The formula, expressive of the strength of a cast-iron beam, is

                           850_bd_^2 = _WL_,

from which we have

                 _b_ = (_LW_)/(850_d_^2) = the breadth,

             and _d_ = √((_L_ × _W_)/(850_b_)) = the depth.


                             WROUGHT IRON.

164.

                           952_bd_^2 = _WL_,

whence

                 _b_ = (_WL_)/(700_d_^2) = the breadth,

                and _d_ = √((_LW_)/(700_b_)) the depth.

[Illustration: Fig. 60.]

165. Mr. Hodgekinson found, that by arranging the material in a
cast-iron beam, as in fig. 60, that the resistance per unit of section
was increased over that of a simple rectangular beam, in the ratio of 40
to 23. He makes the general proportion of such girders as follows:—

                        Length               16
                        Height                1
                        Area of top flange   1.0
                        Area of lower flange 6.1

In this consummate disposition of material, the areas of top and bottom
flanges are made inversely proportional to the power of cast-iron to
resist compression and extension.

166. Mr. Fairbairn found, that in wrought iron flanged girders, (under
which come the various rails, chap. XIII.,) the top web should contain
double the area of the lower one. This agrees with the conclusion
adopted on page 129, as wrought iron resists more extension than
compression.

167. In cast-iron girders, on no account should there be introduced
webs, or openings of any kind, either from economic or ornamental
motives; as the uniformity of cooling is thereby very much opposed.

168. Mr. Hodgekinson gives, as the result of his experiments, the
following formula for dimensioning the cast-iron girder above referred
to.

                          _W_ = (26_ad_)/_L_,

              Where _W_ is the breaking weight in tons,
                    _a_ the area of the bottom flange,
                    _d_ the depth of the girder in inches,
                    _L_ the length in inches.

As it is not considered safe to load a cast-iron beam with more than one
sixth of the breaking load, the formula may be expressed as follows:—

                          _W_ = (26_ad_)/6_L_,

for the weight in tons which may be safely borne, and transforming

                          _a_ = (6_WL_)/26_d_

for the area of the lower flange.

_Example._—Required the dimensions of a cast-iron beam, of Mr.
Hodgekinson’s form, for a span of thirty feet, to support a load of ten
tons at the centre.

      Span   30 feet,             Whence—
      Length 34 feet,           Length       34 feet,
      Load   10 tons at centre. Span         30 feet,
                                Depth        25½ inches,
                                Lower flange 32.58 square inches,
                                Upper flange 5.34 square inches,

          _a_ = (6 × 10 × 12 × 30)/(26 × (34 × 12)/16) = 32.58

and 32.58/6.1 = 5.34.

and the area of the top flange will be

                               36/6 = 6,

whence the following dimensions:—

                     Length       30 feet,
                     Depth        23 inches,
                     Lower flange 36 square inches,
                     Upper flange  6 square inches,


                               OF POSTS.

169. A post may be very well able to resist the compressive strain
thrown upon it by any load, but may bulge, or bend, laterally.

The formula by which beams are dimensioned for this requirement, changes
with the material, and with the form of section. For rectangular posts
of wood, we have the formula below.

                       _W_ = (2240_bd_^3)/(_L_2),

  Where _W_ represents the weight in lbs., which may be safely borne,
        _b_ represents the breadth in inches,
        _d_ represents the depth in inches,
    and _L_ represents the length in feet.

170. The value of the formula for the strength of cast-iron posts, seems
to depend more upon the authority consulted than upon the nature of
iron. For example, assume the length of a post as twenty feet, and the
diameter as ten inches; the load which may be safely borne is, according
to six different authorities, as follows:—

                             _A_ 4,000,000
                             _B_   181,100
                             _C_   370,000
                             _D_   940,000
                             _E_   307,242
                             _F_   300,000

and assuming the length as ten feet, and diameter as ten inches, we have

                             _A_ 8,007,500
                             _B_   204,500
                             _C_ 1,442,500
                             _D_ 3,640,000
                             _E_ 1,170,000
                             _F_   600,000

showing not only a great difference in the unit resistance taken, but
also in the effect of the ratio between the length and diameter.

Such being the discrepancy, there will be given no formula; but in place
of such, the table following, which is calculated from the rules least
opposed to experimental evidence.

 ┌─────────────────────────────────────────────────────────────────────┐
 │ TABLE SHOWING THE LOAD IN POUNDS SAFELY BORNE BY CAST-IRON COLUMNS. │
 ├─────────────────────────────────────────────────────────────────────┤
 │                            HOLLOW CYLINDERS.                        │
 ├──────┬──────────────────────────────────────────────────────────────┤
 │Diame-│                  Length or height in feet.                   │
 │ter in│                                                              │
 │inches│                                                              │
 ├──────┼──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┤
 │      │  6   │  8   │  10  │  12  │  15  │  18  │  20  │  22  │  24  │
 ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │     2│  6000│  5000│  4000│  3000│  2500│  1800│  1500│  1300│  1100│
 │     3│ 16000│ 14000│ 13000│ 11000│  9000│  7000│  6000│  5000│  5000│
 │     4│ 30000│ 29000│ 26000│ 24000│ 22000│ 18000│ 16000│ 14000│ 13000│
 │     5│ 50000│ 37000│ 45000│ 42000│ 39000│ 37000│ 31000│ 28000│ 26000│
 │     6│ 59000│ 57000│ 55000│ 52000│ 49000│ 44000│ 41000│ 38000│ 36000│
 │     7│101000│ 99000│ 96000│ 92000│ 88000│ 81000│ 76000│ 72000│ 68000│
 │     8│131000│129000│126000│122000│118000│109000│105000│100000│ 96000│
 │     9│169000│167000│164000│160000│156000│146000│141000│136000│131000│
 │    10│210000│200000│200000│200000│190000│180000│180000│170000│170000│
 │    11│250000│250000│240000│240000│240000│230000│220000│220000│210000│
 │    12│300000│300000│290000│290000│290000│270000│270000│260000│260000│
 │    14│450000│430000│410000│380000│370000│350000│330000│320000│300000│
 │    16│520000│500000│480000│460000│440000│420000│400000│370000│350000│
 │    18│650000│630000│610000│590000│560000│520000│470000│430000│400000│
 │    20│800000│760000│740000│690000│650000│590000│540000│490000│450000│
 ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │Diame-│  6   │  8   │  10  │  12  │  15  │  18  │  20  │  22  │  24  │
 │ter in│      │      │      │      │      │      │      │      │      │
 │inches│      │      │      │      │      │      │      │      │      │
 ├──────┼──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┤
 │      │                  Length or height in feet.                   │
 └──────┴──────────────────────────────────────────────────────────────┘

 ┌─────────────────────────────────────────────────────────────────────┐
 │ TABLE SHOWING THE LOAD IN POUNDS SAFELY BORNE BY CAST-IRON COLUMNS. │
 ├─────────────────────────────────────────────────────────────────────┤
 │                             H AND + SECTIONS.                       │
 ├──────┬──────────────────────────────────────────────────────────────┤
 │Metal │                  Length or height in feet.                   │
 │thick-│                                                              │
 │ness. │                                                              │
 ├──────┼──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┤
 │      │  6   │  8   │  10  │  12  │  15  │  18  │  20  │  22  │  24  │
 ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │     ¼│  4000│  3000│  2400│  1800│  1400│  1100│  1000│   900│   800│
 │     ⅜│ 12000│ 11000│ 10000│  9000│  8000│  7000│  5000│  4000│  3000│
 │     ½│ 25000│ 23000│ 21000│ 18000│ 16000│ 13000│ 12000│  9000│  6000│
 │     ⅝│ 36000│ 34000│ 31000│ 28000│ 25000│ 23000│ 21000│ 20000│ 18000│
 │     ¾│ 40000│ 38000│ 37000│ 36000│ 35000│ 34000│ 32000│ 30000│ 28000│
 │ 13/16│ 60000│ 59000│ 58000│ 57000│ 56000│ 54000│ 53000│ 51000│ 49000│
 │     ⅞│100000│ 98000│ 96000│ 94000│ 91000│ 88000│ 83000│ 78000│ 70000│
 │     1│140000│130000│126000│120000│114000│110000│106000│100000│ 90000│
 │    1⅛│190000│180000│170000│160000│150000│140000│130000│125000│120000│
 │    1¼│230000│220000│210000│200000│190000│180000│170000│160000│150000│
 │    1½│280000│260000│250000│240000│230000│220000│200000│190000│180000│
 │    1¾│360000│320000│310000│300000│290000│280000│270000│260000│240000│
 │     2│460000│430000│400000│370000│350000│330000│310000│300000│280000│
 │    2½│560000│530000│510000│480000│440000│410000│380000│350000│330000│
 │     3│600000│580000│550000│520000│500000│460000│430000│400000│380000│
 ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │Metal │  6   │  8   │  10  │  12  │  15  │  18  │  20  │  22  │  24  │
 │thick-│      │      │      │      │      │      │      │      │      │
 │ness. │      │      │      │      │      │      │      │      │      │
 ├──────┼──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┤
 │      │                  Length or height in feet.                   │
 └──────┴──────────────────────────────────────────────────────────────┘


                             OF THE TRUSS.

171. The most simple bridge that could be built, consists of a single
piece of timber placed across the opening to be spanned. This form is
applicable to spans under twenty feet. The proper dimensions are found
by the formula:—

                _d_ = √((4_wL_)/(5000_b_)) = the depth.

_Example._—The depth of a beam of twenty feet span, and twelve inches
wide, to support a load of twenty thousand two hundred and fifty lbs. is

        _d_ = √((4 × 20,250 × 20 × 12)/(5000 × 12)) = 18 inches.

A beam 12 × 18, and of 20 feet span, will therefore bear safely a load
of 20,250 lbs., applied at the centre.

In this manner is formed the following table, giving the scantling of
sticks for railroad stringer bridges, of twenty feet span and under.

                     Span. Breadth.     Depth.
                         5       12     12
                        10       12     13
                        12       12     15
                        15       12     18
                        18       12     20
                        20       12     21 inches.


The first scantlings exceed the requirement of the rule, but are none
too large to resist the shocks to which such sticks are exposed.

Cross-ties of plank, 2 or 3 by 6 or 8 inches, and plank braces
underneath, (as shown in the fig. at the end of chapter VIII.,) should
be bolted to the main timbers; the same bolt passing through the tie
beam and plank. The longitudinal pieces should be firmly notched and
bolted to the wall-plates, and these latter either built in or scribed
on to the masonry.

[Illustration: Fig. 61.]

172. For a span of from 20 to 50 feet, we may use the combination shown
in fig. 61. The piece A B, must be so strong as not to yield between A
and D, or D and B. The pieces C E must be stiff enough to resist the
load coming upon them which is as follows. A locomotive engine of the
heaviest class will not exceed fifty tons weight, each pair of driving
wheels will support ten tons, and on each side five tons, 2240 × 5 =
11,200 lbs.; or to allow for shocks and extra strains, 15,000 lbs. Each
brace, then, must support seven thousand five hundred pounds, which for
compression simply would require only seven and one half square inches
of sectional area; but the brace being inclined, the strain is increased
as follows:—

                       A E to E C as 7,500 to X.

And A E being ten feet, and A D fifteen feet, E C becomes eighteen feet,
whence

                   10 to 18 as 7,500 to 13,500 lbs.;

which would require only thirteen and one half inches for compression,
or a piece 4 × 3½. But is this enough for flexure?

On page 124 the load which may be safely borne, by a rectangular post of
wood, is shown by the formula

                      _W_ = (2240_bd^3_)/(_L^2_).

Substituting for _b_ and _d_, the dimensions 4 × 4, we have

        _W_ = (2240 × 4 × 4^3)/(18^2), or 573,440/324, = 1,770,

which is evidently too small.

Placing 6 × 7, for _b_ × _d_, we have

                _W_ = (2240 × 6 × 7^3)/(18^2) = 14,227;

exceeding by a small amount the requirement.

[Illustration: Fig. 62.]

173. It is evidently immaterial whether we _support_ the point D _upon_
C, or _suspend_ it as in fig. 62, provided we prevent any motion in the
feet of the inclines A _c_ B _c_. Abutting them against A B, throws a
tension against A B, found as follows:—

Representing by _c_ D, the applied weight, draw D E parallel to _c_ B;
also E _f_ parallel to A B; E _f_ is the tension. The graphic
construction gives results near enough for practice. Rigorously we have

                     A _c_ D, similar to E _c_ _f_;

also,

                   A _c_, to E _c_, as A D, to E _f_;

and

                       E_f_ = (E_c_ × AD)/(A_c_).

When _a d_ and _c d_ are differently inclined, proceed as follows. See
fig. 102, p. 200 inverted.

[Illustration: Fig. 63.]

Let _d b_ represent the weight; _e h_ shows the tension. The triangles
_a c d_, and _a b e_, are similar; as also _e b h_ and _d b c_; whence

  _b e_ = (_a b_, _c d_)/(_a c_), and _e h_ = (_c b_, _b e_)/(_d c_) =
                                tension.

In practice place _w_ for _b d_; i. e. the actual weight.

In this plan, if the chord is able to resist the cross strain between A
and D, it will also resist the tension. This cross strain is found by
the formula already given and illustrated.

174. From what precedes, we have the following dimensions for bridges
such as are shown in figs. 61 and 62. The details of 62, at _f_ and _c_,
and at E, 61, are shown in figs. 62 A, 62 B, and 61 C.

[Illustration: Fig. 62 A.]

[Illustration: Fig. 62 B.]

[Illustration: Fig. 62 C.]

               Span. Rise.  A B.      C E.     Rod _b_.
                  20     8 12 × 12 (5 ×  8)—2 1¼ inches.
                  25    10 12 × 15 (5 ×  9)—2 1⅜ inches.
                  30    12 12 × 18 (5 × 10)—2 1½ inches.
                  35    13 12 × 20 (5 × 10)—2 1⅝ inches.
                  40    14 14 × 21 (5 × 12)—2 1⅝ inches.
                  45    15 14 × 22 (6 × 12)—2 1¾ inches.
                  50    16 14 × 24 (6 × 12)—2 1¾ inches.

The braces, (column 4,) being in pairs and blocked together. In spans
exceeding twenty-five feet, the braces _d f_, and the rods _f g_, should
never be omitted. The size of the rod _g f_, is found by considering A,
_d_, _f_, as a small bridge.

175. In all light bridges, like the one under consideration, all parts
should be _fastened_ by bolts, to prevent springing by reaction. A
bridge with but little inertia, or dead weight, tends to jump up when
the engine has passed over it. _Fastening_ takes the place of _weight_
in a large span.

As soon as the rise admits, the points C, on each side of the bridge,
should be connected to resist lateral motion. When the height is not
enough for this, the same points may be joined to a floor beam extended
out beyond the truss.

Though the dimensions are given for this plan up to fifty feet span, it
is very seldom advisable to go beyond twenty-five or thirty feet; as
frames consisting of a few long timbers are not so rigid, and free from
vibration, as those made of a greater number of short pieces.

176. In extending this system one hundred or two hundred feet, we see at
once that the pieces A _c_, B _c_, would become very long and would need
to be made large and heavy. We should always so proportion any beam in a
bridge that it is at once able to resist all of the several strains to
which it may be exposed, without being unnecessarily large.

As to compression, the above system might be extended to almost any
amount; but the braces would yield by flexure.

Instead of producing the braces A _c_, A′ _c′_, fig. 64, to their
intersection, we stop at _c_ and _c′_, insert _c c′_; to prevent the
approach of these points, suspend the points B and B′ from _c_ and _c′_,
and commence again with the braces B D, B′ D; and so on as far as
necessary.

To prevent the backward motion of the points B, and B′, either the chord
A A′, or the counter-braces _m_, _m_, are necessary.

[Illustration: Fig. 64.]

The pieces A _c_, A′_c′_ must support all of the load, including the
weight of the bridge, lying within the rectangle B _c_, B′ _c′_. The
next set of braces must sustain that part of the load only which comes
over the centre of the bridge. Thus the braces should decrease in size
as the centre is approached. The rods _c_ B, _c′_ B′, must resist a
tension equal in amount to the pressure on the braces, only being
vertical they do not need the increase given to the braces on account of
their inclination.

177. There is another method of stiffening a beam, as shown in figs. 65
and 66, by trussing rods, and a post. The dimensions being the same, the
forces in both cases will be equal. The second, fig. 66, leaves the
passage beneath the bridge clear.

[Illustration: Fig. 65.]

The tension on the rods A _c_, B _c_, fig. 66, tends to draw the points
A and B together, an effort which is resisted by the top chord A B.

In extending this system, as in art. 176, the rods become either very
long, or very large, from the small angle of inclination; evils which
remedied as before, by supporting the post _c_ B, fig. 64, from the foot
of the first rod, fig. 64, and commencing again from _c_.

[Illustration: Fig. 66.]

To prevent the motion of the triangle _c_ B G, fig. 64, about the angle
B, we must introduce either the upper chord _c c′_, or the counter rod
_c_ A. If the lower chord is omitted the rod D B must be of the same
size as E B. In this truss, either the top or the lower chord simply may
theoretically be omitted, due allowance being made in the size of the
rods. In practice it is never advisable to omit either, as both are
required for lateral bracing, and for support of the road-way.

Having said thus much of the general ideas that apply to all bridges,
let us now look at some of the plans most in use; and to become familiar
with the subject, work out the dimensions of an example of each kind.

178. As rods, nuts, and washers are used in all bridges, the following
table may not be out of place:—

           Column  1 gives the diameter of rod.
           Column  2 strength at 15,000 lbs. per square inch.
           Column  3 the weight per lineal foot.
           Column  4 side of the square nut.
           Column  5 the thickness of the same.
           Column  6 the dimensions of washers.
           Column  7 the thickness of washers.
           Column  8 breadth (side to side) six-sided nut.
           Column  9 breadth (across angles) six-sided nut.
           Column 10 thickness of six-sided nut.
           Column 11 number of screw threads per inch.
           Column 12 gives the diameter of rod.

 ┌─────────┬────────┬──────┬──────┬──────────┬───────┐
 │    1    │   2    │  3   │  4   │    5     │   6   │
 │Diameter.│Strength│Weight│Square│Thickness.│Square │
 │         │of Rod. │ per  │ Nut. │          │  of   │
 │         │        │Foot. │      │          │Washer.│
 ├─────────┼────────┼──────┼──────┼──────────┼───────┤
 │        ½│   2,940│  0.66│    1¼│         ¾│     2½│
 │        ¾│   6,630│  1.49│    1½│         ⅞│      3│
 │        1│  11,775│  2.65│     2│         1│      4│
 │       1⅛│  14,910│  3.36│     2│        1⅛│     4½│
 │       1¼│  18,405│  4.17│    2¼│        1¼│      5│
 │       1⅜│  22,260│  5.02│    2½│        1⅜│     5½│
 │       1½│  26,505│  5.97│    2¾│        1½│      6│
 │       1⅝│  31,095│  7.01│    2⅞│        1⅝│     6½│
 │       1¾│  36,075│  8.13│     3│        1¾│      7│
 │       1⅞│  41,415│  9.33│    3¼│        1⅞│     7½│
 │        2│  47,130│ 10.62│    3½│        1⅞│      8│
 │       2⅛│  53,190│ 12.00│    3¾│         2│     8½│
 │       2¼│  59,640│ 13.40│     4│        2⅛│      9│
 │       2⅜│  66,450│ 15.00│    4⅛│        2¼│     9½│
 │       2½│  73,620│ 16.70│    4¼│        2½│     10│
 ├─────────┼────────┼──────┼──────┼──────────┼───────┤
 │    1    │   2    │  3   │  4   │    5     │   6   │
 └─────────┴────────┴──────┴──────┴──────────┴───────┘

 ┌─────────┬───────┬─────┬──────┬──────┬──────┬─────────┐
 │    1    │   7   │  8  │  9   │  10  │  11  │   12    │
 │Diameter.│  Top  │Six- │ Six- │ Six- │Screw.│Diameter.│
 │         │Washer.│Sided│Sided │Sided │      │         │
 │         │       │Nut. │ Nut. │ Nut. │      │         │
 ├─────────┼───────┼─────┼──────┼──────┼──────┼─────────┤
 │        ½│      ¼│   1⅜│    1½│  9/16│    12│        ½│
 │        ¾│      ¼│   1¾│     2│     ⅞│    10│        ¾│
 │        1│      ⅜│   1⅞│    2¼│    1⅛│     8│        1│
 │       1⅛│      ⅜│   2⅛│ 27/16│    1¼│     7│       1⅛│
 │       1¼│      ½│   2¼│211/16│ 17/12│     7│       1¼│
 │       1⅜│      ½│   2½│    2⅞│ 17/16│     6│       1⅜│
 │       1½│      ½│   2⅝│    3⅛│111/16│     6│       1½│
 │       1⅝│      ⅝│   2⅞│ 35/16│113/16│     5│       1⅝│
 │       1¾│      ⅝│    3│    3½│     2│     5│       1¾│
 │       1⅞│      ⅝│   3¼│    3¾│    2⅛│    4½│       1⅞│
 │        2│      ⅝│   3½│     4│    2¼│    4½│        2│
 │       2⅛│      ¾│   3⅝│ 43/16│    2⅜│     4│       2⅛│
 │       2¼│      ¾│   3¾│ 46/16│    2½│     4│       2¼│
 │       2⅜│      ¾│    4│    4⅝│    2⅝│     4│       2⅜│
 │       2½│      ¾│   4¼│    4⅞│    2¾│    3½│       2½│
 ├─────────┼───────┼─────┼──────┼──────┼──────┼─────────┤
 │    1    │   7   │  8  │  9   │  10  │  11  │   12    │
 └─────────┴───────┴─────┴──────┴──────┴──────┴─────────┘

179. Let us now assume the following data:—

          Span                                      200 feet,
          Rise (centre to centre of chords)          25 feet,
          Width                                      20 feet,
          Length of panel                            15 feet,
          Weight (bridge and load) per lineal ft. 4,000 lbs.


                             HOWE’S BRIDGE.

Fig. 67.

[Illustration: Fig. 67.]

_Lower Chords._—The _tension_, at the centre of the lower chord, is
found _by dividing the product of the weight of the whole bridge and
load by the span_, by eight times the height, or

                       _T_ = (_W_ × _S_)/(8_h_),

which becomes, with the above data,

                _T_ = (800000 × 200)/200 = 800,000 lbs.

Here the tension and the total weight are equal, a result which can
occur only when the rise is one eighth of the span. This is the best
ration between these dimensions, as then the horizontal and vertical
forces are equal.

As to the proportion of the _panel_, (or the rectangle inclosed by the
chords and any two adjacent posts,) the ratio of base to height should
be such as to make the inclination of diagonal about 50° from the
horizontal; if much less, the timbers become large and heavy; and if
more, the number of pieces is unnecessarily increased.

The braces at the end of a long span, may be nearer to the vertical than
those near the centre, as they have more work to do. If the end panel be
made twice as high as long, and the centre panel square, the
intermediates varying as their distance from the end, a good
architectural effect is produced.

To determine the size of the lower chords, to resist the above 800,000
pounds of tension, proceed as follows: Each side truss will support one
half of the whole load, or 400,000 pounds; which, at 2,000 pounds per
inch, will require 200 square inches of section. Four sticks of 8 × 12
inches, give an area of 384 square inches, which must be reduced as
follows: Deduct 72 square inches for the area cut out by the splicing
blocks, 40 inches for the bolts connecting the pieces, 28 inches for
inserting the foot blocks, and 10 inches for inserting the washer, and
we have remaining 234 square inches; which exceeds by a little the exact
demand. This excess (about one seventh) is a necessary allowance for
accidental strain, to which all bridges are subjected.

[Illustration: Fig. 67 A.]

The splices used in bridge framing are shown in fig. 67 A and fig. 67 B.
For the first, the depth of insertion and length of the block depend
upon the tension upon the chord. The following dimensions have been much
used and are perfectly reliable:—

                  Span of Bridge.  A C    B C    C D
                       Feet.      Feet. Inches. Feet.
                               50 1.00  1½      1.50
                              100 1.25  2       2.00
                              150 1.75  2½      2.25
                              200 2.00  3       2.75

There is no need of cutting more than one notch, as in the figure; the
resistance of the triangles is thereby lessened, and the work increased.

[Illustration: Fig. 67 B.]

In fig. 67 B, the rods must of course be able to resist the tension upon
the one piece which is cut.

_Upper Chord._—The upper chords of a bridge suffer compression, to the
same amount numerically, as the tension on the lower chord; as whatever
tension is thrown by any brace upon the lower chord, reacts as just so
much compression upon the upper. In the case at hand, 800,000 lbs. in
all, or 400,000 on each chord.

The resistance to compression being one thousand pounds per inch,
renders necessary four hundred inches of section to each chord; four
pieces 8 × 12 give in all three hundred and eighty-four inches of
section, which requires no reduction, as the whole chord pressing
together and being properly framed is not weakened by splicing. The
splicing blocks in the upper are merely plain pieces, inserted one half
inch, the only duty being to keep the sticks at the proper horizontal
distance.

The spaces between the pieces should be large enough to allow the rods
to pass without cutting the chords; (two inches answers every purpose).
The bolts for splicing, have no very great strain to bear. In small
spans from ½ to ⅝, and in large bridges from ⅝ to an inch is enough.

The object in framing a built beam for a bridge chord, is to make a
stick which shall be uniformly strong. This is done by cutting the
pieces in the centre of the panel, and by having no two joints in either
chord in one panel; though in long spans this cannot always be done.
Figs. 67 D and 67 E (page 153)


                                BRACES.

               The whole load being       800,000 pounds,
               Each truss supports        400,000 pounds,
               Each set of braces         200,000 pounds,
               Each brace (there being 4)  50,000 pounds,

which must be increased for inclination as follows: The length of
diagonal is twenty-nine feet, (the height being twenty-five and length
15,) whence

                   25 to 29 as 50,000 to 58,000 lbs.;

which would need fifty-eight square inches, or 7 × 8 for compression;
which, however, is quite too small for flexure. 12 × 12 placed in the
formula gives

                     _W_ = (2240 × _bd^3_)/(_L^2_),

or

               _W_ = (2240 × 12 × 1728)/841 = 55,296 lbs.

In practice, smaller braces than 12 × 12 would answer, because the four
braces in a set may be fastened together, making a post of four pieces 8
× 12, or in all a built post of 44 × 12 inches; twelve being the depth,
whence

              _W_ = (2240 × 44 × 1728)/841 = 202,511 lbs.;

the forty-four inches being made by blocking the braces four inches
apart. The second set of braces are to be treated in the same manner,
the weight to be supported being only the rectangle included by those
braces; i. e. the whole bridge and load less the two end panels.

As the centre of the span is approached, the pressure on the braces
becomes very small; and the scantling of the braces will be reduced to
about 6 × 7 inches.


                                 RODS.

The weight upon the first set of rods is the same as that upon the end
sets of braces; in the present case 800000 ÷ 2 = 400000 on each side
truss, and 400000 ÷ 2 = 200000 on each end; and if there are five rods
in each set, each rod bears 40,000 lbs. Referring to the table on p.
146, opposite to 41,415 lbs., is the diameter 1⅞ inches; whence the
first set must contain five rods, of 1⅞ inches diameter. The second set
decrease in size as the weight is lessened by the two end panels. The
nut and washer for the rod are also found in the same table.


                            COUNTERBRACING.

180. When a load is placed on the point C′, fig. 64, the truss tends to
sink at that point, and a corresponding rise takes place at C. This
motion changes the figure A B C E, from a rectangle to an oblique angled
figure; the diagonal E B being shortened, and A C lengthened. This
motion is easily checked by the introduction of the counter brace E B.

[Illustration: Fig. 64.]

The action which this timber is called upon to resist, being caused by
the moving or variable load on one panel, the brace must resist the load
coming thereon, (say fifteen feet,) and is thus the same size as the
brace at the centre of the span.

The counter braces may be so confined between the braces, at the
intersection, as not to move laterally or vertically, but must not be
fastened to the braces; because the action of the separate timbers is
thus trammelled.

[Illustration: Fig. 67 C.]

The manner of adjusting the braces and counter braces to the chord is
shown in fig. 67 C. It was formerly the custom to abut the braces
against a block on one side of the chord, and to screw the rod against a
block on the opposite side; the whole strain acting to crush the chord
crosswise. This has been remedied by the arrangement shown in the
figure, the two blocks being cast in one piece and connected by a small
hollow cylinder passing between the chord sticks.

[Illustration: Fig. 67 D.       Fig. 67 E.]

This system is known as Howe’s bridge, and may be seen in almost any
section of the country; and though in many cases badly proportioned, and
of bad material, if properly made answers a very good end.

The following table has been formed for the use of engineers and
builders, giving, together with the table of nuts and washers, all
dimensions required.

   ┌───────┬───────┬───────┬────────┬───────┬───────┬───────┬───────┐
   │ Span. │ Rise. │Panel. │Chords. │  End  │Centre │  End  │Centre │
   │       │       │       │        │braces.│braces.│ rod.  │ rod.  │
   ├───────┼───────┼───────┼────────┼───────┼───────┼───────┼───────┤
   │     50│  10   │      7│2—8 × 10│    7^2│ 5 × 5 │2—1⅛   │  2—1  │
   │     75│  12   │      9│2—8 × 10│    8^2│ 5 × 5 │2—1½   │  2—1  │
   │    100│  15   │     11│3—8 × 10│    9^2│ 6 × 6 │2—1¾   │  2—1  │
   │    150│  20   │     13│4—8 × 12│   10^2│ 6 × 7 │3—2    │  3—1  │
   │    200│  25   │     15│4—8 × 16│   12^2│ 7 × 7 │5—2    │  5—1  │
   └───────┴───────┴───────┴────────┴───────┴───────┴───────┴───────┘


                            PRATT’S BRIDGE.

[Illustration: Fig. 68.]

181. Assume the following data for an example:—

                   Span                    100 feet.
                   Rise                     12 feet.
                   Panel                    10 feet.
                   Weight per lineal ft. 2,500 lbs.

The tension on the lower, or the compression on the upper chord, will be

                    (250000 × 100)/96 = 260,417 lbs.

The manner of dimensioning the chord, and of splicing, is the same as
already described for Howe’s.


                            SUSPENSION RODS.

The first sets of rods, A B, A′ B′, must sustain the whole weight of the
bridge and load; which is 250,000 lbs. Each side 125,000 lbs.; and each
end set of rods 62,500 lbs.; and if each set has four rods, each rod
must support 15,625 lbs.

The rod being inclined, this amount is increased by the following
proportion:—

        12 (height) to 15.8 (diagonal) as 15,625 to 20,573 lbs.

This is half-way between the tabular numbers for rods of 1¼ and 1⅜
inches in diameter; 1⅜ will therefore answer. The next set of rods must
be considered as supporting the whole load, less the two end panels, and
so on as already explained for Howe’s bridge. The manner of applying the
rods to the chords is shown in fig. 68 A. The bevel block should be
connected with the block at the foot of the post, so as to prevent
crushing the chord.

[Illustration: Fig. 68 A.]


                             COUNTER RODS.

As both top and bottom chords are always used in this bridge, the
counter rods have only the variable load on one panel to resist. The
action is, in amount, the same as that on the counter braces in Howe’s
bridge; but acts in a different direction, and in the other diagonal.

The weight of a passing load cannot be more than two thousand pounds per
lineal foot. The panel being ten feet long, the whole weight coming on
two sets of counter rods, (one set in each side truss,) is twenty
thousand pounds; or ten thousand pounds on each set; and if there are
put three rods in each set, we have 3,333 pounds per rod, which increase
for inclination as follows:—

                     12 : 15.8 :: 3333 : 4389 lbs.,

requiring a rod of three fourths inch diameter.

The posts in this structure, correspond to the braces in the Howe
bridge; only being vertical, they need not be so large.

182. The following table gives all the dimensions necessary for
proportioning this truss.

   ┌───────┬───────┬────────┬───────┬───────┬───────┬───────┬───────┐
   │ Span. │ Rise. │Chords. │  End  │C post.│  End  │C rod. │Counter│
   │       │       │        │ post. │       │ rod.  │       │ rod.  │
   ├───────┼───────┼────────┼───────┼───────┼───────┼───────┼───────┤
   │     50│     10│2—8 × 10│ 5 ×  5│    4^2│   2—1⅜│    2—1│   1—1½│
   │     75│     12│2—8 × 10│ 6 ×  6│    5^2│   2—1⅝│    2—1│   1—1½│
   │    100│     15│3—8 × 10│ 7 ×  7│    6^2│   2—1¾│    2—1│   2—1⅛│
   │    125│     18│3—8 × 10│ 8 ×  8│    6^2│   3—1⅞│    3—1│   2—1⅜│
   │    150│     21│4—8 × 12│ 9 ×  9│    6^2│   3—2⅛│    3—1│   3—1⅛│
   │    200│     24│4—8 × 16│10 × 10│    6^2│   5—1⅞│    5—1│   3—1⅛│
   └───────┴───────┴────────┴───────┴───────┴───────┴───────┴───────┘

And the following, the sizes of counter rods, for different panels.

  Length of   Height of  Approximate
   panel.      panel.    diagonal of        Diameter of the rod.
                           panel.
                                      One in a     Two per    Three per
                                        set.        set.        set.
     10          12          16      1⅝              1⅛                ⅞
     11          13          17      1⅝              1¼               1⅛
     12          14          18      1¾              1¼               1⅛
     13          15          20      1¾              1¼               1⅛
     14          16          21      1⅞              1⅜               1⅛
     15          18          23      1⅞              1⅜               1⅛
     16          21          26      2               1⅜               1⅛
     18          25          27      2               1⅜               1⅛

The advantage possessed by this bridge, over Howe’s plan, is that the
panel diagonals may be adjusted by the screws; by which control is had
over the form of the truss, and of the duty done by the several parts.
Change of form cannot be had by working upon verticals. Howe’s bridge
must be adjusted by wedging the braces and the counter braces.

183. The manner of drawing the bevel block in this bridge, is shown in
fig. 68 b. The proportions of the block depend upon the proportions of
the panel; and the dimensions, upon the size of washer used.

Let C C be the centre line of the post, and A B the chord. Let _o m_,
and _o n_, be the panel diagonals, and H and _y_, the length of the
washers.

[Illustration: Fig. 68 B.]

The depth of insertion of the block into the chord, depends upon the
horizontal strain upon it. In a span of one hundred and fifty feet, with
the rods at an angle of 50°, two inches have been found ample at the end
of the truss, and one half inch at centre.

From D, perpendicular to _m m_, lay off D E; equal to H, also from E, at
right angles to _n n_, make E E′ = _y_. From E′ draw the vertical E′ L.

The strain upon the rod _o m_, being represented by _o m_; and that upon
_o n_, by _o n_, the resultant is shown, both in direction and amount,
by _o_ V. It is not necessary that this should pass through the centre
of the post, as the excess of tension on _o m_, over that on _o n_, is
absorbed by the lower chord.

  NOTE.—Screwing up truss bridges, is a more scientific operation than
  is generally supposed. Many builders commence at each end, and lift
  the bridge from the scaffolding. By this method the greater part of
  the load is often borne by a few of the end sets of rods. The better
  method is to begin at the centre and work both ways towards the
  ends, being sure that each set of rods does its duty before the next
  is touched. The lift to be made by each set of rods, should first be
  calculated, and tested while screwing up, with the level.


                            LATTICE BRIDGES.

184. _Town’s lattice_, consists of a simple lattice-work of plank, 3 ×
12 inches, treenailed together at an angle of forty, forty-five, or
fifty degrees. It possesses great stiffness, without by any means having
the material disposed in the best manner. Such bridges might well be
made by the mile, and cut off to order according to the span.

The improved lattice, by Hermann Haupt, Esq., C. E., avoids all of the
evils attendant upon the common lattice, and gives a very cheap, strong,
and rigid bridge. In this plan the braces are placed in pairs, with
vertical tie planks between them; by which the twisting seen in the
common lattice, is removed. The braces are also brought to the vertical,
as the point of support is reached, by which a good bearing is given to
the end sets of timbers.

To vary the size of the braces, as the strain upon them decreases, would
be both inconvenient and expensive; but the same effect may be produced
by varying the distance between them, making it greater as the centre is
approached.


               S. W. HALL’S WOODEN TRUSS AND ARCH BRIDGE.

Inverting Mr. Haupt’s design for a lattice of improved construction,
(which consists of vertical ties and inclined braces,) we have the base
of the above-named bridge; where the inclined timbers are used to resist
tension, as below.

This being a very good plan, and the arrangement for building being such
as to secure the thorough execution of the work in its most minute
detail; it is thought best to extract at some length from a letter from
the inventor, dated July 31st, 1856, not however being confined to the
matter therein.

The first claim, is for a _new form of truss_, formed of posts vertical,
or nearly so, and _tension_ pieces, inclining downwards toward the
centre; thus differing from nearly all other plans. Timber resists
double as much extension as compression; and when large enough to resist
the simple tension, does not have to be increased as in resisting
compression for flexure; but requires a larger allowance for joints, as
tension tends to pull the joints apart, while compression forces them
together.

The following result was obtained, showing the superior strength of
timber work in resisting by _tension_. Two models, containing the same
amount of timber, were tested. The one built with vertical ties and
_braces_, broke by crippling the brace, under 2,400 lbs.; while that
constructed with verticals and _suspenders_, inclining towards the
centre, sustained 4,200 lbs. with no visible change of form.

The second claim is for more efficient bearings and connections than
common, and this with less cutting away of timber. The arch and arch
braces have a full, fair bearing at top and bottom. The first sets of
tension braces, (those extending from the top of the arch braces towards
the centre,) are sustained by two pins at each joint; which gives six
pin bearings, or twelve for one set of braces, of six inches each, (the
pin being two inches in diameter, and plank three inches thick,) equal
in all, to seventy-two inches of bearing surface at least, for each five
feet lineal of bridge, or one hundred and forty-four inches for ten
feet.

The third claim, is that the bearings, at joints, are _central_, and
that the shrinkage of the timber is _towards_ and not _from_ them as in
many plans.

The pin holes are bored by machinery smooth and true; the treenails when
of wood are of seasoned oak or locust, turned to a perfect fit, and when
of iron are made hollow.

These bridges, after three years, stand within an inch of their shape as
framed without exception. One indeed supporting an aqueduct, which
throws upon the truss a constant load of 2¾ tons per foot, not including
the weight of the bridge, without any apparent settling.

The connections being fast, prevent reaction and vibration from variable
loads, the strains in this case are reversed, the bridge tending to
spring up instead of settling.

The fourth claim, is for the small brace connecting the lower with the
intermediate chord; by which additional connections are obtained, and
smaller timbers rendered available.

The fifth claim, is the formation of a stronger chord than by the plan
of using a few large sticks. The chord being made of a great number of
small pieces, the strength is of course less affected at any one point,
by a joint, than when only a few pieces are used.

In the bridges built by the above engineer, are to be seen some of the
most perfect built beams in the country. The following conditions being
observed, the most uniform, and highest average strength possible is
obtained.

  First. To cut but one stick in any one panel.

  Second. To cut no stick at the centre of the bridge.

  Third. To place every joint in the middle of the collateral piece.

The chords are cut by two rows of pins, two inches each; and if the
chord be fifteen inches, the cutting at centre, where there is no joint,
is but four fifteenths of the whole section. To resist the parting of
any two sticks, there is the resistance to shearing of ninety-six pins;
and the section of each being three square inches, the whole resistance
is two hundred and eighty-eight inches of area. If the intermediate
chord has the same number, the whole area to resist shearing, in the
lower chord, is five hundred and seventy-six square inches. The bearing
surface of each pin in the chord stick is 2 × 3 inches, or six inches;
and 96 × 6 = 576: and in both chords 1152 inches.

                                                                 Sq. in.
 The whole chord timber, (both chords,) is (6 × 3 × 14),             252
 In the intermediate chord, (6 × 3 × 12),                            216
                                                                     ———
                      Whole timber section,                          468
 Deduct 4 pins for both chords,
   468 – (4 × 2 × 3 × 6) or 468 – 144 =                              324
 Deduct for joints 3 × 10 + 3 × 8 or 324 – 54, Square inches of
   available area.                                                   270

Comparing the amount thus cut away with that cut away in other plans, we
have the following figures;—

          A. Hall’s Bridge, (actual bridge,)           30/100
          B. Howe’s bridge, (actual bridge,)           35/100
          C. Page 163, (Handbook R. R. Construction,) 39½/100
          D. McCallum’s, (Susquehanna bridge,)         58/100

The sixth claim, is the peculiarly convenient form for applying an
arch,—the superiority consisting in convenience for attachment; in the
connections being less affected by shrinkage than when posts are locked
into arches; in the timbers not being weakened by cutting. The arch is
loaded with the tension timbers, inwardly, and acts as a general arch
brace, transferring at once all of the several tensions to the abutment,
thus really combining the arch with the truss.

The liability of this plan to decay, certainly appears to be less than
that of most plans of wooden bridges now in use; as will be plainly seen
by observing the position of the joints; falling rain finds a much
easier access to almost any other joint than the pin hole. The timber
work being made of plank, all the timbers are small, and are thus much
more likely to be sound.

[Illustration: Fig. 69.]

The bridges built upon this plan upon the Alleghany Valley, and upon the
Williamsport and Elmira roads, illustrate plainly the design.

185. Applying arch braces to lattice bridges, has suggested _The
Arch-brace truss bridge_, in which the whole strength lies in a series
of differently inclined braces, extending from the abutment to the head
of each post; a very light lattice being used to prevent reaction, or as
a counter-brace or stiffener. See fig. 69.

In trusses consisting of a series of triangles, when the span is large,
(150 to 200 feet,) the immense weight coming at the feet of the second
and third sets of braces, causes settling or depressing at twenty or
thirty feet off from the abutment, which can hardly be removed. The
remedy for such settling, is to transfer the load at once to the
abutment; which is completely done in the above-named bridge. Each brace
does its duty directly and well. Before the lattice-work is fastened,
the bridge should be loaded with a maximum load. Then by fastening the
diagonals, the recoil is prevented; and the effect of a passing load is
to ease the counterbracing lattice, without otherwise affecting the
truss.

  NOTE.—A model of this bridge, made by the writer, of the following
  dimensions:—

                        Length,  7 feet.
                        Height,  1 foot.
                        Width,   1 inch.
                        Chords,  ¼ × ½ inch.
                        Braces,  ¼ × ⅓ inch.
                        Lattice, ¼ × 1/16 inch.

  Supported 2,500 lbs. at centre, besides a variable load of 150 lbs.
  applied as a rolling weight in the most disadvantageous manner. It
  represented a span of one hundred and fifty feet, and according to
  Weisbach’s formula for testing a model, proved the actual structure,
  (as far as can be proved by a model,) both strong and rigid to any
  desired amount. The longest bridge ever built upon this principle,
  was that of Schaffhausen, over the Rhine, which had a single span of
  three hundred and ninety feet. This bridge was not stiff, having no
  lattice, but was very strong. B. H. Latrobe, Esq. has adopted this
  form upon the Baltimore and Ohio Railroad.

The calculations for the parts of this bridge are as follows:—

             The Span being                       150 feet,
             The Rise                              20 feet,
             The Panel                             15 feet,
             Weight per foot of bridge and load 3,000 lbs.

The half number of panels is five; the diagonals of which, neglecting
fractions, are

                       √(20^2 + 15^2) = 25 feet,
                       √(20^2 + 30^2) = 37 feet,
                       √(20^2 + 45^2) = 49 feet,
                       √(20^2 + 60^2) = 64 feet,
                       √(20^2 + 75^2) = 78 feet.

The weight upon each of these sets of braces, is the weight of the
length of one panel; which, in the present case, is 3,000 × 15 = 45,000
lbs. As there is a brace under each chord stick, and assuming four
sticks in each chord, we divide by eight, and have, in round numbers,
6,000 lbs. per brace; and correcting for inclination, as follows, we
have the numbers below.

                        20 : 25 :: 6000 : 10000
                        20 : 37 :: 6000 : 15000
                        20 : 49 :: 6000 : 20000
                        20 : 64 :: 6000 : 25000
                        20 : 78 :: 6000 : 30000.

The last column has the several weights coming upon the different braces
at their several inclinations; to resist which, the scantling might be
very small, for compression, but flexure requires larger dimensions.

These braces should be confined laterally and vertically, as they pass
each post, but not connected therewith; as this would not permit a free
action of the brace, without straining transversely the post.

The length of beam, therefore, in which flexure is to be checked, is the
distance between posts in any panel.

                  In panel No. 1, it will be 25 feet.
                  In panel No. 2, it will be 18 feet.
                  In panel No. 3, it will be 17 feet.
                  In panel No. 4, it will be 16 feet.
                  In panel No. 5, it will be 16 feet.

and applying the formula

                       (2240_bd^3_)/(_L^2_) = _W_

we get, in round numbers, the following dimensions, the braces being
bolted and blocked together:—

                For the 1st panel, 25 feet long, 8 × 10
                For the 2d  panel, 37 feet long, 8 × 10
                For the 3d  panel, 49 feet long, 8 × 10
                For the 4th panel, 64 feet long, 8 × 10
                For the 5th panel, 78 feet long, 8 × 10.

For the lattice-work, a double course on each side of each truss, in
long spans, (150 to 200 feet); and a single course in shorter spans, of
3 × 6 plank, treenailed at intersections, is ample.

            GENERAL TABLE OF DIMENSIONS FOR ARCH BRACE TRUSS.

 ┌──────────┬──────────┬──────────┬──────────┬──────────┬──────────────┐
 │  Span.   │  Rise.   │ Chords.  │  Ties.   │ Braces.  │   Lattice.   │
 ├──────────┼──────────┼──────────┼──────────┼──────────┼──────────────┤
 │        50│        10│  2–8 × 10│  1–8 × 10│   2–6 × 6│2 × 9 or 3 × 6│
 │        75│        12│  2–8 × 10│  1–8 × 10│   2–6 × 6│2 × 9 or 3 × 6│
 │       100│        15│  3–8 × 10│  2–8 × 10│   3–6 × 6│2 × 9 or 3 × 6│
 │       150│        20│  4–8 × 12│  3–8 × 10│   4–6 × 8│2 × 9 or 3 × 6│
 │       200│        25│  4–8 × 16│  3–8 × 10│   4–6 × 9│2 × 9 or 3 × 6│
 └──────────┴──────────┴──────────┴──────────┴──────────┴──────────────┘

[Illustration:

  Fig. 69 K.
  Fig. 69 A.
]

Fig. 69 A, shows the method of bringing the arch braces to the chord. To
find the dimensions of the cast-iron block, make a complete drawing of
all of the braces, at their proper angles, and then draw in the block
around the feet, as shown in fig. 69 A.

  NOTE.—The centre of pressure of the braces in fig. 69 A, is not, as
  might seem, at C; because the vertical components of the forces,
  coming down the brace, are much less in the braces at small angles
  than in those at the end of the span. The load applied to each brace
  being the same, and the inclines being found, we find the centre of
  pressure, or the centre of bridge seat as follows:—

  The length of the brace is to the vertical height, as the applied
  load to the vertical pressure. In fig. 69 A, we have the following
  lengths of braces: _a_, 25; _b_, 37; _c_, 49; _d_, 64; _e_, 78; _f_,
  92; and _g_, 106; and the weights corresponding thus,

                     _a_,  25 : 20 :: 6000 : 4800.
                     _b_,  37 : 20 :: 6000 : 3243.
                     _c_,  49 : 20 :: 6000 : 2450.
                     _d_,  64 : 20 :: 6000 : 1870.
                     _e_,  78 : 20 :: 6000 : 1540.
                     _f_,  92 : 20 :: 6000 : 1304.
                     _g_, 106 : 20 :: 6000 : 1132.

In fig. 69 A, assume the foot of the fifth brace (B) as the centre of
pressure, and adding the moments, (or products of vertical components on
the braces by their distance from B,) and we have the sum on the land
side 18,928, and on the water side 16,930; showing that the centre is
taken too far from the land side. In the same manner A will be found too
far from the land side. A third trial will give the place.

[Illustration:

  Fig. 69 B.
  Fig. 69 C.
]

[Illustration:

  Fig. 69 D.       Fig. 69 E.       Fig. 69 F.
  Fig. 69 G.       Fig. 69 H.
]

Fig. 69 B, shows the manner of splicing the arch braces: being subjected
to compression, they are spliced in the same manner as the upper chords.
Fig. C, shows the lower chord spliced. Figs. D and E, the connection of
the posts, chord, and lattice. Figs. F, G, and H, the casting for
applying the upper end of the arch brace to the chord. Fig. 69 K, the
method of supporting the tracks at the end of the span, where the arch
braces will not allow the floor beams to bear upon the lower chord.


                   MCCALLUM’S PATENT RAILROAD BRIDGE.

[Illustration: Fig. 70.]

186. This bridge represents a class of structures in which the upper
chord is curved upwards (7½ feet in 200 in the Susquehanna bridge, New
York and Erie Railroad), which curved chord has the effect of
distributing an applied load at once to all of the braces _directly_, by
means of the chord, as well as _indirectly_, by means of the braces, as
in the common trusses. To this bridge is applied the arch braces A B, A
B, fig. 70, which serves to aid the 2d, 3d, and 4th pair of diagonal
braces in bearing their load.

The great distributing power of the curved chord, is shown by the fact
that a bridge of 125 feet span, actually supported a railroad train
before the diagonal bracing was introduced. The whole strain was thrown
through the curved chord and arch braces to the abutments. The bridge is
counterbraced by the pieces _d d_ and _d d_, adjustable by screws at the
ends.

The following test was applied to a span of 190 feet of this plan of
bridge. Placing the load as near as possible to the centre, the
following deflections were produced.

                           Load.     Deflection.
                         41.40 tons, 0.013 feet,
                         95.35 tons, 0.038 feet,
                        140.70 tons, 0.061 feet,
                        187.20 tons, 0.061 feet.

Upon removing the load, the bridge entirely recovered its form.

187. As the span increases, the benefit derived from the curved chord
also augments; and though in the latter part of the present chapter its
application to small spans is shown, it may not be worth while to adopt
it.

Bridges transferring the load _directly_, from each panel to the
abutment, would not be aided, to an amount worth the increased expense,
by adopting the curved top chord.

In case of any settling at the centre of the span, the reverse effect is
seen from that produced in a truss with horizontal chords; i. e., when
the ends of the upper chords in the latter _draw in_, those of the
former _push out_; and when in such bridges, arch braces are not used,
the top chords of adjoining spans must be _wedged apart_, in place of
_tying together_ as in common plans, over the centre of the piers.


                               THE ARCH.

188. The arch has been applied to long spans for a great while, and when
care has been taken to prevent flexure, answers very well. The repair of
such bridges, if any of the arch timbers decay, is difficult; but is
effected, in the largest arches.

The most correct ideas on wooden arch bridge building, are to be found
in Weibeking’s _Traite d’une parte essential de construire les grandes
pents en charpente_. This engineer, (General Director of Roads and
Bridges in Bavaria,) has built a great number of wooden arches of the
best description, which show him to be master of both the science and
the art.

[Illustration: Fig. 71.]

The general plan of his bridges is shown in fig. 71. They consist of
curved ribs formed of long pieces scarfed and bolted together, from
which the road-way is supported by posts.

The bridges of Neucettringin, Freysingin, Bamberg, Scharding, Wertach,
Vilshoven, and Altenmarkt, all testify to the good judgment of this man.
The spans vary from one hundred to two hundred feet; and the width from
twenty-five to thirty-two feet. The proportions which he gives for the
ratio of rise to span, are valuable; as they are the result of his own
experience. He states, generally, that one tenth of the span is the best
rise; but that for convenience, it is better to keep it lower. The
following table shows the dimensions he has adopted in practice.

189.

   ┌──────────────┬─────────┬─────────┬─────────┬─────────┬─────────┐
   │    Name.     │  Span.  │  Rise.  │ Width.  │ Rad. of │Scantling│
   │              │         │         │         │  Arch.  │of Arch. │
   ├──────────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
   │Bamberg,      │   208   │     16.9│32       │   422   │13½ × 15½│
   │Scharding,    │   194   │     18.8│25       │   258   │12½ × 15½│
   │Vilshoven,    │   179   │     11.1│27       │   378   │13½ × 15½│
   │Freysingin,   │   153   │     11.6│25       │   246   │12½ × 14½│
   │Ettringin,    │   139   │      8.0│25       │   305   │12½ × 15½│
   │Ersingin,     │   126   │      7.0│25       │   285   │11½ × 14½│
   │Augsberg,     │   114   │     10.6│25½      │   158   │12½ × 14½│
   │Neucettringin,│   103   │      6.8│25       │   200   │13½ × 15½│
   └──────────────┴─────────┴─────────┴─────────┴─────────┴─────────┘

The last column shows the scantling of the arch timbers; these being
placed three deep, in spans of less than 150 feet; and in larger spans,
3 deep at centre, and 5 deep at ends. Mr. Weibeking’s formula for
determining the scantling of ribs, is as follows:—

          ((_W_ × (_S_/2)^2)/_Rn_).0011 = Scantling in sq. ft.

                   Where _R_ is the rise of the arch;
                         _n_, the number of ribs;
                         _W_, width of bridge;
                     and _S_, span of bridge.

EXAMPLE.—Required the scantling of the ribs of a bridge of 300 feet
span, 20 feet wide, and 30 feet high. The formula becomes,—

               (20 × 22500)/30 × .0011 = 16½ sq. feet of

section, of all of the arches; or two parallel arches, 2½ feet wide, by
3¼ feet deep each.

        From 100 to 150 feet span, he makes the rise 1/20 span,
        From 150 to 200 feet span, he makes the rise 1/18 span,
        From 200 to 300 feet span, he makes the rise 1/15 span,
        From 300 to 400 feet span, he makes the rise 1/14 span,
        From 400 to 500 feet span, he makes the rise 1/13 span.

190. The bridge built by Mr. Burr across the Delaware at Trenton, New
Jersey, is a good specimen of an arch. It is composed of white pine
planks, from thirty-five to fifty feet long, and of a scantling 4 × 12.
These planks are laid close together, breaking joint, having an entire
depth of three feet. The arches are stiffened by horizontal tie beams,
supporting the road-way, and by diagonal bracing. The spans are 160,
180, and 200 feet, and the rise twenty-seven feet.

191. The bridge over the Susquehanna, at Columbia, built in the same
manner, consists of twenty-nine arches, each two hundred feet clear
span, supported on two abutments and twenty-eight stone piers. The clear
water-way of this bridge is 5,800 feet; and the entire length, including
piers and abutments, one and one fourth miles. There are three sets of
arches, which allow of two carriage roads and one railroad, the whole
width being thirty feet.

192. An arch to support a passing railroad train must be very rigid. It
is customary to connect them with a light truss, which effectually
counter braces the arch, and prevents that change of form which would
otherwise take place; depending entirely upon the arch for strength.

Wherever the load is applied, the arch tends to sink, and a
corresponding rise takes place at the opposite point. A load placed at
E, fig. 71, settles the arch at that point and causes it to rise at C. A
load placed at the curve of the arch depresses the centre, and elevates
the haunches. To counteract these movements a light, stiffening frame
may be used, its strength being able to resist the variable load passing
over the bridge. The strain thrown by the arch upon the truss, advances
from the opposite end to meet the train, passes it at the centre, and
finally goes off from the bridge behind the load.

When the arch _is the truss_, or when a truss is made with curved
chords, the counteracting effect of the truss is not completely
obtained. We should not depend upon the curved chord _as an arch_, but
only as a member of the truss.

193. Many combinations of arch and truss have been built in America for
railroad bridges. The principle of connecting the two systems is by some
thought bad, as they can hardly be made to bear equal parts of the load;
whence each must have more than half the necessary strength of the
whole. Others maintain that by a proper arrangement of parts a perfect
adjustment may be made, by which the load may be placed more or less on
either. There seems to be no very good reason why the two systems should
be combined, as either may be made strong enough to bear the largest
loads.

Both arches and arch braces, however, are very usefully applied to
bridges which have been made too light.

194. The manner of applying arches is well shown in the bridges of the
Pennsylvania Central Railroad, built by Hermann Haupt, Esq.

These bridges are on Howe’s plan, to which have been added strong wooden
arches. The systems are connected by adjusting the counter braces
against the arch by set screws. The arrangement is simple and effectual.
The name of the builder is sufficient to warrant the stability of the
bridge.

195. However nicely we may form an arch, it will settle more or less
when the scaffolding is removed, according to its flatness; which
depression increases with time. Mr. Weibeking expresses it in inches as
follows:—

                              0.806_R_/_S_

                       Where _R_, shows the rise,
                         and _S_, shows the span.

To allow for this settling, the curve when laid down on the platform for
building the arch, should be made a little more convex than the
completed arch is required to be; the amount of excess being that shown
by the formula.

[Illustration: Fig. 72.]

As a bridge composed of a curved rib when the span is large yields at D,
C, and E, fig. 71, when the load is applied in the middle, the strength
must of course be increased by increasing the depth of the rib; and not
to make this too heavy, a framed or built beam should be used as in fig.
72. Here it must be remembered that the two ribs must be so framed as to
resist both tension and compression; for when a load is placed at D, the
lower rib will be extended at _d_, and compressed at _c′_, and _e_;
while the upper one will be compressed at D, and extended at C and E.


                            OF THE ROAD-WAY.

196. The flooring of any system is about the same; consisting of
transverse floor beams, placed either on the top or bottom chords,
(according as the road-way is more or less elevated above the
water-way,) which support longitudinal timbers, upon which are placed
cross-ties. In some cases, two curves of diagonal plank have been placed
across the floor beams, spiked at right angles to each other, by which
the bridge is considerably stiffened laterally.

General dimensions for the floor may be thus:—

       Transverse timbers, 3 feet from centre to centre,  8 × 14
       Track strings, notched 2 inches to floor beams,   12 × 14
       Cross-ties placed one foot apart, (clear,)         3 ×  6

[Illustration: Fig. 73.]


                            LATERAL BRACING.

197. To prevent vibration in a horizontal direction, a system of
diagonal bracing is necessary. The chief pressure upon these braces is
caused by wind; and may be found by considering the bridge as turned
over upon the side, and loaded with a weight equal to the maximum
pressure of the wind, which may be taken as forty pounds per square
foot.

It is unnecessary to vary the size of these braces, except in very long
spans, when they should increase from the centre to the ends. For short
spans, (less than one hundred feet,) a brace 5 × 5 is large enough. For
larger spans 7 × 7 is sufficient.

198. Diagonal bracing, when it can be introduced, is a very desirable
part of a bridge. When the road is on the lower chord this cannot have
place in full, but may be applied as in fig. 74.

[Illustration: Fig. 74.]

By increasing the height of truss in any bridge, the tension and
compression on the chords is lessened; but the length of posts and rods
is increased. As a general thing, _one eighth_ of the span gives the
best results.

199. In framing a large bridge, it is customary to cut the top chord
sticks a little longer than to dimension; to allow for compression in
settling.

200. Bridges in exposed situations have been sometimes blown off from
the masonry. If a bridge _slides off_ from the masonry, the whole force
of the wind must be fifteen twenty-fourths of the whole weight of the
bridge; but if, as is generally the case, the masonry is rough, (and not
hammered,) no amount of wind will cause the bridge to _slide_.

The bridge will upset, turning about its lower edge, when the whole
pressure of the wind, multiplied by half the _height_ of truss,
overbalances the whole weight, multiplied by the half _width_. In very
exposed places the rod A D, fig. 74, answers a very good end; when the
road is upon the upper chord, and a rod from B to the masonry, when upon
the lower.


                            OBLIQUE BRIDGES.

201. The effect of running a train over a skew bridge, is to depress one
side before the other; as the load comes upon the centre of one truss
before it does upon the opposite one. This produces a side rocking in
the engine, dangerous alike to the bridge and to itself.

The floor timbers transferring the load to the chords should not be at
right angles to the axis of the road, but parallel to the abutment. Thus
in fig. 75, a wheel at B, throws one third of its weight upon the
abutment at E; and two thirds upon the chord at C; while in fig. 75 A,
the wheel at B, throws two thirds of the load upon C, but one third also
upon D.

[Illustration: Fig. 75.       Fig. 75 A.]

202. In a very long, oblique span, the floor timbers may be arranged as
in fig. 76, that is, inclined at the entrance and exit of the bridge,
but at right angles at the middle of the span.

[Illustration: Fig. 76.]

203. The preservation of timber in wooden bridges may be accomplished by
covering with boards, whitewashing, painting, and by Kyanizing. Covering
and whitewashing are the best, if care is taken to prevent dry rot by
giving a good circulation of air about the timbers. The oil in paints
prevents the escape of moisture from within as well as the entrance of
that from without; and should not be used unless the wood is well
seasoned. The best plan is to thoroughly whitewash and cover the frame
of the bridge, and to paint the outside of the covering.

204. In framing two or more continuous spans, the chords should always
be connected over the piers; as there is thus given something for the
upper chords to pull against, and a counter thrust for the lower.

205. Bridges should never, when it can be avoided, be placed either upon
a curve or upon a grade; particularly upon the former, as the effect of
a load is thereby very much increased, in the first case causing a
lateral, and in the second a vertical shock.


                             PILE BRIDGING.

206. In shallow water, in marshes, and in similar situations, where an
embankment would be expensive, pile bridging is very useful. Indeed,
whenever we are at liberty to obstruct the passage beneath the road, it
is well to adopt this system, unless over twenty feet high. It is
cheaper than any other, easier to repair, the parts are quite
independent of each other, and such bridges last full as long as other
wooden structures.

[Illustration: Fig. 77.]

[Illustration: Fig. 78.]

Different plans for pile bridging are given in figs. 77 to 82. Figs. 77
to 81 show plans for temporary pile work, to be used during
construction. Nothing lighter than fig. 82, ought to be permanently
used. A pile bridge upon a curve may need stronger lateral bracing upon
the convex, than upon the concave side of the curve; and also in running
water; in which cases, such a form as fig. 81 may do good service.

[Illustration: Fig. 79.]

[Illustration: Fig. 80.]

[Illustration: Fig. 81.]

[Illustration: Fig. 82.]

[Illustration: Fig. 82 A.]

(For pile-driving, and for proper dimensions, see chap. XII.)


                               TRESTLING.

207. Trestling is a system of vertical posts, and of caps and braces,
used both for temporary and for permanent works; temporarily to pass a
road over low ground where embankments are to be made, and permanently
over deep, dry gorges, where the amount of earthwork or masonry would be
too great.

[Illustration: Fig. 83.]

American railroads show all sizes and arrangements of trestling, from
twenty to two hundred feet high. Figs. 83 and 84 show temporary works,
and fig. 85 permanent.

The main part of the design in trestles is to connect the several posts
and caps by well-formed triangles; the equilateral being the best.

[Illustration: Fig. 84.]

The finest example of this system of building is the Genesee high
bridge, over Genesee River near Portageville, on the Buffalo and New
York Railroad; built by H. C. Seymour, Esq. It is eight hundred feet
long, and two hundred and thirty feet above the river. It has eight
stone piers, thirty feet high, upon which are placed trestles one
hundred and ninety feet high, seventy-five feet wide at base, and
twenty-five at top. Upon the top of all is placed a bridge fourteen feet
high. To build this viaduct was used 1,500,000 feet, board measure of
timber, which covered, when standing, two hundred and fifty acres; also,
sixty tons of bolts. The whole time occupied in building was but
eighteen months, the whole cost being $140,000.

[Illustration: Fig. 85.]


                              DRAWBRIDGES.

208. In crossing rivers or bays open to navigation, it is required from
any companies building a bridge, to leave a free passage for shipping.
This is done by making that part of the bridge over the channel movable;
(a draw).

[Illustration: Fig. 86.]

Draws may lift up, (being counterbalanced,) may slide back upon the
fixed part of the bridge, or may turn on a pivot. Fig. 86 shows a draw
much used at present, and answering every purpose. Each half of the
movable part must be calculated as a small bridge. The rods _c c c_
support the overhanging part of the draw while open. The whole revolves
upon a centre pin and a set of rollers.


                                CENTRES.

209. Centres are temporary wooden frames, used in the construction of
stone arches. Their duty is to hold the masonry, while it is unable to
support itself.

For arches from five to fifteen feet span, a centre made of boards or
planks, fig. 87, is all that is necessary. For longer spans, when the
ground beneath the arch can be used, the form, fig. 88, answers well.
When there is no support but the abutments or piers, something similar
to fig. 89 must be adopted. This is the plan adopted by George Rennie,
chief engineer at the Waterloo bridge over the Thames at London.

[Illustration: Fig. 87.]

[Illustration: Fig. 88.]

Centres are strained in a different manner as the arch progresses; first
at the haunches, and last at the crown. Excess of weight at any point
causes a settling at such, and a rise takes place at some other place.
By loading the arch temporarily, such motions are checked.

[Illustration: Fig. 89.]

These frames are placed vertically upon the pieces F F, which being
connected with the braces D D by the folding wedges _c c_, admit of
adjustment of the height of the centre. The distance between the ribbed
frames depends upon the form of the arch, and the span, or upon the
weight to be supported; varying from one to four feet. The centres are
covered with a course of narrow plank, placed parallel with the axis of
the arch, upon which the voussoirs rest.

210. The method of putting a bridge upon the masonry is shown in figs.
90, and 91; the former when the road-way is upon the upper, and the
latter when upon the lower chord.

[Illustration: Fig. 90.]

[Illustration: Fig. 91.]

211. In figs. 92 to 100, are given several plans for spans from five to
seventy-five feet. Fig. 92, shows the simple beam braced beneath with
diagonal plank; the bolts passing through the ties, stringers, and
braces. The stringers are bolted to the wall plates, and when the bridge
is upon a curve notched also, by cutting the bolster. Fig. 92 A shows
the plan. This form answers for openings from five to twenty feet. From
fifteen to thirty feet, we may use figs. 94, 95, 96, and 97. From
twenty-five, to fifty and sixty feet, figs. 93, 97, and 98. And from
fifty to seventy-five feet, figs. 99 and 100.

The following tables give reliable dimensions for bridges upon the above
plans.

[Illustration:

  Fig. 92. 5 to 20 feet.
  Fig. 92 A.
]

    Span.     Bolsters.  Stringers.     Ties.      Braces.     Bolts.
      5        12 × 12     12 × 12     6 × 10      2 × 10      1 inch
     10        12 × 12     12 × 13     6 × 10      2 × 10      1 inch
     15        14 × 14     12 × 18     6 × 10      2 × 10      1 inch
     20        14 × 14     12 × 24     6 × 10      2 × 10      1 inch

The ties being notched three inches on to the stringers, without cutting
the latter.

[Illustration: Fig. 95. 15 to 30 feet.]

    Span.       Rise.     Bolster.    Stringer.    Braces.      Rod.
     15           6        12 × 12     12 × 12    2—5 ×  6     1  inch
     20           7        14 × 14     12 × 12    2—5 ×  8     1¼ inch
     25           8        14 × 14     12 × 15    2—5 ×  9     1⅜ inch
     30          10        15 × 15     12 × 18    2—5 × 10     1½ inch

[Illustration: Fig. 96. 15 to 30 feet.]

     Span.         Rise.       Stringer.       Post.         Rod.
      15             5          12 × 12       8 ×  8          1⅛
      20             6          12 × 13       9 ×  9          1¼
      25             7          12 × 15       10 × 10         1½
      30             8          12 × 18       10 × 12         1⅝

[Illustration: Fig. 94. 15 to 30 feet.]

    Span.       Rise.     Stringer.    Braces.      Rods.     Lattice.
     15           5       2—8 ×  8     2—5 × 5        1        2 ×  6
     20           6       2—8 ×  9     2—5 × 6       1¼        2 ×  8
     25           7       2—8 × 10     2—5 × 8       1⅜        2 ×  9
     30           9       2—8 × 12     2—5 × 9       1½        2 × 10

[Illustration: Fig. 97. 15 to 30 feet.]

    Span.       Rise.     Stringer.     Post.       Rods.      Braces.
     15           5       2—8 ×  8     8 ×  8         1         4 × 5
     20           6       2—8 ×  9     9 ×  9        1⅛         4 × 6
     25           7       2—8 × 10     10 × 10       1¼         5 × 6
     30           9       2—8 × 12     10 × 12       1½         6 × 6

[Illustration: Fig. 93. 25 to 50 feet.]

    Span.       Rise.      Chords.     Braces.     Posts.       Rods.
     25           8       2—6 ×  8      6 × 6      6 ×  8         1
     40          10       2—7 ×  9      6 × 7      8 ×  8        1⅛
     50          10       2—8 × 10      6 × 8      8 × 10        1¼

[Illustration: Fig. 97. 25 to 50 feet.]

    Span.       Rise.      Chords.     Posts.      Braces.      Rods.
     25           8       2—6 ×  8     8 ×  8       5 × 5     1⅛ or 2—⅞
     40          10       2—7 ×  9     9 ×  9       5 × 8    1⅜ or 2—1⅛
     50          10       2—8 × 10     10 × 10      6 × 8    1¾ or 2—1¼

[Illustration: Fig. 98. 25 to 50 feet.]

   Span.      Rise.      Chords.     Posts.      Braces.       Rods.
     25         8       2—6 ×  8     6 ×  8      5 ×  5    2—1  or 1—1⅜
     40         10      2—7 ×  9     6 ×  9      5 ×  8    2—1⅛ or 1—1⅝
     50         10      2—8 × 10     6 × 12      5 × 10    2—1¼ or 1—1¾

[Illustration: Fig. 99. 50 to 75 feet.]

    Span.       Rise.      Chord.      Posts.      Braces.    Lattice.
     50           8       2—8 × 10    1—8 × 10     2—6 × 7      2 × 6
     60           9       2—8 × 10    1—8 × 10     2—6 × 7      2 × 6
     75          10       3—8 × 10    2—8 × 10     3—6 × 8      2 × 6

[Illustration: Fig. 100. 50 to 75 feet.]

  Span.   Rise.   Chords.   Posts.    Braces.   Centre       Rods.
                                                braces.
                                                         No. 1. No. 2.
   50       8    2—8 × 10  1—8 × 10   2—6 × 7    5 × 5     1½     1
   60       9    2—8 × 10  1—8 × 10   2—6 × 7    5 × 5     1⅝     1⅛
   75      10    3—8 × 10  2—8 × 10   2—6 × 8    5 × 6     1¾     1¼

212. In dimensioning small bridges, like the above, in estimating the
maximum load, more regard must be given to the weight of momentary loads
than (as in large bridges) the weight per lineal foot, as the weight of
the bridge itself, when under fifty or sixty feet span, is
inconsiderable. The greatest load that can come upon a single post or
rod, is that from the driving wheels of a locomotive. If the whole
engine weighs forty tons, there will be ten tons on each pair of
drivers, or five tons or 11,200 lbs. on each wheel; which, being applied
over a length of ten feet only, may be considered as at a single point,
and all parts must be able to bear such load. In large spans, where the
weight is great, if the truss is strong enough to support the bridge and
load, it will safely resist the effects of a sudden application of
passing trains.

  NOTE.—_On the Static and Dynamic deflection of Bridges._
  Considerable variance of opinion exists as to the relative
  deflection of bridges, produced by stationary and by moving loads.
  Neither experiment nor theory has exactly settled the point.

  Experiments upon the Elwell bridge, (Epsom and Croydon Railway,
  England).

           Velocity in feet per second. Deflection in inches.
                                      0                 0.215
                                     25                 0.215
                                     31                 0.230
                                     32                 0.225
                                     54                 0.245
                                     75                 0.235

  The bridge being a cast-iron girder of forty-eight feet span, load
  thirty-nine tons.

  Experiments on the Godstone bridge, (S. E. R. R. England).

           Velocity in feet per second. Deflection in inches.
                                      0                  0.19
                                     22                  0.23
                                     40                  0.22
                                     73                  0.25

  Cast-iron girder, thirty feet span, load thirty-three tons.

  Mr. W. H. Barlow, (Eng.) observed, “that in case of a timber
  viaduct, a freight train, at a low speed, produced a certain
  deflection; but an extra train, with a much lighter engine, seemed
  to push the bridge like a wave before it.”

  The Britannia tubular bridge was depressed three fourths of an inch
  by two locomotives and a train of two hundred and eighty tons
  standing still; but at seventy miles per hour, the deflection was
  sensibly less.




                              CHAPTER IX.
                             IRON BRIDGES.

               “A little knowledge is a dangerous thing.”


213. Within the past ten years iron has been brought extensively into
use for railroad bridging; and when employed by those who understand its
chemical and mechanical nature is unequalled for strength, durability,
and elegance of appearance; but when, as is too often the case in
America, it is intrusted to men who neither know nor care for any thing
but the price they get for it, nothing can be more unsafe. No material
requires so complete a knowledge of its properties, to be safely used,
as cast-iron.


                      NATURE AND STRENGTH OF IRON.

214. The table below shows the properties of the several descriptions of
iron used in engineering.

 ┌───────────┬──────────┬───────────┬───────────┬──────────────────────┐
 │  Wrought  │Cast-Iron.│Iron Wire. │  Boiler   │  Designation of the  │
 │   Iron.   │          │           │  Plate.   │       quality.       │
 ├───────────┼──────────┼───────────┼───────────┼──────────────────────┤
 │        480│       450│         ——│        480│Weight per cubic foot │
 │           │          │           │           │  in lbs.             │
 │           │          │           │           │Resistance to         │
 │      15000│      4500│      25000│      12740│  extension in lbs.   │
 │           │          │           │           │  per sq. inch.       │
 │           │          │           │           │Resistance to         │
 │      11000│     25000│         ——│       7500│  compression in lbs. │
 │           │          │           │           │  per sq. in.         │
 │           │          │           │           │Expansion per degree  │
 │   .0000066│ .00000608│  .00000685│   .0000066│  Fahrenheit in       │
 │           │          │           │           │  lengths.            │
 │.0000000424│.000000106│.0000000446│.0000000524│Extension per lb. per │
 │           │          │           │           │  square inch.        │
 │ .000000149│.000000083│         ——│ .000000189│Compression per lb.   │
 │           │          │           │           │  per square inch.    │
 │           │          │           │           │Ratio of extensive to │
 │   90 to 66│ 20 to 111│         ——│  127 to 75│  compressive         │
 │           │          │           │           │  strength.           │
 │           │          │           │           │Resistance to         │
 │      12500│     17500│         ——│         ——│  detrusion, or       │
 │           │          │           │           │  shearing.           │
 │         55│        31│         ——│         ——│Relative transverse   │
 │           │          │           │           │  strength.           │
 └───────────┴──────────┴───────────┴───────────┴──────────────────────┘

_Column four refers to boiler plate when built into tubes._

After wrought iron has become a little compressed, its power to resist a
crushing force is very much increased.

215. The tenacity of wrought iron is increased by heating. Experiments
upon thirty varieties gave the following mean result, the temperature
ranging from 500° to 700° Fahrenheit.

Strength when

                         Cold.   Hot.  Cooled.
                         60,000 64,000 70,000

216. Stirling’s process of toughening cast-iron, by the addition of
malleable scrap, increases the strength in the following ratio:—

      The mean tensile strength of cast-iron being     18,000 lbs.
      And the compressive strength being              105,000 lbs.
      When Stirling-toughened the tensile strength is  23,000 lbs.
      And the compressive strength                    130,000 lbs.

The strength of cast-iron increases rapidly up to the twelfth or
fifteenth recasting, when it is nearly doubled; after the fifteenth
melting the strength decreases.

217. Wrought iron exposed for some time to vibration, as in the case of
railroad axles, or iron which has been wrought with light hammers, loses
its toughness and becomes “short,” (crystalline). The fibre may be
restored in such cases by reheating and cooling slowly.


              218. GENERAL RATIOS OF THE STRENGTH OF IRON.

                       Tension. Compression. Cross Strain.
              Cast,         300        1,666         31.68
              Wrought,    1,000          733         55.40


                   OF THE STRENGTH OF BOILER PLATES.

219. The strength of rolled boiler plates is no greater in the
_direction of the fibres than crosswise_, but is more regular; whence
the length of the fibre must be placed as nearly as possible with the
direction of the force.

A mean of twelve experiments, by Mr. Fairbairn, gives the tensile
strength of wrought iron plates as 50,960 lbs. per square inch; and the
compressive strength of plates, when built into tubes, as 30,464 lbs.,
or for safe use in practice, for extension, 12,740 lbs., and for
compression, 7,500 lbs. In the remarks upon girder bridges the matter of
riveting will be considered.


                    CLASSIFICATION OF IRON BRIDGES.

220. Iron bridges may be classified as follows:—

       Those entirely of _cast-iron_, or Arch and Girder bridge.
       Those of _wrought iron_ alone, or Tubular and Girder.
       Those of _iron wire_, or Suspension bridges.
       Those of _cast and wrought iron_, or Trussed bridges.

The order in which these bridges may be placed as regards cost of
construction, and extent of application, is as follows:—

        Number.      Span.           Description of bridge.
              1  10 to   50 feet Cast-iron girder.
              2  50 to  200 feet Cast and wrought combinations.
              3 200 to 2000 feet Suspension.
              4 200 to  500 feet Cast arch.
              5  25 to  100 feet Boiler plate girder.
              6 100 to  500 feet Tubular.

Numbers 2, 3, and 5, are the forms which are in use upon American roads.
No. 1, is very liable to failure, requires much more knowledge and care
in building, and is far more expensive than a wooden truss, or trussed
girder. No. 4, is very expensive, and causes a greater obstruction to
the water-way than any other. The enormous expense of No. 6, should, and
will prevent its adoption in the United States. Let us look at the
principles of construction of numbers 2, 3, and 5.


                 COMBINATIONS OF CAST AND WROUGHT IRON.

221. Under this head come all of the iron trussed frames used in this
country.

As before observed, skill in bridge construction consists in using
always that material which with the least expense is the best able to
resist the particular strain to which it may be exposed. Thus wrought
iron must always be used to resist tension, and cast-iron compression.
Posts, braces, and upper chords should always be cast, while ties and
lower chords should be made of wrought iron.

The strength of a railroad bridge must be such as to resist all extra
shocks and strains, such as are produced by derailment of engines, and
breakage of axles; also incidental strains arising from change of form
by expansion and contraction of the metal, and from high winds and
gales.

[Illustration: Fig. 101.]

Every part of a bridge not resisting some force is worse than useless,
as it adds to the weight. Lightness not only increases the economy
directly, but indirectly by removing a part of the permanent load.

222. Foremost in class number two stands Wendel Bollman’s Iron
Suspension and trussed bridge. For simplicity of construction and
directness of action, this bridge is unsurpassed. The weight at each
post is transferred at once to the abutment or pier. The upper chord is
of cast iron, hollow, octagonal without, and circular within. The posts
consist of an ¶ᕼ¶ casting, the central web cast open and the flanges
whole. The top is adjusted to the chord, and the bottom to the tension
or suspending rods. These latter are of wrought iron, rectangular in
section, joined when the length requires it by an eye bolt. Each set
after leaving the foot of the post, passes through the chair at A B,
fig. 101, and is secured by a nut. The junction of the tension rod A C,
and the counter rod B C, is attached indirectly to the foot of the post
by a pendulum or link; which serves to equalize the effect of expansion
upon the rods. Vibration and reaction are prevented by the panel
diagonal ties D H, and C E. The floor is supported by flanges at the
foot of each post. The lateral bracing consists of a system of hollow
cast-iron posts, and of wrought diagonal tie rods. A lower chord is
plainly unnecessary, its place being taken by the rods C B, F B, F A, G
A.

A bridge of this description upon the Baltimore and Ohio Railroad of the
following dimensions,

                    Clear span,             124 feet
                    Length of top chord,    128 feet
                    Length of panel,         15 feet
                    Height of truss,         17 feet
                    Width,                   16 feet
                    Lbs. of cast-iron,        65,137
                    Lbs. of wrought iron,     33,527
                    Whole weight,             98,664
                    Weight per lineal foot,      796

was subjected to the following tests.

Three locomotives with tenders attached, and weighing in all one hundred
and twenty-two tons, (nearly one ton per foot,) were run over the bridge
at eight miles per hour, when the deflection at centre was one and three
eighths inches, and at the first post nine sixteenths of an inch. The
following tests were applied to a bridge of seventy-six feet span upon
the Washington branch of the same road:

An engine and tender weighing forty tons, caused a deflection of five
eighths of an inch. A fast passenger train deflected the bridge nine
sixteenths of an inch.

 Two engines and tenders, back to back, at rest, and
   weighing in all 77½ tons, caused a deflection of          11/16 inch,
 The same at ten miles per hour,                             13/16 inch,
 Engines head to head at four miles per hour,                13/16 inch,
 Engines head to head at eight miles per hour,               13/16 inch,
 Engines head to head at twenty miles per hour,              14/16 inch.

The extreme expansion of the one hundred and twenty-eight feet chord
from heat, was five sixteenths of an inch at each end, or five eighths
of an inch in all, or 1/2457th of the length; and that without the
slightest derangement of masonry. The rod C B, being five times as long
as C A, expands five times as much, but at the same time the lengths D
A, D B, being so nearly proportional to C A, and C B, expand also in the
ratio of one to five; and thus no bad result is experienced.

The estimate of strains upon this bridge is extremely simple; the whole
consisting of as many separate systems as there are posts. Each set of
rods sustain a rectangle equal to one panel, i. e., the two adjacent
half panels. Thus A C, and C B, support the rectangle _m m_, _m m_, the
rods A F, F B, the rectangle _n n_, _n n_. Allowance must of course be
made for the inclination of the rods. The dimensions of the central pair
will of course be the same; but those of the other sets will vary. The
diagonals D H, and H L, prevent reaction; and must be able to resist the
action produced by the variable load upon one panel (as noticed in
Chapter VIII).

Any load, one at C D for example, gives to the posts a tendency to
revolve on A, as a centre towards the abutment; to oppose which, there
must be a force in the opposite direction. The most proper direction in
which to resist such motion is the line C K, i. e., the line of the
lower chord. In this bridge there is no lower chord, but in place of
such are put the rods A G, A K, B H, and B C; which prevent the change
of form (by the motion of the triangle) and act against the upper chord.

As an example of the estimate of strains upon this bridge take the
following.

                Span,                           90 feet.
                Rise,                           18 feet.
                Panel,                          15 feet.
                Weight per lineal foot,      2,500 lbs.
                Whole weight,              225,000 lbs.
                Weight on each side truss, 112,500 lbs.
                Weight on each post,        18,750 lbs.

The weight borne by each system, i. e., one post and the two supporting
rods, is 18,750 lbs. The strain to be resisted by any one rod depends
upon its inclination.

The following figures show the elements of the truss in question:—

                                                                Section
 Rod.  Length.         Applied weight.                Increased of the
                                                        strain. bar in
                                                                inches.
 A B =    90.0
 C D =    18.0
 A C =    23.4 (18750 – 3125)  = 15625 which by 23.4/18 = 20312      1⅓
 A H =    35.0 (18750 × 60)/90 = 12500 which by   35/18 = 24306      1⅔
 A F =    48.5 (18750 × 45)/90 =  9375 which by 48.5/18 = 25260      1⅔
 A K =    62.6 (18750 × 30)/90 =  6250 which by 62.6/18 = 21736      1⅓
 A G =    77.6 (18750 × 15)/90 =  3125 which by 77.6/18 = 13472       1

Column 1, gives the name of the rod; col. 2, the calculated diagonal
length; col. 4, the applied weight, (the varying weight by reason of the
varying inclination) found by multiplying the whole weight upon one
panel or post by the distance of that post from the abutment, and
dividing the product by the span. (Thus the load applied to A G is

                              (W × IB)/S,

that on A K is

                              (W × BX)/S,

and so on.) Col. 6, shows the increase found by col. 5 on account of
inclination as noticed in Chap. VIII.; and finally, col. 4 gives the
necessary sectional area of the bars or rods.

The compression on the top chord is evidently the sum of the
compressions of the separate systems; the compression from any one
system is as follows, fig. 102.

[Illustration: Fig. 102.]

Let _a d_, _c d_ be the rods, and _a b c_ the chord; also _b d_, the
post; now if _d b_ represents the weight, _e h_ shows the tension on a
lower, or the compression on an upper chord; the triangles _a c d_ and
_a b e_ are similar; as also _e b h_ and _d b c_; whence

                      _be_ = (_ab_ × _cd_)/(_ac_);

and

                _eh_ = (_cb_ × _be_)/(_dc_) compression.

Numerically we have the following figures:—

In the first system,

                      _be_ = (15 × 77.6)/90 = 13,

also

                      _eh_ = (75 × 13)/77.6 = 12.

In the second system,

                      _be_ = (30 × 62.6)/90 = 21,

also

                      _eh_ = (60 × 20)/62.6 = 20.

In the third system,

                      _be_ = (45 × 48.5)/90 = 24,

also

                      _eh_ = (45 × 24)/48.5 = 23,

that is, the compression from the system A C B, is to the weight on the
post, as twelve is to the length of the post; or actually

                   18 to 12 as 18,750 to compression;

whence

                 compression = (18750 × 12)/18 = 12500

in system one, and in the second system

                      18 to 20 as 18750 to 20833.

In the central system,

                      18 to 23 as 18750 to 24000.

Doubling the sum of the first and second systems, and adding thereto the
central, we have

                 2(12500 + 20833) + 24000 = 90666 lbs.,

as the whole compression upon one side of the bridge.

As to compression only, this would require a section of about four
square inches of cast-iron, which may be obtained by a tube of four and
one half inches inside, and five inches outside diameter. We may however
need to increase this amount to resist flexure, or transverse strains;
in which case the length of tube in one panel is to be regarded as the
height of a post, or the length of a beam; and the size will be found by
the table on page 138.

Each post must bear 18,750 lbs., and these being of cast-iron, to resist
flexure, by the same table above referred to, should, if made as a
hollow cylinder, be a little over four inches in diameter, and one half
inch thick; and if of + or ¶ᕼ¶ section, should have a square of nearly
five inches.

The flooring will be dimensioned by the rules given in Chapter VIII. for
single beams.

There is nothing about this bridge to burn, in case of fire, except the
floor; and that might easily be made of iron.

To use the words of the inventor, “The permanent principle in bridge
building sustained throughout this mode of structure, and in which there
is such gain in competition with any other, namely, the direct transfer
of weight to the abutment, renders the calculation simple, the expense
certain, and facilitates the erection of secure, economical, and durable
structures.”


                        WHIPPLE’S IRON BRIDGES.

223. The bridges built by the above-named engineer are in all respects
well proportioned, rigid, safe, and durable. Cast-iron is used as a top
chord, and wrought iron is employed to resist the tensile forces. The
plan put up upon the New York and Erie Railroad, consists of a hollow
cast-iron top chord, circular in section. Lower chords of wrought iron
rods. Posts cast cruciform in section. Diagonal tension rods, as in
Pratt’s bridge, (Chapter VIII.). The whole structure is in iron exactly
what the above-named bridges are in wood; and the method of calculation
is the same. For spans not exceeding one hundred feet, this form answers
every purpose as a railroad bridge. It is open to the same objection in
larger spans as are all trusses transferring the load by a series of
triangles through which the weight passes successively, namely, the
effect of an enormous pressure at the feet of the second and third pairs
of braces, which should be taken up by arch braces, as in fig. 69; or by
rods from the top of the abutment pillars to the feet of the second and
third sets of posts.

A span of this plan, upon the New York and Erie Railroad, of forty feet,
and which weighed only three tons, supported a load of fifteen hundred
pounds per lineal foot for two days; when the bridge had settled nearly
one half inch. A load of rails weighing 1318 lbs. per foot (of bridge)
was then rolled over, upon a truck without springs, thus making the
whole load upwards of 2,800 lbs. per foot, when the whole deflection was
three fourths of an inch. Upon removing the load the bridge returned to
its original position, within one fourth of an inch.


                          SUSPENSION BRIDGES.

224. Suspension bridges of large span have been generally considered as
entirely unfit for railroad purposes; but John A. Roebling has proved
the contrary by erecting a wire suspension railroad bridge of eight
hundred feet clear span across Niagara River; which with heavy loads and
violent gales has shown itself to be both stiff and strong to any
desired amount. The construction of a bridge upon any other plan would
have been hardly possible at the site of Mr. Roebling’s Niagara bridge,
there being no opportunity for scaffolding or for piers, pontoons or
hydraulic presses.

The simple road-way supported by cables, possesses great strength with
very little stiffness. It must be accompanied by stays and trusses to
check vibration.

No bridge involves more simple calculations, and in none can we proceed
with more absolute safety, than in the wire suspension. European
suspension bridges are generally formed of cables made by linking bars
of wrought iron together. This method is more expensive and more liable
to failure than the American plan of forming cables of iron wire. An
apparently good bar may be defective inside, while we are sure of every
component fibre of the cable; indeed it is very little trouble to test
each wire as it is laid into the cable.

The parts to be considered in proportioning a suspension bridge are

                      The anchoring masonry,
                      The anchor chains,
                      The towers and plate,
                      The suspension cables,
                      The suspending rods,
                      The stiffening arrangement,
                      The road-way.

The data given in the construction of a bridge of this description are

                       The span,
                       The load to be supported.

The assumed data

                     The versed sine of the cable,
                     The width.

And the required elements

  The length of cable,
  Lengths of suspending rods,
  Angle of tangent of cable at point of suspension with axis of tower,
  Tension upon the cables,
  Section of the anchor irons,
  Amount of anchoring masonry,
  Size of the towers,
  Dimensions of trussing and of road-way.


                             OF THE CABLES.

225. The curve formed by the cable of a suspension bridge lies between
the parabola and the catenary. When loaded the curve is nearly the
former, and when unloaded the latter.


                              _Problem 1._

Given the horizontal distance between the points of suspension and the
versed-sine, to find the length of the cable, fig. 103.

[Illustration: Fig. 103.]

Represent C E by _b_, and E F by _a_, and the length of the semi-curve
is

                      _L_ = _b_[1 + ⅔(_a_/_b_)^2].

Let the half span be five hundred feet, and the versed-sine or
deflection eighty feet, the formula becomes

        _L_ = 500[1 + ⅔(80/500)^2] = 500 × 1.0171 = 508.55 feet,

which is the half length of cables between towers.


                              _Problem 2._

226. To find the length of the suspending rods. Calling E the horizontal
distance between the vertical suspenders, we have the formula

                      _X_ = (_Y^2_)/(_b^2_) × _a_,

in which we place E, 2E, 3E, etc., in place of Y, thus calling the rods
one hundred feet apart, we have

 ┌───────────────────────┬───────────────────────┬───────────────────────┐
 │        Centre.        │        Rod 1.         │        Rod 2.         │
 ├───────────────────────┼───────────────────────┼───────────────────────┤
 │           0           │ (_E_^2)/(_b_^2) × _a_ │(4_E_^2)/(_b_^2) × _a_ │
 │           0           │ (100^2)/(500^2) × 80  │ (200^2)/(500^2) × 80  │
 │           0           │         3.20          │         12.80         │
 └───────────────────────┴───────────────────────┴───────────────────────┘

 ┌───────────────────────┬───────────────────────┬───────────────────────┐
 │        Rod 3.         │        Rod 4.         │        Rod 5.         │
 ├───────────────────────┼───────────────────────┼───────────────────────┤
 │(9_E_^2)/(_b_^2) × _a_ │(16_E_^2)/(_b_^2) × _a_│(25_E_^2)/(_b_^2) × _a_│
 │ (300^2)/(500^2) × 80  │ (400^2)/(500^2) × 80  │ (500^2)/(500^2) × 80  │
 │         28.80         │         51.20         │         80.00         │
 └───────────────────────┴───────────────────────┴───────────────────────┘


                              _Problem 3._

227. To find the angle E C G, fig. 103. The formula for the angle
between the axis of the tower, and the tangent to the curve of the cable
at the point of suspension is

                     tang _a_ = E C G = (2_a_)/_b_.

Span being one thousand feet, _b_ is five hundred; and _a_ being eighty
feet, we have

               tang E C G = 160/500 = log 160 – log 500:
       or 2.204120 – 2.698970 = tang 9.505150 = 17° 45′ = E C G.
         Also, 90° – 17° 45′ = 72° 15′ = angle G C A, or A C H.

When the points of suspension are not at the same elevation, we proceed
in the same manner: only using G L, G E, in place of F L, F C, in fig.
103 A.

[Illustration: Fig. 103 A.]

That the resultant of the forces acting upon the top of the tower may be
vertical, the angles G C A, and A C H, fig. 103, must be equal; if not,
the masonry must be so arranged as to cause the resultant to pass
through the centre of gravity. When more than one span is used, and the
openings are unequal, that the intermediate pier or piers shall not be
pulled over, the cable of the largest, and consequently heaviest span,
must have a greater inclination from the horizontal than that of the
shorter span; the product of the tensions by their respective
inclinations must be equal. Mr. Roebling’s plan in connecting several
spans, is to attach the cables of adjacent spans to a pendulum upon the
pier, by which arrangement the difference in tension upon the different
cables swings the pendulums, without racking the masonry.


                              _Problem 4._

228. Given the weight per foot of bridge and load, to find the tension
at the lowest point of the curve. The formula for the minimum tension,
that at the vertex F of the curve, is

                         _T_ = (_ph^2_)/(2_f_);

where _p_ is the weight per foot of bridge and load, _h_ the half
distance between the points of suspension, and _f_ the versed-sine. Thus
the span being one thousand feet, the versed-sine eighty feet, and the
load per lineal foot six thousand lbs., the formula becomes

         _T_ = (6000 × 500^2)/160 = 9375000 lbs. or 4185 tons.

The maximum tension is at the points of support, and is expressed by the
formula

                _T_ = ((_ph_)/(2_f_))[_h^2_ + 4_f^2_]^½:

which, in the case before us, becomes

       _T_ = ((6000 × 500)/160)[500^2 + 4 × 80^2]^½ = 4395 tons.

229. The object of the anchoring is to connect the cable with a
resistance upon the land side, which shall more than balance the weight
and momentum of the bridge and load upon the opposite side. The
anchoring of the Niagara bridge consists of an iron chain made of flat
links, 7 feet long, 7 inches wide, and 1.4 inches thick; the chain links
consist alternately of six and of seven of these bars; see fig. 104.

[Illustration: Fig. 104.]

In the Fribourg bridge (Switzerland) the anchorage is made as in fig.
105, (see p. 220,) by a cable in place of the chain. In M. Navier’s
suspension bridge at Paris, over the Seine, the anchorage depended
somewhat upon the natural cohesion of the earth forming the bank of the
river, and this being destroyed by the bursting of a water-pipe in the
vicinity, the bridge fell. When there is no natural rock for an
anchorage, the masonry of the shaft must, by its own weight, resist the
tension.

230. The height of the towers must be at least as much as the
versed-sine of the cable. Their duty is to support the whole bridge and
load. The breadth and thickness of these columns must be determined more
with a view to opposing lateral, than downward strains. The former
result from the horizontal vibrations of the bridge caused by the action
of the wind. Tremor and vibration caused by a passing load, tend to pull
the towers into the river. The section for weight only might be very
small. From the practice of the best builders, a mean section of one
fifth of the height seems to give the best results; thus, if a tower is
sixty feet high, the mean thickness should be twelve feet; or the top
being 8 × 8 feet, the bottom should be 16 × 16 feet.

If the bridge is so little braced laterally as to swing, a dangerous
momentum will be generated which would very much increase the strain,
both upon the masonry and upon the cables.

231. The object of the stiffening truss is to transfer the weight
applied at any one point over a considerable length, and to prevent
vibration. Its dimensions should, therefore, be those of the
counterbracing in an ordinary truss.

Any applied load produces a certain depression in the bridge: to use the
words of Mr. Roebling, “every train that passes over the bridge causes
an actual elongation of the cables, and consequently produces a
depression. If the train is long, and covers nearly the whole length of
the bridge, and is uniformly loaded, the depression will be uniform. If
the train is short, and covers only a part of the floor, the depression
will be less _general_ and more _local_; and will be the joint result of
an elongation of the cables, and of a disturbance of the equilibrium.
Depressions will be in direct proportion to the loads, and indirectly as
the length of train.” The amount of depression depends on the elongation
of the cables; the elongation upon the length. The depression is shown
by the formula

            _D_ = √(¾[_V^2_ – _d^2_]) – √(¾[_l^2_ – _d^2_]).

        where _D_ = depression,
              _l_ = half length of curve before elongation,
              _V_ = half length of curve after elongation,
              _d_ = half distance between points of suspension.”

The effect of heat, by expanding the cables, is also to depress the
road-way; the amount being shown by the expression

            _D_ = √(¾[_V^2_ – _d^2_]) – √(¾[_l^2_ – _d^2_]).

_V_ being the length of semi-curve as elongated by heat instead of by
tension; the elongations, both by heat and tension, being found by table
on page 193.

Upon the top of the towers is placed a pair of cast-iron plates
separated by rollers; the upper plate (the saddle) is thus enabled to
move over the lower one when pulled either way by the movement of the
cables.

The length of the half cable between towers being generally greater than
the distance from the top of the tower to the anchoring, expands more,
when the saddle moves towards the land side. The dimensions of these
castings must be sufficient to resist the whole weight of bridge and
load.

232. As an example of the preceding formula, take the following:—

           Assume the span as                     1,000 feet.
           Height of towers                         100 feet.
           Deflection of cables                      90 feet.
           Weight per foot (lineal) of bridge     2,500 lbs.
           Weight per foot (lineal) of load       2,000 lbs.
           Whole weight per foot                  4,500 lbs.
           Total weight                       4,500,000 lbs.


                                CABLES.

The formula for the half length of cables between tops of towers is

                      _L_ = _b_[1 + ⅔(_a_/_b_)^2],

which becomes

                  _L_ = 500[1 + ⅔(90/500)^2] = 510.80,

which doubled, is 1021.38. To this add double the distance from the top
of tower to the anchorage, (see page 206,) which is found as follows:—

                        tang E C G = (2_a_)/_b_.

Also, tang E C G = log 2_a_ – log _b_, or 2.255273 – 2.698970 = tang
9.556303 of which the angle is 19° 48′ and 90° – 19° 48′ is 70° 12′ =
angle G C A or A C H.

The height of the tower being one hundred feet, and the angle at the
tower 70° 12′, we have

                    Sin 19° 48′           9,529,864
                    Sin 90° 00′          10,000,000
                    log height (100)      2,000,000
                    log distance (295.2)  2,470,136

which double, and we have 590.4; finally, add twice the breadth of the
tops of the towers, and the whole length of cable is, from anchorage to
anchorage,

                 1021.38 + 590.40 + 16 = 1627.78 feet.

The formula for the maximum tension, (that at the point of suspension,)
is

                _T_ = ((_ph_)/(2_f_))√(_h^2_ + 4_f^2_),

which becomes

         _T_ = ((4500 × 500)/180)√(250000 + 32400) = 2966 tons.

Number 10 iron wire (20 feet per lb.) will support 1,648 lbs. per
strand; this is the ultimate strength; the maximum load for safety is
400 lbs. per strand; whence 2,966 tons, or 6,642,500 lbs. will require
16,606 strands; and if we use two cables, each must have 8,303 wires; or
four cables of 4,151 each. The permanent load on suspension bridges
should never be more than _one sixth_ of the ultimate strength; _one
eighth_ is a good standard. The accidental load should never exceed one
fifth of the whole strength of the cables. The permanent weight
supported by the Niagara bridge is only one twelfth of the ultimate
strength of the cables.


                             ANCHOR CHAINS.

The maximum tension being 6,642,500 lbs. the whole section of the four
anchorings will need to be

                      6642500/15000 = 443 inches,

or 111 square inches for each shaft; which is obtained by eleven links
ten inches wide and one inch thick. If we so attach the anchor chains to
the masonry as to reduce the tension one fourth at the first arch, (see
Fribourg anchoring,) we may fasten three bars of the chain at that
point, and descend from the first to the second arch with eight bars;
and leaving two bars at that point, proceed to the bottom with the
remaining six.

Where there is no natural rock to build the masonry into or against,
enough artificial stone must be put down to balance the bridge and load.


                           ANCHORING MASONRY.

The entire weight of the bridge and load being 4,500,000 lbs. and the
whole tension, as above found, 6,642,500 lbs., or upon each tower
3,321,250 lbs.; this is the tension tending to draw the masonry out of
each shaft. This tension must be reduced on account of the inclination
of the pulling force. The tower is one hundred feet high. The distance
on the line of tension from the top of the tower to the anchoring, as
already found, is 295.2 feet; whence the actual effort to move the
anchor masonry, is thus,

  295.2 to 100 as 1,660,625 to the effort or 562,542 lbs. If rock
  weighs 160 lbs. per cubic foot, which is resisted by a column of
  masonry of 3,321,250/160 = 20,758 cubic feet, or 20 × 20 × 52 feet,
  or by a mass 15 × 15 × 91 feet.


                                TOWERS.

The height of towers being one hundred feet, and the mean thickness
being one fifth of the height, we have mean section 20 × 20; or top 12 ×
12, and base 28 × 28.


                            SUSPENDING RODS.

Assuming the horizontal distances between the centres of the vertical
suspenders as five feet, their lengths, then, will be found by formula

                      _X_ = (_Y^2_)/(_b^2_) × _a_;

and placing for _Y^2_ the distances 5, 10, 15, 20, etc., we have,
commencing at the centre,

 ┌───────┬──────────────┬───────────────┬───────────────┐
 │Centre.│      5       │      10       │      15       │
 ├───────┼──────────────┼───────────────┼───────────────┤
 │   0   │5^2/500^2 × 90│10^2/500^2 × 90│15^2/500^2 × 90│
 │   0   │     .009     │     .036      │     .081      │
 └───────┴──────────────┴───────────────┴───────────────┘

 ┌───────┬───────────────┬───────────────┬───────────────┐
 │Centre.│      20       │      25       │      30       │
 ├───────┼───────────────┼───────────────┼───────────────┤
 │   0   │20^2/500^2 × 90│25^2/500^2 × 90│30^2/500^2 × 90│
 │   0   │     .144      │     .225      │     .360      │
 └───────┴───────────────┴───────────────┴───────────────┘

 ┌───────┬───────────────┬───────────────┬───────────────┐
 │Centre.│      35       │      40       │      45       │
 ├───────┼───────────────┼───────────────┼───────────────┤
 │   0   │35^2/500^2 × 90│40^2/500^2 × 90│45^2/500^2 × 90│
 │   0   │     .490      │     .576      │     .729      │
 └───────┴───────────────┴───────────────┴───────────────┘

 ┌───────┬───────────────┬─────────────────────┐
 │Centre.│      50       │         _d_         │
 ├───────┼───────────────┼─────────────────────┤
 │   0   │50^2/500^2 × 90│(_d_^2)/(_b_^2) × _a_│
 │   0   │     .900      │         _h_         │
 └───────┴───────────────┴─────────────────────┘


and so on, until we arrive at the tower. Whatever distance above or
below the vertex of the curve the road-way is placed, is of course
constant, to be added to or taken from the above lengths.

The manner of putting in any camber is simple both in theory and
practice. The strain upon the suspenders is merely the direct weight of
the road-way and load. If this is 3,500 lbs. per foot, the five feet
supported by two rods (one each side) will weigh 17,500 lbs.; each rod
or wire rope must hold 8,750 lbs.; this can be done by a section of one
half inch area. For extra strains, however, on so large a span as 1,000
feet, one inch of area is not too large.


             OF THE STIFFENING TRUSSES, GIRDERS, AND STAYS.

The object of the girders supporting the rails is to diffuse the applied
weight; these girders may be made of a Howe truss four or five feet
deep, by trussed girders, only simply deep and stiffly framed track
strings. They should be able to distribute the load applied at one point
at least fifteen or twenty feet. The side trusses transfer to a still
greater extent any applied load. Mr. Roebling estimates the combined
effect of trusses and girders in the Niagara bridge as transferring the
weight of a locomotive over a length of two hundred feet. This
transferring counteracts the _local_ depression. The Niagara truss is
formed by a system of vertical posts, five feet apart, and diagonal rods
passing from the top of the first post to the foot of the fifth; the
inclination being 45°, spreads the weight placed upon any one pair of
posts over twice the height of the truss, or about forty feet. As to the
actual dimensions of the girders supporting the rails, if we intend them
to spread an applied weight over forty feet, they must be as stiff as a
bridge of forty feet span. And as regards the truss, if we would
effectually distribute the applied weight and check vibration, the
trussing should be as strong as the counterbracing in a large span upon
the ordinary plans. The principle of trussing a suspension bridge may be
thus explained. See fig. 106. Suppose that in place of supporting the
three trusses D _s w_, _s m m′_, and _m′ m d_, upon piers at _w_ and
_m′_, we suspend these points from the cable A _c_ B. The cable is
flexible, and when we apply a load at _m_, the truss will assume the
position D _s c n d_, but between D and _s_, _s_ and _n_, _n_ and _d_,
the truss will be quite stiff. What we require, then, is to make the
figure _o p m m′_, incapable of changing its form, which is done by
diagonal bracing.

[Illustration: Fig. 106.]

233. Undoubtedly the finest specimen of a bridge of large span upon the
suspension principle, or indeed upon any principle, is that built by
John A. Roebling, across the Niagara River, a short distance below the
falls. The dimensions below of this admirable structure are from the
final report of the above-named engineer.

   Length of bridge from centre to centre of tower      821′ 4″
   Length of floor between towers                        800 ft.
   Number of wire cables                                   4
   Diameter of each                                      10″
   Solid wire section of each cable                    60.40 sq. in.
   Total section of four cables                       241.60 sq. in.
   Whole section of lower links of anchor irons          276 sq. in.
   Whole section of upper links of anchor irons          372 sq. in.
   Ultimate strength of chains                        11,904 tons.
   Whole number of wires in cables                    14,560
   Average strength of a wire                          1,648 lbs.
   Ultimate strength of four cables                   12,000 tons.
   Permanent weight supported by cables                1,000 tons.
   Resulting tension                                   1,810 tons.
   Length of anchor chains                                66 ft.
   Length of upper cables                              1,261 ft.
   Length of lower cables                              1,193 ft.
   Deflection of upper cables (mean temperature)          54 ft.
   Deflection of lower cables (mean temperature)          64 ft.
   Number of suspenders                                  624
   Aggregate strength of suspenders                   18,720 tons.
   Number of over-floor stays                             64
   Aggregate strength                                  1,920 tons.
   Number of river stays                                  56
   Aggregate strength                                  1,680 tons.
   Elevation of grade above mean water                   245 ft.
   Depth of river                                        200 ft.
   Cost of the bridge                              $400,000.

231. The following items are extracted from the report above referred
to:—

“The trains of the New York Central, and Canada Great Western Railroads
have crossed regularly at the rate of thirty trips per day for five
months. (At present over two years.)

“A load of forty-seven tons caused a depression at the centre of five
and a half inches.

“An engine of twenty-three tons weight, with four driving wheels,
depressed the bridge at the centre 0.3 feet. The depression immediately
under the engine was one inch; the effect of which extended one hundred
feet.

“The depression caused by an engine and train of cars is so much
diffused as scarcely to be noticed.

“A load of three hundred and twenty-six tons produced a deflection of
0.82 feet only. The Conway tubular bridge deflects 0.25 feet under three
hundred tons; the span being only one half that of the Niagara bridge.

“The specified test for the wire was, that a strand stretched over two
posts four hundred feet apart should not break at a greater deflection
than nine inches; also, that it should withstand bending square and
rebending over a pair of pliers without rupture. This test corresponds
to a tensile strain of 90,000 lbs. per square inch, or I,300 lbs. per
wire of twenty feet per pound.”

The wire is preserved from oxidation by coating with linseed oil and
paint. Upon the durability of wire cables employed for suspension
bridges the following fact came to light: Upon taking down the cables of
the footbridge, put up in 1848, by Mr. Ellet, the wire was found so
little impaired that Mr. Roebling did not hesitate to work it into the
new cables; also, the original oil was found to be still soft and in
good condition, having been up six years.

That iron-work lying under ground has been completely covered with
cement grout, as this is found by the above-named engineer to be an
effectual guard against oxidation.

Engineers wishing to study the details of the Niagara bridge, will find
the final report of Mr. Roebling full of valuable matter, both as
regards the making of cables, anchoring, stiffening, and the effect of
passing trains.

  NOTE.—This engineer is at present engaged upon a still greater work,
  namely, a railroad suspension bridge across Kentucky River, of 1,224
  feet span, 300 feet above the water. There is no lower road-way in
  this bridge, the cross section being a triangle base upwards.

  235. NOTE.—The Britannia tubular bridge, across the Menai Straits,
  is doubtless a great work, and also an enormously extravagant one.
  If no other structure were possible it would be admissible; but it
  is equalled in strength and by far surpassed in economy by Mr.
  Roebling’s system of trussed suspension bridges. The cost of
  material alone in one span of the Britannia bridge, of 460 feet,
  exceeds the entire cost of the Niagara bridge of 800 feet span; add
  to this that we are sure of the strength of wire cables, but not of
  tubes, and that the 800 feet span of the Niagara bridge weighs only
  1,000 tons in itself against 1,400 in a 460 feet span of tube, and
  it will not be difficult to prove the superiority of the suspension
  over the tubular system; thus,

          A suspension bridge of 800 feet span costs $400,000.
          A tubular bridge of 460 feet span costs $500,000.

  When we double the linear dimensions we increase the weight by the
  cube; and the cost of a tube is very nearly as the weight; whence a
  tubular bridge of 800 feet span will cost 2 × 2 × 2, or eight times
  500,000, or $4,000,000 against $400,000. Thus,

                        Suspension   400,000  1
                        Tubular    4,000,000 10

[Illustration: Fig. 105.]

Fig. 105, shows the anchoring of the Fribourg bridge.

[Illustration: Fig. 107.]

[Illustration: Fig. 108.]

Fig. 107, the manner of fastening the ground stays of the Niagara
bridge.

Fig. 108, connection between cable and suspender.

[Illustration: Fig. 109.]

[Illustration: Fig. 109 A.]

Figs. 109, 109 A, another method of effecting the same.

[Illustration: Fig. 110.]

[Illustration: Fig. 111.       Fig. 112.]

Fig. 110, floor beam attachment to suspender.

Figs. 111, 112, floor beam attachment in Niagara bridge.

[Illustration: Fig. 113.]

Fig. 113, connection of land and water cables in Fribourg bridge.

[Illustration:

  Fig. 114.
  Fig. 114 A.
]

Figs. 114, 114 A, fastening of cables at G, (fig. 105).

[Illustration: Fig. 115.]

Fig. 115, Mr. Roebling’s pendulum connection for the cables of two
adjacent spans.


                         BOILER PLATE BRIDGES.

                       Spans from 25 to 100 feet.

236. These structures fulfil every requirement of safe, durable, and
rigid bridges; being open however to the contingency attendant upon all
similar structures of wrought iron, namely, the becoming crystalline
when exposed to vibration. Time only will show whether this is a
sufficient cause for their non-adoption.

Each side truss consists as it were of a top and bottom chord connected
by a vertical web. The whole being of wrought iron, requires that the
section of the upper chord should be to that of the lower, as ninety to
sixty-six.

The general plan of such bridges is shown in fig. 116. This is the
patent wrought iron girder bridge of Mr. Fairbairn. The upper chord is
formed by connecting the four plates _a a a a_, by angle irons. The web
is formed either by a single or a double plate, stiffened laterally by T
iron placed at the vertical plate joints, as shown generally at B, and
detailed at C and D; or by a pair of plates separated by a space as at
B′, thus forming a rectangular tube. The lower chord is made by bending
horizontally the lower part of the web, and to the flanges thus formed
riveting the plate _m m_. The suspending rod _f_ is applied to the upper
chord by a washer as at E.

[Illustration: Fig. 116.]

The central connecting web, acting as do the braces and ties in a wooden
truss, should be more stiff at the ends of the span than at the centre.
This is easily effected by joining the web plates towards the end by
stronger T irons than at the centre. The joints for the rib, or the
vertical plates, either single or double, are shown in figs. C and D.

An example of the need of such increased stiffness towards the ends, was
given to the experimenters upon the Britannia model tube, which (tube)
was found to yield by buckling near the ends of the span sooner than
elsewhere. Thus advised, the vertical plates were made thicker as the
end of the span was approached. Examination of the principles of
proportioning a common wooden truss would have shown this without
experiment.

The tensile and compressive strength of rolled boiler plates (by the
table on page 193,) is, extension 12,740 lbs. per square inch,
compression 7,500 lbs. The strength of such work depends in a very great
measure upon the size and disposition of rivets. In plates exposed to
compression, the strength is not so much affected by riveting as in
those subjected to tensile strains; as to whatever amount the plate is
cut away, by the same amount is the resistance to tension reduced.

237. Mr. Fairbairn found that to obtain the maximum strength of riveted
plates, the section of the rivets should equal that of the plates, that
is, in a plate four inches wide, if there are two rivets, the area of
each must be one inch; or the diameter 1⅛ inches; thus leaving a section
of

                          4 – 2¼ = 1¾ inches,

which divided by four gives seven sixteenths of an inch as the distance
from the edge of the plate to the side of the first rivet; and seven
eighths of an inch between rivets. If the bolt yields by shearing, the
rim is destroyed by _detrusion_, or crushing across the fibres. That the
rivets and plates may be equally strong, their products of area of
section by the actual strength per unit of area must be equal. The
detrusive strength of wrought iron (see page 193) is 12,500 lbs. per
inch, whence the proportion

                       12,500 : 15,000 :: 1 : _d_

where 1 is the resisting length of the plate at right angles to tension,
and _d_, the sum of rivet diameters. Thus suppose we have a plate 13.2
inches wide, to be fastened with nine rivets of 0.8 inch diameter; we
have

                          9 × 0.8 = 7.2 = _d_,

and the above proportion becomes

                  15,000 : 12,000 :: 7.2 to 6 inches,

which is the length of plate section at right angles to tension. As
there are nine rivets, there will be eight spaces between them, and one
space at each edge of the plate, half as large as those between; or
reducing all to the same size,

                        8 × 2 = 16, 16 + 2 = 18;

and as the whole plate section after punching is six inches,

                          6/18 = .33 or ⅓ inch

for the edge space, and two thirds inch between rivets. Proceeding thus,
the result compares with the practice of Mr. Fairbairn as follows:—

                     Diameter of rivet.   Distance between rivets.
     Mr. Fairbairn ⅝ inch, or 0.625 inch,                      0.8
     Handbook      ⅔ inch, or 0.666 inch,                      0.8

The difference between the results, or 0.041 inch, less than one
sixteenth inch, will be partially absorbed by the remark of Mr.
Fairbairn that the area of the rivet should be _nearly_ as much as that
of the plate, and partly by the difference in results showing the
detrusional force of iron.

[Illustration: Fig. 117.]

238. In experimenting to determine the resistance of rivets, Mr.
Fairbairn found that by the common plan of riveting, fig. 117, the
strength of plates when whole, single, and double riveted, was as
follows, the section of the punched plate being in each case equal to
that of the whole one.

                          Whole plate,    100.
                          Single riveted,  56.
                          Double riveted,  70.

This loss of strength made him fearful of the ability of the tension
plates of the Britannia bridge to do their duty; and he was led to adopt
what he terms “chain riveting,” which consists in placing the rivets as
in fig. 118, or _in the same line of tension_. The strength of plates
thus made he considers as great at the joints as elsewhere.

239. As to the diameter of rivets, we have the following results of the
practice of the best English engineers.

     Thickness of plate, ¼, 5/16, ⅜, 7/16, ½, 9/16,  ⅝, 11/16,  ¾.
     Diameter of rivet,  ⅝,  6/8, ⅞,    1, 1,   1⅛, 1¼,    1⅜, 1½.

240. As to the distance _in the direction of the force_ from rivet to
rivet, also from the first rivet to the plate end, we gather the
following from the best executed works in boiler plate. See fig. 118.

Plates exposed to compression,

                    _cb_ = 2 diam., _df_ = 1½ diam.

Plates exposed to extension,

                    _cb_ = 2½ diam., _df_ = 2 diam.

the diameter being that of the rivet.

The distance at right angles to the force has already been given.

241. If we knew the lateral adhesion of rolled plates, that is, the
resistance of the fibres to sliding horizontally past each other; we
should determine the distance of rivets in the direction of tension as
follows:—

Let _R_, equal the resistance per unit of area for _detrusion_ or
shearing, _R′_ the lateral adhesion of rolled plates, and we should have

                   _R_ × _a_ = _R′_ × (2 _d_ × _t_);

                whence _d_ = (_R_ × _a_)/(2_R′_ × _t_);
                 where _a_ = area of rivet,
                       _d_ = distance,
                       _t_ = plate thickness.

also

                   2_d′_ + _d_ = (_R_ × _d_)/(_R′_);

and

                   2_d′_ = (_R_ × _d_)/(_R′_) – _d_;

whence

                  _d′_ = [(_R_ × _d_)/(_R′_) – _d_]/2

and finally

                   _d′_ = ½[(_R_ × _d_)/(_R′_) – _d_]

supposing the piece 1, 2, 3, 4, fig. 118, to split out.

The diameter of the semi-spherical head of the rivet should be three
times the thickness of the plate to be riveted; that of the conical head
four times; and the height of both of the heads, one and one half the
plate thickness.

242. Examples of the application of the preceding remarks.

Suppose we wish to build a boiler plate bridge of one hundred feet span,
twelve feet rise, weight of bridge and load 3300 lbs. per lineal foot.
The tension by formula

                 _T_ = (_WS_)/(8_h_) (see Chap. VIII.)

becomes

                       33000000/96 = 343,750 lbs.

Each side truss will bear one half of this or 171,875 lbs., and as
wrought iron resists eleven thousand pounds of compression per square
inch, the required section of the top chord will be

                   171875/7500 = 22.9 square inches.

Also the lower chord resisting fifteen thousand pounds per square inch,
must have

                   171875/12740 = 13.5 square inches

of area nearly.

If we make the tube at top of one fourth inch iron, and 8 × 10 inches;
fastening the plates by one fourth inch angle iron, four inches on the
side, the section becomes

              One top plate    10 × ¼ = 2½ square inches.
              One bottom plate 10 × ¼ = 2½ square inches.
              Two side plates   8 × ¼ = 4  square inches.
              Four angle irons  ¼ × 8 = 8  square inches.
                                        —
                               In all,  17 square inches.

In the lower chord, if we bend the web plates (of ⅜ inch) so as to form
a flange of eighteen inches in width, and to that rivet a bottom plate
18 × ¼, we shall have

                      In the flanges, 18 × ⅜ =  6¾
                      Bottom plate,   18 × ¼ =  4½
                                               ———
                          In all,              11¼

The web acting as both ties and braces, must be able to support the
following load.

   Whole weight of bridge and load is, in round numbers, 344,000 lbs.
   One half,                                             172,000 lbs.
   And upon each end of the truss,                        86,000 lbs.

to resist which, at eleven thousand pounds per square inch, requires
eight inches nearly, regarding the plate as a brace.

Now the side of the bridge being one hundred feet long, and twelve feet
wide, will contain any system of bracing that we choose to draw thereon.
Suppose, for example, that we chalk a line upon the erected bridge
representing an arch-brace, extending from the end to the centre. Such a
brace has actual existence in the bridge; and the same idea holds good
for any system of braces that may be assumed. We ought, therefore, to
take the most disadvantageous system that can have place, and giving
such a good bearing upon the abutment, estimate its width and thickness.
Suppose that we draw a natural size representation of Howe’s bridge, the
end braces must support a load of eighty-six thousand pounds, which at
eleven thousand lbs. per inch, requires a section of nearly eight
inches; and if the plate is one half inch thick, the brace must be
sixteen inches deep. The manner, however, in which the plate would yield
is by bulging laterally; which is to be checked by the before-mentioned
T connecting irons at the sides. It may be thought that the above method
of considering the plates as braces, would give very little thickness by
assuming very wide plates. The answer to this is, that the side plates
must not be so thin as to need more stiffening angle irons by weight,
than a thicker plate with less stiffening. Of course the weight should
be minimum.

243. As an actual example of this plan we have the following, built by
Mr. Fairbairn for the Blackburn and Bolton Railroad, across the Leeds
and Liverpool Canal.

                      Span,               60 feet,
                      Length,             66 feet,
                      End bearings, each,  3 feet,
                      Rise,                5 feet,
                      Width,              28 feet,

for a double track. Top chord of three eighths iron, web of five
sixteenths, lower flange of three eighths, and vertical web plates
stiffened by T irons.

This bridge was tested as follows:—

Three engines, weighing twenty tons each, running from five to
twenty-five miles per hour, deflected the bridge .025 feet. Two wedges,
one inch high, being placed upon the rails, and the engines being
dropped from that height, the bridge was deflected at the centre .035
ft.; with wedges of one and one half inches the deflection was .045 ft.
The cost of this bridge (in England) was estimated by Mr. Fairbairn at
$4,500, while that of a cast-iron bridge of the same span was $7,150.

244. _Example 2._—Manchester, Sheffield, and Lincolnshire Railroad
(England) Bridge, at Gainsborough, on the river Trent. Two spans, each
one hundred and fifty-four feet. Rise twelve feet. Top chord, double
rectangular tube, 36¾ × 16 inches, vertical web as before, and
horizontal plate for the lower chord. The floor beams are wrought iron
girders, cruciform in section, ten inches wide, and one foot three
inches (15″) deep, placed four feet apart.

245. _Example 3._—Fifty-five feet boiler plate bridge, built by James
Millholland, in 1847, for the Baltimore and Susquehanna Railroad
Company. Each truss consists of two vertical plates 55 × 6 feet, formed
of plates thirty-eight inches wide by six feet deep, the plates being
fastened together by bolts passing through cast-iron sockets. The lower
chord is formed by riveting two bars 5 × ¾ inches to each side of each
truss plate; making in all eight. Top chord—one bar of the same size on
each side of each plate, compression being made up by a wooden chord
between the plates. Height of bridge, six feet; length, fifty-five feet;
width, six feet; weight, fourteen tons; cost, $2,200, or forty dollars
per foot. The inventor thinks thirty dollars per foot enough when a
considerable amount of such bridging is wanted.

  NOTE.—White, buff, or some light color should be used in painting
  iron bridges, as such throw off, and do not absorb heat from the
  sun.




                               CHAPTER X.
                             STONE BRIDGES.


A complete treatise on stone bridging would be of little practical value
to the American engineer, and would occupy too much of the necessarily
small space allowed here. The object in the present chapter is to give
the manner of dimensioning stone arches of from ten to sixty feet span,
and of proportioning retaining walls, piers, and abutments.


                     CONTRACTION OF THE WATER-WAY.

246. In building a bridge across a stream, we must be careful not to
obstruct the water-way so as to prevent free passage to the highest
floods. Regard must be had to this in fixing the size of the spans, and
the thickness and number of the piers. By contracting the width of the
stream the velocity is increased beneath the arches, the same amount of
water being obliged to pass through a smaller space, and when the bottom
is of such a nature as to yield to this action, there is danger of the
foundation being undermined. If the form and size of the piers be so
arranged as not to increase the velocity, such danger will be avoided
and floods will pass without harm. In bridges crossing navigable
streams, if the bottom is not destroyed the velocity may be made so
great as to impede navigation.

247. The following table is from Gauthey, _Construction des Ponts_,
showing the velocities which are just in equilibrium with the material
composing the bottom of the stream.

  State of the water. Velocity in feet per second. Nature of bottom.
  Torrents,                                 10′ 0″ Large rocks.
  Floods,                                    3′ 3″ Loose rocks.
  Common,                                    3′ 0″ Gravel and stones.
  Regular,                                   2′ 0″ Fine gravel.
  Moderate,                                  1′ 0″ Sand.
  Slow,                                      0′ 6″ Clay.
  Very slow,                                 0′ 3″ Common earth.

248. If _b_ represents the width of the natural water-way; _c_, that as
reduced by the structure; _V_, the velocity of the stream in the natural
state; then the augmented velocity is expressed by

                          _W_ = _mV_(_b_/_c_);

                         and _c_ = (_mbV_)/_W_;

where _m_ is a constant quantity expressing the contraction which takes
place in passing the narrow place, which, according to Du-Buat, is 1.09;
but depending somewhat upon the form of the bridge piers; adopting which
value, we have

                        _W_ = 1.09_V_(_b_/_c_);

                       and _c_ = (1.09_bV_)/_W_.

_Example._—Let the bottom be gravel, the width of the natural water-way
one hundred feet, the velocity one foot per second: now for a gravel
bottom the velocity must not exceed two feet per second, whence

                  _c_ = (1.09 × 100 × 1)/2 = 54½ feet;

which is the width of the contracted water-way; and 100 – 54½, or 45½
feet may be occupied by piers or other obstructions.

The amount of fall which the water suffers in passing the pier is found
by the following formula, the notation being the same,

              fall = ((_V^2__m^2__b^2_) – _c^2_)/(64_c^2_)

Thus the velocity being one foot per second, _m_ being 1.09 and _b_ =
100; also, _c_ = 54½, we have

          (1 × 1 × 1.09 × 1.09 × 100 × 100) – (54½ × 54½)
   fall = ——————————————————————————————————————————————— = 0.047 ft.
                            64 × 54½ × 54½

The velocity of a river is greatest at its surface and at the centre of
the stream. In the same river the velocity is nearly as the square root
of the depth; thus the surface velocity being known, that for any other
depth may be easily found. The velocity of streams should always be
noted at the times of the highest floods. For measuring the velocity of
running water a bottle enough filled with water to maintain an upright
position, with a small rod placed through the stopper having a red flag
upon the upper end, answers very well. Velocities of undercurrents may
also be measured by so loading the bottle as to cause it to float two,
four, six, or ten feet below the surface.


                        OF THE FORM OF THE ARCH.

249. There are three general forms which may be given to the intrados of
a stone arch.

  _Semicircular_, or one hundred and eighty degrees.

  _Segmental_, less than one hundred and eighty degrees.

  _Basket handle_, nearly elliptical, being formed by a number of
  circular curves.

Full centre (semicircular) arches offer the advantages of great solidity
and ease of construction; but unless the springing lines are high,
contract considerably the water-way.

Segmental arches give the freest passage to the water, are easily built,
but throw a great horizontal strain upon the abutments.

The basket handle gives free passage to the water, when not too flat are
very strong, are easily adjustable to different ratios between the span
and the distance between grade and the spring line, and except making
the centres, are easily built. Whatever the form of the arch, the line
of arch springing should not be below high water.

The manner of tracing the full centre and segmental curves is too simple
to need remark.

250. In tracing the basket handle curve, the following conditions must
be observed:—

       _The tangents at springing must be vertical._
       _The summit tangent must be horizontal._
       _The curve at springing must inclose the ellipse._
       _The radius of summit must not be greater than the span._

The number of arches composing the curve must not be less than three,
nor more than eleven; and must be uneven. Perronet’s fine bridge of
Neuilly, over the Seine at Paris, has eleven centres. In spans of sixty
feet and under, it is unnecessary to use more than five centres.

[Illustration: Fig. 119.]

251. The three centred curve is described as follows, fig. 119:—

Let A B represent the span, and _c_ D the rise, with _c_ as a centre and
_c_ A as radius, describe the quadrant A F E; make the angle A C F 60°.
Parallel to F E draw D G, and parallel to F C draw G K. H is the centre,
and A G the arc of the springing curve; also GD is the arc, and K the
centre of the summit curve.


                        THE FIVE CENTRED CURVE.

252. The common construction of the five centred curve leaves the radii
of the extreme curves to be assumed. The following method fixes all of
the dimensions when the span and rise are given:—

  Let _c_ B be half the span and _c_ D the rise.

  Join D B.

  Draw _n_ K through _n_ perpendicular to D B.

  Make B _a_ equal to _c_ D.

  Also _c e_ to _c a_.

  Draw _e_ K′ _o_ and K _a m_.

  K H′ and K′ are the centres, and H′ _m_ and H′ _o_ the lines
  separating the several curves.

For spans of from twenty-five to one hundred feet, the five centred arch
answers every purpose; making a strong and well proportioned structure.


                 THICKNESS OF VOUSSOIRS, (RING STONES).

253. The thickness of the voussoir, or arch stone, depends upon the form
and size of the arch, the nature of the masonry, and the character of
the stone. No authority gives more reliable results than Gauthey, who,
for stone of average quality, with hammer dressed beds, laid in cement,
gives the following proportions between the span and depth of key:—

  For spans _under six feet_ the depth should be _thirteen inches_.

  From six to fifty feet, 13 inches plus 1/48 of the span.

  From fifty to one hundred feet, 1/24 of the span.

  For over one hundred feet, 1/24 of 100 plus 1/48 of the remainder.

Thus for a span of one hundred and ninety-six feet we have

                     (100 × 12)/24 + (96 × 12)/48,

or, 50 + 24 equal in all to seventy-four inches, or six feet and two
inches; whence the following table:—

 Span of arch in feet.         Thickness of voussoir in inches.
                     6                             13 +  0 = 13
                     8                             13 +  2 = 15
                    10                             13 +  3 = 16
                    12                             13 +  3 = 16
                    15                             13 +  4 = 17
                    18                             13 +  5 = 18
                    20                             13 +  6 = 19
                    25                             13 +  7 = 20
                    30                             13 +  8 = 21
                    35                             13 +  9 = 22
                    40                             13 + 10 = 23
                    45                             13 + 11 = 24
                    50                             13 + 13 = 26
                    60                                     = 30 inches.


                    THICKNESS AND FORM OF ABUTMENTS.

254. The above depend upon the span and form of the arch, the height of
the abutment, and character of the masonry.

Different methods of determining the thickness of an abutment have from
time to time been given; several very correct rules have been arrived
at, but difficult of application. The most simple rule is given by
Hutton in the course of mathematics edited by Rutherford; it is as
follows:—

[Illustration: Fig. 120.]

Let A B, C D, fig. 120, be one half of the arch and A G F the abutment.

From the centre of gravity K of the arch, draw the vertical K L; then
the weight of the arch in the direction K L will be to the horizontal
thrust, as K L to L A. For the weight of the arch in the direction K L,
the horizontal thrust L A, and the thrust K A will be as the three sides
of the triangle K L, L A, K A; so that if m denotes the weight of the
arch,

                          (_LA_)/(_KL_) × _m_,

will be its force in the direction L A, and

                       (_LA_)/(_KL_) × _GA_ × _m_

its effect on the lever G A to overturn the wall, or cause it to revolve
about the point F.

Again, the weight or area of the pier is as EF × FG, and therefore EF ×
FG × ½FG, or ½FG^2 × EF, is its effect upon the lever ½FG, to resist an
overthrow. Now that the abutment and the arch shall be in equilibrium
these two effects must be equal to each other; whence we must have

              ½_FG^2_ × _EF_ = (_LA_)/(_RL_) × _GA_ × _m_;

whence

             _FG_ = √((2_GA_ × _LA_)/(_EF_ × _RL_) × _m_).

The following table has been calculated for the use of builders and
engineers, giving the thickness of abutments for different spans and
heights.

                255. THICKNESS OF RECTANGULAR ABUTMENTS.

        │      Semicircular arch.       │      Basket-handle arch.
        │                       The height being.
  Span. │   5       8      10      15   │   5       8      10      15
       6│   3       3      3¼      3½   │  3½       4       4       5
       8│  3½       4      4¼      4½   │   4      4½      5¼       6
      10│   4       5       5       5   │  4½      5¾      6¼       7
      15│  4½      5¼      5½       6   │   5      6½      7¼       8
      20│   5      5½       6       7   │   6      7¼       8       9
      25│  5½       6      6½      7¼   │   7      7½      8¼      9½
      30│   6       7       8      8½   │   8      8½      9¼      10
      35│  6½       7      8¼       9   │   9      9¼      10      11
      40│   7      7½      8¾      9½   │  9½      10      11      12
      45│  7½      8¼      9¼      10   │  10      10¾     11½     12½
      50│   8       9      10      11   │  10¼     11½     12¼     13

[Illustration:

  Fig. 121.
  Fig. 121 B.
  Fig. 121 A.
]

256. The form of a bridge abutment will depend upon the locality and
upon the use to which the bridge is to be put, whether used for a
railroad, or for common travel; whether near a large city, or in a
location where appearance need not be regarded. Where a river acts
dangerously upon a shore, wing walls will be necessary. These wings may
be curved or straight, and may be simply the abutment produced, or may
be swung around into the bank at any required angle, until the winged
abutment, as in figs. 121, 121 A, 121 B, becomes the U abutment, fig.
124; or by moving the walls, W and W, parallel to themselves, takes the
form of the T abutment, fig. 122.

[Illustration: Fig. 122.]

The curved wing, in fig. 121, being arched, requires a little less
thickness, but at the same time is longer. B B, show the bridge seats.
The slope of the wings may be battered with an inclined coping, or
off-setted at each course. Wing walls, subjected to special strains or
to particular currents of water, require positions and forms
accordingly. In skew bridges, as in Chap. V., the wing, at the acute
angle, is longer and inclines less from the face of the abutment than
that at the obtuse angle. The more the wing departs from the face line
and swings round into the slope, the greater the thrust becomes upon it,
as the centre of pressure is raised; the thrust becomes a maximum when
the wing is inclined from forty-five to seventy degrees from the face of
the abutment. The body of an abutment, as well as any other retaining
wall, may be much stronger by giving it a trapezoidal instead of a
rectangular section, as the resisting leverage is thereby much
increased. Abutments may be to advantage buttressed in order to resist
special strains, as in case of the arches or braces of wooden bridges.

[Illustration: Fig. 123.]

[Illustration: Fig. 124.]

257. Railroad abutments except for a double track, require but little
breadth on top, except where the truss itself rests. The common T
abutment originated by Captain John Childe, and now in very extensive
use, seems to fulfil any requirement of a good abutment, see fig. 122,
page 242. B B is the bridge seat, and the mass T T takes the place of
wings. The difference of level of the top and of the bridge seat depends
upon the difference between the height of the bearing of the lower chord
of the bridge, and grade. The line of contact between the earth and the
wall is shown by _s s′ s″ s‴_. The length of the top of the masonry is
found thus. Suppose the slope to be one and one half to one, and the
whole height thirty feet, the whole horizontal length of slope is then
forty-five feet; from this we take the sum of the horizontal distances,
_s s′_ and _s′ s″_, and suppose these to be, respectively, six and eight
feet, we have the whole operation thus:—

                  30 × 1½ – 6 + 8 = 45 – 14 = 31 feet.

It may be advisable in very high abutments to lighten the masonry by an
arched opening as in fig. 123. The walls, also, of the U abutment (see
fig. 124), when large, may be pierced with arches to save masonry.

Probably the cheapest mode of bringing a bridge to the embankment is
that shown in fig. 125; A being the bridge seat for the main truss, and
B that for the trussed girder.

[Illustration: Fig. 125.]


                                 PIERS.

258. The thickness of a pier may be considered either as depending upon
the weight of the superstructure, or as resisting the thrust of arches
or braces. For the first requirement, very little thickness would
suffice; for the second, it may require to be considerable. The
objection to thick piers is the expense, and the contracting too much
the water-way; the benefit, a large bearing surface, and in stone
bridges where there are several continuous spans, a saving of centring;
as where the piers are not able to resist the thrust of the arches, they
must all be carried up at once.

259. Piers supporting truss bridges, require very little thickness
provided a good foundation is obtained. The following table shows the
sufficient dimensions for the piers of wooden or iron trussed bridges,
when the masonry is good. (See First Class Masonry, specification, Chap.
IV.) From ten to twenty feet in height the batter is assumed at one
twelfth; from twenty to fifty feet in height at one twenty-fourth.

             Span.        Length of bridge seat.  Width of seat.
        20 to   40 feet,         20 feet,         4  feet,
        40 to   60 feet,         20 feet,         4½ feet,
        60 to   80 feet,         22 feet,         5  feet,
        80 to  100 feet,         23 feet,         5½ feet,
       100 to  125 feet,         23 feet,         6  feet,
       125 to  150 feet,         24 feet,         6½ feet,
       150 to  200 feet,         24 feet,         7  feet.

260. Upon the form of the up-stream end of the pier, or the starling,
depends, in a considerable degree, the contraction of the water-way. In
sluggish water the form is not of much importance, but in swift flowing
rivers a great deal depends upon the choice. The forms in use are the
rectangle, the rectangle terminated by right-lined triangles, and the
same terminated by curved-lined triangles, and finally the ellipse.

The latter is that which causes the least disturbance to the water, but
is also the most costly.

The effect of gyration at the shoulder, deserves notice, as it may be
the cause of the ruin of the foundation when the bottom is of yielding
material.

River beds being porous, springs work up through them with a force equal
to the whole depth of water; and whenever there is a means of escape for
such, its pressure will act upwards against any structure that comes
within its reach; and if four or five feet deep, is capable of moving
enormous weights. Such springs gave a great deal of trouble at the
foundation of the United States Dry Dock, at Brooklyn, N. Y. When
checked in one place they burst up in another, and to proceed with the
work it was necessary to allow them a passage through which to flow.

[Illustration: Fig. 126.]

261. However proper it may be to give to piers the proper form to cause
as little contraction as possible to the water, it is no less necessary
to give them strength to oppose the shocks to which they are subject
from floating ice, timber and shipping. The best method of breaking up
ice, when it comes in large masses, is by inclining the front of the
pier, as shown in fig. 126. The angle of the front being inclined from
30° to 50°. The ice running up this slope breaks by its own weight, and
falls off on either side.

The foundations of piers may be protected by sheet piling, (see chap.
XII.,) or the bottom, if soft, may be dredged out for a few feet and
filled in with loose rock.

The form of the down-stream end is not of so much importance as of the
upper one, but deserves consideration; as when the water is swift or the
bottom soft and yielding, the eddies caused by sharp angles wear upon
the soil in a dangerous manner.




                              CHAPTER XI.
                                MASONRY.


                                STONES.

262. The varieties of this material most commonly used in engineering
operations are granites, limestones, sandstones, slates, brick, and
artificial stones; the latter being made by compounding clays, limes,
and cements.

Rock taken from the surface, which has been exposed to the atmosphere,
is of an inferior quality to that found at a depth where it has been
exposed to a strong pressure; and is consequently denser. Therefore, in
opening a quarry it is advisable to excavate upon a hill-side and come
at once to the sound stone. Rock is generally found in beds, divided by
joints or seams, at which the natural adhesion is broken and the layers
are easily separated. When the quarry shows no natural line of
separation, one may be produced by drilling a line of holes at equal
distances from each other, into which conical steel pins are driven, and
the stone splits; the pins being placed in the plane of the required
seam.

263. Stone is used almost entirely to resist a compressive strain; as in
the voussoirs of an arch, or in the courses of a pier. The resistance of
stone to crushing, is as follows:—

                                    Pounds per square inch.
            Granite                        10,000 to 16,000
            Limestone                      12,000 to 14,000
            Sandstone                                10,000
            Marble                          9,000 to 14,000
            Firm, hard burned brick                   2,600
            Yellow burned brick                       1,500
            Red brick                                 1,200
            Pale-red brick                              900
            Chalk                                       750

264. When stone cannot be found, brick forms an excellent substitute;
being made from clay earths, which can be found in almost any locality.
Bricks are well fitted for nice work, are cheap, and easy of transport.
The French, at Algiers, have used concrete, rammed in boxes so as to
make large cubes and other shapes. The structures built of this material
are found to be very nearly if not quite as strong as those of natural
rock.


                LIMES, CEMENTS, MORTARS, AND CONCRETES.

265. Nothing is more important in the construction of masonry than good
cement; and generally, no part of construction is intrusted to more
ignorant persons. Under the above head are to be considered limes,
cements, sands, common mortar, hydraulic mortar, and concrete.

266. Lime is obtained by burning off the carbonic acid from the pure
limestones; when it is put up in air tight barrels and is unslacked
lime. Natural cements are composed of pure lime mixed with argil,
magnesia, iron, and manganese. Artificial cements are prepared by mixing
with pure lime, calcined clay, forge scales, powdered bricks which are
underburnt, and other materials of like nature. Cements made thus
artificially, are as good as those naturally hydraulic.

Lime is termed rich, poor, hydraulic, and eminently hydraulic, according
to its properties.

Rich or fat limes are those which double their volume in slacking and
dissolve in fresh water to the last particle. They absorb about 300 per
cent. of their weight of water.

Poor limes do not much increase their volume, do not dissolve
completely, and absorb 200 per cent. of water.

Hydraulic limes set in fifteen or twenty days after immersion, and
continue to harden as they grow older. After one year their consistency
is about that of hard soap.

Eminently hydraulic limes set in five or six days, and continue to
harden.

Limes are said to set when they will bear, without depression, a rod of
1/20 of an inch diameter loaded with ten or twelve ounces.

  NOTE.—The following test was applied to every tenth cask of
  Rosendale cement used upon the masonry of the United States Dry Dock
  at the Brooklyn (N. Y.) Navy Yard. Cakes two inches in diameter and
  three fourths of an inch in thickness, after being immersed five
  days, were required to bear a rod of one twenty-fourth of an inch
  diameter loaded with fifty lbs. Two bricks united with the cement
  and immersed five days, were required to resist one hundred lbs.
  before separating. The following shows the progress of hardening.
  The force required to thrust a rod one twenty-fourth of an inch in
  diameter through a cake three fourths of an inch in thickness, was,
  after

                           24 hours,  65 lbs.
                           48 hours,  70 lbs.
                           72 hours,  75 lbs.
                           15 days,  150 lbs.
                           50 days,  390 lbs.


                                 SAND.

267. Sand is the product of the decomposition of granitic and schistose
rocks, and weighs, per unit of bulk, somewhat less than one half of the
rock producing it; owing to the spaces between the grains. The amount of
lime necessary to fill these spaces must be known before we can form a
solid mass with the least lime. The amount of void may be found by
filling a measure with sand, and then pouring in water: the volume of
water is that of the spaces. In pebbles of one half inch in diameter the
void amounts to about one half, in gravel about five twelfths, in common
sand two fifths, and in very fine sand, one third. Clean sharp sand
obtained from the beds of rivers is the best for mortars.

268. In mixing the ingredients for mortar, the lime is first spread on a
platform and wet by sprinkling with water, which causes it to give off a
great deal of heat and vapor, and fall into a powder. The sand is then
applied, and the whole brought with water to a consistent paste.

The proportions for common mortar for dry work are

                             Sand, 1½ to 2
                             Lime,       1

It is well always to use a small quantity of cement; the parts which
have in practice been found perfectly satisfactory are

                               Cement, 1
                               Lime,   3
                               Sand,   6

For hydraulic mortar the following proportions have been used with
success:—

                               Cement, 2
                               Sand,   3

269. Concrete is made by mixing broken stone, brick, or shells, with
cement mortar; it is used for foundations, backing of arches, and for
making artificial stone. The common proportions are

                         Cement,       1  or  2
                         Sand,         1½ or  3
                         Broken stone, 5  or 10

The cement and sand are first mixed as for cement mortar; the broken
stone is added and the whole well mixed and immediately applied before
it has time to set. Both concrete and cement mortar should be made as
required for use, and in no case applied after standing over three
hours.


                            FLASHING MORTAR.

270. Flashing consists of a thin coat of cement mortar made with a very
large part of cement. It is used to protect the face of walls exposed to
the wet; such as the top of arches. Stone liable to disintegration may
be protected by flashing.


                            POINTING MORTAR.

271. Pointing is used to protect the joints of masonry, and is made by
mixing cement and sand with a minimum of water. The joint is first cut
out to the depth of from one half to one inch, carefully brushed clean,
moistened with water, and filled with the mortar, which is well rubbed
with a steel tool. To give architectural effect, plaster of Paris
(Gypsum) is sometimes used in pointing.


                                 GROUT.

272. Grout is thin-tempered mortar, composed almost entirely of cement
and water. It is run into the joints, and is useful in filling crevices
in masonry which cannot be filled with mortar.


                        CONSTRUCTION OF ARCHES.

273. The foundations being secured, and the piers and abutments being
carried up to the springing line of the arch, the centres are carefully
adjusted to their places and the arch is commenced. When the voussoirs
begin to bear upon the centre (which is when the angle of the joint with
the horizontal is greater than the angle of repose of one stone upon
another), the frame is liable to change of form, (particularly when the
arch is flat,) which must be provided for by counter loading the centre
in various points as the work proceeds. Great care should be taken to
make each stone point in the direction of the radius of the arch. To do
this effectually, their thickness should be marked upon the outer rib of
the centre. The line of the joint may then be fixed by a straight-edge
placed both on the centre and the rib mark, or by a template so cut that
when one side is level the other shall stand at the proper angle. Excess
of weight upon one side of the centre causes a depression at that point,
and a corresponding rise at the opposite side of the arch. Both sides
being loaded, the haunches settle, and the crown rises. The point where
the centre is first loaded will determine the point where the frame is
to be temporarily weighted. Such precautions, however, need only to be
taken in arches of over fifty feet span, unless the curve is quite flat.
The keystone should be put into the proper place, but not driven until
the rest is finished. The back joints are then closely wedged and
cemented with thin tempered mortar, and the whole is left to set. The
masonry of the spandrels is brought up to about one fourth the height of
the arch, or enough to prevent by their weight any change of form of the
curve. The centres are then struck and the soffit and voussoir joints
cleaned and pointed. The facing and road-way may next be carried up; the
parapet coping and drains finished off; and the whole pointed. Parapets
are shown in figs. 127 and 128. The spandrels, fig. 129, may be carried
up solid or hollow; their weight must be enough to stiffen sufficiently
the arch. It should, at least, be carried up solid to the line _c c c_;
the shaded mass being of well-cemented rubble. Above this the filling
may be of masonry, solid or arched, or even of well-rammed layers of
earth. The road-way should, in all cases, be well drained, that the
water may not sink through to the masonry.

[Illustration: Fig. 127.       Fig. 128.]

[Illustration: Fig. 129.]

The apparatus for handling stone (cranes, lewises, and derricks) is much
better understood by inspection than by description.

Wherever walls support masses of earth, the thrust may be somewhat
lessened by ramming the earth behind the wall in layers inclining
backward. In laying up the courses each should be well cleaned and
moistened before the mortar is laid upon it. When a stone has been once
placed upon the mortar bed, it should not be moved at all _laterally_,
but may be gently mauled on top.


                          CULVERTS AND DRAINS.

274. Small culverts are made by covering two side walls with large flat
stones; the bottom being paved with stone at least nine inches deep,
laid dry. The general dimensions of such structures depend somewhat upon
the class of masonry, but as this is generally the _third_ or _fourth_,
will not vary much.

                   Opening. Side walls. Cover. Heads.
                    2 × 2     3  × 2      12   2 × 10
                    2 × 3     3  × 3      12   3 × 10
                    3 × 3     3  × 3      12   3 × 11
                    3 × 4     3½ × 4      15   4 × 12
                    4 × 4     3½ × 4      15   4 × 13
                    4 × 5     3½ × 5      18   5 × 15
                    5 × 5     4  × 5      18   5 × 16
                    5 × 6     4  × 6      18   6 × 18

Figs. 130, 131, and 132, show plans for culverts of from 5 to 25 feet
span.

[Illustration: Fig. 130.]

[Illustration: Fig. 131.       Fig. 132.]


                            RETAINING WALLS.

275. A wall made to sustain a mass of earth or water, to resist
overthrow, requires a certain thickness. A body of earth assumes what is
termed the natural slope, the inclination of which depends upon the
adhesion of the soil, but may be taken as one and one half horizontal,
to one vertical, (1½ to 1), as an average.

The problem is, knowing the height of the wall and the form of the mass
of earth to be supported, to find the thickness of the wall.

Let A B 6 F, represent the thickness of the wall. Its centre of gravity
is at O, and is horizontally projected at _m_. The centre of gravity of
the thrusting triangle of earth, B 4 6, is C, (found by the cutting of
lines joining any two angles to the centre of the opposite sides,) is
horizontally projected at C^{_a_}, and the horizontal component of the
thrust is exerted at 2, tending to overthrow the wall with a leverage, 6
2.

[Illustration: Fig. 133.]

The overthrowing power is, then, the area of the triangle B46 × the
weight of the unit of area × the leverage 6 2. And the resisting power,
the area AB × B6 × the weight of a unit of area by one half breadth, or
_m_ 6; or, calling _w_ the weight of the wall, and _w′_ that of the
triangle, B 4 6, and _L_ and _L′_ the leverage respectively of the wall
to resist and of the earth to overthrow; we must have at least

                             _wL_ = _w′L′_,

and to insure stability,

                             _wL_ > _w′L′_

or,

                          _L_ = (_w′L′_)/_w_,

and as _L_ = half base finally, the thickness, or

                          2_L_ = (2_w′L′_)/_w_

276. _Example._—Let the height of wall be twenty feet, slope one and one
half to one; if a cubic foot of earth weighs one hundred lbs., and of
masonry, one hundred and sixty lbs., we have the overthrowing force,

                     20 × 15 × 1 × 100 × 2 × 20/3,

and the resisting force, (assuming the thickness as eight feet, in order
to get the area),

                        20 × 8 ×  1 × 160 × 8/2.

Or performing the operations,

                     For overthrowing, 100,000 lbs.
                     For resisting,    102,400 lbs.

If the wall in place of retaining only the mass B 4 6, retains the bank
B E F^{_a_}, the pressure will evidently be increased. The centre of
gravity of the trapezoid B E F^{_a_} 6, is at C′, which is horizontally
projected at C′^{_a_}, and the horizontal component of the thrust acts
at 3 with the leverage 63.

Any superincumbent load, as a train of cars at E F^{_a_}, will again
increase the pressure, not only by reason of weight, but from shocks and
vibration.

For resisting lateral pressure, the beds of masonry are best when rough
dressed. For vertical loads, hammer dressed beds are the best.

The leverage of resistance is very much increased by battering the wall
in front, as at A D. The centre of gravity is then horizontally
projected at _m′_, but the distance D _m′_ is much greater than F _m_.

[Illustration: Fig. 134.]

The amount of masonry remaining the same, by decreasing the top, and
increasing the base, the strength is very much increased.

When retaining walls are exposed to shocks or pressures special
directions, they may be very much aided by buttresses opposing directly
such forces, as in fig. 134.

The increase of strength thus made by a small bulk of masonry is very
great.

All abutments, wing-walls, and side walls of culverts, come under the
head of retaining walls.

When the face of the wall does not by its position admit of buttresses,
as in fig. 134, it may be dovetailed into the earth; the latter being
firmly rammed around the masonry, as in fig. 135.

[Illustration: Fig. 135.]

277. The weight of the different earths and stones are shown in the
following table.

               Name of material.        Weight per cubic foot.
         Brick, common                               97 to 125
         Brick, stock                               115 to 135
         Brickwork, (average,)                       90 to  95
         Chalk,                                     144 to 166
         Granite,                                   164 to 187
         Marble,                                    111 to 117
         Mortar, (hair,) dry                         80 to  86
         Puzzolano,                                 160 to 178
         Slate,                                     157 to 180
         Stone, (average,)                          140 to 150
         Clay, (common,)                            110 to 125
         Clay and gravel,                           150 to 170
         Earth, common,                              95 to 126
         Gravel,                                    100 to 110
         Quick-lime,                                 50 to  55
         Quartz sand,                               170 to 175
         Common sand,                                88 to  93
         Shingle,                                    88 to  92
         Earth, loose                                90 to  95
         Stone work, (hewn,) in wall,               160 to 175
         Stone work, (unhewn,) in wall,             125 to 140




                              CHAPTER XII.
                              FOUNDATIONS.


278. Foundations may be divided into four classes.

                 Those on _firm_, dry land.
                 Those on _unfirm_ dry land.
                 Those on _solid_ bottom, under water.
                 Those on _unfirm_ bottom, under water.

Foundations upon firm dry land require only to be placed at a sufficient
depth to be out of the way of frost; varying from one foot in the
Southern, to two and three feet in the Middle, and four and five feet in
the Northern States. The first course should consist of small, flat
stones placed dry, but well packed by hand, upon the bottom; upon the
top of this layer, the mortared or cement masonry should be commenced.
The object of the first course of small stones is to apply the weight of
the superincumbent masonry as equally as possible to the ground. All
boulders and rounded stones should be carefully kept out of the
foundation.

Unfirm soils are prepared by driving piles, upon which a platform
holding the masonry is placed; or by placing the lower courses directly
upon the heads of the piles. Sand piles are made either by driving and
withdrawing a wooden pile and filling the hole thus made with sand; or
by digging trenches and filling such with sand. The applied weight is
thus spread over the entire surface of the sides and bottom, instead of
being placed upon the bottom only. When the weight of a heavy structure
is thrown upon a few small points of support, they may be made the piers
and abutments of a series of inverted arches, by which the whole surface
beneath the structure is made to assist in bearing the load. Foundations
upon yielding or sandy and wet soils may be secured by piling around the
whole structure; by which the earth is kept from spreading. Foundations
upon dry land do not generally give much trouble to the engineer; but
operations carried on under water require all the science and patience
that he is master of.

279. Three methods of founding under water may be noticed,

                           By driving piles.
                           By coffer-dam.
                           By caisson.

In very shallow water, where no danger arises from contracting the
water-way, we may throw in loose stones until the surface is reached;
and commence thereon the lower courses of the masonry. This is termed
“Enrockment.”


                             PILE DRIVING.

This operation has for its object the consolidation of naturally weak
bottoms; for piles driven close together tend to prevent that
compression that might take place under a heavy structure. Piles may
resist either by friction against the soils through which they are
driven, or by bearing upon a firm substratum at too great a depth to be
reached by uncovering. Piles driven in clay have sometimes acted as a
conductor to water, which, insinuating itself along the side of the
wood, produced settling which would not otherwise have taken place.

Experience has shown that four feet apart from centre to centre, when
there is a good substratum, is near enough to bear the heaviest loads.

The fact that a pile refuses to enter further, does not show that it has
reached a bed strong enough to bear the required load; for though it may
bear upon a solid bottom, or resist penetration by side friction, when
the load has been for some time upon the pile, it may be found too weak
to stand. Piles have in some cases refused to enter the ground from the
blow of a 1,500 lbs. ram, falling twenty feet, when first driven, and
have afterwards gone down three feet from a ram of 1,000 lbs.

The following formula, showing the resistance which a pile should offer,
is given by _Weisbach_ in Mechanics of Engineering, Vol. I. p. 285.
First, when the ram remains upon the pile after the blow,

                 _P_ _s_ = (_G′^2_ × _H_)/(_G_ + _G′_).

And, second, when the ram does not remain upon the pile,

                 _P_ _s_ =(_G′_/(_G_ + _G′_))^2 × _GH_

_Example._—A pile weighing five hundred lbs. is driven two feet, by
forty blows of a 1,000 lbs. ram falling six feet. Required the weight
which may be safely supported by the pile without further penetration.

The notation in the formula above is thus,

                     _G_  = the weight of the pile.
                     _G′_ = the weight of the ram.
                     _H_  = the fall of the ram.
                     _s_ = penetration per blow.
                     _P_ = the weight in lbs.

The penetration per blow will be 2/40 or .05 feet; and the formula for
the second case

          (1000/(1000 + 500))^2 × (500 × 6)/.05 = 48,000 lbs.

Of which _one tenth_ or _one twelfth_ only is the maximum load which
should be placed upon the pile permanently. The surest test of the power
of a pile is to load it temporarily, when the time and place admit.

Perronet considered fifty tons, or 112,000 lbs. as not too great for a
twelve inch pile; and allowed twenty-five tons for a pile of nine inches
in diameter.

That the point of the pile may not be shattered by contact with the hard
earth, an iron shoe is sometimes fitted to the lower end; and that the
head may not split, an iron ring is driven on to the top.

The force of the blow given by a ram depends upon the weight of the ram
or monkey, and upon the velocity at which it strikes the pile; the
velocity depends upon the height from which it falls. The velocities of
bodies falling freely being as the times, and the spaces fallen through
as the squares of the times, we have the following rules; and from them
the table succeeding.

Given the _velocity_ of a body to find the _space_ through which it must
fall,

          ((Velocity in feet per second)/8)^2 = space in feet.

Thus a weight to acquire a velocity of two hundred feet per second, must
fall through a height of

                         (200/8)^2 = 625 feet.

Given the _space_ fallen through, to find the _velocity_.

        √(height in feet × 64.3) = velocity in feet per second.

Thus the velocity of a body falling twenty feet will be

                   √(20 × 64.3) = 36 feet per second.

_Momentum_ is the product of weight by velocity; therefore, to find the
force of the blow given by a ram of given weight, falling a given
height, we find, first, the velocity by rule two. Also, given the weight
of ram, the necessary velocity to produce any required effect being
found, it is easy to find the height, and the reverse.

_Examples._—Suppose we have a ram weighing 2,000 lbs. and wish to strike
a blow of 25,000 lbs.; the velocity must be

                   25000/2000 = 12½ feet per second;

and to acquire that velocity, the height fallen must be (rule one)

                         (12½/8)^2 = 2.43 feet.

Again, if we have a pile-engine which admits of a fall of fifteen feet,
and we wish to strike a blow of 18,000 lbs., we first find the velocity
(rule two) thus:—

               √(15 × 64.3) = 31 feet per second nearly,

whence the weight

                          18000/31 = 581 lbs.

The form of the common pile-engine is too well known to need
description.

Mr. Nasmyth’s system of pile-driving consists in forcing the pile into
the ground by a great number of blows following each other in rapid
succession. Piles were driven by his engine at the United States Dry
Dock, at Brooklyn, (N. Y.,) as follows: A pile was sunk fifty-seven feet
by a hammer of 4,500 lbs.; it was driven forty-two feet in seven minutes
by three hundred and seventy-three blows.


                         MITCHELL’S SCREW PILE.

Mitchell’s screw pile is a cast-iron column, around the lower part of
which is a spiral flange. It is screwed into the ground, and offers
great resistance to vertical pressure, on account of the large bearing
surface obtained.


                    DR. POTTS’S ATMOSPHERIC SYSTEM.

280. All methods of placing foundations in difficult positions must
yield to the above plan, which consists in exhausting the air from a
hollow cast-iron cylinder; when the pressure upon the surface of the
ground, outside of the cylinder, forces the earth immediately under the
pile to its interior; at the same time the pile sinks into the opening
thus made, both by its weight and by the atmospheric pressure from the
outside. The earth is moved from the interior of the pile; and when sunk
to the necessary depth, the interior is filled with concrete.

A very successful application of the above system was made at the
Goodwin Sands, at the mouth of the Thames River, (England). These sands
change their position with every violent storm, and are yet so compact
that a steel bar could be driven only eight feet with a sledge hammer;
and a pointed rod three inches in diameter, when sunk thirteen feet
deep, required forty-six blows from a one hundred lbs. ram falling ten
feet to drive it one inch. But a hollow pile two and a half feet in
diameter was sunk seventy-eight feet, at the rate of ten feet per hour
for a part of the time. In case of meeting with rock, the pile may be
converted into a diving-bell, and the obstruction moved.

The pile is cast in lengths of ten or twelve feet, and flanged together
with cemented joints.

In founding a bridge at Rochester, (England,) a pile of this nature was
loaded with thirty tons of iron rails, which caused a settlement of
three fourths of an inch. The rails being removed and the air exhausted,
by a single effort the pile descended six and a half feet. One hundred
tons of rails were then placed upon the pile, when the settlement was
again three fourths of an inch. (This small depression was owing to the
compression of the soil.)

The piles supporting the Shannon bridge, on the Midland Great Western
Railroad, (England,) were sunk by this system; and are ten feet in
diameter, and filled with concrete.

After wooden piles have been driven, they are cut off at the proper
level to receive the lower courses of the masonry. In some cases square
timber caps are placed upon the pile heads, and thereon a plank floor.
In others, the spaces between the piles are filled with cement and
concrete.


                              COFFER-DAM.

281. In founding in water from five to twenty-five feet deep, a
contrivance called a “coffer-dam,” is sometimes used. It is formed by
driving a double or triple row of piles around the foundation; which
rows are made water tight, either by tongued and grooved square piles,
or by round piles, to which is fastened a sheathing of plank. The space
between the courses of piling is emptied of water and packed closely
with clay or other material impervious to water. The interior of the dam
is then pumped dry and the masonry laid as on dry land. The thickness of
the dam depends upon the depth of water; the pressure upon the lower
part being of course much greater than that at the upper. If it was
considered as a mass resisting by its weight, overthrow from the
pressure of the water, the thickness would be easily calculated. Thus,
if the water is twenty feet deep the whole hydrostatic pressure upon
each lineal foot of the dam is 20 × 1 × 10 × 62½ = 12,500 lbs.; and as
the weight of water increases in the order of the terms of an
arithmetical progression, as also the pressure, it may be expressed by
the elements of a triangle, of which the height is the depth; and as the
centre of gravity of a triangle is at two thirds of the height from the
vertex, the pressure may be regarded as concentrated at one third of the
depth from the bottom; and the leverage of the above 12,500 lbs. is

                           20/3 = 6.67 feet;

and the overthrowing force is 83,375 lbs. The resisting force of a clay
dam twenty feet high and ten feet thick, would be

                  20 × 10 × 110 × 10/2 = 110,000 lbs.

Determining the thickness thus, would make the dam, when in deep water,
very thick; and it is generally best to brace the inside against the
ground, and when the masonry will admit, against that.

Dams of the following thickness have proved perfectly secure:—

                       Depth of water. Thickness.
                               6 feet.    3 feet.
                              10 feet.    5 feet.
                              15 feet.    8 feet.
                              20 feet.   12 feet.
                              25 feet.   14 feet.

The best form for a large coffer-dam is circular, or elliptical; as the
pressure is thus resisted more equally in all places than when there are
flat sides and angles in the plan.

To keep the dam dry while the work is going on, pumps are rigged along
one side of the dam the lower ends of which are placed in a trench or
well which drains the bottom.

The piers of the Victoria bridge at Montreal, (Canada,) are put down by
coffer-dams. Some of the piers being in but few feet of water, and upon
a rocky bottom, which did not admit of the driving of piles; the dams
for such were built in sections, floated to the site and anchored.


                         FOUNDATION BY CAISSON.

282. In deep water the coffer-dam becomes very expensive, on account of
the size and length of the piling, and the quantity of bracing required.
In such cases recourse is had to the caisson; which is simply a box in
which the masonry is built, and afterwards sunk to the proposed site.
The manner of putting down a piece of masonry by caisson will best be
shown by an example.

Suppose we wish to sink a pier thirty feet long, twenty feet high, and
six feet wide, in twenty feet of water.

Let the caisson bottom be of two courses of square 12 × 12 timbers,
fastened strongly at right angles to each other. Let the courses of
masonry be two feet thick. Assume the weight of a cubic foot of stone as
one hundred and sixty lbs., a cubic foot of wood at thirty, and of water
sixty-two lbs. per foot.

Every floating body will sink until it has displaced a quantity of water
equal to its own weight.

If the bottom is ten feet wide and thirty-five feet long, it will weigh

                     35 × 10 × 2 × 30 = 21,000 lbs.

one course of masonry weighs

                     30 × 6 × 2 × 100 = 57,600 lbs.

one course of side timbers, 12 × 12, which are laid upon the sides of
the raft,

                   (2 × 35 + 2 × 8) × 30 = 2,580 lbs.

Now load the bottom with one course of masonry and three courses of side
timbers, and we have

                     Stone              57,600 lbs.
                     Bottom of caisson  21,000 lbs.
                     Three side courses  7,740 lbs.
                                        ——————
                     In all:            86,340 lbs.

which divided by 62, gives 1,392; which divided by the area of the
caisson bottom, gives

                            1392/350 = 3.98

or nearly four feet, for the depth at which the caisson will float. This
leaves the sides one foot above the water surface.

Putting on a second course of masonry and three more side courses of
timber, we have

                    Floor                21,000 lbs.
                    Two courses masonry 115,200 lbs.
                    Six side courses     15,480 lbs.
                                        ———————
                    In all              151,680 lbs.

which divided by 62, and by 350, gives seven feet very nearly; leaving
the top one foot above the surface.

In the same manner we proceed until the caisson grounds upon the bed,
which has been previously prepared, either by pile-driving or by
dredging. The bottom being reached, the sides are taken off, and the
masonry remains upon the floor. The caisson may at any time be grounded
by filling with water, and may be raised again by pumping out. The
masonry may be laid either from barges or rafts at the site, or at the
shore. Guide piles are necessary to insure the descent in the proper
manner, and to prevent overturns.

In laying stone under water, it is to be remembered that masonry
submerged loses 62/100 nearly of its weight, and is consequently more
liable to be injured by shocks than when above the surface.




                             CHAPTER XIII.
                            SUPERSTRUCTURE.


283. Nothing aids more the proper accomplishment of any object than a
correct idea of what is wanted. The following definition is given by Mr.
W. B. Adams, of what good superstructure should be:—

“The principal requirements of permanent way are: That it shall be well
drained, especially in contiguity to the substructure; that the weight
and damaging power of the locomotives and rolling stock should be
considered the data for calculation; that the strength, hardness, and
tenacity of rails, and the immobility of the substructure should be
adapted to the hardest work to which the railway is to be subjected;
that the substructure should have an amount of bearing surface
proportioned to the load to be borne, and the nature of the rail and
ballast; and a sufficiently fair hold in the ground to prevent looseness
or lateral motion, from the side lurches of the engines and trains; that
the rails should possess so much vertical and lateral stiffness, either
in themselves or in their fastenings, as to prevent all deflection; and
have sufficient hardness of surface not to laminate or to disintegrate
beneath the rolling loads; also, to have sufficient breadth or tread
surface to diminish the crushing effect of the wheels.

“They should be as smooth as possible, to prevent concussion, and be
laid at the proper angle, and the curves regularly bent, so as to insure
the accurate tread of the wheels. The joints should be so made that the
rails may practically become continuous bars, yet with freedom to
contract and expand without being too loose. And with all this there
should be interposed between the rails and the solid ground, some medium
sufficiently elastic to absorb the effect of the blows of the wheels,
without being crushed or forced down into the ballast, and yet stiff
enough to keep the upper surface of the rails in a uniform plane.”


                              TIMBERWORK.

284. The timber-work supporting the rails consists either of cross ties
of wood, hewn flat on top and bottom, of dimensions from 6 × 7 to 7 × 9,
and 2½ or 3 feet longer than gauge; or of longitudinal sawed timbers
rectangular in section, placed directly beneath the rail, and giving it
a bearing throughout the whole length.

Longitudinal bearings seem to possess no advantage over cross ties, but
are subject to some decided disadvantages. In case of removal, two rails
at least must be taken up to admit of the replacing a timber; while with
cross ties any one may be taken out and replaced without even affecting
the immediate passing of a train. A continued bearing is no better than
a broken one, as the strength of the timber itself offers very little
resistance to the weight of a locomotive. Strength is not to be expected
in the timber-work; it is only the elastic medium between the rail and
the ground serving to maintain the rail in a proper position. The
strength is in the rail. The distance at which to place cross ties
depends upon the weight of engines traversing the road, the nature of
the ballast, and the strength of the rail; somewhere between two and
four feet from centre to centre.

The amount of superficial bearing which the timber-work ought to give
per lineal foot of rail, is differently estimated by different
engineers.

Upon the 4′ 8½″ gauged roads of America, 1¾ square feet per lineal foot
of rail has been allowed.

Several of the English roads give the following:—

       Name of road.       Gauge. Square feet per lineal foot of rail.
 London and N. W. Railway, 4′ 8½″ 3
 Great Western,            7′ 0″  2½
 S. and W. of Ireland,     5′ 3″  3⅔
 Midland G. W. of Ireland, 5′ 3″  27/12

If ties are made eight inches wide, and eight feet long; we have the
following amounts of bearing surface per lineal foot of the rail with
different distances of the ties.

        Distance C to C of tie. Superficial feet per lin. foot.
        2                       2.66
        2½                      2.13
        3                       1.78
        3½                      1.53

Of course the longer the tie is made the greater may be the distance
between, provided the rail will bear it. Mr. Peter Barlow, in his report
of August, 1835, to the directors of the Liverpool and Manchester
Railway, fixes the following dimensions for superstructure.

                 Distance between insides of ties being
                                  3′   3′ 9″    4′     5′     6′
      Weight in lbs. per yard.    50     59     61     67     79
      Depth of rail in inches.    4½     4⅝     4¾     5    55/16

At the time these dimensions were given, however, much less weight was
applied to the rails than at the present day. As the bearing is
increased, the rail must become heavier and more expensive; but the
number and cost of the ties is lessened. The report above referred to,
concludes that five feet bearings, involving heavier rails, would cost
no more, after the road bed is consolidated, than shorter ones; but that
on embankments and soft subsoils, it would be at first somewhat more
expensive.

285. The object of the ballast is, first, to transfer the applied load
over a large surface; second, to hold the timber-work in place,
horizontally; and third, to carry away the rain water from the
superstructure; it also furnishes the means of adjusting the timber-work
to the proper position. It should be at least one half way up the depth
of the tie, and deep enough below the under surface to prevent the
timber being forced down by the passing weight. From various
observations it appears that there should be one and a half times the
depth of the tie of ballast, beneath the under surface; or the whole
depth of ballast should be from two to two and one half times the depth
of tie.

For ballast, broken stone, gravel, or other dry, durable, and porous
material, is suitable.

A perfectly inelastic road bed is not to be desired. Something is
necessary to absorb the shocks given by the wheels, and prevent their
reaction against the machinery. To supply this amount of elasticity, and
to transmit the weight evenly to the ground, is the duty of the ballast
and timber-work.

Of late years there has been applied, in England, cast-iron
hemispherical bowls, designed to take the place of both tie and chair.
Such answers very well when there is no lack of ballast, and where
wooden ties are worth from seventy-five cents to one dollar each.


                          SECTION OF THE RAIL.

286. A good rail must be able to act as a girder, or supporter, between
the ties, as a lateral guide upon curves; and must possess a top surface
of sufficient hardness and size to resist the rolling wear of the
wheels.

                                         Lbs. per yard.  Tons per mile.
                                                          (2,240 lbs.).
 One square inch of rail section weighs,       9.9            15.72
 Two inches      of rail section weighs,      19.8            31.42
 Three inches    of rail section weighs,      29.7            47.14
 Four inches     of rail section weighs,      39.6            62.84
 Five inches     of rail section weighs,      49.5            78.56
 Six inches      of rail section weighs,      59.4            94.28
 Seven inches    of rail section weighs,      69.3           110.00
 Eight inches    of rail section weighs,      79.2           124.50
 Nine inches     of rail section weighs,      89.1           140.01
 Ten inches      of rail section weighs,      99.0           155.57
                                         Single line of  Double line of
                                             rails.          rails.

Thus, at sixty dollars per ton, each square inch of section costs
$943.20 per mile, or $94,320 per one hundred miles, whence the necessity
of rolling the rail to the form which shall give the greatest strength
with the least weight.

The sections most in use in America are shown in fig. 136, and 137.

[Illustration: Fig. 136.]

Fig. 136 gives the most direct bearing, is compact, and brings the
fibres at top and bottom more directly in opposition with the
compressive and extensive strains. The top of the rail being curved to a
radius of ten or twelve inches, the load is applied nearly to a single
point; whence the whole resistance in fig. 137, depends upon the lateral
resistance of the piece _a b c d_ to being pushed down.

An objection is sometimes made to fig. 136, on the ground that it splits
off on the line _n n_: this will not be the case when the head is joined
to the web by a proper curve, as in fig. 136. This splitting off happens
full as often in fig. 137 as may be seen where it is in use; and it
might be supposed to act in that manner; because if the weight is
transferred at all from the point of application to the web, it must be
in the direction _e f_.

[Illustration: Fig. 137.]

The rails in present use upon our roads, weigh from fifty to
seventy-five lbs. per lineal yard; and are laid upon cross ties placed
at a distance of from two and one half to four feet from centre to
centre.


                   OF THE ACTUAL DIMENSIONS OF RAILS.

Digesting carefully the results of the experiments of Barlow, Fairbairn,
and Hodgekinson, and the experience of Mr. W. B. Adams, and other
English engineers; also the conclusions arrived at by the Berlin
Convention of 1850, appointed to determine the best form of section, we
come to the following limiting dimensions.


                               THE HEAD.

Mr. Barlow limits the width of head at two and one half inches as the
maximum; the Berlin Convention, at two and one fourth inches; W. B.
Adams, at two and one half; and all of the above recommend supporting
the edges of the head well from the rib.


                           THE VERTICAL RIB.

The experiments of the Prussian engineers fix the thickness for a rail
four inches high, at one half of an inch, and a rail four and one half
inches high, at 0.6 or 6/10 inch. Mr. Barlow makes it six tenths of an
inch for a four and one half inch rail, and 0.75, or three fourths inch
for a rail four and five eighths inches high, and for four and three
fourths inches high, 0.8, eight tenths inch.


                           THE BOTTOM FLANGE.

The use of this is more for bearing and fastening, than for supporting
strength. The Prussian engineers make three and one half inches an ample
base for a rail five inches high. The edge for one half or three fourths
of an inch, should be nearly horizontal, or parallel with the base, to
allow the spike to have a good bearing.


                          OF THE INCLINATION.

As the tread of the wheel is conical, the top of the rail must be
inclined to fit this cone, otherwise the wear will come upon the inner
edge of the rail only. This may be done in two ways; by placing the rail
base level, and inclining the vertical axis of the cross section of the
rail, and making the tread square with that axis; or by making the rail
section true, and inclining the base, either by cutting the tie, or by a
wedge placed between the rail and the tie.


                         OF THE HEAD CURVATURE.

If the top surface of the rail were perfectly flat, and the wheel tire
does not happen to fit it exactly, (from want of the proper position of
the rail, by settling, or other cause,) the wheel will bear entirely
upon one edge, and would soon destroy the rail. To remedy this, a slight
convexity is given to the top. Mr. Clark (in R. R. Mach.), recommends
the top to be curved to a radius of _ten_ or _twelve_ inches.


              OF THE VERTICAL DEPTH (HEIGHT) OF THE RAIL.

Mr. Barlow’s general results are as follow:—

         Distance from inside to inside of tie. Height of rail.
                         3′ 0″                        4½″
                         3′ 9″                        4⅝″
                         4′ 0″                        4¾″
                         5′ 0″                        5″
                         6′ 0″                      51/16″

In the London edition (1836) of Barlow’s Strength of Materials, page
402, in a report to the London and Birmingham Railway Co., upon the best
form and upon the strength of rails; after a carefully conducted set of
experiments, and an elaborate theoretical deduction of results, the
writer comes to the following five sections of rails possessing the
maximum strength, with the least weight.

            Dimensions.         No. 1. No. 2. No. 3. No. 4. No. 5.
     Height,                      4½     4⅝     4¾     5    55/16
     Breadth at top,              2¼     2¼     2¼     2¼     2¼
     Depth of top,                1      1      1      1      1
     Thickness of rib,           0.6    0.75   0.8    0.85   1.0
     Width of lower flange,       1¼     1½     1½     1⅔     1⅔
     Depth of lower flange,       1      1      1      1⅛     1½
     Weight per yard,            51.4   58.8   61.2   67.4    79
     Distance C. to C. of ties,   3′    3′9″    4′     5′     6′

This table shows the ratio of material which should be placed in the top
and bottom.

With the above dimensions, and joining the curve of the head to the rib
at two and one fourth inches from the top of the head, we obtain a
strong and well-shaped rail, with the least material possible. See fig.
136.

As an example of the application of the above, the table below has been
formed, showing four standard forms, which will be found to unite all of
the requirements of good rails; the general form being that of fig. 136.

           Dimensions.           The weight of the rail being, in lbs.,
                                    60        65        70        75
 Width of head,                     2½        2½        2½        2½
 Rad. of top,                       12        12        12        12
 Height of rail,                     4        4¼        4½        4¾
 Thickness of rib,                  0.6       0.6      0.65       0.7
 Breadth of base,                   3½        3½        3¾         4
 Depth of head at point A B,        2¼        2¼        2½        2½
 Thickness at edge of lower web,     ½         ½         ½         ½

and the following figures show the weights which should be applied to
differently spaced sleepers.

  Distance centre to centre of tie. Distance clear.  Weight of rail.
                           1½ feet,        1  feet, 60 lbs. per yard.
                           2  feet,        1½ feet, 60 lbs. per yard.
                           2¼ feet,        1¾ feet, 60 lbs. per yard.
                           2½ feet,        2  feet, 60 lbs. per yard.
                           2¾ feet,        2¼ feet, 65 lbs. per yard.
                           3  feet,        2½ feet, 65 lbs. per yard.
                           3¼ feet,        2¾ feet, 70 lbs. per yard.
                           3½ feet,        3  feet, 75 lbs. per yard.

The amount of inclination or bevel to be given to the cross section of
the rail, depends _directly_ upon the cone of the wheel, and
_indirectly_ upon the gauge of the track. (See Chapter XIV. part 2.) The
radius of curvature being averaged at 2°, or 2,865 feet,

                                             Feet or Inches.
           For the 4′ 8½″ gauge it should be  .0017   .020
           For the 5′ gauge,                  .0017   .020
           For the 5½′ gauge,                 .0019   .022
           For the 6′ gauge,                  .0021   .025

in the width of the rail, or two and one half inches.

The above dimensions embrace all of the best results of experiment and
experience, and at the same time satisfy the conditions demanded by the
mechanical and physical nature of the material—iron.


                           CHAIRS AND JOINTS.

287. The chairs most common at present are made of a wrought iron plate,
with two lips, either cut and punched up, or forged up, to hold the
lower web of the rail. Such chairs weigh from six to ten pounds each,
and are less liable to break than the common form of cast-iron chairs.
It is probable that a cast-iron chair may be made, however, with
properly shaped lips, and so hollowed out as to be at once strong and
light. (See Clarke’s R. R. Machinery, “Permanent Way.”)

Of late the chair of Mr. David L. Davis, of Dedham, Mass., has attracted
considerable attention, and bids fair to be the means of obtaining a
better rail surface than has heretofore been possible. This gentleman
has been for twenty years Road-master of the Boston and Providence
Railroad, and has had ample opportunity for considering the subject of
track laying in every respect. The rail bears upon a cap of wrought
iron, which rests upon a piece of rubber, lying in the chair. The
testimony of the leading managers of the New England Railroads bears
witness of the excellence of the arrangement.

The practice of notching _each end_ of the rail causes the expansion to
be exerted directly _against_ the fastenings, which should not be the
case. Some point should be _fixed longitudinally_, to resist the end
shocks from the wheel. This point should be either the _centre_ or _one
end_ of the rail. End chairs may hold the rail laterally, and
vertically, but not longitudinally.

The weakest part of the track is that, where, to resist the concussions
of the wheels it should be strongest, namely, at the joint: here we lose
the strength of the rail and depend entirely upon the tie. The flattened
ends of rails which have been laid for a few years show the bad effect
of the common joint. The complete remedy for this is, so splicing the
rail that it is as strong at the joint as elsewhere. The method termed
“fishing,” is not much more expensive than the ordinary method of
jointing, it is perfectly effectual, and has had the test of long and
successful use. It consists in bolting a plate two and one half feet
long, two and one half or three inches wide, and from one third to one
half inch thick, to the ends of both rails making the joint; one plate
being placed on each side. The plates are convexed a little from the
rail as in fig. 138, so that being sprung by screwing on the nuts, the
latter shall not work loose by the vibration of the rail.

[Illustration: Fig. 138.]

In the above arrangement there is no tie below the joint, but the latter
lies midway between two sleepers.

Another method of “fishing” is, to place a piece of ¶ᕼ¶ or ¶⊤¶ iron
beneath the rail, bolting it firmly to the lower flanges.

In bolting rails together at the ends, the bolt holes must be cut a
little larger than the bolt, to allow for the expansion of the iron.

The effect of the joint upon the passing carriage, is the jumping
motion; the middle of each rail being a summit, and the end a
depression, (the strength at the joint being taken away); and if the
joints are not opposite to each other, there is generated a very
injurious and dangerous side rocking. Figs. 138, 138 A, and 138 B, show
the methods of fishing.

[Illustration:

  Fig. 138 A.
  Fig. 138 B.
]

[Illustration: Fig. 139.]

To avoid the wear caused by frequent joints, various forms of compound
rails have been proposed; consisting of two or more parts breaking
joint. One form has been contrived in which the section is vertically
halved; another of three parts, a head placed on top of a double
vertical web. Fig. 139 shows what would seem to answer any purpose (if
compound rails are at all allowable). The joint is here divided into
four parts, so that the strength of the bar at any point is reduced only
one fourth. In bolting the parts together the joints should be left open
enough (see in advance) to allow for contraction; and the bolt-holes, as
before noticed, should be longer than the bolts. (This enlargement,
extending only in the direction of contraction, and not in the line of
the force.) The upper part of such a rail should be hardened to resist
the rolling of the wheels, while the webs must possess the strength to
act as a girder.

It is questionable whether, by dividing the rail, particularly when it
is done horizontally, we do not prevent the mutual extensile and
compressive actions which ought to have place in the top and bottom; for
we cannot make the bolts perfectly tight because of expansion.

Some of the compound rails which have been laid in America have given
good results, others have not.

Mr. W. B. Adams observes, that a compressed rail to be as strong as a
sixty pound whole rail, must weigh ninety lbs. per yard.

Some engineers have proposed such a rail that when one side becomes worn
it may be turned over so that the lower may become the upper table. This
is quite wrong in principle; as when the lower fibres have been
subjected for some time to extension, they are entirely unfitted to
oppose compression.


                         OF THE LIFE OF RAILS.

288. The time which a rail will last, depends upon the form and weight,
and _on the quality of the iron_; and upon the number, weight, and speed
of engines and cars passing over it.

  NOTE.—The effect of _quality_ is altogether too little regarded in
  America. How worthy of attention it is may be seen by the following.

  Upon the same road were used two kinds of seventy-two pound rails,
  each five inches deep, and having a bearing surface of 2.7 inches in
  width. The one was worn out with a tonnage of 41,000,000 tons, the
  other of 22,000,000 tons; the difference being entirely in the
  _quality_ of the iron.

  Upon the Philadelphia and Reading Railroad there have been used
  forty-five pound rails of reheated and refined iron, which have
  lasted for eighteen years; and that with a very heavy traffic upon
  them. While upon other American roads, English sixty pound rails
  have required renewing in one, two, three, and four years.

The durability of rails is practically independent of time, and depends
entirely upon the amount of work done. The repairs of iron, depending
upon flaws and other physical defects, will be greater at the
commencement of operations than afterwards. After the first one or two
years the regular depreciation begins. The first Liverpool and
Manchester rail weighed thirty-five lbs. per yard, and the locomotive
seven and a half tons. As the traffic increased, so did the necessary
weight of engines, and a corresponding increase in the strength and
weight of rails was also rendered necessary. In 1831, the average weight
of engines with tenders was eighteen tons. In 1855, the maximum engine
with tender, fuel, and water weighed sixty tons; and in like manner the
rails increased from thirty-five to eighty-five lbs. per yard.

Messrs. Stephenson and Locke, in a report to the London and
North-western Railroad Company, in 1849, recommend the adoption in
future of an eighty-five lb. rail.

Upon the roads of Belgium are used rails of fifty-five and sixty-four
lbs. per yard; but it is asserted that an eighty lb. rail would allow of
ten times more traffic.

For the average of American roads, when the iron is good, (_in
quality_,) fifty-five, sixty, and at most sixty-five lbs., will probably
be found ample for the heaviest traffic: the rail being of the form
already given, and supported on ties not more than two and a half feet
from centre to centre.

Mr. Belpaire, (of the Belgium engineers,) concludes, from many
experiments, that in sixty miles, each engine abrades 2.2 lbs.; each
empty car 4½ oz.; and each ton of load 1.4 oz.; the amounts being in
direct ratio to the several weights.

Captain Huish, of the London and North-western Railroad, (England,)
estimates (Report of April, 1849) that fifty trains per day, or 18,250
trains per annum, for twenty years, would wear out a seventy lb. rail.

The Belgian engineers have concluded that 3,000 trains per annum, for
one hundred and twenty years, would wear out a fifty-five lb. rail.

Now 120 × 3,000 = 360,000 Belgian, and 20 × 18,250 = 365,000 English, a
very satisfactory coincidence, as the different observers did not know
of each other’s proceedings. The difference, 5,000 trains, being
accounted for by the use of heavier engines upon the roads of England.

From the above results the following table is formed, showing the life
of rails under from two to one hundred trains per day. American roads
being less nicely finished, as regards the road-bed, will of course wear
out rails faster than the roads of Europe. The table will serve as a
base for estimates.

     Trains per day. Trains per year. No. of years’ life of rails.
                   2              600                          604
                   4            1,200                          302
                   6            1,800                          201
                   8            2,400                          151
                  10            3,000                          121
                  12            3,600                          100
                  14            4,200                           86
                  16            4,800                           75
                  18            5,400                           67
                  20            6,000                           60
                  30            9,000                           40
                  40           12,000                           30
                  60           18,000                           20
                  80           24,000                           15
                 100           30,000                           12

Probably one half of the above numbers of years would show the full life
of rails upon American roads.

As those rails which are most used wear out the soonest, they should be
made accordingly heavier. Such are those at depot grounds and at
sidings.

  NOTE.—From the reports of the Reading (Penn.) Railroad it appears
  that in 1846 153/209 of the damaged rails were split; and that in
  1845 285/295 were split.

  As regards the _quality_ of railroad iron, it is generally
  notoriously bad, and its makers know it as well as those who buy it.
  Railroad companies are not willing to pay for good iron. Comparisons
  between American and English iron amount to little. First rate iron
  can be made in England or in America, and so can that which will
  last about two years. Time will convince companies that the most
  expensive iron is the cheapest.


            TABLE OF THE WEIGHT PER MILE OF DIFFERENT RAILS.

            Weight in lbs.  Tons per mile.  Tons per mile.
               per yard.     (2,000 lbs.)    (2,240 lbs.)
                  50             44.00           39.29
                  55             48.00           43.21
                  60             52.80           47.19
                  62             54.56           48.71
                  64             56.32           50.28
                  66             58.05           51.86
                  68             59.84           53.43
                  70             61.60           55.00
                  72             63.36           56.57
                  74             65.12           58.14
                  76             66.88           59.71
                  78             68.64           61.28
                  80             70.40           62.86


                             TRACK-LAYING.

289. As wrought iron expands 0.0000068 of its length per degree
(Fahrenheit) of heat, a change of 130° will cause the following
expansions:—

                      In a 15 feet rail .0135 ft.
                      In a 18 feet rail .0162 ft.
                      In a 20 feet rail .0176 ft.

and that the track may be kept in the right vertical and horizontal
line, rails laid in cold weather must not be placed in contact; but
separated by space enough to allow expansion to take place. In hot
weather they may be placed close together. Calling 100° the maximum and
-30° the minimum, we form the following table for the average lengths of
rail, (20 feet).

           At 100° place the rails in contact.
               90° at a distance of .00136 feet .016 inches.
               80° at a distance of .00272 feet .032 inches.
               70° at a distance of .00408 feet .049 inches.
               60° at a distance of .00544 feet .065 inches.
               50° at a distance of .00680 feet .082 inches.
               40° at a distance of .00816 feet .092 inches.
               30° at a distance of .00952 feet .114 inches.
               20° at a distance of .01088 feet .131 inches.
               10° at a distance of .01224 feet .147 inches.
                0° at a distance of .01360 feet .163 inches.
              -10° at a distance of .01496 feet .179 inches.
              -20° at a distance of .01632 feet .196 inches.
              -30° at a distance of .01768 feet .212 inches.

[Illustration: Fig. 140.]

The proper distance of rails may be fixed by the use of the steel plates
shown in figs. 140 and 140 A, which are marked with the temperature,
according to their thickness, as in the above table.

To incline the rail base may be used, when the rail is not bevelled,
wedges one foot long and six inches wide, spiked with the rail to the
tie. When the chairs are of cast-iron, they may be cast to the required
slope.

[Illustration: Fig. 140 A.]


                                 FROGS.

290. When one line of rail crosses another, a contrivance called a frog
is used; see figs. 141 and 142.

[Illustration: Fig. 141.]

That the wheel may run smoothly from _a_ to _c_, fig. 141, the rail _b
f_ must be cut at D, and the rail _a c_ must be cut at the same point.
Cutting the two gives the form shown in the figure, and further
developed in fig. 142.

In order that the flange of the wheel shall not leave the line _a c_,
when at the break D, the guard rail _m m_ is used to confine the
opposite wheel. It should be placed at a distance of two inches from,
and parallel with, the main rail _g g_, from opposite six inches below
the frog point at _s_, to six inches above the shoulder at _s′_. From
the ends of the parallel line _n n_ the guard rail should gently curve
away at both ends. Thus the wheel will be gradually brought into the
right line, kept so until the break in the rail is passed, and finally
easily released. To place and maintain the guard rail in the right
position, it is well to put both it and the main rail into a double
chair, which is spiked to the sleeper.

[Illustration: Fig. 142.]

The form and dimensions of the cast-iron frog depends upon the angle at
which the cutting rails cross, and upon the size of the wheel tire.

To draw the frog, proceed as follows:—

[Illustration: Fig. 142 A.]

Let _a c b_ be the angle. Parallel with and two inches from _b c_ draw
_d e_, _e_ being in _a c_ produced. In the same manner fix the point
_g_. At the width of the rail head (from 2¼ to 2½ inches) draw, parallel
to _a c_, L 8. The point 8 is the limit to the solid steel. At double
the rail width, or 4½ inches, draw, also, parallel to _a c_, 16. 6; 5. 6
is the limit of the flat steel, generally about half an inch in
thickness. This is the least amount of steel allowable; it is best to
steel the whole tongue, and all of that part of the wings acted upon by
the wheels. The geometric point is generally very thin, and is omitted
to a distance far enough back to make the point a third or half an inch
wide, which is rounded off; _e L_ and _d k_ are made two and a half
inches; as also _f m_ and _g n_; _k_ 10 and _m_ 11 are made six or seven
inches, and joined to _d_ and _f_ by a curve, abrupt at first, but
afterwards more gentle. The distances, 5 _a_ and 6 _b_ must be such that
_a_ 9 is three and one eighth inches, (depending upon the breadth of
rail base,) _o m″_ is from three to four inches. At the other end of the
frog _e h_ must be enough to make _s t_ at least an inch, when _e h_ and
_i g_ are from three to four inches; _i m′_ being, as at the other end,
three or four inches. The steel plates N N are one half inch in
thickness. The surface, N, is two inches above the bottom, M. The lower
plate, M, is two inches thick. A B, C D, and E F are six or seven inches
wide, and one inch thick. The spike holes 11/16 square, the spike being
one half inch. The sharp edges, _i g_, _e h_, _a c_, _b c_, should be
rounded off to fit the wheel at A, fig. 142 A. The surface of the tongue
N 9 should be formed to a double incline to fit the wheel cone.

  NOTE.—Fig. 142 A gives the shape and dimensions of the largest
  tires.

Another method of making a frog is to cut and weld the rails _a_ and _b_
of the track, as in fig. 143. The continuations of these rails are bent
as shown in the figure.

[Illustration: Fig. 143.]

The whole angle is placed upon a firm wooden bearing.

There is no weaker part of the track than the frog. To make up the
strength at such places a heavy longitudinal timber twelve feet long
will answer a good end.


                               SWITCHES.

291. The object of the switch is to adjust a single line of rails to two
or more pairs, so that any two lines may be made continuous. The form in
general use consists of two rails, as at _a b_, _a b_, fig. 144, moving
upon _a_ and _a_ as centres. Here the tangent point of the turnout curve
is at _c_. The data given for the switch are the length of switch rail
and the motion at the toe (_c_) (which determine the direction of the
starting tangent) and the radius of curvature of the turnout curve. The
required elements are, the angle of frog at _b_ and the distance from
_a_ to the point of the frog.

[Illustration: Fig. 144.]

The following formula and table are by Josiah Hunt, Esq., (at present
chief engineer of the Hannibal and St. Joseph Railroad, Mo.). The
formula was first published in Appleton’s Mechanics’ Magazine, vol. 1,
p. 575.

   _D_ = 2(_g_ – _s_) × (cot. _S_ × cot. _F_)/(cot. _S_ + cot. _F_).

                      Where _S_ = angle of switch.
                            _F_ = angle of frog.
                            _s_ = the movement.
                            _g_ = the gauge.

_Example._—How far from the toe of the switch is the point of the frog,
the gauge being 4′ 8½″, the rail twenty feet long, and moving five
inches; the frog being six feet long, six inches wide across the head,
and three inches at the mouth?

We have

   _D_ = 2(4.708 – .417) × (240/5 + 72/(6 + 3))/(240/5 + 72/(6 + 3))

           or, _D_ = 8.582 × (48 × 8)/(48 + 8) = 58.85 feet.

In laying the rails, the distance from the point to the end of the frog
(towards the switch) is to be taken from the above.

Table showing the distance between the frog and switch, gauge 4′ 8½″,
movement of switch-rail five inches. Frog six inches across head, and
three inches at mouth. Main track being straight.

            ┌───────────────┬─────────────────────────────┐
            │Length of frog.│   LENGTH OF SWITCH RAIL.    │
            ├───────────────┼────┬────┬────┬────┬────┬────┤
            │               │ 12 │ 14 │ 16 │ 18 │ 20 │ 22 │
            ├───────────────┼────┼────┼────┼────┼────┼────┤
            │       3       │29.1│29.7│30.1│30.4│30.7│30.9│
            │      3½       │33.3│34.0│34.5│35.0│35.3│35.6│
            │       4       │37.3│38.2│38.8│39.4│39.8│40.2│
            │      4½       │41.1│42.2│43.0│43.7│44.3│44.7│
            │       5       │44.8│46.1│47.1│47.9│48.5│49.1│
            │      5½       │48.3│49.8│51.0│51.9│52.7│53.2│
            │       6       │51.7│53.4│54.8│55.9│56.8│57.6│
            │      6½       │55.0│56.9│58.5│59.8│60.8│61.7│
            │       7       │58.1│60.3│62.1│63.4│64.7│65.7│
            │      7½       │61.2│63.6│65.6│67.2│68.5│69.6│
            └───────────────┴────┴────┴────┴────┴────┴────┘

292. When the switch rail is short, the angle between the main line and
the switch rail, when switched, is considerable; and causes quite a
shock to the passing engine. The switch shown in fig. 145 remedies the
evil, makes the machinery compact, and the calculation simple. The
tangent point of the turnout curve is at _n n_ (the usual heel). In
place of adjusting the single to the double line of rails, the double is
adjusted to the single line. The data given are the gauge and radius of
curve; and as before, the elements required the frog angle and distance
from switch to frog point.

[Illustration: Fig. 145.]

Now

              Rad.^2 – (Rad. _less_ gauge)^2 = distance^2,

                   or _R^2_ – (_R_ – _g_)^2 = _D^2_,

                  and _D_ = √(_R^2_ – (_R_ – _g_)^2).

The angle of frog is also

            Sin angle of frog = (Sin 90 log _D_)/(log _R_).

The length of this switch rail depends upon the radius of curvature. The
distance between the two rails at S must be enough to admit the wheel
flange, that is, at least two inches.

Let A B, fig. 146, be the straight rail; E D the curved one. Draw G H
parallel with and two inches distant from the inner edge of A B. No
point of the curved rail must fall within G H; whence E is the
turning-point, and E D the length, found as follows.

Let _R_ equal the radius of curve to outside of outer rail; _d_ equal
two inches plus width of rail, or _i e_, and _D_ equal _D E_.

Then

                    _D_ = √(_R^2_ – (_R_ – _d_)^2).

[Illustration: Fig. 146.]

_Example._—Let the radius of outer rail be five hundred feet, and the
gauge five feet. We have, then, the distance

          (A.) _D_ = √(500^2 – 495^2) = 72 feet, very nearly.

            Also, Sin _E C D_ = (Sin 90 log _D_)/(log _R_),

              (B.) or (Sin 90 log 72)/(log 500) = 8° 17′,

and the length of switch

              (C.) √(500^2 – 499.65^2) = 18¾ feet nearly.

Five hundred feet is, therefore, about the longest radius for which such
switches should be used.


                         SIDINGS AND CROSSINGS.

Crossings occur where two tracks cross, and consist of four frogs, with
the corresponding guard rails, as in fig. 147.

[Illustration: Fig. 147.]


                    ELEVATION OF THE EXTERIOR RAIL.

293. The motion of a train of cars around a curve is accompanied by a
tangential force, depending in amount upon the velocity of the train and
the radius of curvature. This force tends to throw the cars from the
track; and is counteracted by elevating the exterior rail.

The centrifugal force of any body in motion in a curved line is shown by
the formula

                           (_WV^2_)/(32_R_).

               Where _W_ is the weight in lbs.
                     _V_ the velocity in feet per second.
                     _R_ the radius of curvature,
                and 32 the accelerating force of gravity.

The force tending to throw the car from the rail is not _centrifugal_
but _tangential_, but it matters not whether the body is kept in
position by _tension_ upon the _inside_ or by _compression_ on the
_outside_; the amount of the force is the same.

[Illustration: Fig. 148.]

The horizontal projection of the centre of gravity of the car, when at
rest, is at _c_, fig. 148, and when in motion the direction of the
weight should be _a b_; and the inclination, _c′ a′ b′_, must be such
that _a b_ will be perpendicular to _c′ a′_; to effect which, _c′ b′_
should be to _a′ b′_ as the weight to the tangential force; or _E_ being
the elevation of the rail, _g_ the gauge, _W_ the weight, and _c_ the
tangential force; we have

                         _E_ : _g_ :: _c_ : _W_,


          or _E_ = (_cg_)/_W_, and _c_ being = (_WV^2_)/(32_R_);

 finally  _E_ = ((_WV^2_)/(32_R_))_g_/_W_ or (_V^2__g_)/(32_R_) = _E_.

       Where _W_ = weight of a car.
             _V_ = speed of train in feet per second.
             _g_ = gauge of road.
             _R_ = radius of curve.
             _E_ = elevation of outer rail in feet and decimals.

_g_ and _R_ are the only fixed quantities in the formula; and the
average weight and speed of a car must be assumed.

Examination of the formula shows how important it is that all trains
should run at such a velocity as to demand the same elevation of rail.
The absolute elevation must be arranged to meet the requirement of the
fastest trains; and other trains must conform, even at a disadvantage.

  NOTE.—The subject of the mechanics of traversing railroad curves, is
  yet quite in the dark. The action of the train, as caused by its own
  momentum, is _tangential_; while the action of the engine tends to
  pull the cars against the _inner_ rail, being _opposed_ to the first
  motion. This might require a reduction of the elevation given by the
  formula when the engine is exerting a strong tractive power, but
  when running without steam the full elevation is needed, (see
  chapter III.)

[Illustration: Fig. 149.]

In laying and maintaining the rails to the proper elevation, a
clinometer attached to a rail gauge, as in fig. 149, answers a good end:
the small arc being graduated according to the different elevations
required by curves of different radii. Thus the index of the level being
placed at 2°, when the rails are fitted to A and B, the elevation is
correct for a 2° curve; or for a curve of 2,865 feet radius.

The difference in gauge of one foot makes a difference in the elevation
of but 0.009 feet, or about ⅒ of an inch.

The following table is calculated for the average of the different
gauges in use, thus,—

                                        4.7
                                        5.0
                                        5.5
                                        6.0
                                     ——————
                                     4)21.2
                                     ——————
                      Average gauge,    5.3 feet.


                    TABLE OF ELEVATION OF OUTER RAIL.

 ┌───────────────┬─────────────────────────────────────────────────────┐
 │Radius of curve│  ELEVATION OF OUTER RAIL IN FEET AND DECIMALS, THE  │
 │in feet, being │          VELOCITY IN MILES PER HOUR BEING           │
 ├───────────────┼────────┬────────┬────────┬────────┬────────┬────────┤
 │               │  10.   │  15.   │  20.   │  25.   │  30.   │  40.   │
 ├───────────────┼────────┼────────┼────────┼────────┼────────┼────────┤
 │            250│  .130  │        │        │        │        │        │
 │            500│  .070  │        │        │        │        │        │
 │          1,000│  .037  │  .079  │        │        │        │        │
 │          2,000│  .018  │  .040  │  .074  │  .111  │        │        │
 │          3,000│  .013  │  .026  │  .048  │  .074  │  .106  │        │
 │          4,000│  .009  │  .020  │  .037  │  .058  │  .079  │  .154  │
 │          5,000│  .007  │  .016  │  .031  │  .045  │  .065  │  .119  │
 │          6,000│  .006  │  .013  │  .024  │  .037  │  .053  │  .095  │
 │          7,000│  .005  │  .011  │  .021  │  .033  │  .046  │  .086  │
 │          8,000│  .004  │  .010  │  .018  │  .029  │  .039  │  .077  │
 │         10,000│  .003  │  .008  │  .010  │  .022  │  .032  │  .059  │
 └───────────────┴────────┴────────┴────────┴────────┴────────┴────────┘




                              CHAPTER XIV.
                               EQUIPMENT.


                                PART I.
                              LOCOMOTIVES.

As the locomotive engine is the power by which railroads are worked, and
as its proportions and dimensions are so intimately connected with the
physical character of the road, it is thought proper to take space
enough at this point to examine the general principles of its
construction, and of its adaptation to the work required of it upon
railroads.

Under the general principles, we recognize the production and
consumption of steam, the disposition of weight upon the several pairs
of wheels which shall secure the necessary adhesion, the application of
the power generated in the boiler to the moving of the wheels, and that
general arrangement of parts which shall render the use of power
economical.


                  BIRTH AND GROWTH OF THE LOCOMOTIVE.

294. The first idea of the application of steam to locomotion, is due to
the unfortunate Solomon de Caus, of Normandy (France), who was confined
in a madhouse for insisting that steam could be made to move wheeled
carriages.

295. In the year 1784, William Murdoch, the friend and assistant of
James Watt, built a non-condensing steam locomotive engine, on a scale
of about one inch per foot, having

                          Cylinders, ¾ × 2 inches,
                          Wheels,    9½ inches,
                      and Weight,    10 lbs.

This little engine, however, accomplished the speed of ten miles per
hour.

296. In 1802, Richard Trevethick patented the application of the
non-condensing steam-engine to the propelling of carriages on railroads;
his engine was fitted with one horizontal cylinder, which applied its
power to the wheels by means of spur gear.

297. In 1825, the truck was first applied, to relieve the driving wheels
of a part of the weight, and to enable the engine to pass freely around
curves.

298. In 1827, Timothy Hackworth applied the blast pipe, for the purpose
of draft. He applied, also, spring balances to the safety-valves, and
used the waste steam to heat the feed water. This engine drew one
hundred tons, at five miles per hour, and forty-five tons on a fifty
feet grade.

299. In 1828, M. Seguin (France) introduced the multitubular boiler.

300. In 1829, the directors of the Liverpool and Manchester Railroad
offered a premium for the best locomotive, which should draw three times
its own weight, at ten miles miles per hour. The “Rocket,” by Robert
Stephenson, of Newcastle on Tyne, was the successful competitor, and
drew the load required, seventy miles, at an average speed of 13.8 miles
per hour; its maximum velocity was twenty-nine miles per hour; it
evaporated 5.4 lbs. of water per pound of coke, and 18.24 cubic feet per
hour of water.

301. From 1830 to 1840, the changes that were made were rather those of
dimension, proportion, and arrangement, than of essential elements of
steam producing.

302. In 1840, several truck frame engines were sent to England from the
Norris Works of Philadelphia. These locomotives would draw a load of one
hundred and twenty tons over a sixteen feet grade, at the rate of twenty
miles per hour.

303. In 1845, the Great Western Railroad, of England, was supplied with
an engine of twenty-two tons weight, having cylinders 15¾ × 18, wheels 7
feet, heating surface 829 square feet. This locomotive carried
seventy-six and one half tons at a velocity of fifty-nine miles per
hour. The consumption of coke was 35.3 lbs. per mile, and of water,
201.5 cubic feet per hour.


                    THE ENGLISH LOCOMOTIVE OF 1850.

304. The “_ne plus ultra_” for the seven feet gauge (Great Western
Railway) by Gooch, has inside cylinders 18 × 24 inches, one pair of
eight feet driving wheels, grate area twenty-one square feet. Fire-box
surface, one hundred and fifty-three feet. Three hundred and five two
inch tubes, giving 1,799 feet of surface. Total heating surface, 1,952
square feet. Weight of engine, empty, thirty-one tons; of tender, eight
and one half tons; whole weight with wood and water, fifty tons.
Evaporating power, three hundred cubic feet of water per hour. This
engine can draw two hundred and thirty-six tons, at forty miles per
hour.

The maximum for the London and North-western Railroad, four feet, eight
and one half inches gauge (Crampton’s patent), has cylinders 18 × 24
inches; wheels, eight feet; two hundred two and three sixteenths inch
(outside diameter) tubes; grate, twenty-one and one half square feet;
fire surface, one hundred and fifty-four feet; tube surface, 2,136 feet;
whole heating surface, 2,290 square feet; weight, loaded, thirty-five
tons; twelve tons upon driving wheels; tender, twenty-one tons, loaded;
whole weight, fifty-six tons.


                    THE AMERICAN LOCOMOTIVE OF 1855.

305. The engine “Charles Ellet, Jr.,” drew on the 9th of August, 1854,
forty tons, over a grade of two hundred and seventy-five feet per mile,
and over grades of two hundred and thirty-eight feet, upon curves of
three hundred feet radius. This engine has wheels four and one half feet
in diameter coupled seven feet apart; cylinders 14 × 26 inches; and
weighs, including wood and water, 53,058 lbs. This is a tank locomotive,
the tender is dispensed with, and in its room a tank containing one
hundred cubic feet of water, and one cord of wood is used. This engine
was built by Richard Norris and Son.

An engine built by the Cuyahoga Steam Furnace Co. of Cleveland, Ohio,
performed the following feat.

An ordinary passenger train was carried one hundred and one miles, over
a total ascent of 1,255 feet of grades, making twenty stops, at an
average speed of twenty-five miles per hour, with a consumption of only
ninety cubic feet of wood.

The same engine drew an average load of three and one third cars four
hundred and thirty miles, making seventy-five stops, surmounting a total
ascent of 5,439 feet, averaging twenty-five miles per hour, with one
tender full of wood only.

In the months of July and August, 1856, two engines upon the Pacific
Railroad (Missouri), one by R. K. and G., and one by Palm & Robertson,
ran each one hundred and twenty-five miles, with three passenger and one
baggage cars, using only one cord of wood.

  NOTE.—For an interesting example of what can be done by the American
  locomotive, and an illustration of engineering peculiarly American,
  the reader is referred to a description of the “Mountain top track”
  at the Rock-fish Gap crossing of the Blue Ridge (Va.), by the
  Virginia Central Railroad, given by the engineer under whose
  direction the work was proposed and executed (Charles Ellet, Esq.),
  from which is extracted the following:—

  “The eastern slope is 12,500 feet long, and rises 610 feet; the
  average grade being 2574/10 feet, and the maximum 29568/100 feet per
  mile. The least radius of curvature 234 feet; upon which curve the
  grade is 2376/10 feet per mile. The western slope is 10,650 feet
  long, and falls 450 feet; the average grade being 223⅒, and the
  range 27984/100 feet per mile.

  “The engines, which have taken loads ranging from twenty-five to
  fifty tons up one slope at seven and one half miles per hour, and
  down the opposite one at six miles per hour, making four trips of
  eight miles per day for three years, were designed and built by M.
  W. Baldwin & Co., Philadelphia, and have three pair of forty-two
  inch wheels all coupled, the flange base being 9′ 4″, cylinders 16½
  × 20 inches, weigh, with wood and water, 55,000 lbs., or
  twenty-seven and one half tons. They run without a tender, the
  engine carrying its own feed; thus gaining the double advantage of
  increasing the adhesion of the engine, and avoiding the resistance
  of a tender.”


                          GENERAL DESCRIPTION.

306. The locomotive is a non-condensing, high pressure engine, working
at a greater or less degree of expansion, according to the labor to be
performed, and placed upon wheels which are so connected with the
piston, that any motion of the latter is communicated to the former, by
which the whole is moved.

The power exerted in the cylinder and referred to the circumference of
the driving wheel, is called _traction_; its amount depends upon the
cylinder diameter and steam pressure, upon the diameter of wheel and
stroke, this latter being the distance between the wheel centre and
point of application of power.

The means by which the “traction” is rendered available for moving the
engine and its load, is the resistance which the wheel offers to
slipping on the rail, or its bite, and is called adhesion; it is
directly as the weight applied to the wheels, but depends also upon the
state of the rails. It varies from nothing, when there is ice on the
rail, to one fifth of the weight upon the driving wheels when the rail
is clean and dry, and in some cases has reached as high as nearly one
third. It should be enough to resist the maximum force of traction, that
is, the wheel should not slip when the engine is doing its greatest
work.

_Steam producing_, _Traction_, and _Adhesion_, are the three elements
which determine the ability of an engine to perform work. The
proportions and dimensions of the machine depend upon the duty required
of it; sufficient adhesion for a required effect should be obtained
rather by a proper _distribution_, than by _increase_ of weight.

Fig. 150 shows the relative position of parts in the locomotive engine
as at present constructed in America.

 1 2,         Grate upon which the fuel is placed.
 1 2 3 4,     Interior fire-box.
 5 6,         Exterior fire-box.
 7 7 8 8,     Shell of the boiler.
 9 9,         Boiler flues.
 10 11 12 13, Exhaust chamber, or smoke box.
 14,          Steam dome, entrance to steam pipe.
 15,          Steam pipe.
 16,          Piston.
 18,          Piston rod.
 19,          Connecting rod.
 20,          Crank.
 21,          Driving wheel.
 22,          Blast pipe.
 23,          Chimney.
 27 28,       Leading wheels, supporting the front end of the engine,
                turning on a swivel, 29.
 30,          “Blow off” safety-valve.

[Illustration: Fig. 150.]

307. The operation of generating and applying steam for the production
of motion is as follows:—

The boiler and the space between the two fire-boxes being filled with
water, (high enough at least to cover the flues and the top of the inner
box,) fire is applied to the fuel placed upon the grate; the heat which
fills the fire-box and tubes, is communicated to the water and converts
the same to steam; which entering the mouth of the pipe, 15, flows to
the cylinder, where it forces the piston to the end of the stroke. This
motion is transferred through the connecting rods and cranks to the
wheels, which revolving, move the engine upon the rails. At the same
time the eccentrics, placed upon the driving axle, give a motion to the
valve gear, and thence to the valves, by which the admission of steam is
stopped at the first end of the cylinder, and commenced at the other.
The volume of steam which entered during the first half stroke is forced
out of the cylinder by the returning piston, up the blast pipe, and out
at the chimney, where a vacuum is produced, which can be supplied with
air only from the chamber 10 11 12 13; after a few strokes the air is
exhausted from the _chamber_, which can be refilled only by the external
air _drawn through the fuel, furnace, and tubes_. The more complete this
vacuum, the stronger the current of air drawn through the fire, which
(current) is the draft. The admission of fresh air is regulated by a
damper placed at 2. The fuel is placed upon the grate by means of a door
in the rear of the fire-box. The necessary height of water is maintained
in the boiler by pumps worked by the engine, in such a manner as to
secure at all times the proper supply. The proportions and dimensions of
the boiler, the engine, and the carriage, with the rules for obtaining
the same will be considered shortly.


                 DUTIES EXPECTED OF LOCOMOTIVE ENGINES.

308. The work required of any engine depends upon the nature and amount
of traffic, and upon the physical character of the road.

The nature of the traffic, whether bulky or compact, and whether
requiring quick or slow transport, determines somewhat the number and
size of the trains, and consequently the number and power of the
engines.

A road with steep grades and sharp curves, with the same amount of
traffic, will need stronger engines than a road with easy grades and
large curves.

The amount of motive power and cost of working it, depends in a great
degree upon the disposition of grades as regards the direction of the
traffic movement. The most economically worked road will be either a
level one, or one where the bulk of the traffic is moved _down_ hill.

The mineral, commercial, or agricultural nature of the country,
determines the direction of the traffic, and the physical nature, the
arrangement of the grades.

The different kinds of labor required of locomotives, necessitate the
employment of engines of different proportions; and the different
classes of railways, require engines possessing different amounts of
power.

309. The classification of locomotives should be determined according to
the following relations.

               _Department_ depends upon commercial duty.
               _Division_ depends upon character of road.
               _Order_ depends upon weight of trains.
               _Class_ depends upon speed of trains.

  NOTE.—The general classification is given at the end of this
  chapter.

High rates of speed are generally combined with light loads, and heavy
trains are required to move at the lower velocities.

Great speeds require the rapid production and consumption of a large
bulk of steam of but little density; large wheels and short stroke, that
the ratio of velocities of piston and wheel may be as great as possible.

Heavy trains consume less steam by bulk, per mile, but of a much greater
density, and combine a long stroke with a small wheel, by which great
leverage is obtained.

In general, engines for winter use should be heavier than those for
summer, upon the same ground, as natural causes are more liable to
resist adhesion in the winter.

The locomotive engine may be so proportioned as to run at any speed from
ten to sixty miles per hour, over grades from ten to two hundred feet
per mile, and to carry loads from two hundred to two thousand tons.

The rules by which the necessary dimensions to perform any required duty
are fixed, depend upon the very simplest mechanical laws.

  NOTE.—The formulæ expressing the most proper relations to exist
  between the several steam-producing and steam-consuming parts are
  more reliable than the assertions of any machinist in America, and
  though taken from books, are the result of the experience of the
  most able and practical men for twenty years. Operatives are too apt
  to despise book knowledge, forgetting that the very knowledge so
  despised is the result of more practice than a lifetime can afford
  them. Railroad managers are too apt to receive as indisputable, the
  opinions of men who are _practical_, simply because they understand
  nothing of _principle_.

  Since the work of D. K. Clark (England) has appeared, any dimension
  from the beginning to the end of a locomotive may be fixed, to the
  eighth of an inch, with absolute correctness, and there is no excuse
  for departing from the proper proportions. It does not follow that
  because a locomotive does actually start off and draw the train,
  that it is properly made. A race-horse can draw a plough, and a yoke
  of oxen a “trotting buggy,” but this is by no means the correct
  adaptation of power.

310. The elements which govern the requirements of power are

                        The maximum grades.
                        The weight of the train.
                        The required speed.

And the elements which govern our ability to produce the power needed,

                    The grate area.
                    The heating surface.
                    The cylinder diameter.
                    The steam pressure.
                    The stroke.
                    The diameter of wheels.
                    The weight upon driving wheels.


  MECHANICAL AND PHYSICAL PRINCIPLES GOVERNING THE CONSTRUCTION OF THE
                           LOCOMOTIVE ENGINE.


              RESISTANCE TO THE MOTION OF RAILROAD TRAINS.

311. The exact resistance to the motion of a railroad train cannot be
determined, as some of the elements are so variable; for example, the
state of the weather. An approximate estimate, near enough for practice,
is easily obtained. To arrive at correct data the observations must be
made upon trains working under the same conditions that they are subject
to in practice.

The whole resistance is made up of several partial resistances, some of
which are constant at all speeds, and some of which increase with the
velocity.

The engine and tender resistance is composed of the friction of pistons,
cross heads, slide valves, cranks, eccentrics, pumps, the back pressure
of the blast, and various erratic movements, rolling, twisting, and
pitching together with both wheel and axle friction, which is common to
the engine and tender.

The atmospheric resistance is not due to the direct action of the air
upon the front and sides of the train entirely, but chiefly to the
exhausting action in the rear. The train has, as it were, to pull along
a large column of air like the water in the wake of a ship; form or
amount of frontage has little or no effect. The resistance depends upon
the bulk of the train and its velocity. A train with the same frontage
offers more resistance as its bulk increases.

Oscillatory resistance is caused by irregularities in the surface of the
rails, and increases with the velocity, and also with increase of height
of the centre of gravity of the car or engine.

Frictional resistance may be divided into wheel and axle friction. That
of the axle is composed of two parts, the direct vertical friction on
the journal, and the side friction on the collar, consequent upon
lateral motion. The vertical friction is independent of the surface
pressed or of velocity, but is directly proportional to the pressure,
and the same remark applies to that of the collars. As the diameter of
wheel increases, the oscillation is increased, the centre of gravity
being raised. The direct cause of the vertical friction is the weight of
the car or engine, and of the lateral irregularities in the surface of
the rails, which cause the car to sway from side to side. Wheel friction
which acts between the periphery of the wheel and the surface of the
rail increases with the load, and decreases as the wheel diameter
augments.

For the total resistance to the motion of a railroad train, D. K. Clark
gives the following formula:—

                         (_V^2_)/171 + 8 = _R_,

              Where _R_ is the resistance in lbs. per ton,
                and _V_ the velocity in miles per hour.

From this expression we form the following table:—

        Velocity in miles per hour. Resistance in lbs. per ton.
                                 10                       8.585
                                 12                       8.842
                                 15                       9.315
                                 20                      10.339
                                 25                      11.655
                                 30                      13.263
                                 40                      17.356
                                 50                      22.620
                                 60                      29.052
                                100                      66.480

From a great number of experiments made by Mr. Clark, the relative
resistance to the motion of inside and outside connected engines is as
follows:—

                         Inside connections  17
                         Outside connections 14

The effect of curves, bad state of the road, and adverse winds, amounts
(according to the same author) to the following percentages:—

                     Bad state of the road      40
                     Curves                     20
                     Strong head and side winds 20
                                                —
                     In all                     80


The resistance due to grades depends entirely upon the rate of incline,
and is quite independent of all other considerations. The _relative_
effect of grades decreases with the absolute increase of resistance on a
level. Thus common roads admit of steeper grades than do railroads,
because the level resistance is much more upon the former than on the
latter.

The exact determination of the resistance due to any grade depends upon
the very simple mechanical principle, regulating motion upon the
inclined plane. For each foot rise of grade per mile, the resistance per
ton is

                             2240 × 1/5280.

Thus the resistance to one ton upon a forty feet grade is

                       2240 × 40/5280 or 17 lbs.

And if we are moving at thirty miles per hour the sum of all other
resistances is, by the formula, or the table at the end of Chapter XIV.,
part I., 13.3 lbs. per ton; whence the whole resistance to the motion of
one ton, at thirty miles per hour, upon a forty feet grade, is

                         17 + 13.3 or 30.3 lbs.

and one hundred tons would be one hundred times as much. Table 1, at the
end of Chapter XIV., part I., gives the whole resistance to the motion
of trains of from fifty to one thousand tons, moving at speeds varying
from ten to one hundred miles per hour, and table 2 gives the resistance
upon grades from ten to one hundred feet per mile.


                         TRACTION AND ADHESION.

312. The whole steam pressure upon both pistons, referred by means of
the crank, connecting, and piston rods, and wheel, to the rail, is
called “traction.” It is the _drawing_ power of the engine. Its amount
depends upon the diameter of cylinder, steam pressure, stroke, and
diameter of wheel.

By increasing the steam pressure, we increase the power. By increasing
the cylinder diameter, we increase the power. By increasing the stroke,
we increase the power. By decreasing the wheel diameter, we increase the
power. And by adjusting the dimensions of the above parts, we may give
any desired amount of power to the engine.

The formula expressing the tractive power of an engine, of any
dimensions, is

                        ((2_A_) _P_ × 2_S_)/_C_.

      Where _A_ = the area of one piston.
            _P_ = the steam pressure in cylinder per square inch,
            _S_ = the stroke in inches.
            _C_ = the circumference of the wheel in inches.

The formula is expressed verbally as follows: Double the stroke and
multiply it by the total steam pressure on both pistons; divide the
product by the circumference of the driving-wheel in inches.


                               ADHESION.

313. As observed on page 307, the adhesion or the bite of the wheels
upon the rail is, as an average, from one fifth to one sixth of the
weight; one fifth when the rail is in a good state, and less when wet or
greasy; we cannot depend upon more than one sixth in practice.
Therefore, if the tractive power of an engine is 3,000 lbs. we must, to
make it available, place 3,000 × 6 or 18,000 lbs. upon those wheels
which are connected with the machinery, (driving wheels).


                                 FUEL.

314. The fuels employed in the locomotive engine for the evaporation of
water are wood, coal, and coke. In England the latter is used
exclusively. In America the first has, on account of its cheapness, been
quite generally adopted; but of late railroad companies have been
turning their attention to coal and coke.

The immense beds of coal distributed throughout the United States will
furnish fuel to railroad companies almost without limit. Its position as
well as its amount will render its adoption practicable in nearly all of
the States. Ohio alone contains more coal than all of Great Britain. The
following table is from the iron manufacture of Frederick Overman.

           Name of State.        Area of Coal-fields.
           Georgia                         150 square miles.
           Maryland                        550 square miles.
           Alabama                       3,400 square miles.
           Tennessee                     4,300 square miles.
           Michigan                      5,000 square miles.
           Missouri                      6,000 square miles.
           Indiana                       7,700 square miles.
           Ohio                         11,900 square miles.
           Kentucky                     13,500 square miles.
           Pennsylvania                 15,437 square miles.
           Virginia                     21,195 square miles.
           Illinois                     44,000 square miles.
                                       ———————
           In all                      133,132 square miles.

315. The following table (also from the works of Overman) gives the
nature and evaporative power of the different American coals.

 ┌────────────────────┬──────┬──────────┬──────────┬────────┬──────────┐
 │                    │State │          │ Steam of │Quantity│Percentage│
 │   Name of Coal.    │where │Percentage│   212°   │of heat │of coke by│
 │                    │found.│of carbon.│evaporated│   by   │ weight.  │
 │                    │      │          │ per lb.  │volume. │          │
 ├────────────────────┼──────┼──────────┼──────────┼────────┼──────────┤
 │                    │      │          │          │        │          │
 │   _Anthracite._    │      │          │          │        │          │
 │Beaver Meadow,      │ Pa.  │   88.9   │      10.4│   94   │          │
 │Forest Improvement, │ Pa.  │   90.7   │      10.8│   94   │          │
 │Lehigh,             │ Pa.  │   89.1   │       9.6│   94   │          │
 │Lackawanna,         │ Pa.  │   87.7   │      10.7│   94   │          │
 │                    │      │          │          │        │          │
 │      _Coke._       │      │          │          │        │          │
 │Midlothian,         │ Va.  │          │      10.3│   92   │   .66    │
 │Cumberland,         │ Md.  │          │      10.3│   92   │   .75    │
 │                    │      │          │          │        │          │
 │   _Bituminous._    │      │          │          │        │          │
 │Maryland,           │ Md.  │   73.5   │      11.2│   85   │          │
 │Cumberland,         │ Md.  │   74.3   │      11.0│   85   │          │
 │Blossburg,          │ Pa.  │   73.4   │      10.9│   85   │   .83    │
 │Karthans,           │ Pa.  │   73.8   │       9.8│   85   │   .88    │
 │Cambria County,     │ Pa.  │   69.4   │      10.2│   85   │          │
 │Clover Hill,        │ Va.  │   56.8   │       8.5│   85   │   .68    │
 │Tippecanoe,         │ Va.  │   64.6   │       8.5│   85   │          │
 │Pittsburgh,         │ Pa.  │   55.0   │       8.9│   85   │   .68    │
 │Missouri,           │ Mo.  │          │          │        │   .57    │
 └────────────────────┴──────┴──────────┴──────────┴────────┴──────────┘

316. The employment of the several varieties of wood depends more upon
the commercial than the chemical character. The following table shows
the specific gravity, the nature and the evaporative value of the
different species.

 ┌────────────┬────────┬────────┬────────┬──────────┬────────────┐
 │  Species.  │Specific│Specific│Specific│Degrees of│  Species.  │
 │            │gravity │gravity │gravity │heat which│            │
 │            │ green. │  air   │  kiln  │  may be  │            │
 │            │        │ dried. │ dried. │generated.│            │
 │            │        │        │        │          │            │
 ├────────────┼────────┼────────┼────────┼──────────┼────────────┤
 │Hickory,    │        │        │        │   3000   │Hickory.    │
 │White Oak,  │  1.07  │  0.71  │  0.66  │   3000   │White Oak.  │
 │Black Oak,  │        │        │        │   3000   │Black Oak.  │
 │Red Oak,    │  1.05  │  0.68  │  0.66  │   3000   │Red Oak.    │
 │Beech,      │  0.98  │  0.59  │  0.58  │   3000   │Beech.      │
 │Birch,      │  0.90  │  0.63  │  0.57  │   3000   │Birch.      │
 │Maple,      │  0.90  │  0.64  │  0.61  │   3000   │Maple.      │
 │Yellow Pine,│        │        │        │   2800   │Yellow Pine.│
 │Chestnut,   │        │        │        │   3000   │Chestnut.   │
 │Pitch Pine, │        │        │        │   2800   │Pitch Pine. │
 │White Pine, │  0.87  │  0.47  │  0.38  │   2800   │White Pine. │
 ├────────────┼────────┼────────┼────────┼──────────┼────────────┤
 │  Species.  │Specific│Specific│Specific│Degrees of│  Species.  │
 │            │gravity │gravity │gravity │heat which│            │
 │            │ green. │  air   │  kiln  │  may be  │            │
 │            │        │ dried. │ dried. │generated.│            │
 │            │        │        │        │          │            │
 └────────────┴────────┴────────┴────────┴──────────┴────────────┘

 ┌────────────┬──────────┬────────┬──────┬────────┬────────────┐
 │  Species.  │Percentage│Quantity│Weight│Relative│  Species.  │
 │            │    of    │of heat │of one│value as│            │
 │            │Charcoal. │ as to  │ cord │ fuel.  │            │
 │            │          │volume. │  in  │        │            │
 │            │          │        │ lbs. │        │            │
 ├────────────┼──────────┼────────┼──────┼────────┼────────────┤
 │Hickory,    │  44.69   │   25   │ 4469 │  1.00  │Hickory.    │
 │White Oak,  │  21.62   │   25   │ 3821 │  0.81  │White Oak.  │
 │Black Oak,  │  23.80   │   25   │ 3254 │  0.71  │Black Oak.  │
 │Red Oak,    │  22.43   │   25   │ 3254 │  0.69  │Red Oak.    │
 │Beech,      │  32.36   │   25   │ 3236 │  0.65  │Beech.      │
 │Birch,      │          │   25   │      │        │Birch.      │
 │Maple,      │  27.00   │   25   │ 2700 │  0.57  │Maple.      │
 │Yellow Pine,│  24.63   │   23   │ 2463 │  0.54  │Yellow Pine.│
 │Chestnut,   │  25.25   │   25   │ 2333 │  0.52  │Chestnut.   │
 │Pitch Pine, │  19.04   │   23   │ 1904 │  0.43  │Pitch Pine. │
 │White Pine, │  18.68   │   23   │ 1868 │  0.42  │White Pine. │
 ├────────────┼──────────┼────────┼──────┼────────┼────────────┤
 │  Species.  │Percentage│Quantity│Weight│Relative│  Species.  │
 │            │    of    │of heat │of one│value as│            │
 │            │Charcoal. │ as to  │ cord │ fuel.  │            │
 │            │          │volume. │  in  │        │            │
 │            │          │        │ lbs. │        │            │
 └────────────┴──────────┴────────┴──────┴────────┴────────────┘

Of the relative value of wood and coal, we have the following results of
experience.

In the engines of the Baltimore and Ohio Railway 2.55 lbs. of pine wood
were found equal to one pound of Cumberland coal.

On the Reading Railroad (Pennsylvania), three pounds of pine wood equal
to one pound of Anthracite coal.

Mr. Haswell estimates the best varieties of wood fuel to contain twenty
per cent. of carbon.

Walter R. Johnson found that one pound of wood, upon an average,
evaporated two and one half pounds of water.

The average percentage of coke from American bituminous coal from the
above table is seventy-three per cent., and the average percentage of
carbon, sixty-seven and one half per cent.

317. The following table shows the relative properties of good coke,
coal, and wood.

 ┌───────────────────────────────────────────────────┬─────┬─────┬─────┐
 │                   Name of fuel.                   │Coke.│Coal.│Wood.│
 ├───────────────────────────────────────────────────┼─────┼─────┼─────┤
 │Weight per cubic foot, in lbs.                     │ 63  │ 80  │ 30  │
 │Degrees of heat generated.                         │4300 │4000 │2800 │
 │Percentage of carbon, in the fuel.                 │ 95  │ 88  │ 20  │
 │Economic bulk, or cubic feet required to stow one  │ 80  │ 44  │ 107 │
 │  ton.                                             │     │     │     │
 │Economic, or stowage weight per cubic foot.        │ 28  │ 51  │ 21  │
 │Cubic feet of air to evaporate one lb. of water.   │22.4 │ 32  │ 16  │
 │Equivalent economic bulk, to evaporate the same    │ 13  │ 10  │ 60  │
 │  weight of water.                                 │     │     │     │
 │Weight of water evaporated per lb.of fuel in       │ 8½  │  6  │ 2½  │
 │  ordinary practice.                               │     │     │     │
 │Relative value as fuel, disregarding the actual    │ 100 │ 71  │ 29  │
 │  cost.                                            │     │     │     │
 └───────────────────────────────────────────────────┴─────┴─────┴─────┘

The power of fuel depends upon the amount of carbon in it.

Pure coke is solid carbon.

Hence its superior value as a heat generator.


                       OF THE PROCESS OF COKING.

318. Anthracite coal is used for locomotive fuel in its natural state.
It is employed chiefly upon those roads on the eastern slope of the
Alleghanies. The bituminous coal lies in the Mississippi valley, and may
be found anywhere between the summits of the Alleghanies and the Rocky
Mountains. This, in its natural state, contains so much pitchy matter as
to render it unfit for locomotive purposes. Upon being heated, it melts,
runs into a mass, and clogs the grate; requiring frequent poking and a
strong draft. But when the bitumen is burnt off by slow and careful
baking, (as described below,) no fuel equals it.

Just as carbonized wood is charcoal, so carbonized coal is coke. Coke is
bituminous coal deprived of its bitumen, the raw coal being baked in
ovens having vents so regulated as to admit air enough to char, without
consuming the coal. The ovens being closed at the proper time, the fire
is gradually extinguished, and the coke, compacted into large masses,
requiring to be broken up before taken out. Coal may be coked by piling
loosely in heaps, covering with earth, and firing through openings,
which, after forty or fifty hours, are closed. In preparing coke,
however, in the large quantities required for railroads, and that it may
be of the very best quality, a good deal of care must be taken.

Probably in no place more or better coke is made, or the operation more
skilfully carried on, than at the Camden-town station of the London and
North-western Railroad, (England).

The company have built eighteen ovens, in two rows, all discharging
their volatile gases into a horizontal flue terminating in a chimney one
hundred and fifteen feet high; having an internal diameter of eleven
feet, and being three feet thick, (making the external diameter
seventeen feet). The ovens are elliptical, 11 × 12 feet inside, with
walls three feet thick. The height is ten feet, the first three feet
from the ground being solid, and furnished with a fire brick floor, on
which the coal is placed. Each oven communicates with the flue by an
opening in the top two and one half feet by twenty-one inches; which
opening is closed by an iron damper, to regulate the draft. The openings
for the doors are three and one half feet square outside, and two and
three fourths inside, being closed with iron doors four and one half by
five feet, lined with fire brick, and balanced in opening by
counterweights. (The object of the chimney and horizontal flue is to
carry the smoke and unburned gases so far up that they shall not be a
nuisance. In America we might allow the smoke of each oven to escape
through a low chimney of its own, (ten or twelve feet high,) and save
the cost of a large stack; like the coking ovens in our foundries).

The operation of coking is carried on as follows:—Each alternate oven is
charged between eight and ten A. M. every day, with three and one half
tons of good coals. A whisp of straw is then thrown in, which takes fire
from radiation from the top, and inflames the smoke then arising from
the surface, by the reaction of the hot sides and bottom upon the body
of the fuel. In this way the smoke is consumed at the very point of the
process, where it would otherwise be the most abundant. The coking
process is a complete combustion of the volatile principles of the coal.
The mass of coal being first kindled at the surface, where it is
supplied with an abundance of oxygen, because the doors in front and
vents in the rear are open, no more smoke goes from the chimney than
from that of a common kitchen fire. The gas generated from the slightly
heated coal cannot escape destruction in passing up to the bright flame
of the oven. Any deficiency in oxygen for consuming the smoke is
supplied by the air entering the grooves of the dampers.

As the coking process advances most slowly from the top to the bottom,
only one layer is consumed at a time; while the surface is covered with
red-hot cinders, ready to consume any particles of carburetted or
sulphuretted hydrogen gases which may escape from below. The greatest
mass cannot emit more gases than the smallest heap.

The coke being perfectly freed from all smoky and volatile matters, by a
calcination of forty hours, is cooled down to a moderate ignition by
sliding in the dampers and opening the doors, which had been partly
closed during the latter part of the operation.

The coal is now converted into a clean, crystalline, porous, columnar
mass, of a steel-gray color, and so hard as to cut glass. This is broken
up and taken out—coke. It is sometimes extinguished by a watering-pot.
This is wrong, it ought not to be wet, and even more, ought to be
immediately shut up in fire-proof boxes and bins. Even left to itself in
the air, it absorbs moisture rapidly, which must be burned off in the
boiler; it should by all means be kept in a dry place. Mr. Woods
(England) observes, that coke may absorb as much as eight per cent. of
water in going from the oven to the storehouse. The amount of absorption
depends upon the nature of the coke. D. K. Clark records the following,
the coke being immersed in water.

  No. 1. Close-grained and good, absorbed 14.5 per cent. of water.

  No. 2. Porous and ordinary, absorbed 21 per cent.

  No. 3. Very close-grained and good, 9 per cent.

The time of coking may be stated generally as fifty hours, though it is
somewhat improved by being allowed forty hours more; this gives time for
a better consolidation, and gives a firmer, brighter, and more
crystalline mass.

Mr. Gooch, of the Great Western (England) Railroad, experimented upon
the time of coking with the following results.

     In oven.      Yield per ton of  Water evaporated       Result.
                         coal.       per lb. of coke.
     48 hours         12.71 cwt.         7.1 lbs.            902.
     72 hours         12.00 cwt.         7.7 lbs.            924.

Thus, though the yield per ton is decreased by a greater time, the value
of the coke per pound is augmented, and the increase overbalances the
decrease.

Firstrate coal gives from seventy-five to eighty per cent. by weight, of
compact glistening coke, weighing about 14 cwt. per chaldron,
(thirty-six bushels). The bulk is increased from ten to fifty per cent.

In breaking out the coke from the ovens, a great deal is unavoidably
reduced too fine for use in the locomotive furnace under a strong draft;
such may, however, be used in firing up, in standing still, and at the
stations.

In taking the coke from the ovens it should be separated into the three
following classes.

              Large coke.  Cubes of 9 inches to the side.
              Medium coke. Cubes of 6 inches to the side.
              Small coke.  Cubes of 3 inches to the side.

Pittsburgh coal carefully coked for forty-eight hours, gives
seventy-five per cent., by weight, and one hundred twenty-five per cent.
by bulk, of firstrate, firm, bright, clean coke.

The best test for coke is to place it in water. Water, weighing
sixty-two and one half pounds per cubic foot, should not float good
coke, which ought to weigh sixty-three pounds per cubic foot, therefore
if the coke floats it is too light.

Much of the bituminous coal in the Mississippi valley does not coke, but
burns up. A large part cokes moderately well, but not so well as the
Pittsburgh coal. In estimating for a comparison of fuels, the particular
coal of any location must be tested.


           OF THE COMPARATIVE VALUE OF WOOD, COAL, AND COKE.

This question divides itself into two parts,

                 The relative cost of the different fuels,
             and The relative power to produce heat.

319. It does not follow that because coke in England, anthracite in
Pennsylvania, or wood in New England, is the most economical fuel, that
either of the above will be so in Ohio, Indiana, or Illinois, or because
wood is the cheapest in some parts of a State, that it is so throughout,
or even that one fuel should be applied to the whole length of a single
road.

The heat used to evaporate water in the locomotive boiler is developed
by combustion; combustion is produced by chemically combining the oxygen
of the air with the carbon of the fuel; whence, that material containing
in a given cost the largest amount of carbon will produce heat the most
economically.

From the table on page 320, we see that, by bulk, thirteen of coke are
equal to sixty of wood; that one pound of coke evaporates eight and one
half pounds of water; that one pound of wood will evaporate two and one
half pounds of water. Tables of specific gravity give as an average
weight per cubic foot of hard wood, thirty pounds. A cord of wood, by
very careful measurement, contains one hundred cubic feet _solid_, or
one hundred twenty-eight feet _as piled_, taking the average size of
wood; whence a cord will weigh three thousand pounds. And we have as the
relative evaporative efficiency of a cord of wood and a ton of coke,

                           2240 × 8½ = 19040,
                           3000 × 2½ =  7500.

Now if the cost of a cord of wood is to the price of a ton of coke as
7,500 to 19,040, it is immaterial which we use.

As an example of the use of the above proportion, when the absolute cost
of wood, coal, coke, and labor are known, take the following.

If wood, cut and ready for burning, costs $3.00 per cord, how much may
be given for a ton of coke?

           As 7,500 is to 19,040, so is 300 to 762, or $7.62.

From the same proportion we form the following table.

            Cost per cord of wood    Price that may be paid
             ready for burning.         per ton for coke.
                  (Cents.)                  (Cents.)
                     200                       508
                     225                       571
                     250                       635
                     275                       698
                     300                       762
                     325                       825
                     350                       877
                     375                       952
                     400                      1016
                     425                      1079
                     450                      1143
                     475                      1206
                     500                      1270

In the comparison above, the maximum evaporative power of wood has been
used, 2½ lbs., and the ordinary power of coke, 8½ lbs. of water per
pound of fuel.

320. In making coke in large quantities, the ovens should be at the
mines, as we thus save transporting the extra weight of coal over coke.

The cost of making coke, exclusive of the cost of the coal, is
approximately as follows:—

     10 ovens capable of making annually 5,000 tons of coke, $5,000
     Sheds, and apparatus to correspond,                      3,000
                                                             ——————
                             In all,                          8,000

           Annual interest at 6 per cent.,      480
           Annual cost of attendance, 2 men,  1,000
                                             ——————
           The sum of which is,              $1,480
           And the cost per ton,                    0.296/10

or in round numbers, thirty cents per ton; and if coal is $1.50 per ton,
adding twenty-five per cent. we have $1.87 as the cost of coal that will
make one ton of coke, to which add the cost of making per ton, thirty
cents, and we have as the whole cost of one ton of coke $2.17; and from
the rule on page 327 we see that wood must not cost over $0.85 per cord
to be as economical as coke at $2.17; of course inferior qualities of
coal will give less good coke and change the comparison.


                              COMBUSTION.

321. The combustible element in all fuels is carbon; the heat necessary
for steam producing, is obtained by combining the carbon of the fuel
with the oxygen of the air, forming carbonic acid gas.

Carbonic acid gas consists of

                        Oxygen     16} Parts by
                        Carbon      6} weight.

Atmospheric air consists of

                        Oxygen      8} Parts by
                        Nitrogen   28} weight.

Whence, for the combustion of one pound of carbon, we require

                              Carbon 1.00
                              Oxygen 2.66

But to obtain 2.66 of oxygen from the atmospheric air, we also use
nitrogen in the proportion of 28 nitrogen to 8 oxygen; whence, for
converting one pound of carbon to carbonic acid, we require

                Oxygen    2.66
                Nitrogen  9.31
                         —————
                Or       11.97 lbs. of atmospheric air.

From careful observations on the gases passing through the chimneys of
well-constructed boilers, oxygen is found free, varying in amount from
one quarter to one half of the quantity necessary for combustion; this
is owing to the mechanical obstructions to the perfect conversion of the
air arising from leakage through the fuel.

More than the above 11.97 lbs. of air should, therefore, be applied to
the fire for each pound of carbon consumed. Twenty-five per cent. is
found by experience to be a sufficient surplus allowance to convert the
carbon.

      Whence, to  11.97
      add          3.03
                  —————
      and we have 15.00 lbs. of atmospheric air per lb. of carbon.

Air weighs .075 lbs. per cubic foot, whence 15/.075 or 200 cubic feet of
air are necessary for the proper combustion of one lb. of pure carbon.

Knowing the necessary amount of air for one lb. of carbon, and also the
percentage of carbon in the different kinds of fuel, it becomes a simple
arithmetical operation to fix the bulk of air required for any species
of coal, coke, or wood. The result of such a calculation is shown in the
seventh column of the table on page 320.

“There are two causes why all the heat which fuel may furnish is not
obtained. First, that the inflammable gases evolved by the heat are not
all consumed from want of a sufficient supply of oxygen, the air drawn
through the fire being only sufficient to decompose more fuel than when
decomposed it could burn, or supply with oxygen. The thick smoke that
escapes from a chimney when fresh fuel is thrown on a hot fire, is
unconsumed gas; decomposed from the fuel, but without oxygen enough to
burn—although there may have been a sufficient supply of heat. From this
cause it is, perhaps, that flame is seen coming from the top of a
steamboat chimney which appears to be continuous from the furnace; but
which, in fact, is ignited by contact with the air, having retained
sufficient heat for that purpose.

“All smoke-consuming furnaces are simply means of admitting fresh air to
the unconsumed gases above the fire, which, in a common chimney, will
effect the object, as so large a mass of smoke retains the necessary
amount of heat. This only prevents the nuisance of smoke. To render the
gases thus reheated useful in evaporating water, this supply of oxygen
must be added while the gases are yet in the flues.” This might seem
difficult. Mr. McConnell (England) divides the flues of his locomotives
into two parts, connecting the front ends of the first part and the back
ends of the second part by a space of twelve or fifteen inches, (called
by him a ‘combustion chamber,’) into which he admits any required amount
of fresh air. (See appendix E.)

“A second cause why the full value of the fuel produced is not obtained
is, that so much is abstracted from the gases in passing through long
tubes, that there is not enough left to continue combustion, although
the inflammable gas is still there. That a tube or any substance in the
way of the hot gases does absorb the heat enough to prevent the burning
of the gas, is proved by the action of Davy’s Safety Lamp; this is a
common light surrounded by a wire gauze, which so absorbs the heat from
the flame as to extinguish the latter at the wire; by applying fire
above the gauze, the gas is again kindled, showing plainly that want of
heat above had quenched the flame.” See Stöckhardt’s Chemistry;
translation by C. H. Peirce, M. D., Cambridge, Mass., 1852, page 105.

We require, then, in every boiler, first, to have a sufficient supply of
oxygen to decompose the fuel; next, a quantity above the fire to consume
the produced gases; third, such an arrangement of communicating surface
that so much heat shall not be abstracted from the gases as to deaden
their combustion, until just as they are discharged, at which period
they ought to be consumed. (See appendix E.)


                          GENERATION OF STEAM.

322. The means of producing the power is of course of the first
importance.

The heat generated in the fire-box is conducted through the tubes to the
exhaust chamber; during which passage it is imparted to the metal, and
from thence absorbed by the adjacent water, which being thereby made
lighter, rises to the surface and gives place to a new supply. The duty
of the furnace is to _generate_, and of the tubes to _communicate_,
heat.

The power of a plain surface to generate steam, depends upon its
position and on the ability of the material to transmit heat An
experiment recorded in Clark’s Railway Machinery, gave the following
results: A cubic metallic box submerged in water and heated from within,
generated steam from its upper surface more than twice as fast as from
the sides when vertical, while the bottom yielded none at all. By
slightly inclining the box the elevated side produced steam much faster,
while the depressed one parted so badly with it as to cause overheating
of the metal.

Acting upon this result, most builders of engines of the present day
give an inclination of from one inch to one quarter of an inch per foot
to the sides of the inner fire-box. That the heat should be applied in
the most effectual manner to the water, the latter should _circulate_
freely around the hot metal, carrying off the heat as soon as it reaches
the surface. As the heat is applied to the _inside_ of the furnace and
tubes, it must, therefore, be the _inside_ dimensions which determine
the amount of heating surface.

  NOTE.—If we multiply the interior surface of a tube by the intensity
  of heat applied, and divide the product by the exterior surface, we
  shall have the intensity at the outside. We also _apply more heat_
  to the _outside_ of a tube, which, passing to the inner surface,
  augments in intensity per unit of area.

The area of the inner fire-box is not all available for heating, but
requires to be reduced as follows:—

                        For the fire-door.
                        For the ferrule area.
                        For the top stays.
                        For the side stay bolts.

The area is, therefore,

            Sides, twice length by height, less stay bolts.
            Back, height by width, less fire-door.
            Front, height by width, less ferrule area.
            Top, length by width, less top stays.


                                 TUBES.

323. The tubes or flues, varying in number from one hundred to three
hundred, in diameter from one and a half to three inches, and in length
from eight to sixteen feet, furnish the real communicating surface. The
amount of heating surface thus obtained for any length, number, and
diameter, is given in table 10, Chapter XIV., Part I. The surface of a
single tube is found by the formula

                           (_Ld_3.1416)/144.

               Where _L_ = the length,
                 and _d_ = the diameter, both in inches.

The efficiency of circular tubes is a matter not yet fully understood.
They certainly give a large amount of surface in a small boiler. Pambour
considered the value of tube area per unit of surface, in terms of the
furnace area, as one third only; that is, three square feet of tube
surface as equal to one foot of furnace area, in power of generating
steam. D. K. Clark makes no distinction between the two surfaces, but
observes “there is reason to believe that in the upper semicircular part
of each tube the efficiency principally resides. The winding progressive
motion, observable in tubes of considerable diameter, confirms this
conclusion, as it is with much probability due to the cooling of the
upper portion of the gases of combustion, which, as they cool also,
become heavier and descend laterally, to make room for the hotter smoke
next the bottom of the flue; the general result of which is the spiral
motion of the current in its progress onwards.” Certainly the upper half
of the tube would part much easier with the steam than the under one,
even supposing the applied heat to be the same.

At page 340 of “Overman’s Mechanics,” is the following: “The application
of heat to a _concave_ surface is wrong in principle. The heat in gases
is conducted to other bodies, and among themselves by _convection_ only.
This quality of gases causes the convex form of a vessel to be the most
profitable in absorbing the heat of ascending gases, because the motion
of the gas causes a constant change of particles on the convex body. On
a _concave_ surface exposed to the influence of moving gases, but little
effect is produced; because the particles of gas in the concavity are at
rest. A plane surface is for the same reason an imperfect form for
absorbing heat; it must be exposed at an angle of 45° to obtain the best
effect of the heating gases. In all cases if we wish to obtain the best
effect from the fuel, we should expose a convex surface to the current
of hot air. The direction of the motion of the hot gases decides the
position of the metal which is to absorb the heat; if the current is
horizontal the pipes must be vertical. Gases do not convey heat by
radiation. Tubes and other vessels containing water must be so placed
that the hot gases play around the outside.

“If we lead a current of hot air around a cylinder we shall observe that
a particle of air plays but a short time upon its surface, when it gives
way to another; the particles play almost around the cylinder, and a
concentration or increase of density behind the pipe is the result. The
relative position of pipes in the range is not indifferent, and the
distance of one from the other must be related to their diameter.”

The conducting power of the metal composing the fire-box and tubes, is
one condition which limits the rate of evaporation, when the heat is
abundant on the one side and circulation free on the other, as the water
certainly carries off the heat as fast as it arrives at the outer
surface.

All the heat should be extracted if possible from the gases before they
enter the smoke box. We should so arrange the flues, that without so
much contracting the passage for the exit of the gases as to need too
strong a blast, yet to confine the gases until their full value is
extracted.

Several attempts have been made to apply the ideas of Clark and Overman,
but as yet they have been very indirect and have met with only moderate
success. (See Appendix, E.)


            EVAPORATION, PRESSURE, TEMPERATURE, AND DENSITY.

324. The character of work to be done determines the nature of the steam
to be used.

The quantity of work to be done shows the amount of steam to be
produced.

The amount and character of the steam required, fixes the dimensions and
proportions of the boiler.

A cubic foot of water, at a temperature of 62°, weighs 62.321 lbs.

A cubic foot of steam, generated at 212° Fahrenheit, under the
atmospheric pressure (14.7 lbs. per square inch) weighs .03666 lbs.

Whence one cubic foot of water boiled at 212°, makes 1,700 cubic feet of
steam.

The total heat of saturated steam (steam produced in contact with the
water), consists of two parts at all temperatures; the _latent_ and the
_sensible_. The sensible heat is that shown by the thermometer, and
varies with the pressure. The latent heat absorbed during the generation
of steam, amounts to three fourths of the whole. As the temperature at
which the steam is produced increases, the bulk produced from a given
unit of water _decreases_, but the pressure and the total heat increase.
(See C. R. M. p. 59, 61, Regnault’s experiments.)

Table 8, Chapter XIV., Part I., gives the properties of saturated steam,
produced under pressures varying from fifty to one hundred and fifty
pounds per square inch.

The steam produced over water is called saturated, and an application of
heat to an isolated volume of this steam, raises both the temperature
and pressure, the volume and density remaining the same. The saturation
is then no more, and the steam is surcharged. If the heat be withdrawn,
pressure and density fall, and a precipitation of water takes place. The
priming of steam in a cylinder is an illustration of this. D. K. Clark,
in Railway Machinery, urges the necessity of thoroughly drying the steam
before applying it to the pistons in this manner, he says, ten per cent.
may be gained at low velocities, and in some cases forty per cent. at
high speeds.


                       MOTION OF STEAM IN PIPES.

325. Steam may flow from any vessel into a vacuum, into the open air, or
into steam of a less density. The velocity of efflux of steam is the
same as that of a stream of water flowing under a pressure equal to that
of the steam. Steam flowing into the atmosphere of course has 14.7 lbs.
per inch resistance to meet, which is equivalent to a reduction of 14.7
lbs. of its pressure. The following numbers show the velocity of efflux
of steam into the open air under different pressures.

                Pressure. Velocity, in feet per second.
                       50             1791
                       60             1838
                       70             1877
                       80             1919
                       90             1936
                      100             1957
                      110             1972
                      120             1990
                      130             2004


            LOSS OF PRESSURE CAUSED BY THE MOTION OF STEAM.

326. The loss of power suffered by the steam during its motion from the
boiler to the cylinder is caused by condensation in passing through cold
pipes, and by friction and sharp bends. The total fall that may be
caused by a combination of circumstances is from ten to fifteen per
cent. at low velocities, and from fifty to sixty per cent. at high
speeds. The fall of pressure decreases as the square of the velocity of
motion, that is, the fall at a velocity of 1,600 feet per second is four
times as great as the fall at a velocity of eight hundred feet. By well
protecting the steam pipes and cylinders, and by drying, it may be
worked at nearly its initial pressure.


                         APPLICATION OF STEAM.

327. The steam being generated in the boiler, and conveyed to the
cylinders, is admitted alternately to the opposite sides of the piston,
by which its reciprocations are produced. The first valve applied to
regulating the admission of steam to the cylinder was so arranged that
the steam was admitted during the whole stroke; at the end of which,
ingress stopped and egress commenced at the first end, and ingress
commenced at the second end simultaneously; this caused an unnecessary
resistance to the return movement, by preventing the quick escape of the
first cylinder-full, which had to be _pushed_ out, instead of _flowing_
out. The continuance of the full pressure upon the piston also, until
the end of the stroke, caused a dangerous momentum to be given to the
reciprocating machinery.

These evils are obviated by causing the exhaust passage to open, and the
entering port to close a little _before_ the end of the stroke. This is
effected by moving the valve bodily forward.

Now it is well ascertained, that with very free steam entrances, if we
allow the cylinder to be only partially filled, and then cause the steam
to expand itself, more work is accomplished with a given bulk than when
the cylinder is completely filled. That the steam may have time thus to
expand itself, the return of the piston must not take place until after
the suppression (the stopping of admission).

328. There are four positions of the valve during each half stroke, and
three distinct actions of steam in the same period, which are as
follows:—

                  Position of valve. Action of steam.

                  Admission (A).
                                     Entrance.
                  Suppression.
                                     Expansion.
                  Release.
                                     Compression.
                  Admission (B).

The longer the time between suppression and release, of course the more
complete will be the expansion. The entire force of the steam should not
(even if possible) be extracted, as a certain force is necessary to
produce a blast.

The time of expansion is regulated by the proportions of the valve
cover; which may be so adjusted as to fix suppression or release at any
desired part of the stroke.

By the above means any rate of expansion may be established, but when
once fixed will remain the same, the valve being invariably connected
with the eccentric, and thus partaking of its motion.

329. The great step which has been taken in locomotive construction
since 1840 is the invention of the “link motion,” by Williams, which,
perfected by Howe, admits of varying the travel of the valve, and thus
using the steam under any desired rate of expansion. By this
arrangement, the power of regulating the force applied to the piston,
according to the work to be done, is placed in the engineer’s hands, to
be used at any time under whatever conditions the engine may be working.

By this arrangement, two eccentrics to each cylinder are required, (and
in some dispositions of the link, only one). Fig. 150 shows the general
plan of varying the expansion. A fixed relation evidently exists between
the points A and B, two distinct motions are communicated by the
eccentrics C and D through the rods E and F, to the two ends G H, of the
curved link L; the eccentrics are so adjusted upon the driving axle as
to cause the two ends of the link to move in opposite directions, whence
at some point midway there is no motion; the link is movable
(vertically) upon the suspended point L, so that by bringing L to one
end or the other, the motion given to the rod _m_ partakes of the motion
of that eccentric which is nearest to it. Thus the movement of the valve
may be checked, or even reversed in a second, while the engine is in
motion, and that without sudden shocks.

The link is moved by the levers _n n′ n″_ terminating in the bar O,
placed at the foot board of the engine in reach of the engineer. Applied
to this is an iron sector _h h′ h″_ made fast to the frame of the
engine. Now when the point L is in such a part of the link as to place
the valve in a position admitting steam for any fraction of the stroke,
let the point at which the bar O stands upon the sector be marked for
that admission; and so also for any number of different degrees of
expansion. It is plain that the engineer may thus, by fixing the lever
O, use any percentage of admission that is required; and may always know
just what duty the engine is doing. Five minutes’ examination of the
reversing gear upon an engine will render the operation plain.

330. If we cut the steam off at half stroke and then allow it to expand,
of course the mean pressure during the whole stroke is less than that at
entering. The effective mean pressure obtained by any degree of
expansion is shown by the following formula, deduced from a mean of
forty-nine experiments with the Great Britain locomotive, (Great Western
Railroad, England,) having cylinders 18 × 24.

                   13.5(√(_a_) – 28) = mean pressure

where _a_ is the percentage of admission.

From this formula, table 11 is made.

331. Mr. Clark deduces as general results, from a very extensive and
carefully conducted system of experiments, the following.

That the maximum useful admission is seventy-five per cent.

The minimum useful admission is ten per cent.

The greatest possible gain by working expansively is one hundred per
cent., which is effected by an admission of ten per cent.

The best admission for engines having ports 1/14 of the area of the
piston, and blast area from 1/13 to 1/16 of piston, at high speeds (from
thirty to sixty miles per hour) and with considerable loads, is from
sixty to sixty-six per cent. With a wider port and blast area, the best
admission is seventy-five per cent.

The resistance due to the back pressure of the blast, varies as the
speed squared, and inversely as the square of the area of blast orifice.

332. From the experiments made by Daniel Gooch, with the engine “Great
Britain,” the following results appear.

The loss of fuel at seventy-five per cent. admission, the blast orifice
being from ⅒ to 1/11 of piston at sixty miles per hour, is from ⅓ to ⅒;
at thirty or forty per cent. admission, the loss is from ⅛ to 1/50; and
at thirty miles per hour, (seventy-five per cent. admission,) from 1/11
to 1/40.

The resistance from steam compressed in the cylinder, increases with the
speed, and also with the degree of expansion; it varies from eight per
cent. in full gear, (seventy-five per cent.,) to twenty-eight per cent.
at an admission of forty per cent.

At the highest velocities, the whole resistance from back pressure is
nearly the same for all expansions; for compression increases as blast
pressure decreases.

The above deductions hold good for speeds under forty miles per hour,
with steam ports at least 1/14, and blast orifice from 1/12 to 1/15 of
the piston area.


                         OF BOILER PROPORTIONS.

333. The dimensions of American locomotives seem to depend more upon the
shop whence they come, than upon any special duty required of them. It
is not surprising that the utmost economy is seldom attained when a
railroad president orders a lot of locomotives, from the cheapest
builder, to suit his own ideas of an engine; or when engines are ordered
by a superintendent of machinery who does not know the difference
between a sixty foot grade and a level. It is the affair of the
company’s agent and not of the machinist to know just what a railroad
needs. It is a common, and most absurd practice, for a man who is
completely ignorant of machinery to order five or ten engines, without
the least regard to the character of the road or of the traffic.

334. The particular characteristics of each class of engines is entirely
a matter of figures. There is no reason why a general table should not
be formed embracing all divisions, orders, and classes of locomotives,
in which the requirements and general dimensions corresponding thereto
should be laid down for machine shop reference. Such a table would at
once establish a mutual understanding between railroad companies and
builders. Such a general classification is shown hereafter. The
dimensions of engines are not given, as it was thought best to let each
person fill it up according to his own ideas. By so doing some valuable
general proportions may be arrived at.

335. Thus far experience has been the only guide to proportion (in
America at least). Practice, in many things, is the only correct path to
the right results, but locomotives are too expensive for philosophical
apparatus; correct experiments upon imperfect machines will lead to the
means of avoiding errors. The following is the _modus operandi_ of D. K.
Clark in his “Railway Machinery.”

A number of engines of different proportions are chosen, and
observations made upon the amounts of fuel and water consumed upon the
work done, and under what conditions. These results are so tabulated as
to show the effect in difference of construction upon the performance of
the engine, whence the proportioning of parts becomes a simple
arithmetical operation. The reduction of experiments to tables, and the
deduction from tables of formulæ, is a simple operation compared with
the skill and care required in observing the operation of a machine,
subject to so many disturbances as a locomotive engine in rapid motion.
None have had a better opportunity of observing, have conducted
experiments with more care, or have obtained results which show fewer
discrepancies than the English engineers Clark and Gooch, and the French
and German observers Le Chatlier and Nollau.

336. Three essential parts of the locomotive are the _grate area_,
_heating surface_, and _cylinders_. No two writers upon this subject
arrive at the same dimensions to perform the same work. They not only
differ, but differ widely. They cannot all be right; all but one, or all
must be wrong. American builders have fixed the dimensions of their
engines by observing the performance of constructed machines, not by
rules deduced from any systematic experiments, but upon a system of
remedying visible errors. If a chimney diameter of ten inches is found
too small and twenty too large, fifteen has been assumed as about right.

337. As an example of the difference in the results obtained by
different authors, take the following:—

An engine to do the same work must have, according to

     Zerah      Norris.[7]     D. K.        D. K.
  Colburn.[6]                Clark.[8]    Clark.[9]
       18 × 22      18 × 22      18 × 22      18 × 22 Cylinders.
             5            5            5            5 Wheels.
         13.00        13.86        14.00        19.60 Grate area.
          1114          812         1327         1327 Heating surface.
           250          324          134          134 Area of chimney.
             4           23           28           28 Area of blast.
            59           73           ——           —— Steam room.
           100           73           ——           —— Water room.

Footnote 6:

  Colburn on the Locomotive Engine.

Footnote 7:

  Norris’s Handbook for Locomotive Engineers and Machinists.

Footnote 8:

  D. K. Clark’s Railway Machinery, calculated for coke.

Footnote 9:

  D. K. Clark’s Railway Machinery, calculated for wood.

From these figures, the work done being the same, Mr. Clark gives forty
per cent, more grate area than either Colburn or Norris, an easier
blast, and greater heating surface. Norris makes the steam and water
room equal, while Colburn makes the latter almost double the former. It
is to be observed that Colburn gives only rules adopted by different
builders, not vouching for their correctness, while Norris lays down his
rules as fixed and right. The engines used by the English experimenters
in their observations, vary in dimension between the following wide
limits, whence the universal application of their results.

             Grate area        9 to    24 square feet.
             Fire surface     50 to   100 square feet.
             Tube surface    400 to 1,000 square feet.
             Whole surface   450 to 1,100 square feet.
             Blast orifice    10 to    20 sq. inches, area.
             Speed of engine  12 to    20 miles per hour.

338. The result of some sixty experiments upon forty-five different
engines (detailed in Clark’s Railway Machinery, page 156), gives the
following formula, expressing the relations which ought to exist between
grate area, heating surface, and consumption of water; that evaporation
may be carried on in the most economical manner.

                    _S_ = √(_ac_) × 21.2 = surface.

      Where _S_ is the heating surface in square feet.
            _a_ is the grate area in square feet.
            _c_ is the hourly consumption of water in cubic feet.

From which we deduce the value of _a_ or _c_ thus,

                 _a_ = ((_S_/21.2)^2)/_c_ = grate area;

        and _c_ = ((_S_/21.2)^2)/_a_ = hourly water consumption.

The maximum evaporation which should be carried on per square foot of
grate is found, by Mr. Clark, to be sixteen cubic feet per hour. Thus,
if we wish to evaporate 160 cubic feet of water per hour, we must have a
grate area of at least 160/16 or ten square feet.

339. The above formula for the grate area gives the dimension for a
coke-burning furnace. Locomotives burning wood or coal require a
modification of the above, as follows:—

To produce a given amount of heat, a certain amount of carbon must be
burnt. As wood contains much less carbon than coke, a correspondingly
larger bulk must be burnt, and a larger grate is necessary; not,
however, larger in proportion to the larger bulk of fuel, as we may have
a deeper wood than coke fire. The relative depth of fire being as the
stowage bulk, and the actual depth of a coke fire being 1.9 feet, that
of a wood fire will be 2.5 feet.

Now let _A_ be the number of lbs. of coke per foot of water evaporated.

_B_ the number of lbs. of coal per foot of water evaporated.

_C_ the number of lbs. of wood per foot of water evaporated.

Call _d_ the depth at which if is the most economical to burn coke; _d′_
the same depth for coal, and the depth for wood _d″_. Then will the area
of a coke grate be

                                _A_/_d_;

Of a coal grate

                               _B_/_d′_;

And of a wood grate

                               _C_/_d″_.

To be able to fix the proper grate area for any fuel, we must know its
evaporative power, and a depth of a layer in the furnace. Knowing the
absolute value for coke, it remains only to obtain the relative value
for any other. Thus far we have disregarded the difference in _time_ of
burning wood and coke. To produce a given amount of heat, we burn a
certain chemical value of fuel; a much larger bulk of wood than of coke
is needed. If we burn wood and coke _at the same depth_ and _in the same
time_, the grate areas would be proportional to the bulks of fuel to
produce the same heat; but, _first_, we burn fuel in a depth
proportioned to the economic stowage bulk, or as 2.5 to 1.9, which
decreases the wood area; and, _second_, a layer of coke 1.9 feet deep
burns in one hour, while a layer of wood 24 feet deep burns in fifteen
minutes; whence 60 m. divided by 15 m. = 4 layers of 2½ feet deep each,
or in all ten feet, which into the bulk (equal to a mass of coke 1 foot
square × 1.9 high) or 1 foot square by 14 high, gives 14 ÷ 10 = 1.4; or,
finally, the area of the wood grate should be 1.4 times that of a grate
to burn coke.


                 OF THE SIZE AND USE OF THE SMOKE BOX.

340. The smoke box is the general termination of the flues, and the
place where the vacuum is produced, which causes the draft. The size of
the boiler being the same, the vacuum varies directly as the blast
pressure. The power of the blast is of course affected by the capacity
of the smoke box. Mr. Clark fixes the capacity of the exhaust chamber at
three cubic feet per square foot of grate. The vacuum in the furnace
varies from one to two thirds of that in the smoke box. The less the
resistance to the hot gases experienced in the flues, the less may be
the vacuum. Upon the vacuum depends the amount of air drawn through the
grate; upon the bulk of air drawn through the grate depends the
combustion; upon the combustion the evaporation. Whence the evaporation
_cet. par._ depends the vacuum in the smoke box.

The velocity of any fluid depends upon the power applied to it, (being
as the square root,) the pressure applied to the gases in the furnace of
a locomotive is the vacuum in the smoke box; thus the combustion or rate
of evaporation is as the square root of this vacuum. To double the
evaporation it is necessary to quadruple the vacuum.


                              BLAST PIPE.

341. The blast pipe conducts the waste steam from the cylinder, which
drives the air from the chimney and produces the vacuum in the smoke
box; its form should permit the freest escape of the steam from the
cylinder. The blast pipe area should nowhere be smaller than the exit
port, except at the contraction at the top. “Too much care,” says Mr.
Clark, “cannot be taken to adjust the blast pipe concentrically with the
chimney; one half inch has been known to spoil the draft of a
locomotive.” “The area of orifice is the most critical and most
important item in the composition of the locomotive.”

For the form, dimensions, and influence of this important member, the
reader is referred to Clark’s Railway Machinery.

As the grate area increases, the blast may decrease. The greater the
flue area the easier may be the blast; decrease of smoke box capacity
and of chimney diameter, both allow a milder blast.

342. The following proportions are collected from the work of Mr. Clark.
The order in which the different parts of the engine stand in importance
with relation to the blast, is shown in column 1. The figures show the
ratios (the best) which may be had under the most favorable
circumstances.

    Grate area                                                  1
    Ferrule area (area of section of tubes at back flue sheet)  ⅕
    Tube, sectional area                                        ¼
    Capacity of smoke box, cubic feet                           3
    Chimney, height four diameters, area of section            1/15
    Blast orifice                                              1/75

The vacuum in the smoke box is somewhat regulated by a damper placed in
front of the ash pan, by a valve in the chimney, or by a Venetian blind
covering the front ends of the tubes.


                        TUBE SECTION AND LENGTH.

343. The section of the tubes (crosswise) is the space through which the
hot gases pass off. By increasing the length or decreasing the diameter,
we of course require a stronger blast.

That the steam may escape as soon as generated, there must be a certain
clearance between the tubes, which Mr. Clark fixes as follows:—

Divide the number of tubes by thirty and the result is the clearance in
eighths of an inch; or algebraically

               _C_ = ((_N_/30))/8 = clearance in inches;

Or otherwise

                  _C_ = _N_/240 = clearance in inches.


                  PROPORTIONS OF CYLINDERS AND WHEELS.

344. The above proportions depend entirely upon the nature and amount of
work to be done, and upon the character of the road. Small wheels and
long stroke are to be applied to heavy trains and steep grades. Short
stroke and large wheels to fast trains and level roads.

There are some advantages in a long cylinder, even with a constant ratio
between the stroke and wheel diameter. The steam has more time to
expand; the action of the machinery is slower, and the erratic movements
of the engine caused by the movement of the reciprocating machinery are
lessened, at the same time the centre of gravity is raised and
oscillation increased.


                            OF THE CARRIAGE.

345. The arrangement of the wheels, axles, springs, and draw-link, and
the distribution of the weight of the engine upon its several bearings
so as to provide the necessary adhesion, and to run steadily upon the
rails, is a matter well worthy of more attention than is commonly given
to it.

The frame is the base of the engine, to which every thing should be
attached. The cylinders and the wheel both being attached to it, it of
course becomes the counterpart to the piston and connecting rod; the
former holding the cylinder and wheel together, while the latter pushes
them apart. The frame _should_ form a rigid connection between the
piston and the wheel; and its strength must be able to resist the whole
power of the engine, applied alternately as compression and as
extension.

The wheels of a locomotive answer three several purposes, and are
classed as follows:—

                            Leading wheels.
                            Driving wheels.
                            Trailing wheels.

The duty of the driving wheels is to transfer the power of the engine to
the rails, by which the motion is produced. That of the leading wheels,
to guide the engine; and that of the trailing wheels, to support the
after end of the engine.

The weight upon the driving wheels must be enough for sufficient
adhesion. That upon the leading wheels, sufficient to guide the engine
upon curves, (decreasing as their distance from the centre of gravity
becomes greater, and increasing with the speed.)

The centre of gravity of an engine is generally at a distance of from
one quarter to one sixth of the length of the barrel from the furnace
horizontally and forwards, and in the lower part of the barrel,
vertically.

The weight upon any one pair of wheels is as their distance from the
centre of gravity; by changing their position we change the applied
weight.

The flange base[10] must increase as the engine becomes heavier, when
applied to fast trains, as more leverage is necessary to keep it on the
rails. Heavy freight engines with four or five pairs of wheels, and no
truck, wear the rails and strain themselves very much. We should make
the wheels of such very small and near together, in order to contract
the flange base.

Footnote 10:

  _Wheel base_,—Horizontal length between centres of extreme wheels.
  _Flange base_,—Horizontal length between centres of extreme fixed
  flanged wheels.


                        DISTRIBUTION OF WEIGHT.

346. Suppose the whole load upon the wheels is 60,000 lbs. If the centre
of gravity is half-way between the wheels (there being two pairs), each
will support 30,000 lbs. If the centre of gravity is twice as near to
one axle as to the other, the furthest one will support 20,000 lbs., and
the nearest one 60,000–20,000, or 40,000 lbs.

Suppose the engine has six points of support, or three points in the
side elevation, (the ordinary four driving wheels and a truck engine).
Let the centre of gravity be one foot behind the middle axle and the
distances between the wheel centres eight feet.

The weight upon the middle axle being _H_, that upon the hind axle is
_H_/7, because that axle is seven times more distant from the centre of
gravity than the middle one, and for the same reason the weight upon the
front axle is _H_/9.

                 Now _H_ + _H_/7 + _H_/9 = 60,000 lbs.

                        Whence _H_ = 47,976 lbs.

                        Also, _H_/7 = 6,853 lbs.

                         And _H_/9 = 5,331 lbs.

And the same laws (see article Lever, in any work on Mechanics) apply to
any arrangement of wheels and to any position of centre of gravity.

Springs are employed to absorb the shocks received by the wheels from
irregularities in the surface of the rails. They must be equally stiff
on both sides of the engine, or lateral rocking will be generated.

When, as is generally the case, the springs are connected by
compensating levers, their stiffness being as the load upon them, the
arms of the connecting lever must be inversely proportional to the
applied weights. The shock received by one wheel is by the lever
communicated to the whole four, (or even more when there are such). The
truck springs of some builders are also connected by an equalizing
lever.

According to Mr. Clark, not more than twelve tons should ever be placed
upon one axle; whence engines requiring a tractive power of twelve tons
and less may be of the form shown in fig. 151. Between twelve and
twenty-four tons, of the form fig. 152; and over the forms figs. 153,
154, and 155.

[Illustration: Fig. 151.]

The weight upon the leading wheels of fast passenger engines should be
as much as one fifth of the whole weight. Upon freight engines it need
not be more than one sixth.

[Illustration: Fig. 152.]

The line of traction of a locomotive ought to be as near as possible at
the same vertical height as the driving wheel centres. If much below
this the load will tend to lift the engine off from the leading wheels,
upon the drivers as a fulcrum, thus increasing the adhesion and
lessening the leading power.

[Illustration: Fig. 153.]

If the traction bar (draw link) is above the wheel centres, it will tend
to lift the rear of the engine from the rails.

[Illustration: Fig. 154.]

The general form of engines used in America are shown in figs. 151, 152,
153, 154, and 155.

[Illustration: Fig. 155.]

Fig. 151 is the express passenger locomotive.

Fig. 152 is the ordinary passenger, mail, and mixed engine.

Fig. 153 is the heavy freight engine.

We have, also, engines with three, four, and five pairs of small wheels
without a truck, for heavy grades and large amounts of work.


                         OF ERRATIC MOVEMENTS.

347. The erratic movements of a locomotive in motion are due to three
separate causes.

              To the motion of the machinery.
              To the arrangement of the frame and wheels.
              To the state of the surface of the rails.

Those caused by the motion of the machinery are as follows:
_Longitudinal fore and aft movement_, generated by the reciprocations of
the piston rod, cross head, connecting rod, and crank; and depending in
amount upon the weights of the moving parts, steam pressure, and
velocity of motion. _Pitching_ of the engine, arising from the oblique
action of the cross heads upon the guides, which tends to lift the front
end of the engine from the rails; and depends in amount upon the ratio
between the stroke and length of connecting rod. _Rocking_ laterally,
arising from the difference of time of action of the cross heads; one
acting with its greatest vertical power, when the opposite one acts with
none. _Vibration in plan_ about the centre of gravity of engine,
produced by the pressure between the piston and crank pin, and by the
momentum of the reciprocating machinery. This last, combined with
lateral rocking, produces _sinuous_ or _spiral_ motion.

The amounts of these several irregularities depend considerably upon the
arrangement of carriage; that is, upon the position of wheels; being
less as the base included by the bearing points is greater.

The influence of the state of the rails is shown by the vertical and
lateral shocks arising from the rail joints and from bad adjustment,
both horizontally and vertically.

The amounts of these irregularities increase very rapidly with the
speed. Le Chatelier’s experiments make them increase nearly as the
square of the velocity.

Longitudinal fore and aft motion is nearly balanced by applying a
counterweight to the wheel, opposite the point to which the connecting
rod is attached. The remedy for pitching consists in placing the guide
bars under the heaviest part of the engine; by which, a great weight is
opposed to the vertical action of the cross heads. Crampton’s engine is
quite free from this disturbance, as the guide bars are almost directly
under the centre of gravity.

The only counteracting effort (remedy it is not) for sinuous motion yet
applied, is extension of wheel and flange base, thus giving the guiding
wheels more control over the mass of the engine.

The remedy, however, which applies at once to all of the erratic
movements, is reduction of speed, as when we divide the velocity by two
we decrease the disturbances nearly fourfold.


           REVIEW OF THE FORMULÆ AND FORMATION OF THE TABLES.


                                 No. 1.

348. Given the weight and velocity of a train, to find the necessary
traction on a level.

                               _Formula._

                               _W_ × _R_,

_W_ being the weight of the train in tons, and _R_ the resistance in
lbs. per ton; found by the formula

                         (_V^2_)/171 + 8 = _R_.

By this formula is formed table 1, giving the traction required to move
trains of from fifty to one thousand tons weight, at speeds from ten to
one hundred miles per hour.


                                 No. 2.

349. To find the traction due to a grade.

                               _Formula._

                             _W_ × _R_/_L_,

where _W_ is the weight of the train in tons, _R_ the rise, and _L_ the
length of the incline. By this rule is formed table 2, giving the
necessary traction to overcome grades from ten to one hundred feet per
mile, with loads from one to one thousand tons.

To obtain the whole traction required, add the amounts taken from tables
1 and 2; thus the traction necessary to draw five hundred tons at twenty
miles per hour over fifty feet grades is,

                        By table 1,  5,170 lbs.
                        By table 2, 10,605 lbs.
                                    ——————
                        In all,     15,775 lbs.

or, algebraically,

                    (_W_ × _R_) + (_WR_/_L_) = _T_,

the letters standing for the same quantities as above.


                                 No. 3.

350. To find the weight to place on the driving wheels.

                               _Formula._

                                 6_T_,

where _T_ is the whole tractive power. (Table 3.)


                             Nos. 4 and 5.

The tractive power of an engine is expressed by

                     _T_ = ((2_A_)_P_ × 2_S_)/_C_,

           Where _T_ is the tractive power.
                 _P_, steam pressure in lbs. per square inch.
                 _S_, stroke in inches.
                 _C_, circumference of wheel in inches.
                 _A_, area of one piston in inches.

From this formula we get the values of the several factors as follows:—

        The steam pressure, or _P_ = (_TC_)/((2_A_)2_S_).      (A.)

           The stroke, or _S_ = (_CT_)/((2_A_)(2_P_)).         (B.)

            The piston area, or _A_ = (_TC_)/(4_SP_).          (C.)

    The wheel circumference, or _C_ = (2_A_ × _P_ × 2_S_)/_T_. (D.)

And from (C) we get the diameter of piston by the following:—

                          _d_ = √(area/.7854).

And in like manner from (D) the diameter of wheel by

                           _d_ = _c_/3.1416.

(See tables 4 and 5.)


                                 No. 7.

351. To find the capacity of cylinders of any dimension.

                               _Formula._

                     (_D^2_ × .7854 × Stroke)/1728.

This gives the capacity in cubic feet. The dimensions above (see D and
S) being in inches. (Table 7.)


                                 No. 6.

352. To find the hourly steam consumption in terms of the capacity of
one cylinder, (that is, the number of cylinderfuls per hour).

                               _Formula._

                           _N_(5280/_c_) × 4,

where _N_ is the number of miles per hour, _c_ the wheel circumference.
(Table 6.)


                                 No. 8.

353. Knowing the hourly consumption of steam, to reduce it to water.

                               _Formula._

                                _B_/_N_,

_B_ being the bulk of steam in cubic feet, and _N_ the relative volume
of steam and water. (The values of _N_ are given in table 8.)


                                 No. 9.

354. Knowing the hourly water consumption, to find the grate area and
heating surface.

  First, (Cubic feet of water per hour)/16 = grate area in square ft.

            Second, _S_ = √(_ac_) × 21.2 = heating surface,

where _a_ is the grate area, and _c_ the hourly consumption of water in
cubic feet.

From the same formula,

Grate area, or

                        _a_ = ((_S_/21.2)^2)/_c_

Also water consumption, or

                        _c_ = ((_S_/21.2)^2)/_a_

(See table 9.)


                                No. 10.

355. To find the necessary number of tubes to give any amount of heating
surface.

                               _Formula._

                           _N_ = _S_/(_Ld_π),

when _N_ is the number, _S_ the required surface, _L_ the length, _d_
the diameter, both in feet, and π = 3.1416. (See Table 10.)


                                No. 11.

356. To find the mean cylinder pressure for any percentage of admission.

                               _Formula._

                            13.5√(_a_) – 28,

where _a_ is the percentage of admission. (See Table 11.)

As to the internal arrangement of the barrel of the boiler, we must of
course have the length of tubes the same as that of the barrel, (that
is, in the general plan of boiler, some makers have moved the back flue
plate ahead). The length of tubes will of course be the same as the
distance between the tube sheets. The number is governed by their
diameter and by the proper clearance, which is found by the formula,

         (_N_/|30|)/8 in eighths of inches, or _N_/240 inches.

The upper fifteen to eighteen inches of the barrel must be left for
steam room.


                       OF THE DIAMETER OF BARREL.

357. To find the diameter of a barrel to contain a given number of
tubes,

            Represent the inside diameter of boiler by _D_,
            Diameter of one tube                       _d_,
            Clearance between tubes                    _c_,
            Number of tubes                            _n_,
            Sectional area of boiler, in inches        _A_,
            Water section, in inches                   _B_,

we shall have as the area of water room per tube,

                             (_d_ + _c_)^2,

and the whole area of water room,

                          (_d_ + _c_)^2 × _n_,

the whole section of the barrel,

                       _A_/_B_[(_d_ + _c_)^2_n_],

and the diameter of that area,

               _D_ = √(([(_d_ + _c_)^2_n_]_A_/_B_)/.7854)

which is the boiler diameter in inches, to which add _D_/16 on each
side, or in all _D_/8 as the room to be left between the sides of the
boiler and first tube.

The _diameter_ finds its maximum limit in the gauge less the two half
breadths of tire, and two or three inches allowance for attachment to
the frame and other mechanical incidentals. The _length_ must be enough
to carry the leading wheels a sufficient distance from the centre of
gravity of the engine.


 ADAPTATION OF THE LOCOMOTIVE ENGINE TO THE MOVEMENT OF RAILWAY TRAINS.

358. First, as regards the nature of the traffic.

There are certain necessary causes of a bad application of power upon
railroads; for example, when the trains are very much heavier in one
direction than in the other, as we are obliged to use the same engine
both ways, because when it arrives at one end of the road it must go
back to start again. Where the traffic requires to be worked chiefly up
hill, we use an engine much heavier to _ascend with the load_ than is
necessary to _descend without a load_. Different objects of transport
require different speeds. Perishable freight, such as ice, beef, pork,
cattle, &c., requires to be moved in much less time than grain, lumber,
flour, coal, and manufactured articles. As a general thing, the
difference between the characters of freight engines, as regards the
nature of the traffic, can be adapted only with a view to amount,
disregarding the nature.

With passenger traffic, however, there is a great variety of speeds made
use of, and consequently may be a greater difference in the proportions
of engines depending entirely upon the nature of the traffic.


       ADAPTATION AS REGARDS THE PHYSICAL CHARACTER OF THE ROAD.

The best adaptation of locomotive power to any system of grades, would
be that which should render the mileage a minimum; and this will be
done, as nearly as possible, by applying engines, the strength of which
shall be proportional to the resistance to be overcome. The best mode of
comparing different adaptations of power is by reducing the grades to a
level; or by equating for grades by means of the capacity of motive
power.

This is done as follows:—

 The length of an incline being                                    _L_,
 The resistance on a level being                                   _R_,
 The ratio of the resistance due to the grade to the resistance on
   a level by                                                      _r_,
 The equivalent horizontal length by                               _L′_,

and we shall have,

                         (_R_ + _r_)_L_ = _L′_.

_Example._—Let the length of a grade be seventy-five miles; the value of

                              _r_ = _R_/3;

and we have

             (3/3_R_+_R_/3)_L_ = ((4_R_)/3)75 = 100 miles.

Let us now compare the mileage of some of the large roads of America, as
given by a good, and also by a bad adaptation of power.

The Massachusetts Western Railroad may be divided into the four sections
below (including the Boston and Worcester road).

                                   Length miles. Maximum grade.
        Boston to Worcester,       44                  30
        Worcester to Springfield,  54½                 50
        Springfield to Pittsfield, 52                  83
        Pittsfield to Albany,      49½                 45

Assume the speed of freight trains as fifteen miles per hour, the
resistance on a level will be 9.3 lbs., or for simplicity call it ten
pounds per ton.

    The resistance due to a    30 feet grade is  13   lbs. per ton.
    The resistance due to a    50 feet grade is  21   lbs. per ton.
    The resistance due to a    83 feet grade is  35   lbs. per ton.
    The resistance due to a    45 feet grade is  19   lbs. per ton.
    And the value of _r_ for a 30 feet grade is 13/10 lbs. per ton.
    And the value of _r_ for a 50 feet grade is 21/10 lbs. per ton.
    And the value of _r_ for a 83 feet grade is 35/10 lbs. per ton.
    And the value of _r_ for a 45 feet grade is 19/10 lbs. per ton.

And the relative length of the several sections will be,

     Boston to Worcester,       10/10 + 13/10 = 23/10 of 44  = 101
     Worcester to Springfield,                  31/10 of 54½ = 169
     Springfield to Pittsfield,                 45/10 of 52  = 234
     Pittsfield to Albany,                      29/10 of 49½ = 144
                                                         ———   ———
           And the sums,                                 200   648

the equated distance being 3¼ times the actual length. This length
assumes the resistance of the several sections to be for their whole
length that given by their maximum grade. This might seem erroneous; but
its correctness will be seen when it is remembered that the greatest
load that can be taken over any section is limited by its maximum grade.

Now suppose that the engine employed is of the following dimensions (as
it is very nearly).

                       Cylinders 16 × 20 inches,
                       Wheels         54 inches.

Assume the cylinder pressure 110 lbs., and the tractive power of the
engine is 5,287 lbs.

 A load of 500 tons, upon a 30 feet grade, requires a        11,500 lbs.
   traction of

 Upon a 50 feet grade,                                       15,500 lbs.

 Upon an 83 feet grade,                                      22,500 lbs.

 Upon a 45 feet grade,                                       14,500 lbs.

 To move the above load from Boston to Worcester we should   2 engines,
   require

 From Worcester to Springfield,                              3 engines,

 From Springfield to Pittsfield,                             5 engines,

 From Pittsfield to Albany,                                  3 engines,

And the products of the number of engines by the lengths of the
corresponding divisions, are

               Boston to Worcester,       44  × 2 =   88
               Worcester to Springfield,  54½ × 3 = 163½
               Springfield to Pittsfield, 52  × 5 =  260
               Pittsfield to Albany,      49½ × 3 = 148½
                                                    ————
                                                     660

Suppose that by making the engines on the several sections strong in
proportion to the resistance of those sections, one engine is capable of
taking the whole load over all of the grades. The mileage becomes as
follows:—

            Boston to Worcester,       44  × 1 =  44
            Worcester to Springfield,  54½ × 1 = 54½
            Springfield to Pittsfield, 52  × 1 =  52
            Pittsfield to Albany,      49½ × 1 = 49½
                                                 ———
                                                 200 miles.

            The mileage before was               660 miles,
            And the saving therefore             400 miles.

or about 70 per cent. of the first mileage.

359. From a recent report of the New York and Erie Railroad it appears
that the same power will draw

                    28 tons on the Western division,
                    80 tons on the Susquehanna division,
                    85 tons on the Delaware division,
                and 20 tons on the Eastern division,

neglecting the assistance required from Susquehanna to Deposite. In the
following table are given the actual lengths of the several divisions,
and the sum of the products of three lengths both by the relative and a
uniform resistance on each.

                          Miles run  Miles run by
    Division.   Length.     by an     an engine   Difference.
                         engine not    adapted.
                          adapted.
   Western,       128    128 × 3.04   128 × 1.0        261.12
   Susquehanna,   139    139 × 1.06   139 × 1.0          8.35
   Delaware,      104    104 × 1.00   104 × 1.0          0.00
   Eastern,        88     88 × 4.25    88 × 1.0        286.00
                                                       ——————
                Sum of differences,                    555.47 miles,

that is, the miles run by engines adapted to the work on the several
divisions will be 555.47 less than the miles run by engines not adapted.
(See Appendix F.)


                     PENNSYLVANIA CENTRAL RAILROAD.

360. The physical character of this road is as follows:—

                                        Length. Max. grades.
            Philadelphia to Harrisburg,   106        45
            Harrisburg to Altoona,        131        21
            Altoona to Johnstown,         48½        92
            Johnstown to Pittsburgh,      78½        53

The value of _r_ will be here

                         45 feet grades, 19/10
                         21 feet grades,  9/10
                         92 feet grades, 39/10
                         53 feet grades, 25/10

Whence the equation,

                        106 × (10/10 + 19/10) =  307
                        131 × (10/10 +  9/10) =  249
                        42½ × (10/10 + 39/10) =  208
                        78½ × (10/10 + 25/10) =  275
                        ———                      ———
                   Sum, 358                Sum, 1039
                         and 1039 – 358 = 681.

361. On the Baltimore and Ohio Railroad we have,

                                          Miles. Max. grade.
            Baltimore to Harper’s Ferry,  80         82
            Harper’s Ferry to Cumberland, 98         40
            Cumberland to Raccoon,        88.2       116
            Raccoon to 148⅔ miles,        60.5       40
            148⅔ miles to Wheeling,       51.3       80

And as before,

                      80   × (10/10 + 35/10) = 360
                      98   × (10/10 + 17/10) = 265
                      88.2 × (10/10 + 49/10) = 520
                      60.5 × (10/10 + 17/10) = 163
                      51.3 × (10/10 + 35/10) = 231
      Sum of Col. 1 = 378, Sum of Col. 3 = 1539; difference 1161.

Thus by the most correct adaptation of power, upon the above-named
railroads, the following percentages of mileage may be saved.

                       Massachusetts Western, 70
                       New York and Erie,     55½
                       Pennsylvania Central,  68
                       Baltimore and Ohio,    75

Of these roads the Baltimore and Ohio is that which has actually the
best adaptation; and the Western road of Massachusetts that which has
the worst.

362. To determine the actual dimensions of the engines which should be
used upon any road, from the tables, proceed as follows:—Let the load be
one hundred tons, the maximum grade thirty feet per mile, and speed
twenty-five miles per hour.

Referring to the tables in succession we have,

 By table 1, Traction for 100 tons, on a level, at 25 miles   1,550 lbs.
   per hour,

 By table 2, Traction for 100 tons, on a 30 feet grade,       1,273 lbs.

                                                              —————

                   Whole traction required,                   2,823 lbs.

By the formula, table 3, the weight upon the drivers must be

                   2823 × 6 = 16938 lbs., or 8 tons.

By table 4, with a wheel five feet in diameter, and a stroke of twenty
inches, we have the decimal .2122.

By table 5, the mean cylinder pressure being sixty pounds per inch, and
piston twelve inches in diameter, we have as the total pressure

                On both pistons,             13,572 lbs.
                And finally, 13572 × .2122 =  2,880 lbs.
                The requirement being         2,823 lbs.

By table 6, we see that five feet wheels at twenty-five miles per hour,
use 33,600 cylinders of steam per hour.

By table 7, the capacity of a cylinder 12 × 20 is 1.31 cubic feet; also
33600 × 1.31 = 44016 cubic feet of steam per hour.

Assuming the mean cylinder pressure at sixty pounds, and the entering
pressure at eighty pounds, also the loss in passing from the boiler at
twenty pounds, we must generate the steam at one hundred pounds per
square inch.

By table 8, we see that when steam is produced under one hundred pounds
pressure per inch, each cubic foot of water makes 293 cubic feet of
steam; whence

                            44016/293 = 150,

is the number of cubic feet of water to be evaporated per hour. At
sixteen cubic feet of water per hour per square foot of grate, we thus
require

                      15.0/16 or 9.4 feet, nearly;

and by table 9, we find the heating surface necessary to evaporate 150
cubic feet of water per hour, with nine square feet of grate surface, to
be 779 square feet; and by the formula, with 9.4 square feet, we have,

              _S_ = √(9.4 × 150) × 21.2 = 797 square feet,

the fuel being coke; for wood, multiply the grate area (as mentioned
before) by 1.4 and the grate area will be 1.4 × 9.4 = 13.16. The tube
surface of course remains the same, as, when the necessary amount of
heat is developed, the same surface only is enough to apply it to the
water.

To obtain 779 square feet of heating surface, we see, by table 10, that
it is given by

               100 tubes 17  feet long and 1¾ inch diameter,
            or 100 tubes 16  feet long and 1⅞ inch diameter,
            or 100 tubes 15  feet long and 2  inch diameter,
            or 100 tubes 14  feet long and 2⅛ inch diameter,
            or 100 tubes 12½ feet long and 2⅜ inch diameter,
            or 100 tubes 12  feet long and 2½ inch diameter,

or by consulting the table, and having given the number and length, the
number and diameter, or the length and diameter, we may easily find the
third factor of the surface. Thus the length being eleven feet, and
diameter two inches, 779 feet is obtained by

                  779/(11 × 3.1416 × 167) = 135 tubes.

To obtain the diameter of barrel to contain 135 two inch tubes, we use
the formula

               D = √((_A_/_B_[_n_(_d_+_c_)^2])/(.7854)).

We have already found _d_ = 2 inches, _n_ = 135, whence _c_ will be by
formula,

                         _c_ = _N_/240 = 0.54,

and

                           _d_ + _c_ = 2.54,

also,

                         (_d_ + _c_)^2 = 6.45,

and

                           135 × 6.45 = 871+;

and allowing three fourths of the boiler cross section to be filled with
tubes, we have,

                           4/3 of 871 = 1161;

also,

                           1161/.7854 = 1478,

the square root of which is 38.5 nearly, to which add 38.5/8 or 4.8
inches, (see page 359), and we have

                       38.5 + 4.8 = 43.3 inches,

as the inside diameter of boiler, whence the following locomotive to
meet the requirement as stated.

          Weight upon driving wheels, 16,938 lbs.,
          Cylinders,                  12 × 12 inches,
          Wheels,                     5 feet,
          Tubes,                      135—11 feet × 2 inches,
          Grate,                      13.16 square feet,
          Barrel, (inside diameter,)  43.3 inches,

and under the most favorable circumstances, the chimney may be 40 inches
high, 12.7 inches in diameter; the blast orifice 5.8 inches in diameter;
and the capacity of smoke box 39½ cubic feet.

363. We may vary the tractive power of an engine by using the steam at a
greater or less degree of expansion, but the adhesion remains the same.
If an engine was built able to work a road partly level, and partly on
steep grades, varying the power simply by varying the expansion, it
would be unnecessarily heavy for the easy parts of the road. The
expansive principle may be advantageously employed in adjusting the
power to the difference of resistance on any one division of a road, and
also to the varying load which each day’s traffic will present.

Suppose we would move a load of two hundred tons over the road below;
and suppose, also, that we require the cylinder pressures set opposite
the several divisions.

                 10 miles, level,             60 lbs.,
                 10 miles, 10 feet per mile,  80 lbs.,
                 10 miles, 20 feet per mile, 100 lbs.,
                 10 miles, 30 feet per mile, 120 lbs.

The boiler pressure being 150 lbs., and the pressure at entering the
cylinder 145 lbs.,

    An admission of 71 per cent. gives a mean pressure of 120 lbs.,
    An admission of 55 per cent. gives a mean pressure of 100 lbs.,
    An admission of 40 per cent. gives a mean pressure of  80 lbs.,
    An admission of 28 per cent. gives a mean pressure of  60 lbs.,

        And if the  1st notch of the sector admits, 75 per cent,
        And if the  2d  notch of the sector admits, 70 per cent,
        And if the  3d  notch of the sector admits, 65 per cent,
        And if the  4th notch of the sector admits, 60 per cent,
        And if the  5th notch of the sector admits, 55 per cent,
        And if the  6th notch of the sector admits, 50 per cent,
        And if the  7th notch of the sector admits, 45 per cent,
        And if the  8th notch of the sector admits, 40 per cent,
        And if the  9th notch of the sector admits, 35 per cent,
        And if the 10th notch of the sector admits, 30 per cent.

We should work the engine as follows:—

                From  0 to 10 miles, use the 10th notch,
                From 10 to 20 miles, use the  8th notch,
                From 20 to 30 miles, use the  5th notch,
                From 30 to 40 miles, use the  2d  notch,


            APPLICATION OF LOCOMOTIVE ENGINES TO RAILROADS.

                     364. _Department 1. Freight._


                        GENERAL CLASSIFICATION.

 ┌─────────┬─────────┬───────────┬─────┬─────┬─────┬─────┬─────┬─────┐
 │         │         │           │Order│Order│Order│Order│Order│Order│
 │Number of│ Maximum │Designation│  1  │  2  │  3  │  4  │  5  │  6  │
 │division.│ grades. │ of parts. │ 50  │ 100 │ 250 │ 500 │ 750 │1,000│
 │         │         │           │tons.│tons.│tons.│tons.│tons.│tons.│
 ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤
 │         │         │Grate area.│     │     │     │     │     │     │
 │         │         │   Tube    │     │     │     │     │     │     │
 │    1    │ Level.  │ surface.  │     │     │     │     │     │     │
 │         │         │Cylinders. │     │     │     │     │     │     │
 │         │         │  Wheels.  │     │     │     │     │     │     │
 │         │         │  Weight.  │     │     │     │     │     │     │
 ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤
 │    2    │ 10 feet │           │     │     │     │     │     │     │
 │         │per mile.│           │     │     │     │     │     │     │
 ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤
 │    3    │ 20 feet │           │     │     │     │     │     │     │
 │         │per mile.│           │     │     │     │     │     │     │
 ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤
 │    4    │ 40 feet │           │     │     │     │     │     │     │
 │         │per mile.│           │     │     │     │     │     │     │
 ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤
 │    5    │ 60 feet │           │     │     │     │     │     │     │
 │         │per mile.│           │     │     │     │     │     │     │
 ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤
 │    6    │ 80 feet │           │     │     │     │     │     │     │
 │         │per mile.│           │     │     │     │     │     │     │
 ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤
 │    7    │100 feet │           │     │     │     │     │     │     │
 │         │per mile.│           │     │     │     │     │     │     │
 └─────────┴─────────┴───────────┴─────┴─────┴─────┴─────┴─────┴─────┘

The speed is assumed from twelve to fifteen miles per hour. The mean
cylinder pressure is assumed at sixty lbs. per square inch; the initial
pressure at ninety pounds, and the boiler pressure at 120 lbs. per
square inch. The grate areas are designed for coke; for wood multiply
the same by 1.4.

365. _Department 2. Passenger._

 ┌───────────────────────┬───────┬───────┬───────┬───────┬─────────────┐
 │                       │Order 1│Order 2│Order 3│Order 4│ Designation │
 │    Classification.    │  50   │  100  │  150  │  200  │  of parts.  │
 │                       │ tons. │ tons. │ tons. │ tons. │             │
 ├────────────┬──────────┼───────┼───────┼───────┼───────┼─────────────┤
 │            │          │       │       │       │       │ Grate area. │
 │ Division 1 │ 25 miles │       │       │       │       │Tube surface.│
 │   Level.   │per hour. │       │       │       │       │ Cylinders.  │
 │            │          │       │       │       │       │   Wheels.   │
 │            │          │       │       │       │       │   Weight.   │
 ├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤
 │ Division 2 │ 25 miles │       │       │       │       │             │
 │20′ grades. │per hour. │       │       │       │       │             │
 ├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤
 │ Division 3 │ 25 miles │       │       │       │       │             │
 │40′ grades. │per hour. │       │       │       │       │             │
 ├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤
 │ Division 4 │ 25 miles │       │       │       │       │             │
 │60′ grades. │per hour. │       │       │       │       │             │
 ├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤
 │ Division 5 │ 25 miles │       │       │       │       │             │
 │80′ grades. │per hour. │       │       │       │       │             │
 ├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤
 │ Division 6 │ 25 miles │       │       │       │       │             │
 │100′ grades.│per hour. │       │       │       │       │             │
 └────────────┴──────────┴───────┴───────┴───────┴───────┴─────────────┘

The engines in the Northern States require more power in winter than in
summer.

To the above classification might be added, an engine for “making up
trains,” and similar station work; such an engine should be able to
start easily the extreme weights of trains, from fifty to one thousand
tons, and should be fitted with a power of varying its adhesion.

                                FORMULA.

                     _W_ × [(_V^2_)/171 + 8] = _R_.

                               _Example._

The speed being thirty miles per hour, and load 250 tons.

          _R_ will be [((30 × 30))/171 + 8] × 250 = 3315 lbs.

366. Table 1. Showing the required traction on a level for loads from
fifty to one thousand tons, and for velocities from ten to one hundred
miles per hour.

  ┌─────────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
  │Velocity.│  50   │  75   │  100  │  250  │  500  │  750  │ 1000  │
  │         │ Tons. │ Tons. │ Tons. │ Tons. │ Tons. │ Tons. │ Tons. │
  ├─────────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
  │       10│    429│    643│    858│   2146│   4292│   6435│   8585│
  │       12│    442│    663│    884│   2210│   4421│   6630│   8842│
  │       15│    465│    698│    931│   2328│   4657│   6982│   9315│
  │       20│    517│    773│   1034│   2585│   5170│   7735│       │
  │       25│    582│    874│   1165│   2912│   5825│       │       │
  │       30│    663│    994│   1326│   3315│   6630│       │       │
  │       40│    868│   1302│   1736│   4340│       │       │       │
  │       50│   1131│   1696│   2262│   5655│       │       │       │
  │       60│   1452│   2180│   2905│       │       │       │       │
  │      100│   3324│   4986│   6648│       │       │       │       │
  └─────────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘

                                FORMULA.

                               _WR_/_L_.

                               _Example._

The tractive power to overcome the resistance of 750 tons upon a sixty
feet grade is

                         750 × 60/5280 = 19050.

367. Table 2. Showing the tractive power necessary to overcome grades
from ten to one hundred feet per mile with loads from one to one
thousand tons.

 ┌──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┐
 │Grade.│1 Ton.│  50  │  75  │ 100  │ 250  │ 500  │ 750  │ 1000 │Grade.│
 │      │      │Tons. │Tons. │Tons. │Tons. │Tons. │Tons. │Tons. │      │
 ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │    10│     4│   212│   318│   424│  1061│  2121│  3181│  4240│    10│
 │    20│     8│   424│   636│   848│  2122│  4242│  6362│  8480│    20│
 │    30│    13│   636│   955│  1273│  3170│  6363│  9545│ 12730│    30│
 │    40│    16│   848│  1272│  1696│  4244│  8484│ 12724│ 16960│    40│
 │    50│    20│  1060│  1590│  2120│  5305│ 10605│ 15905│ 21200│    50│
 │    60│    26│  1272│  1910│  2546│  6340│ 12726│ 19050│ 25460│    60│
 │    70│    30│  1500│  2240│  3000│  7500│ 15000│ 22400│ 30000│    70│
 │    80│    33│  1697│  2545│  3393│  8489│ 16969│ 25459│ 33950│    80│
 │   100│    40│  2120│  3180│  4240│ 10610│ 21210│ 31810│ 42400│   100│
 ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │Grade.│1 Ton.│  50  │  75  │ 100  │ 250  │ 500  │ 750  │ 1000 │Grade.│
 │      │      │Tons. │Tons. │Tons. │Tons. │Tons. │Tons. │Tons. │      │
 └──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

                                FORMULA.

                                 6_T_.

                               _Example._

Required traction 5,000 lbs.; upon driving axles the weight is 5000 × 6
= 30,000 lbs.

368. Table 3. Giving the weight which should be placed upon the driving
axles to secure any amount of adhesion; the latter being one sixth of
the weight.

                    ┌─────────┬─────────┬─────────┐
                    │Required │Weight in│Weight in│
                    │traction.│ pounds. │  tons.  │
                    ├─────────┼─────────┼─────────┤
                    │      500│     3000│     1.34│
                    │     1000│     6000│     2.69│
                    │     2000│    12000│     5.36│
                    │     3000│    18000│     8.04│
                    │     4000│    24000│    10.80│
                    │     5000│    30000│    13.40│
                    │     6000│    36000│    16.07│
                    │     7000│    42000│    18.75│
                    │     8000│    48000│    21.43│
                    │     9000│    54000│    24.11│
                    │    10000│    60000│    26.80│
                    │    12000│    72000│    32.14│
                    │    14000│    84000│    37.50│
                    │    16000│    96000│    42.86│
                    │    18000│   108000│    48.22│
                    │    20000│   120000│    53.60│
                    └─────────┴─────────┴─────────┘

                                FORMULA.

                              (2_S_)/_c_.

         Where _S_ = stroke.
               _c_ = circumference of wheel, (both in inches.)

                               _Example._

Let stroke be twenty inches, and diameter of wheel five feet, the ratio
will be

                           40/188.4 = 0.2122.

369. Table of decimals, which, multiplied by the total piston pressures
(table 5) will give the traction in pounds, or ratio between double
stroke and wheel circumference. Table 4.

   ┌──────┬─────────────────────────────────────────────────┬──────┐
   │Wheel.│                STROKE IN INCHES.                │Wheel.│
   ├──────┼────┬────┬────┬────┬────┬────┬────┬────┬────┬────┼──────┤
   │      │ 18 │ 20 │ 22 │ 24 │ 26 │ 28 │ 30 │ 32 │ 34 │ 36 │      │
   ├──────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼──────┤
   │3½    │2728│3031│3334│3638│    │    │    │    │    │    │3½    │
   │3¾    │2553│2837│3120│3404│3688│    │    │    │    │    │3¾    │
   │4     │2386│2652│2918│3182│3444│3708│    │    │    │    │4     │
   │4¼    │2250│2500│2750│3000│3250│3500│3750│    │    │    │4¼    │
   │4½    │2151│2390│2593│2830│3071│3294│3529│3764│    │    │4½    │
   │4¾    │2012│2235│2459│2682│2905│3129│3352│3575│3800│    │4¾    │
   │5     │1910│2122│2334│2546│2766│2979│3192│3405│3617│3830│5     │
   │5½    │1736│1929│2122│2315│2500│2692│2885│3077│3273│3473│5½    │
   │6     │1591│1768│1945│2122│2321│2500│2678│2857│3036│3215│6     │
   │6½    │1468│1632│1796│1958│2131│2295│2459│2623│2790│2951│6½    │
   │7     │1364│1516│1667│1819│1970│2121│2273│2424│2576│2727│7     │
   │7½    │1272│1414│1556│1691│1831│1972│2114│2254│2394│2535│7½    │
   │8     │1194│1326│1417│1592│1688│1818│1948│2078│2208│2337│8     │
   ├──────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼──────┤
   │Wheel.│ 18 │ 20 │ 22 │ 24 │ 26 │ 28 │ 30 │ 32 │ 34 │ 36 │Wheel.│
   ├──────┼────┴────┴────┴────┴────┴────┴────┴────┴────┴────┼──────┤
   │      │                STROKE IN INCHES.                │      │
   └──────┴─────────────────────────────────────────────────┴──────┘

                                FORMULA.

                      2(_d^2_ .7854 × _p_) = _P_.

                     Where _d_ = diameter.
                           _p_ = pressure per inch.

                               _Example._

The whole pressure at one hundred pounds per inch on two sixteen inch
pistons will be

                   2[16 × 16 × 0.7854 × 100] = 40212.

370. Table 5. Total pressures upon pistons from ten to twenty-four
inches in diameter, and for steam pressures from fifty to one hundred
and fifty pounds per square inch.

 ┌──────┬───────┬──────────────────────────────────┬──────┐
 │Diam. │Area of│ WHOLE PISTON PRESSURE ON BOTH    │Diam. │
 │  of  │  one  │PISTONS, AT A PER INCH PRESSURE OF│  of  │
 │cyl’r.│Piston.│                                  │cyl’r.│
 ├──────┼───────┼──────┬──────┬──────┬──────┬──────┼──────┤
 │      │       │  50  │  60  │  70  │  80  │  90  │      │
 ├──────┼───────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │    10│   78.5│  7950│  9420│ 10990│ 12560│ 14130│    10│
 │    11│   95.0│  9500│ 11400│ 13300│ 15200│ 17100│    11│
 │    12│  113.1│ 11310│ 13572│ 15834│ 18096│ 20358│    12│
 │    13│  132.7│ 13270│ 15924│ 18564│ 21232│ 23906│    13│
 │    14│  153.9│ 15390│ 18468│ 21546│ 24624│ 27702│    14│
 │    15│  176.7│ 17670│ 21204│ 24738│ 28272│ 31806│    15│
 │    16│  201.1│ 20110│ 24132│ 28154│ 32176│ 36198│    16│
 │    17│  227.0│ 22700│ 27240│ 31780│ 36320│ 40860│    17│
 │    18│  254.5│ 25450│ 30540│ 35630│ 40720│ 45810│    18│
 │    19│  283.5│ 28350│ 34020│ 39690│ 45360│ 51030│    19│
 │    20│  314.2│ 31420│ 37704│ 43988│ 50272│ 56556│    20│
 │    21│  346.4│ 34640│ 41568│ 48496│ 55424│ 62352│    21│
 │    22│  380.1│ 38010│ 45612│ 53214│ 60816│ 68418│    22│
 │    23│  415.5│ 41550│ 49860│ 58170│ 66480│ 74790│    23│
 │    24│  452.4│ 45240│ 54288│ 63336│ 72384│ 81432│    24│
 └──────┴───────┴──────┴──────┴──────┴──────┴──────┴──────┘

 ┌──────┬─────────────────────────────────────────┬──────┐
 │Diam. │ PISTONS, AT A PER INCH PRESSURE OF      │Diam. │
 │  of  │                                         │  of  │
 │cyl’r.│                                         │cyl’r.│
 ├──────┼──────┬──────┬──────┬──────┬──────┬──────┼──────┤
 │      │ 100  │ 110  │ 120  │ 130  │ 140  │ 150  │      │
 ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │    10│ 15700│ 17270│ 18840│ 20410│ 21980│ 23550│    10│
 │    11│ 19000│ 20900│ 22800│ 24700│ 26600│ 28500│    11│
 │    12│ 22620│ 24882│ 27144│ 29406│ 31768│ 33930│    12│
 │    13│ 26540│ 29194│ 31848│ 34502│ 37156│ 39810│    13│
 │    14│ 30780│ 33858│ 36756│ 40014│ 43092│ 46170│    14│
 │    15│ 35340│ 38874│ 42408│ 55942│ 49476│ 53010│    15│
 │    16│ 40220│ 44242│ 48264│ 52062│ 56308│ 60330│    16│
 │    17│ 45400│ 49940│ 54480│ 59020│ 63560│ 68100│    17│
 │    18│ 50900│ 55990│ 61080│ 66170│ 71260│ 76350│    18│
 │    19│ 56700│ 62370│ 68040│ 73710│ 79380│ 85050│    19│
 │    20│ 62840│ 69124│ 75408│ 81692│ 87976│ 95260│    20│
 │    21│ 69380│ 76208│ 83136│ 90064│ 96992│103920│    21│
 │    22│ 77020│ 83622│ 91224│ 98826│106428│114030│    22│
 │    23│ 83100│ 91410│ 99720│108030│116340│124650│    23│
 │    24│ 90480│ 99528│108576│117626│126672│135720│    24│
 └──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

                                FORMULA.

                          _N_ = 5280/_c_ × 4.

                    Where _N_ = the number.
                          _c_ = wheel circumference.

                               _Example._

Speed twenty-five miles per hour, wheels four and a half feet, the
number of cylinders per hour is

                   25 × 5280/(4 × 3.1416) × 4 = 37348

371. Table 6. Showing the hourly consumption of steam in terms of the
capacity of one cylinder, with wheels from three and a half to eight
feet, and speeds from ten to sixty miles per hour.

 ┌──────┬───────┬───────────┐
 │Wheel.│ Wheel │Revolutions│
 │      │  in   │ per mile. │
 │      │inches.│           │
 ├──────┼───────┼───────────┤
 │      │       │           │
 ├──────┼───────┼───────────┤
 │3½    │  42   │    480    │
 │3¾    │  45   │    449    │
 │4     │  48   │    421    │
 │4¼    │  51   │    397    │
 │4½    │  54   │    373    │
 │4¾    │  57   │    361    │
 │5     │  60   │    336    │
 │5½    │  66   │    306    │
 │6     │  72   │    281    │
 │6½    │  78   │    259    │
 │7     │  84   │    240    │
 │7⅛    │  90   │    224    │
 │8     │  96   │    211    │
 └──────┴───────┴───────────┘

 ┌──────┬─────────────────────────────────────────────────────┐
 │Wheel.│    NUMBER OF CYLINDERS PER HOUR AT A VELOCITY OF    │
 │      │                                                     │
 │      │                                                     │
 ├──────┼─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┤
 │      │ 10  │ 12  │ 15  │ 20  │ 25  │ 30  │ 40  │ 50  │ 60  │
 ├──────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
 │3½    │19200│23040│     │     │     │     │     │     │     │
 │3¾    │17960│21552│26940│     │     │     │     │     │     │
 │4     │16840│20208│25260│33681│     │     │     │     │     │
 │4¼    │15880│19056│23820│31760│39700│     │     │     │     │
 │4½    │14920│17904│22380│29840│37300│     │     │     │     │
 │4¾    │14440│17328│21660│28880│36100│     │     │     │     │
 │5     │     │     │20160│26880│33600│     │     │     │     │
 │5½    │     │     │18360│24480│30600│36720│     │     │     │
 │6     │     │     │     │22480│28100│33720│44960│     │     │
 │6½    │     │     │     │20720│25900│31080│41440│51800│62160│
 │7     │     │     │     │19200│24000│28800│38400│48000│57600│
 │7⅛    │     │     │     │     │22400│26880│35840│44800│53760│
 │8     │     │     │     │     │21109│25320│33760│42200│50640│
 └──────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘


                                FORMULA.

                  (_D^2_ × .7854 × Stroke)/1728 = _C_.

                               _Example._

Cubic content of a cylinder 15 × 24 is

            (15 × 15 × 0.7854 × 24)/1728 = 2.44 cubic feet.

372. Table 7. Capacity of cylinders in cubic feet of from ten to
twenty-four inches in diameter, and from eighteen to thirty-six inches
stroke.

        ┌──────┬───────────────────────────────────────┬──────┐
        │Diam. │ CAPACITY OF CYLINDERS IN CUBIC FEET,  │Diam. │
        │  of  │             STROKE BEING              │  of  │
        │cyl’r.│                                       │cyl’r.│
        ├──────┼───┬───┬───┬───┬───┬───┬───┬───┬───┬───┼──────┤
        │      │18 │20 │22 │24 │26 │28 │30 │32 │34 │36 │      │
        ├──────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼──────┤
        │  10  │082│091│100│109│118│127│136│145│   │   │  10  │
        │  11  │093│104│115│126│137│148│159│170│181│   │  11  │
        │  12  │118│131│144│157│170│183│196│209│222│235│  12  │
        │  13  │133│149│165│181│197│213│229│245│261│277│  13  │
        │  14  │160│178│196│214│232│250│268│286│304│322│  14  │
        │  15  │184│204│224│244│264│284│304│324│344│364│  15  │
        │  16  │208│232│255│278│301│324│347│370│393│416│  16  │
        │  17  │235│263│289│315│341│367│393│419│445│471│  17  │
        │  18  │263│294│323│352│381│410│439│468│497│526│  18  │
        │  19  │   │   │361│394│427│460│493│526│559│592│  19  │
        │  20  │   │   │400│437│474│511│548│585│622│659│  20  │
        │  21  │   │   │   │481│521│561│601│641│681│721│  21  │
        │  22  │   │   │   │528│572│616│660│704│748│792│  22  │
        │  23  │   │   │   │   │625│674│723│772│821│876│  23  │
        │  24  │   │   │   │   │681│733│785│837│889│941│  24  │
        └──────┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴──────┘

373. Table 8. Giving the volume, pressure, temperature, and density of
steam.

 ┌──────────┬──────────┬────────────┬──────────┬──────────┬──────────┐
 │          │ Relative │            │          │          │          │
 │          │volume or │            │          │Weight of │          │
 │  Steam   │cubic feet│Temperature.│  Total   │ a cubic  │  Steam   │
 │pressure. │of steam, │            │  heat.   │  foot.   │pressure. │
 │          │  water   │            │          │          │          │
 │          │ being 1. │            │          │          │          │
 ├──────────┼──────────┼────────────┼──────────┼──────────┼──────────┤
 │    50    │   552    │    281     │   1200   │   1129   │        50│
 │    60    │   467    │    293     │   1203   │   1335   │        60│
 │    65    │   434    │    298     │   1205   │   1436   │        65│
 │    70    │   406    │    303     │   1206   │   1535   │        70│
 │    75    │   381    │    307     │   1208   │   1636   │        75│
 │    80    │   359    │    312     │   1209   │   1736   │        80│
 │    90    │   323    │    320     │   1212   │   1929   │        90│
 │   100    │   293    │    328     │   1214   │   2127   │       100│
 │   110    │   269    │    335     │   1216   │   2317   │       110│
 │   120    │   249    │    341     │   1218   │   2505   │       120│
 │   130    │   231    │    347     │   1220   │   2698   │       130│
 │   140    │   216    │    353     │   1221   │   2885   │       140│
 │   150    │   203    │    358     │   1223   │   3070   │       150│
 └──────────┴──────────┴────────────┴──────────┴──────────┴──────────┘

                                FORMULA.

                          _S_ =√(_ac_) × 21.2.

               Where _S_ = surface.
                     _a_ = grate area.
                     _c_ = cubic feet of water per hour.

                               _Example._

Grate area sixteen square feet, cubic feet of water per hour two
hundred, surface is

                     √(16 × 200) × 21.2 = 1199.92.

374. Table 9. Showing the necessary amount of grate area and heating
surface for an hourly consumption of water.

 ┌──────┬─────────────────────────────────────────────────────────────┐
 │Cubic │                                                             │
 │ft. of│                                                             │
 │water │                 GRATE AREAS IN SQUARE FEET.                 │
 │evap’d│                                                             │
 │ per  │                                                             │
 │hour. │                                                             │
 ├──────┼───┬───┬───┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┤
 │      │ 7 │ 8 │ 9 │ 10 │ 11 │ 12 │ 13 │ 14 │ 15 │ 16 │ 17 │ 18 │ 19 │
 ├──────┼───┴───┴───┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┤
 │      │           HEATING SURFACE CORRESPONDING TO ABOVE            │
 │      │               GRATE AREAS AND TO SIDE COLUMN.               │
 ├──────┼───┬───┬───┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┤
 │   100│561│599│636│ 670│ 703│ 734│ 764│ 793│ 821│ 848│ 874│ 900│ 924│
 │   110│588│628│667│ 702│ 737│ 770│ 802│ 831│ 861│ 888│ 916│ 943│ 969│
 │   120│614│657│697│ 734│ 770│ 805│ 837│ 869│ 900│ 927│ 957│ 985│1013│
 │   130│639│683│725│ 764│ 801│ 837│ 871│ 904│ 936│ 965│ 996│1025│1053│
 │   140│663│709│752│ 793│ 831│ 869│ 904│ 938│ 972│1003│1034│1064│1093│
 │   150│686│734│779│ 821│ 860│ 900│ 935│ 971│1006│1038│1070│1101│1131│
 │   160│   │758│805│ 848│ 889│ 927│ 966│1004│1039│1073│1106│1138│1169│
 │   170│   │782│829│ 874│ 916│ 957│ 996│1034│1071│1106│1140│1173│1205│
 │   180│   │805│853│ 900│ 943│ 985│1025│1064│1102│1138│1173│1207│1240│
 │   190│   │   │877│ 924│ 969│1013│1053│1093│1132│1169│1205│1240│1274│
 │   200│   │   │900│ 948│ 995│1039│1081│1122│1161│1199│1236│1272│1307│
 │   210│   │   │928│ 974│1019│1064│1107│1149│1189│1229│1264│1298│1336│
 │   220│   │   │   │1000│1042│1089│1133│1176│1217│1258│1291│1324│1365│
 │   230│   │   │   │1019│1067│1114│1159│1203│1245│1286│1323│1359│1398│
 │   240│   │   │   │    │1091│1138│1184│1229│1272│1314│1354│1393│1431│
 │   250│   │   │   │    │1111│1162│1208│1254│1298│1341│1380│1422│1458│
 │   260│   │   │   │    │    │1184│1232│1278│1323│1367│1406│1450│1484│
 │   270│   │   │   │    │    │1207│1256│1303│1349│1401│1433│1478│1515│
 │   280│   │   │   │    │    │    │1279│1327│1374│1435│1460│1505│1546│
 │   290│   │   │   │    │    │    │1302│1351│1400│1452│1486│1532│1573│
 │   300│   │   │   │    │    │    │    │1374│1425│1469│1512│1558│1600│
 │   320│   │   │   │    │    │    │    │    │1469│1516│1564│1610│1654│
 │   340│   │   │   │    │    │    │    │    │    │1564│1612│1658│1704│
 │   360│   │   │   │    │    │    │    │    │    │    │1658│1706│1754│
 │   380│   │   │   │    │    │    │    │    │    │    │    │1753│1802│
 │   400│   │   │   │    │    │    │    │    │    │    │    │1800│1848│
 │   425│   │   │   │    │    │    │    │    │    │    │    │    │    │
 │   450│   │   │   │    │    │    │    │    │    │    │    │    │    │
 │   475│   │   │   │    │    │    │    │    │    │    │    │    │    │
 │   500│   │   │   │    │    │    │    │    │    │    │    │    │    │
 └──────┴───┴───┴───┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘

 ┌──────┬──────────────────────────────────────────────────────┐
 │Cubic │                                                      │
 │ft. of│                                                      │
 │water │             GRATE AREAS IN SQUARE FEET.              │
 │evap’d│                                                      │
 │ per  │                                                      │
 │hour. │                                                      │
 ├──────┼────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┤
 │      │ 20 │ 21 │ 22 │ 23 │ 24 │ 25 │ 26 │ 27 │ 28 │ 29 │ 30 │
 ├──────┼────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┤
 │      │       HEATING SURFACE CORRESPONDING TO ABOVE         │
 │      │           GRATE AREAS AND TO SIDE COLUMN.            │
 ├──────┼────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┤
 │   100│ 948│ 972│ 995│1017│1039│1060│1081│1102│1122│1142│1161│
 │   110│ 994│1018│1042│1066│1089│1111│1133│1155│1176│1197│1217│
 │   120│1039│1064│1089│1114│1138│1162│1184│1207│1229│1251│1272│
 │   130│1081│1107│1133│1159│1184│1208│1232│1255│1278│1300│1323│
 │   140│1122│1150│1177│1203│1229│1254│1279│1303│1327│1351│1374│
 │   150│1161│1190│1218│1245│1272│1298│1323│1350│1373│1398│1422│
 │   160│1199│1229│1258│1286│1314│1341│1367│1393│1419│1444│1469│
 │   170│1236│1266│1296│1325│1354│1382│1409│1436│1462│1488│1514│
 │   180│1272│1303│1334│1364│1393│1422│1450│1478│1505│1532│1558│
 │   190│1307│1339│1370│1401│1431│1461│1490│1518│1546│1573│1600│
 │   200│1341│1374│1406│1437│1468│1499│1529│1558│1586│1614│1642│
 │   210│1374│1408│1441│1473│1505│1536│1566│1596│1625│1654│1683│
 │   220│1406│1441│1475│1508│1541│1572│1603│1634│1664│1693│1722│
 │   230│1437│1473│1508│1542│1575│1607│1639│1663│1701│1724│1761│
 │   240│1468│1505│1541│1575│1609│1642│1675│1692│1738│1754│1799│
 │   250│1499│1533│1572│1606│1642│1675│1709│1733│1774│1797│1836│
 │   260│1529│1560│1603│1636│1675│1708│1743│1774│1809│1840│1872│
 │   270│1557│1592│1634│1668│1692│1741│1776│1808│1843│1875│1908│
 │   280│1586│1624│1664│1700│1738│1774│1809│1842│1877│1910│1943│
 │   290│1614│1653│1693│1729│1754│1804│1841│1873│1910│1939│1977│
 │   300│1642│1682│1722│1758│1799│1834│1872│1904│1943│1968│2011│
 │   320│1696│1738│1778│1816│1859│1894│1932│1970│2008│2024│2078│
 │   340│1748│1792│1833│1872│1915│1954│1993│2032│2069│2096│2141│
 │   360│1800│1844│1886│1928│1971│2012│2050│2090│2128│2166│2204│
 │   380│1848│1894│1938│1982│2025│2066│2107│2148│2187│2226│2264│
 │   400│1900│1944│1990│2034│2077│2120│2162│2204│2244│2284│2322│
 │   425│1950│2014│2056│2077│2142│2187│2226│2268│2317│2353│2396│
 │   450│2014│2056│2120│2150│2190│2200│2300│2332│2374│2417│2459│
 │   475│    │    │2175│2210│2268│2310│2353│2416│2445│2480│2523│
 │   500│    │    │    │    │2332│2370│2412│2459│2523│2565│2608│
 └──────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘

                                FORMULA.

                 _N_ = _S_/(_Ld_π) or _S_/(_Ld_3.1416).

                     Where _S_ = whole surface,
                     Where _L_ = length,
                     Where _d_ = diameter, in feet,
                     Where  π  = 3.1416,
                     Where _N_ = the number.

                               _Example._

Diameter two inches, surface 1466, length fourteen feet, we have,

                _N_ = 1466/(14 × 0.167 × 3.1416) = 200.

375. Table 10. Giving the number and dimensions of tubes to obtain any
given amount of surface.

 ┌──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┐
 │L’gth.│Diam. │Diam. │Diam. │Diam. │Diam. │Diam. │Diam. │Diam. │L’gth.│
 │      │  1½  │  1¾  │  1⅞  │   2  │  2⅛  │  2¼  │  2⅜  │  2½  │      │
 ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤
 │     8│   314│   336│   397│   419│   445│   471│   504│   523│     8│
 │    8½│   334│   389│   422│   445│   473│   500│   535│   556│    8½│
 │     9│   352│   411│   447│   471│   507│   530│   566│   588│     9│
 │    9½│   372│   435│   471│   497│   523│   559│   597│   621│    9½│
 │    10│   392│   457│   496│   524│   556│   589│   628│   655│    10│
 │   10½│   411│   480│   521│   549│   584│   618│   659│   687│   10½│
 │    11│   431│   503│   545│   576│   612│   647│   690│   720│    11│
 │   11½│   451│   526│   570│   602│   640│   677│   721│   753│   11½│
 │    12│   471│   549│   595│   628│   667│   705│   752│   786│    12│
 │   12½│   490│   572│   620│   654│   695│   735│   783│   818│   12½│
 │    13│   510│   595│   645│   681│   723│   764│   814│   851│    13│
 │   13½│   530│   617│   669│   707│   750│   793│   845│   884│   13½│
 │    14│   549│   640│   695│   733│   778│   823│   876│   916│    14│
 │   14½│   569│   663│   719│   759│   806│   852│   907│   949│   14½│
 │    15│   589│   686│   744│   785│   834│   882│   938│   982│    15│
 │   15½│   608│   708│   769│   811│   861│   911│   969│  1015│   15½│
 │    16│   628│   731│   794│   837│   889│   941│  1000│  1048│    16│
 │   16½│   648│   754│   819│   863│   917│   971│  1031│  1081│   16½│
 │    17│   668│   777│   843│   889│   945│  1000│  1062│  1114│    17│
 └──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

                                FORMULA.

                            13.5√(_a_) – 28,

where _a_ is the percentage of admission.

                               _Example._

What is the mean pressure, with an initial pressure of one hundred
pounds, and sixty per cent. admission.

    13.5√(60) – 28 = (13.5 × 7.7)  – 28 = 76/100 of 100, or 76 lbs.

376. Table 11. Showing the mean cylinder steam pressure for any
percentage of admission, the initial pressure being from 50 to 150 lbs.
per inch.

   ┌────────┬───────────────────────────────────────────────────────┐
   │Initial │                                                       │
   │pressure│ MEAN CYLINDER PRESSURE, ADMISSION BEING IN HUNDREDTHS │
   │   in   │                    OF THE STROKE.                     │
   │pounds. │                                                       │
   ├────────┼───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┤
   │        │10 │15 │20 │25 │30 │35 │40 │45 │50 │55 │60 │65 │70 │75 │
   ├────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┤
   │      50│  7│ 12│ 16│ 20│ 23│ 26│ 28│ 31│ 33│ 36│ 38│ 40│ 42│ 44│
   │      60│  9│ 14│ 19│ 24│ 28│ 31│ 34│ 37│ 40│ 43│ 46│ 49│ 51│ 53│
   │      70│ 10│ 17│ 22│ 28│ 33│ 36│ 40│ 43│ 47│ 50│ 54│ 57│ 59│ 62│
   │      80│ 12│ 19│ 26│ 32│ 38│ 42│ 41│ 49│ 54│ 58│ 62│ 65│ 68│ 71│
   │      90│ 13│ 22│ 29│ 36│ 42│ 47│ 51│ 54│ 60│ 65│ 69│ 73│ 76│ 80│
   │     100│ 15│ 24│ 32│ 40│ 47│ 52│ 57│ 62│ 67│ 72│ 77│ 81│ 85│ 89│
   │     110│ 16│ 26│ 35│ 44│ 52│ 57│ 63│ 68│ 74│ 79│ 85│ 89│ 93│ 98│
   │     120│ 18│ 29│ 38│ 48│ 56│ 62│ 68│ 74│ 80│ 86│ 91│ 97│102│107│
   │     130│ 19│ 31│ 42│ 52│ 61│ 68│ 74│ 81│ 87│ 94│ 99│105│110│116│
   │     145│ 21│ 34│ 45│ 56│ 65│ 73│ 80│ 87│ 94│101│107│113│119│125│
   │     160│ 22│ 36│ 48│ 60│ 70│ 78│ 85│ 93│100│108│114│121│127│134│
   └────────┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘


                                PART II.
                                 CARS.


                           WHEELS AND AXLES.

377. Of the mechanical details of car building it is not necessary here
to speak; but of those matters which fit a car for special duty, and
depend upon particular characteristics of any road, such as the gauge,
something must be said.

The trend of the wheel tire, as remarked in Chapter XIII., is not turned
cylindrical, but conical. A perfectly straight road would of course
require no cone upon the wheels; the object of the latter being to vary
the wheel diameter when upon curves. The general practice is to give a
certain standard cone to all wheels, for all gauges. This is quite
wrong, as will be seen by the following formula, which is from “Pambour
on the Locomotive Engine.”

[Illustration: Fig. 156.]

Let _m m′_, fig. 156, represent the outer rail, and _n n′_ the inner
one. The circumferences upon the same axles must evidently vary as the
length of these curves, which are included between the same radii.

Let _D_, be the diameter of the first wheel, and _d_, that of the
second; and we shall have,

                   (_mm′_)/(_nn′_) =  (π_D_)/(π_d_),

or otherwise

                          _mm′_ = 3.1416 _D_,

and

                          _nn′_ = 3.1416 _d_.

We have also,

                    (_mm′_)/(_nn′_) = (_mo_)/(_no_).

Expressing the radius of curvature by _r_, and the half gauge by _e_,
the above proportion may be expressed by

               (_mm′_)/(_nn′_) = (_r_ + _e_)/(_r_ – _e_),

and also

                   _D_/_d_ = (_r_ + _e_)/(_r_ – _e_),

and finally

                    _D_ – _d_ = (2_eD_)/(_r_ + _e_).

This equation shows the difference in diameters that ought to exist
between the inner and outer wheels, that the required effect, (no
dragging of the outer and no slipping of the inner wheel,) is produced.

                               _Example._

               Let the radius of curvature be 1,000 feet.
               The gauge of the road,             6 feet.
               The wheel diameter,                4 feet.

And the formula becomes

               (2_ed_)/(_r_ + _e_) = 24/1003 = .024 feet,

or .288 inch on both wheels, or 0.144 inch for each wheel; which for
four inches breadth, gives a curve of 1/28 of the width, or decimally,
0.144, and vulgarly, ⅐ of an inch. For a three feet wheel, the rule
gives a cone of 0.11 inch.

  NOTE.—Messrs Bush and Lobdel cone their wheels 0.08 inches in a four
  inch tire; or ¼ inch per foot. The formula above for a three feet
  wheel, and 4′ 8½″ gauge, gives a curve of 0.09 inches.

The wheel most used upon American roads is made of cast-iron, in one
piece, and consists either of two side plates, connected by a hub and
rim, or of a central plate ribbed on the sides. Messrs Whitney and Son,
(Philadelphia,) pass all their wheels through an annealing process,
which renders them much less liable to fracture from shocks and from
cold than when the wheel is allowed to cool at once, when hot from the
foundery.

The wheels used upon English roads are made with a wrought iron rim and
spokes, with a cast hub, the tire being, put on separately. Such wheels
are less liable to fracture, but cost more than the American wheel.

378. A very frequent cause of accident upon railroads, is the breakage
of axles. Experiments made at Wolverhampton, (England,) upon differently
formed axles, show very plainly that it is quite wrong to reduce the
diameter of the axle at the middle. That if any variation exists it
should be in making the middle the largest. That the effect of a
shoulder behind the wheel was to decrease very much the strength.
Probably the strongest and most economical railroad axle, would be a
wrought iron tube. Certainly a hollow axle is much stronger in resisting
tension than a solid one containing the same amount of material.

  NOTE 1.—Thomas Thorneycroft, of Wolverhampton, England, an educated
  man, and a manufacturer of railway axles, observes:—That the various
  forms of axles, as generally made, possess within themselves the
  elements of destruction. That there are certain fixed principles to
  be observed in proportioning axles, and that just as such principles
  are departed from, just so much is liability to failure increased.

  He says:—It is doubtful whether the wheel is the support and the
  journal the loaded part, or the reverse. If the latter is the case,
  then the cone of the wheels causes a lateral strain, tending to bend
  the axle; and should that bending extend no further than one half of
  the elastic limit, if long continued, fracture must result; and
  should the elastic limit be exceeded, the plane of the wheel will be
  removed from that in which it ought to revolve.

  The object of the first experiment was to determine the effect of
  the form of the longitudinal section of the axle upon its elastic
  limit.

  By reducing the diameter of the axle from 45/16 inches at centre, to
  3¾ inches; the limit of elasticity was reduced from .343 to .232
  inches; and the load, to produce that elasticity, from fourteen to
  seven tons.

  Experiment second was to ascertain the effect of a reduction of
  diameter at the centre, upon the ability to resist sudden shocks.
  One half of the axle was made 4½ inches in diameter from middle to
  end, and the other half was reduced from 4½ to four inches at
  centre. The wheel being fixed, and a ram allowed to fall upon the
  journal, when the following result was obtained. Under forty-six
  blows, the unreduced end was bent to an angle of eighteen degrees.
  Under sixteen blows, the reduced end was bent to twenty-two degrees.

  Experiment third was to ascertain the effect of a shoulder behind
  the wheel, one end being turned with a shoulder of one eighth of an
  inch, as a stop to the wheel, the other end turned plain. Tested by
  hydraulic pressure, the shouldered end broke with sixty tons, the
  plain end with eighty-four tons.

  The object of the fourth experiment was to find the influence of the
  position of the wheel, as regards the end of the journal. An axle
  was fastened into a cast-iron frame, in a line with the neck of the
  journal, when the latter was broke with seven blows of a ram falling
  ten feet. The other end was keyed into the frame, with the neck of
  the journal projecting 1½ inch, and broke at the twenty-fourth blow
  of the same ram, falling ten feet.

  The results of the trials are thus summed up by the
  experimenter:—That axles should never be smaller at the centre than
  at the ends, but on the contrary, that if a difference in size is
  made, the centre should be the largest.

  The best authorities on the strength of materials, give the hollow
  tube as three times stronger in resisting twisting, than the solid
  bar possessing the same weight. Thus an axle with an external
  diameter of five inches, and an internal diameter of 3¾ inches, is
  three times as strong as a solid axle of 3¾ inches diameter.

                  *       *       *       *       *

  NOTE 2.—The following experiments were prepared by M. Bourville, and
  executed by the Austrian government. The apparatus consisted of a
  bent axle, which was firmly fixed up to the elbow in timber, and
  which was subjected to torsion by means of a cog-wheel connected
  with the end of the horizontal part. At each turn the angle of
  torsion was twenty-four degrees. A shock was produced each time that
  the bar left one tooth to be raised by the next. An index adapted to
  the apparatus, indicated the number of revolutions and shocks. Seven
  axles, submitted to this trial, presented the following results:—

  1st. The movement lasted one hour; 10,800 revolutions and 32,400
  shocks were produced. The axle, two and six tenths inches in
  diameter, was taken from the machine and broken by an hydraulic
  press. No change in the texture of the iron was visible.

  2d. A new axle, having been tried four hours, sustained 129,000
  torsions, and was afterwards broken by means of an hydraulic press.
  No alteration of the iron could be discovered, by the naked eye, on
  the surface of rupture; but tried with a microscope, the fibres
  appeared without adhesion, like a bundle of needles.

  3d. A third axle was subjected, during twelve hours, to 388,000
  torsions, and broken in two. A change in its texture, and an
  increased size in the grain of the iron, was observed by the naked
  eye.

  4th. After one hundred and twenty hours, and 3,888,000 torsions, the
  axle was broken in many places; a considerable change in its texture
  was apparent, which was more striking towards the centre; the size
  of the grains diminished towards the extremities.

  5th. An axle, submitted to 23,328,000 torsions during seven hundred
  and twenty hours, was completely changed in its texture; the
  fracture in the middle was crystalline, but not very scaly.

  6th. After ten months, during which the axle was submitted to
  78,732,000 torsions and shocks, fracture, produced by an hydraulic
  press, showed clearly an absolute transformation of the structure of
  the iron; the surface of rupture was scaly like pewter.

  7th. Finally, as a last trial, an axle submitted to 128,304,000
  torsions, presented a surface of rupture like that in the preceding
  experiment. The crystals were perfectly well defined, the iron
  having lost every appearance of wrought iron.


                        CLASSIFICATION OF CARS.

379. Railroad cars come under three general heads,

                     Those for passenger transport,
                     Those for freight traffic,
                     Those for repairs of the road.

380. The American passenger car consists of a body about fifty feet
long, ten feet wide, and seven feet high, containing seats for about
sixty passengers, being cushioned, warmed, lighted, and ventilated.
Except for emigrants, second and third class cars are but little used in
America.

House, box, or covered freight cars, differ from the “flat,” or platform
car, only in having a simple rectangular house, about six feet high and
nine feet wide, built upon the floor. This is used for the protection of
such freight as will not bear exposure; as furniture, books, dry goods,
hardware, and small machinery. Carriages, boxes, bales, masts, lumber,
and fuel are carried by platform cars. Bulky machinery, and first and
second class freight too large for the box cars, should be protected by
tarpaulins.

381. The general arrangement of wheels, springs, and brakes, is the same
for the several classes of cars, the chief difference being in the ease
of springs. Each car rests upon two “trucks,” consisting of four, six,
or eight wheels, so connected by levers and springs, as best to absorb
shocks, and connected with the body by a pin only, by which the passage
of curves is made quite easy.

Cars used for the movement of earth are so arranged as to allow the body
to be tipped up, that the contents may be quickly “dumped,” either at
the sides, ends, or middle, as desired.

382. Upon some roads, a continuous draw bar is passed under the whole
train, the several cars being attached to it, and to each other by
safety chains only. By adopting this, and at the same time by springing
the buffer beams tight upon each other, the whole train becomes one
piece; and the jerks at stopping and at starting are in a great measure
avoided.

As lightness combined with strength is a desideratum in all cases, it
will be found best to truss the longitudinal frame pieces of the car
with rods, rather than to use large and heavy beams, as done by many
builders.


                          RETARDING OF TRAINS.

383. As regards the mode of retarding trains of cars, the practice of
applying blocks to the wheels is justly considered by many as quite
wrong. The brake should be applied to the rail and not to the wheel.
Blocks drawn against the wheel are supplied with friction by means of
levers worked by a brakeman, who can at pleasure cause the wheels to
slide upon the rail. A shoe, sliding upon the rail, may be supplied with
friction from the whole weight of the car.

The retarding force should be applied at once to every car alike; if too
much in front, the rear cars are driven against those in advance; if too
much behind, the train is liable to break.

The proper place for the brakeman is upon the top of the train, where
all signals may be quickly seen.




                              CHAPTER XV.
                               STATIONS.


                      CLASSIFICATION OF BUILDINGS.

384. The entire establishment of buildings for operating a railroad,
consists of the

                               ┌──────────┐
                      Terminal,│Passenger,│Stations.
                               │ Freight, │
                               ├──────────┤
                           Way,│Passenger,│Stations.
                               │ Freight, │
                               └──────────┘
                         Engine houses.
                         Repair shops, (for engines).
                         Repair shops, (for cars).
                         Wood sheds.
                         Water tanks.

And appertaining to these, scales for the weighing of cars and freight;
turntables, transfer tables, switch and gate houses.


                         LOCATION OF BUILDINGS.

385. The location of the several buildings mentioned above will depend
upon the situation of the terminus, the character of the traffic, and
the number of trains arriving and departing.


                       TERMINAL PASSENGER HOUSE.

386. The passenger house should be at the most convenient point of
access to the persons using it. The freight buildings should be at the
most convenient point for receiving, shipping, and distributing
merchandise.

The engine and car houses, with the shops for repair, may be placed
where the land is cheap, and so distant from dwelling-houses as not to
cause inconvenience to the inmates thereof by smoke and noise. The wood
sheds, tanks, turntables, etc., etc., are generally at the engine
houses; weigh scales, etc., at the freight buildings.

387. A railroad which connects the interior with a seaport, would
probably bring two classes of freight; one for export and one for home
consumption. The first should be carried at once to the wharves and
loaded into the ships with one transshipment; while the second should be
delivered as near as possible to the centre of home trade.

The departments of arrival and departure should be kept quite distinct,
when the amount of business transacted is considerable; otherwise
operating will become complicated. The arrival part of a large passenger
house requires a great number of doors, that exit may be easy to the
large number of passengers that arrive at once. The departure rooms
require few doors, as departing passengers come singly or in small
bodies. Thus, in large cities the front of a long rectangle is given to
departure, while a long side, communicating with an outside platform,
forms the arriving room.

One thing in particular ought to be looked to by American railroad
companies,—the arrangement of public vehicles that shall secure
travellers from the impositions and extortions of hack-drivers. No
person whatever should have access to any building except passengers and
the railroad officials. The places of the several carriages, and the
rates of pay for the same, should be fixed by the company; the fare
being paid by checks bought by the traveller from a company agent at the
station.


                        TERMINAL FREIGHT HOUSE.

388. The terminal freight house should contain all of the apparatus
necessary for receiving and embarking freight. When the central part of
the building is occupied by tracks, and the sides by platforms, the
landing platform should incline gently from the car to the door; and
that for loading, from the door to the car. This arrangement facilitates
the handling of freight. The interior of the building may be divided
into departments, either according to the destination or the class of
the freight.


                    ENGINE HOUSE AND APPURTENANCES.

389. A terminal engine house, with a table in the centre, to contain

               10 engines, must be 145 feet in diameter.
               15 engines, must be 150 feet in diameter.
               20 engines, must be 167 feet in diameter.
               25 engines, must be 183 feet in diameter.
               30 engines, must be 200 feet in diameter.
               35 engines, must be 217 feet in diameter.
               40 engines, must be 233 feet in diameter.
               45 engines, must be 250 feet in diameter.
               50 engines, must be 267 feet in diameter.

The diameter of the table being forty-five feet, and the engine
occupying, when off from the table, fifty feet. Again, thirty-two
engines would require a diameter of

               (32 × 10)/3.1416 + (2 × 50) = 202 nearly.

The engines within the house may be supplied with water from small tanks
between each alternate pair of pits, (each tank holding five thousand
gallons,) or the entire building may be furnished from a cast-iron pipe
running around the whole, and being in connection with a large tank. In
such pipe there should be a gate over the centre of each pit, and near
its upper end. It may be convenient to connect all to a series of small
tanks, by a pipe, that the water level may be kept nearly constant.

Repair shops for engines and for cars, may be plain, rectangular
buildings, so arranged as to accommodate the necessary machinery.

Turntables consist of simply a circular framework of wood or iron,
placed at the centre upon a solid iron pintle which bears the whole
weight, and guided at the circumference by a series of fifteen,
eighteen, or twenty wheels fourteen or fifteen inches in diameter. The
wheels are placed in an independent spider frame, and run upon a curved
rail placed on the bottom masonry, and the table runs upon the top of
the wheels, so that the motion of the circumference of the table is
double that of the wheels.

The frame consists, first, of a pair of timbers ten or twelve inches
wide and fifteen or sixteen inches deep, upon which the rails are
placed, strongly trussed so as to throw the load upon the centre. At
right angles to these are placed, at a distance of eight or ten feet,
timbers 5 × 10, also trussed, which serve to connect the load more
completely with the wheels. The whole is stiffened by diagonal bracing,
and is strongly floored. The table is turned by a pinion upon itself,
working into a rack fastened to the foundation or to the side masonry.
The trusses, as also the centre bearing, should be capable of adjustment
vertically.

The cost of the table, exclusive of masonry, is from $1,200 to $1,800.

Weigh scales are made similar to, but stronger than, the ordinary
hay-scales, being rigid and strong enough to bear the weight of a
locomotive. Every car (freight) placed upon the road should have the
number and the exact weight painted upon it in some conspicuous place,
so that the contained load may, at any time, be found by placing the car
upon the scale.


                          WOOD SHED AND TANK.

At _way_ stations the freight and passenger houses, wood and water
station, may all be combined; the plan and size depending upon the
location and importance of the station. The relative position of the
tank, wood shed, and passenger house should be such that when the tender
is at the proper place for receiving its supplies the centre of a
passenger train of ordinary length shall be at the passenger door.


                          OF THE WATER SUPPLY.

390. The number of engines leaving the terminus of a road determines the
amount of water necessary at the _principal_ stations; and the character
of the road and of the traffic fixes the location and size of the _way_
water stations. The amount of traffic being pretty equally distributed
over the length of the road, the tanks should be placed at equal equated
distances; thus the engines will need to water at closer points upon
steep grades than upon level roads. Generally, however, the water is
taken where it can be got, the location of streams and springs fixing
the place. Steam, hydraulic, wind, human, or animal power may be
employed to raise the water to the tank. Oftentimes high springs will
fill the tanks without the application of artificial power. As we find
the liquid water in nature it is more or less impregnated with
vegetable, gaseous, and saline matter, which often impairs its fitness
for mechanical purposes. These admixtures are derived from the rocks and
ground over or through which the water flows. The incrustations which
form in boilers are caused by the precipitation of the impurities in
consequence of the concentration of water in the boiler. They may be
effectually removed, no matter what their nature, by boiling charcoal in
the water. If the water, previous to filtration, can be heated, to expel
all the air and carbonic acid gas, which is often the solvent of the
foreign matter, the filtering process will be accelerated, and will be
more effectual. Rain water is more pure than any other; practically,
perfectly so. River water comes next to it. Spring water is generally
adulterated with basic salts in various forms, most of which may be
precipitated by gently heating and filtering through charcoal.

391. Fig. 157 shows a convenient form for a tank house, with pump and
heater.

[Illustration: Fig. 157.]

  A shows half interior section of the tank.

  B, half elevation of tank.

  C, pump; C′, supply pipe; _d_, suction pipe and strainer.

  E, heater.

  _e_, the short, and _h_, the long pipe.

  H, the discharge pipe.

  G, discharge valve.

  I, counter weight for discharge pipe.

  K, wheel for weight rope.

  L, scale showing amount of water in the tank.

The heater shown in the cut is made of a coil of two inch pipe of iron.
The short pipe descends from within six inches of the bottom of the tank
to within two or three feet of the floor; then bending four or five
times around spirally, turns up through the centre of the coil, and runs
three or four feet into the tank. A small grate is placed in the lower
part of the coil, and the whole apparatus is cased in sheet iron. By
such an arrangement of pipe, circulation is obtained, and the water in
the tank is kept quite warm. The following rules and tables may be found
convenient.

392. The velocity of water in any pipe necessary to discharge a given
quantity, in a fixed time, is expressed by

                             (144_C_)/_a_.

Where _C_ is the number of cubic feet per hour, and _a_ the area of the
pipe.

393. The head necessary to send water through a given length of pipe, of
any diameter, is shown by the formula

                        _C_/(_D_ + _C′_) = _H_.

              Where _C_  = a constant.
                    _C′_ = constant for diameter of pipe.
                    _D_  = diameter of pipe.
                    _H_  = heads required.

The experimental values of _C_ and _C′_ are as follows: Let _V_ equal
the velocity in feet per minute, and we have

                               V.   C.
                                60  8.62
                                70 11.40
                                80 14.58
                                90 17.95
                               100 21.56
                               120 29.70
                               140 38.90
                               150 44.00
                               180 62.13

Also, the values of _C′_ are

                         Diameter of pipe. C′.
                                 2         .000
                                 3         .006
                                 4         .028
                                 5         .053
                                 6         .078
                                 7         .104
                                 8         .134


                   EXAMPLE OF USE OF PRECEDING RULES.

Required the head of water necessary to send 1,333 cubic feet of water,
or 10,000 gallons per hour, through an eight inch pipe one thousand feet
long.

The velocity by rule _one_ will be

 (1333 × 144)/(8^2 × .7854) = 3818 feet per hour, or 64 feet per minute.

By rule _two_ (the value of _C_ for 60 being 8.62, and for 70 11.40,
that for 64 is 10 nearly), we have

                         10/(8 + 0.134) = 1.23,

which multiplied by ten (the number of times that one hundred is
contained in one thousand feet, the distance), gives the result, twelve
inches or one foot, which is the required head; and if the entrance to
the tank is twenty feet high, we have, as the necessary head, 20 + 1 =
21 feet.

394. The formula expressing the power of an engine to raise a given
amount of water is

                             (_WV_)/33000.

Where _W_ is the weight of a column of water, and _V_ the velocity in
feet per minute; also 33,000 the expression of a horse-power. For
example, how many horse-power must an engine possess to raise one
thousand cubic feet of water per hour through a six inch pipe fifty feet
high?

The velocity will be

           (1000 × 144)/(6^2 × 0.7854) = 5093 feet per hour,

or eighty-five feet per minute. The weight of a column of water fifty
feet high and six inches in diameter is

            (6^2 × 0.7854 × 50 × 12)/1728 × 62½ = 613.6 lbs.

Also,

               (612½ × 83)/33000 = 1½ horse-power nearly.

395. Among the pumps now in use for raising water at railroad stations
are Carpenter’s rotary, Worthington’s, McGowan’s, and that of Messrs.
Perkins and Bishop, either of which answers every purpose.


   396. TABLE SHOWING THE WEIGHT AND COST PER FOOT OF CAST-IRON PIPE.

    Diameter of      Thickness of    Weight of pipe     Cost of pipe
       bore.            metal.      per lineal foot. per lineal foot.
      Inches.          Inches.            Lbs.            Cents.
         1                ¼               3.06              15
         1¼               ¼               3.67              18
         1½               ¼               4.29              21
         1¾               ⅜               7.81              39
         2                ⅜               8.73              44
         2¼               ⅜               9.65              48
         2½               ½              14.70              73
         2¾               ½              15.93              80
         3                ½              17.15              86

The weight of a cubic foot of cast-iron being 450 lbs., and the price
being five cents per lb.


      TABLE SHOWING THE CAPACITY OF McGOWAN’S DOUBLE ACTING PUMPS.

 ┌─────────────────────────────┬─────────┬─────────┬───────────────────┐
 │                             │         │         │ Time required to  │
 │        Explanation.         │ No. 1.  │ No. 2.  │fill a 6600 gallons│
 │                             │         │         │       tank.       │
 ├─────────────────────────────┼─────────┼─────────┼───────────────────┤
 │Stroke in inches,            │        5│       8½│      Hours.       │
 │Diameter of plunger,         │       2⅝│       3⅛│                   │
 ├─────────────────────────────┼─────────┼─────────┼─────────┬─────────┤
 │Area of plunger,             │5.278 in.│ 7.70 in.│  Small  │  Large  │
 │Cube of half stroke in       │    0.114│    0.283│pump, No.│pump, No.│
 │  gallons,                   │         │         │   1.    │   2.    │
 ├─────────┬─────────┬─────────┼─────────┼─────────┼─────────┼─────────┤
 │Discharge│ At  10  │  Full   │    136.8│    339.6│       49│       19│
 │   in    │ At  20  │ strokes │    273.6│    679.2│       24│       10│
 │ gallons │ At  30  │   per   │    410.4│   1018.8│       16│        7│
 │per hour.│ At  40  │ minute. │    547.2│   1358.4│       12│        5│
 │         │ At  50  │         │    684.0│   1698.0│       10│        4│
 │         │ At  60  │         │    820.8│   2037.6│        8│       3½│
 │         │ At  70  │         │    957.6│   2377.2│        7│        3│
 │         │ At  80  │         │   1094.4│   2716.8│        6│       2½│
 │         │ At  90  │         │   1231.2│   3058.4│        5│       2¼│
 │         │ At 100  │         │   1368.0│   3396.0│        5│        2│
 └─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┘




                              CHAPTER XVI.
                              MANAGEMENT.


  All that is required to render the efforts of railroad companies in
  every respect equal to that of individuals, is a rigid system of
  personal accountability through every grade of service.—_D. C.
  McCallum._


                       ORGANIZATION OF EMPLOYEES.

397. Railroad management may be divided into two grand departments,—

                         Financial management.
                         Operating management.

The first of these does not properly come into a work of the present
kind. It embraces the entire system of accounts. Its officers are a
president, secretary, treasurer, attorney, and directors.

398. The operating management is subdivided as follows:—

                      _The mercantile department._
                      _The mechanical department._

The first embracing every thing relating to the adjusting of tariffs,
the transport of passengers and freight, the embarking and delivering of
goods, and the weighing and measuring, ticket and receiving offices,
steamboat, stage, and railroad connections. The second, the maintaining
the road-bed, superstructure, bridging, masonry, buildings, and fixed
stock in working order; making all repairs, renewals, enlargements, and
alterations, and the purchase, inspection, maintaining, and operating of
the rolling stock. These departments are again divided and subdivided
until we come to the minutest details.

  NOTE.—That part of Chapter XVI. in italics is extracted, by
  permission, from the elaborate Report of D. C. McCallum to the
  stockholders of the New York and Erie Railroad, (March 25, 1856).

399. The following general principles govern the formation of an
efficient system of operations.

_First. A proper division of responsibilities._

_Second. Sufficient power conferred to enable the same to be fully
carried out, that such responsibilities may be real in their character._

_Third. The means of knowing whether such responsibilities are
faithfully executed._

_Fourth. Great promptness in the report of all derelictions of duty,
that evils may at once be corrected._

_Fifth. Such information to be obtained through a system of daily
reports and checks that will not embarrass principal officers nor lessen
their influence with their subordinates._

_Sixth. The adoption of a system, as a whole, which will not only enable
the general superintendent to detect errors immediately, but will also
point out the delinquent._

400. _A system of operations to be efficient and successful should be
such as to give to the principal and responsible head of the running
department a complete daily history of details in all their minutiæ.
Without such supervision the procurement of a satisfactory annual
statement must be regarded as extremely problematical. The fact that
dividends are made without such control does not disprove the position,
as in many cases the extraordinarily remunerative nature of an
enterprise may insure satisfactory returns under the most loose and
inefficient management._

All subordinates should be accountable to, and directed by, their
_immediate superiors only_. Each officer must have authority, with the
approval of the general superintendent, to appoint all persons for whose
acts he is held responsible, and to dismiss any subordinate when in his
judgment the interests of the company demand it.

401. The following table shows the rate and direction of subordination
for a first class railroad:—

                                               {Section men.
                {Superintendent   {Road-master.{Section men.
                {  of Road.       {Road-master.{Section men.
                {                              {Section men.
                {
                {                 {Foreman Machine shop, Machinists.
                {                 {Foreman Blacksmith shop, Blacksmiths.
                {Superintendent   {Foreman Car shop, Carpenters,
                {  of Machinery.  {Foreman Paint shop, Painters.
                {                 {Engineers (not on trains), Firemen.
                {                 {Car-masters, Oil men and cleaners.
                {
                {                 {Conductors     {Brakemen.
                {                 {Mail agents.   {Engineers (on trains).
                {                 {               {Ticket collectors.
 General        {                 {
  Superintendent{General passenger{Station agents.{Hackmen.
                {  agent.         {               {Switchmen.
                {                 {
                {                 {Express agents.
                {                 {Police.
                {
                {                 {Conductors.    {Brakemen.
                {                 {               {Engineers (on trains).
                {General freight  {Station agent.
                {  agent.         {Weighers.
                {                 {Gaugers.
                {                 {Yard-masters.
                {
                {Supply agent.    {Clerks, Teamsters furnishing supplies.
                {Fuel agent.      {All men employed about the wood sheds.



                          DUTIES OF EMPLOYEES.

402. _The General Superintendent_ has entire control of all of the heads
of departments; he issues his orders to the heads only, and is the main
agent for transferring the resolves of the directors to the operating
department, and the channel through which the reports of the departments
go to the directory.

_The Superintendent of the Road_ has complete charge of the road-bed,
superstructure, bridging, masonry, and buildings; also all removals,
enlargements, and alterations. He should be a thorough civil engineer,
able in every respect to build a railroad from beginning to end.

_The Superintendent of Machinery_ has charge of the purchase,
inspection, repair, and operating of all of the rolling and fixed
machinery, of shops, engine houses, turntables, tanks, and weigh scales.
He is responsible for the good condition, proper adaptation and
efficiency of the entire equipment of engines and cars.

_The General Passenger Agent_ fixes, under the direction of the
president and general superintendent, the prices of passenger
transportation, has charge of all conductors, ticket sellers, station
police, mail and express agents, of stage, steamboat, and railroad
connections, and of all operations incident to transporting passengers.

_The General Freight Agent_ has charge of all persons occupied at all of
the stations in forwarding and receiving merchandise, in measuring and
weighing, in receiving money, and bookkeeping, station agents, and train
hands. He makes and regulates, with the approval of the president and
general superintendent, the tariff for freights; contracts with
connecting roads, and insures the benefits of such agreements, examines
all claims for damages to freight, and sees that such are properly
settled.

_The Agent for Wood_ contracts, with the approval of the general
superintendent, for the supply of the necessary amount of fuel; attends
the measurement, inspection, and delivery at the proper places;
registers each month the amount of fuel supplied and used, and the
location and amount on hand.

_The Supply Agent_ has charge of the supply of all materials in use in
all departments; iron, timber, engines, rails, bridges, and every thing
in use upon the road; charging each department with its correct quantity
and quality of material received.

_Road-masters_ will have charge, under the superintendent of the road,
of the maintenance of the road-bed and superstructure of divisions of
from twenty-five to fifty miles in length, depending upon the care that
the road-way may need. They will have charge of gravel trains, and of
wood trains, which run under the orders of the superintendent of the
road. They should pass over their divisions at least once per day. Under
them are placed section men, having care of ten miles each, being
supplied with the proper tools and signals. They must pass over their
respective sections at least once per day in a hand car. They should see
that every switch, frog, chair, and rail on their section is in proper
order, and report at once any defects, which cannot be remedied by them,
in the track, to the road-master.

_Engineers_ are subject to the superintendent of machinery when off, and
to the conductor when on, the trains. None but a man well acquainted
with the details of machinery, and who has served in a locomotive
machine shop, and is in every respect temperate and steady, should fill
this berth.

_Foremen_ of the blacksmith, machine, carpenter, and car shops, are
subject to the superintendent of machinery, and have charge of the
repairs and cleaning of the engines, cars, and other machinery.

_Car-masters_ have charge of the men employed in cleaning, oiling, and
examining the cars and their wheels. The cars should be thoroughly
examined at the end of each trip, and at each stop, by an inspector who
accompanies the train and looks to the wheels, axles, boxes, and brakes.

_Conductors._—A conductor of a train should be a machinist, a prompt,
active man, who should station himself on the top of the cars in such a
position as to see the whole train, and able at any moment to
communicate with the engineer. He should direct the running of the
train, and control the engineer and the person who takes the fares. The
latter should confine himself to the inside of the cars.


                      NUMBER OF TRAINS TO BE USED.

403. This is determined by the quantity and quality of the material to
be transported, and by the character of the road. The train should not
be so heavy as to be beyond the power of the engines upon the steepest
grades, nor so light as to increase unnecessarily the number. A road
doing a large passenger business must accommodate the public as far as
possible as regards the time of departure and arrival, and the
connections with other roads. A freight road must regard more the
character of the road. Some classes of freight (ice, beef, etc.) do not
admit of delay. As we increase the number of trains, the ratio of time
employed in actual work to the whole train under steam is decreased, as
there must be much time lost on sidings in waiting for trains to pass.
Liability to accidents is also incurred. Commercial circumstances, more
than any other, will determine the proper number and class of trains.


                     AMOUNT OF SERVICE OF ENGINES.

404. This is much less than is generally supposed. The number of engines
required to perform any amount of work is considerably greater than the
number actually in motion, because of liability to accident, time
required for cleaning and repair. The New York State Engineer’s Report
for 1854 gives, as the number of engines on 2,500 miles, 668, or one
engine per 3¾ miles. Also, 668 engines run per annum 11,393,000 miles,
or 17,055 miles per annum per engine; thus requiring .00005863 of an
engine per mile run per annum.

This is very nearly fifty-five miles per day, (313 days per annum).
Also, 968/2500 gives 27/100 of an engine per mile of road, and the same
report gives the following:—

               One locomotive for 3¾ miles of road.
               One passenger car for 2½ miles of road.
               One freight car for 32/100 miles of road.

Or each mile needs

                       27/100 of a locomotive.
                       40/100 of a passenger car.
                       3 freight cars.

Or to one engine 781/100 passenger cars, and 1072/100 freight cars. From
Lardner’s Railway Economy it appears that the average daily run of an
engine is forty-two miles, or seventy-five miles per day, working four
days in the week. That the daily service is two hours working, and three
and three quarters hours standing with steam up. The maximum annual
mileage mentioned by Lardner is that upon the Belgium lines, and was
21,737. The maximum in America has been, as far as we have been able to
ascertain, 22,000, and this for eighteen years.

  NOTE 1.—Two little eight ton, four wheeled, Stephenson engines,
  cylinders 10 × 16, four and a half feet drivers, inside connection,
  copper fire-boxes, have averaged 22,000 miles per annum, with trains
  weighing forty tons exclusive of engine and tender, for eighteen
  years, costing about $700 per annum each for repairs, or $3.18 cents
  per mile run, upon the Bangor and Oldtown Railroad (Maine).

  NOTE 2.—In the Report of the Railroad Commissioners of the State of
  New York for the year ending September 30, 1855, is the following:—

  One engine is required for each three and a half miles; or one
  engine in constant use for five and a quarter miles. The average run
  per annum by each engine in actual use is 22,823 miles; or 16,302 to
  all of the engines. Also, as regards the work done by cars.

                     Effective in     Miles per car.   Distance run per
                     constant use.                      annum per car.
 Passenger,                      650                 4            45.126
 Baggage,                        246                11                ——
 Freight,                       7500              0.35            11.970

  the number of miles being 2,615.


                      EXPENSES, RECEIPTS, PROFITS.


                               EXPENSES.

405. American railroad reports as a general thing do not analyze the
cost of working. The gross expense is given, and in some cases is
primarily divided. Besides the retrospective use of a minute division of
expenses, which enables us to see what system is the most economical,
there is a prospective use, namely, the formation of estimates for
future operations and a correct base for establishing tariffs. If the
circumstances of the traffic remain the same, an estimate of what the
cost will be at any time is easy; but if they change, the data for the
estimate change also. That we may at all times possess these data, we
should know every year just the cost of working each article of traffic.
It is not enough that the gross receipt exceeds the whole expense; even
then the road may be working unprofitably. Unless each item of transport
pays for itself, we are taxing unjustly some other item, (except,
indeed, in such cases as adopting low rates in order to fill trains
running in one direction which would otherwise run empty). An analysis
of cost will also show whether or not it is best to attract an increased
amount of business by a reduction of rates.

406. The whole cost of operating and of maintaining a railroad may be
generally and specially divided as follows:—

                                            {Cost of Road-bed.
                                            {Cost of Superstructure.
 (A) Interest on construction and equipment {Cost of Buildings.
       capital.                             {Cost of Engines.
                                            {Cost of Cars.
                                            {Fixed machinery.

                                   {Road-bed.          {Material.
                                   {                   {Labor.
                                   {
 (B) Maintenance of way and works. {Buildings.         {Material.
                                   {                   {Labor.
                                   {
                                   {Superstructure.    {Material.
                                   {                   {Labor.

                    {            {            {             {Fuel, oil, and
                    {            {            {Working.     { waste.
                    {            {Passenger.  {             {Salaries.
                    {            {            {
                    {            {            {Maintaining. {Material.
                    {            {            {             {Labor.
                    {Locomotives.{
                    {            {            {             {Fuel, oil, and
                    {            {            {Working.     { waste.
                    {            {Freight.    {             {Salaries.
                    {            {            {
                    {            {            {Maintaining. {Material.
                    {            {            {             {Labor.
 (C) Maintenance of {
      the fixed and {            {            {             {Warming,
      rolling stock.{            {            {Working.     { lighting, and
                    {            {            {             { cleaning.
                    {            {Passenger.  {             {Oil and waste.
                    {            {            {
                    {Cars.       {            {Maintaining. {Material and
                    {            {                          { labor.
                    {            {
                    {            {            {Working.     {Oil and waste.
                    {            {Freight.    {Maintaining. {Material and
                    {            {            {             { labor.
                    {
                    {Fixed       {In shops.   {Machinery.   {Oil and waste.
                    { machinery. {On road.    {Tanks and    {Materials and
                    {            {            { tables.     { labor.

                                    {           {Conductors.
                                    {           {Ticket Sellers.
                                    {Passenger. {Clerks.
                                    {           {Brakemen.
 (D) Salaries of hands employed in  {           {Porters.
       and about trains.            {
                                    {           {Conductors.
                                    {Freight.   {Station agents.
                                    {           {Brakemen.
                                    {           {Weighers and gaugers.

                       {Passenger. {Warming and lighting.
                       {           {Police.
 (E) Station expenses. {
                       {Freight.   {Warming and lighting.
                       {           {Police.

                              {Salaries.
                              {Travelling expenses.
 (F) General superintendence. {Office expenses.
                              {Stationery.
                              {Advertising, &c., &c.

The actual _general_ division of the operating expenses upon the New
York State system of roads was, for 1854, as follows. (See State
Engineer’s Report).

     Way and works,                1,123 dollars per mile of road.
     Machinery,                    2,072 dollars per mile of road.
     Salaries on and about trains,   640 dollars per mile of road.
     Stations,                        30 dollars per mile of road.
     General superintendence,        333 dollars per mile of road.
                                   —————
     Total,                        4,198 dollars per mile of road.

That the detailed expenses may be charged to the proper departments, and
that we may be able to take out the exact cost of working any one class
of trains, or of carrying any article of transport, the following form
should be filled.



 ┌──────────────────────────────────────────────────────┐
 │ 407. TABLE SHOWING THE GENERAL AND DETAILED EXPENSES │
 │ OF WORKING AND MAINTAINING THE RAILROADS OF NEW YORK │
 │ STATE, FOR 1854, AND THE NEW YORK AND ERIE RAILROAD  │
 │       FOR THE YEAR ENDING SEPTEMBER 30, 1855.        │
 ├──────────┬───────────────────────────────────────────┤
 │          │                                           │
 │          │                                           │
 │          │              WAY AND WORKS.               │
 │          │                                           │
 │          │                                           │
 ├──────────┼─────────┬───────────────┬──────────┬──────┤
 │          │         │               │          │      │
 │Nature of │         │               │          │      │
 │ the item │         │               │          │      │
 │ is shown │Road-bed.│Superstructure.│Buildings.│Total.│
 │    in    │         │               │          │      │
 │horizontal│         │               │          │      │
 │ columns. │         │               │          │      │
 │          │         │               │          │      │
 │          │         │               │          │      │
 │          │         │               │          │      │
 │          │         │               │          │      │
 │          │         │               │          │      │
 │          │         │               │          │      │
 │          │         │               │          │      │
 ├──────────┤         │               │          │      │
 │ Name of  │         │               │          │      │
 │railroad. │         │               │          │      │
 │          │         │               │          │      │
 ├──────────┼─────────┼───────────────┼──────────┼──────┤
 │Cost, in  │         │               │          │      │
 │dollars,  │         │               │          │      │
 │per mile, │      351│            140│        22│F. 513│
 │upon N. Y.│         │               │          │      │
 │State     │         │               │          │      │
 │Railroads │         │               │          │      │
 │          │      453│             88│        27│P. 568│
 ├──────────┼─────────┼───────────────┼──────────┼──────┤
 │Cost in   │         │               │          │      │
 │cents, per│         │               │          │      │
 │ton, or   │         │               │          │      │
 │per       │         │               │          │    F.│
 │passenger │     .020│           .161│      .010│  .191│
 │per mile  │         │               │          │      │
 │run, N. Y.│         │               │          │      │
 │and Erie  │         │               │          │      │
 │Railroad. │         │               │          │      │
 │          │         │               │          │      │
 │          │     .035│           .207│      .011│    P.│
 │          │         │               │          │  .253│
 ├──────────┴─────────┴───────────────┴──────────┴──────┤
 │                             NOTES.                   │
 └──────────────────────────────────────────────────────┘

 ┌───────────────────────────────────────────────────────┐
 │ 407. TABLE SHOWING THE GENERAL AND DETAILED EXPENSES  │
 │ OF WORKING AND MAINTAINING THE RAILROADS OF NEW YORK  │
 │ STATE, FOR 1854, AND THE NEW YORK AND ERIE RAILROAD   │
 │       FOR THE YEAR ENDING SEPTEMBER 30, 1855.         │
 ├──────────┬────────────────────────────────────────────┤
 │          │                                            │
 │          │                                            │
 │          │    LOCOMOTIVE ENGINES, CARS, AND FIXED     │
 │          │                 MACHINERY.                 │
 │          │                                            │
 ├──────────┼────────────────────────────────────────────┤
 │          │                                            │
 │Nature of │                                            │
 │ the item │                                            │
 │ is shown │            LOCOMOTIVE ENGINES.             │
 │    in    │                                            │
 │horizontal│                                            │
 │ columns. │                                            │
 │          │                                            │
 │          ├────────────────────────────────────────────┤
 │          │                                            │
 │          │                                            │
 │          │           Passenger Locomotives.           │
 │          │                                            │
 │          │                                            │
 ├──────────┼─────┬──────┬────────┬──────┬────────┬──────┤
 │ Name of  │     │ Oil  │        │      │        │      │
 │railroad. │Fuel.│ and  │Salaries│Whole.│Repairs.│Total.│
 │          │     │waste.│        │      │        │      │
 ├──────────┼─────┼──────┼────────┼──────┼────────┼──────┤
 │Cost, in  │     │      │        │      │        │      │
 │dollars,  │     │      │        │      │        │      │
 │per mile, │     │      │        │      │        │      │
 │upon N. Y.│     │      │        │      │        │      │
 │State     │     │      │        │      │        │      │
 │Railroads │     │      │        │      │        │      │
 │          │  395│    50│     140│   585│     237│   822│
 ├──────────┼─────┼──────┼────────┼──────┼────────┼──────┤
 │Cost in   │     │      │        │      │        │      │
 │cents, per│     │      │        │      │        │      │
 │ton, or   │     │      │        │      │        │      │
 │per       │     │      │        │      │        │      │
 │passenger │     │      │        │      │        │      │
 │per mile  │     │      │        │      │        │      │
 │run, N. Y.│     │      │        │      │        │      │
 │and Erie  │     │      │        │      │        │      │
 │Railroad. │     │      │        │      │        │      │
 │          │ .157│  .021│    .107│  .285│    .109│  .394│
 │          │     │      │        │      │        │      │
 │          │     │      │        │      │        │      │
 ├──────────┴─────┴──────┴────────┴──────┴────────┴──────┤
 │                         RECAPITULATION.               │
 └───────────────────────────────────────────────────────┘

 ┌───────────────────────────────────────────────────────────────┐
 │     407. TABLE SHOWING THE GENERAL AND DETAILED EXPENSES      │
 │     OF WORKING AND MAINTAINING THE RAILROADS OF NEW YORK      │
 │     STATE, FOR 1854, AND THE NEW YORK AND ERIE RAILROAD       │
 │           FOR THE YEAR ENDING SEPTEMBER 30, 1855.             │
 ├──────────┬────────────────────────────────────────────────────┤
 │          │                                                    │
 │          │                                                    │
 │          │   LOCOMOTIVE ENGINES, CARS, AND FIXED MACHINERY.   │
 │          │                                                    │
 │          │                                                    │
 ├──────────┼────────────────────────────────────────────────────┤
 │          │                                                    │
 │Nature of │                                                    │
 │ the item │                                                    │
 │ is shown │                LOCOMOTIVE ENGINES.                 │
 │    in    │                                                    │
 │horizontal│                                                    │
 │ columns. │                                                    │
 │          │                                                    │
 │          ├─────────────────────────────────────────────┬──────┤
 │          │                                             │      │
 │          │                                             │Total │
 │          │            Freight Locomotives.             │ cost.│
 │          │                                             │      │
 │          │                                             │      │
 ├──────────┼─────┬──────┬─────────┬──────┬────────┬──────┼──────┤
 │ Name of  │     │ Oil  │         │      │        │      │      │
 │railroad. │Fuel.│ and  │Salaries.│Whole.│Repairs.│Total.│      │
 │          │     │waste.│         │      │        │      │      │
 ├──────────┼─────┼──────┼─────────┼──────┼────────┼──────┼──────┤
 │Cost, in  │     │      │         │      │        │      │      │
 │dollars,  │     │      │         │      │        │      │      │
 │per mile, │     │      │         │      │        │      │      │
 │upon N. Y.│     │      │         │      │        │      │      │
 │State     │     │      │         │      │        │      │      │
 │Railroads │     │      │         │      │        │      │      │
 │          │  202│    31│      122│   355│     191│   546│  1368│
 ├──────────┼─────┼──────┼─────────┼──────┼────────┼──────┼──────┤
 │Cost in   │     │      │         │      │        │      │      │
 │cents, per│     │      │         │      │        │      │      │
 │ton, or   │     │      │         │      │        │      │      │
 │per       │     │      │         │      │        │      │      │
 │passenger │     │      │         │      │        │      │      │
 │per mile  │     │      │         │      │        │      │      │
 │run, N. Y.│     │      │         │      │        │      │      │
 │and Erie  │     │      │         │      │        │      │      │
 │Railroad. │     │      │         │      │        │      │      │
 │          │ .205│  .018│     .080│  .303│    .081│  .384│  .778│
 │          │     │      │         │      │        │      │      │
 │          │     │      │         │      │        │      │      │
 ├──────────┴─────┴──────┴─────────┴──────┴────────┴──────┴──────┤
 │                                                               │
 └───────────────────────────────────────────────────────────────┘

 ┌─────────────────────────────────────────┐
 │   407. TABLE SHOWING THE GENERAL AND    │
 │    DETAILED EXPENSES OF WORKING AND     │
 │  MAINTAINING THE RAILROADS OF NEW YORK  │
 │  STATE, FOR 1854, AND THE NEW YORK AND  │
 │    ERIE RAILROAD FOR THE YEAR ENDING    │
 │           SEPTEMBER 30, 1855.           │
 ├──────────┬──────────────────────────────┤
 │          │                              │
 │          │LOCOMOTIVE ENGINES, CARS, AND │
 │          │       FIXED MACHINERY.       │
 │          │                              │
 │          │                              │
 ├──────────┼──────────────────────────────┤
 │          │                              │
 │Nature of │                              │
 │ the item │                              │
 │ is shown │            CARS.             │
 │    in    │                              │
 │horizontal│                              │
 │ columns. │                              │
 │          │                              │
 │          ├──────────────────────────────┤
 │          │                              │
 │          │                              │
 │          │       Passenger cars.        │
 │          │                              │
 │          │                              │
 ├──────────┼──────────┬────────────┬──────┤
 │ Name of  │          │            │      │
 │railroad. │Operating.│Maintaining.│Total.│
 │          │          │            │      │
 ├──────────┼──────────┼────────────┼──────┤
 │Cost, in  │          │            │      │
 │dollars,  │          │            │      │
 │per mile, │          │            │      │
 │upon N. Y.│          │            │      │
 │State     │          │            │      │
 │Railroads │          │            │      │
 │          │        50│         145│   195│
 ├──────────┼──────────┼────────────┼──────┤
 │Cost in   │          │            │      │
 │cents, per│          │            │      │
 │ton, or   │          │            │      │
 │per       │          │            │      │
 │passenger │          │            │      │
 │per mile  │          │            │      │
 │run, N. Y.│          │            │      │
 │and Erie  │          │            │      │
 │Railroad. │          │            │      │
 │          │      .020│        .079│  .099│
 │          │          │            │      │
 │          │          │            │      │
 ├──────────┴──────────┴────────────┴──────┤
 │              SUMMARY.                   │
 └─────────────────────────────────────────┘

 ┌─────────────────────────────────────────────────────────────────────┐
 │ 407. TABLE SHOWING THE GENERAL AND DETAILED EXPENSES OF WORKING AND │
 │ MAINTAINING THE RAILROADS OF NEW YORK STATE, FOR 1854, AND THE NEW  │
 │   YORK AND ERIE RAILROAD FOR THE YEAR ENDING SEPTEMBER 30, 1855.    │
 ├──────────┬──────────────────────────────────────────────────────────┤
 │          │                                                          │
 │          │                                                          │
 │          │      LOCOMOTIVE ENGINES, CARS, AND FIXED MACHINERY.      │
 │          │                                                          │
 │          │                                                          │
 ├──────────┼─────────────────────────────────────┬──────────┬─────────┤
 │          │                                     │          │         │
 │Nature of │                                     │          │  Whole  │
 │ the item │                                     │          │ cost of │
 │ is shown │                CARS.                │  FIXED   │machinery│
 │    in    │                                     │MACHINERY.│oiling on│
 │horizontal│                                     │          │the road.│
 │ columns. │                                     │          │         │
 │          │                                     │          │         │
 │          ├──────────────────────────────┬──────┼──────────┤         │
 │          │                              │Total │ Repairs, │         │
 │          │                              │ cost │ oil and  │         │
 │          │        Freight Cars.         │  of  │  waste,  │         │
 │          │                              │cars. │labor, and│         │
 │          │                              │      │machinery.│         │
 ├──────────┼──────────┬────────────┬──────┤      │          │         │
 │ Name of  │          │            │      │      │          │         │
 │railroad. │Operating.│Maintaining.│Total.│      │          │         │
 │          │          │            │      │      │          │         │
 ├──────────┼──────────┼────────────┼──────┼──────┼──────────┼─────────┤
 │Cost, in  │          │            │      │      │          │         │
 │dollars,  │          │            │      │      │          │         │
 │per mile, │          │            │      │      │     44 F.│      841│
 │upon N. Y.│          │            │      │      │          │         │
 │State     │          │            │      │      │          │         │
 │Railroads │          │            │      │      │          │         │
 │          │        45│         206│   251│   446│     55 P.│     1072│
 ├──────────┼──────────┼────────────┼──────┼──────┼──────────┼─────────┤
 │Cost in   │          │            │      │      │          │         │
 │cents, per│          │            │      │      │          │         │
 │ton, or   │          │            │      │      │          │         │
 │per       │          │            │      │      │          │         │
 │passenger │          │            │      │      │   .015 F.│     .466│
 │per mile  │          │            │      │      │          │         │
 │run, N. Y.│          │            │      │      │          │         │
 │and Erie  │          │            │      │      │          │         │
 │Railroad. │          │            │      │      │          │         │
 │          │          │            │      │      │          │         │
 │          │      .022│        .045│  .067│  .166│   .018 P.│     .511│
 │          │          │            │      │      │          │         │
 ├──────────┴──────────┴────────────┴──────┴──────┴──────────┴─────────┤
 │                                                                     │
 └─────────────────────────────────────────────────────────────────────┘

 ┌───────────────────────────────────────────────────────────┐
 │  407. TABLE SHOWING THE GENERAL AND DETAILED EXPENSES OF  │
 │ WORKING AND MAINTAINING THE RAILROADS OF NEW YORK STATE,  │
 │ FOR 1854, AND THE NEW YORK AND ERIE RAILROAD FOR THE YEAR │
 │                ENDING SEPTEMBER 30, 1855.                 │
 ├──────────┬─────────┬───────────┬────────────────┬─────────┤
 │          │         │Salaries of│                │         │
 │          │ Station │ employees │    General     │  Grand  │
 │          │expenses.│  in and   │superintendence.│ Total.  │
 │          │         │   about   │                │         │
 │          │         │  trains.  │                │         │
 ├──────────┼─────────┼───────────┼────────────────┼─────────┤
 │          │         │           │                │Cost per │
 │Nature of │ Repairs │Conductors.│  Stationery.   │passenger│
 │ the item │   and   │ Brakemen. │   Salaries.    │ or per  │
 │ is shown │material.│ Weighing. │    Offices.    │ton, per │
 │    in    │ Warming │ Loading.  │  Travelling.   │mile run,│
 │horizontal│   and   │ Porters.  │  Advertising.  │ or cost │
 │ columns. │lighting.│ Watchmen. │   Agencies.    │per mile │
 │          │         │           │                │of road. │
 │          │         │           │                │         │
 │          │         │           │                │         │
 │          │         │           │                │         │
 │          │         │           │                │         │
 │          │         │           │                │         │
 │          │         │           │                │         │
 ├──────────┤         │           │                │         │
 │ Name of  │         │           │                │         │
 │railroad. │         │           │                │         │
 │          │         │           │                │         │
 ├──────────┼─────────┼───────────┼────────────────┼─────────┤
 │Cost, in  │         │           │                │         │
 │dollars,  │         │           │                │         │
 │per mile, │        —│        371│             180│     1905│
 │upon N. Y.│         │           │                │         │
 │State     │         │           │                │         │
 │Railroads │         │           │                │         │
 │          │        —│        246│             170│     2056│
 ├──────────┼─────────┼───────────┼────────────────┼─────────┤
 │Cost in   │         │           │                │         │
 │cents, per│         │           │                │         │
 │ton, or   │         │           │                │         │
 │per       │         │           │                │         │
 │passenger │     .023│       .240│            .045│     .965│
 │per mile  │         │           │                │         │
 │run, N. Y.│         │           │                │         │
 │and Erie  │         │           │                │         │
 │Railroad. │         │           │                │         │
 │          │         │           │                │         │
 │          │     .026│       .159│            .053│    1.002│
 │          │         │           │                │         │
 ├──────────┴─────────┴───────────┴────────────────┴─────────┤
 │                   DEDUCTIONS.                             │
 └───────────────────────────────────────────────────────────┘

408. The following general measures are recommended by Lardner in his
Railway Economy, as being the means of obtaining increased economy in
the working of railroads.

1st. So to manage the traffic as to cause the cars to carry more
complete loads.

2d. To encourage the transport to long distances.

3d. To regulate the tariff so as to give the largest possible number of
cars to each engine.

4th. To adjust the tariffs where the business is chiefly in one
direction, so as to attract return traffic, that the cars may not run
without a load.

5th. Not to increase the number of trains beyond a reasonable
accommodation of traffic.

6th. To diminish as far as possible express trains, if it be not
practicable to abolish them altogether.


                         RECEIPTS AND PROFITS.

409. The distribution of expenses, as we have seen, is somewhat
complicated, and is systematically done upon a very few roads. The
classification of receipts is, however, very easy, and is properly
detailed in nearly all railroad reports. Upon the New York State
railroads, the following was the division for the year 1854.

Average receipts per mile of road,

                        Passengers,    $4,074.16
                        Freight,        3,776.72
                        Extras,           427.28
                                       —————————
                        Whole,         $8,278.16
                        Whole expense, $4,710.14

or fifty-seven per cent. of the receipts.

Receipts per mile run by trains,

               Passengers,                          $1.32
               Freight,                              2.02
               Extras,                               1.67
                                                    —————
               Whole,                               $5.01
                                                    —————
               Average,                              1.67
                                                    —————
               Whole expense per mile run by train, $0.97

Average receipts per passenger and per ton, per mile,

            Passenger,                           1.95 cents,
            Ton,                                 2.79 cents,
                                                 ————
            Average of passenger or ton,         2.37 cents,
                                                 ————
            Average expense of passenger or ton, 1.38 cents,

410. Upon the New York and Erie Railroad for the year ending September
30, 1856.

Receipts per mile of road,

               Passengers,                      $3,397.34
               Freight,                          7,143.42
               Express and mail,                   397.84
                                               ——————————
               Whole,                          $10,938.60
               Whole expense per mile of road,   5,263.00

or forty-eight per cent, of the receipts.

Receipts per mile run by trains,

                           Passengers, $1.16
                           Freight,     2.13

Average receipts per passenger and per ton, per mile,

                         Passenger, 2.02 cents,
                         Ton,       2.37 cents.

411. Upon the New York State roads,

 Average number of passengers per mile run,                         57.4
 Average distance travelled by passengers,                          81.4
 Average tons per mile run,                                         90.0
 Average distance, whole number of tons carried,                   177.0
     Length,                                            496 miles,
     Freight tonnage,                           150,673,997 miles,
     Passenger,                                  84,069,398 miles.

412. It is of course an object on every railroad to make the gross
receipts overbalance the gross expense by the largest possible amount.
The elements which determine the gross receipts are,

                  The charge per mile, for transport,
                  The number of units transported,
                  The distance carried,

of which the company’s directors can control the first only, except as
adjustment of rates may attract business.

Reduction of tariff, to a certain degree, has the effect of increasing
the receipts by augmenting the number of fares; but the reduction may be
carried too far. So, also, for a certain distance, increased rates will
increase the whole receipts; but in this case, also, the extreme must be
avoided. The point to be arrived at is, evidently, that at which the
difference of expense and receipt is the greatest, and this is not
necessarily when receipts are the greatest.

We can make the receipts nothing either by making the charges so large
that nothing can bear them, or so small as to vanish. Even when the
receipts are 0, we still have the expense of moving the empties.

By forming a table in which one column shall show the different charges,
and the second the corresponding amounts transferred, with the
consequent receipts and cost of working, we shall find which rate of
charge will give the greatest difference between expense and receipt.


                            EXPRESS TRAINS.

413. Express trains are a source of vast expense, directly and
indirectly, which can never be repaid by any practicable tariff to be
levied upon them. Dr. Lardner, (1850):—

Resolved, That this meeting recommend the adoption of a higher rate of
fare upon express passenger trains, corresponding in some degree to the
increased cost of such trains.—American Railroad Convention of 1854.


                       INCREASED COST OF WORKING.

This is due to the extra wear and tear of engines, cars, and road, from
increased speed, and also to the delays occasioned to other trains in
motion at the same time.

The influence of express trains is felt not only by themselves, but by
nearly all the trains upon the road.

  NOTE.—To determine the most economical speed, regard need only be
  had to the variable elements of cost, namely: cost of power, and
  maintenance of superstructure, and rolling stock; assuming the power
  expended as the resistance, and the cost of repairs of machinery and
  superstructure as the velocity, we form the following table:—

 Velocity in Resistance  Hours con.  Product of    Cost of
  miles per   in pounds   in going   column 2 ×   repairs.     Result.
    hour.     per ton.   300 miles.      3.
     10          8.6         30          258         100         358
     15          9.3         20          186         150         336
     20         10.3         15          154         200         354
     25         11.6         12          139         250         389
     30         13.3         10          133         300         433
     35         15.2        8.60         131         350         481
     40         17.3        7.50         130         400         530
     45         19.8        6.67         132
     50         22.6          6          136
     60         29.1          5          145
     100        66.5          3          200

  The result is found by adding the product of columns 2 and 3, or
  column 4 to column 5, from which the minimum cost is seen to be
  produced by a very little more than fifteen miles per hour. The
  variable (and above assumed) element is the rate of increase of cost
  of maintenance.

All trains in motion at the same time within a certain distance of the
express, must be kept waiting with steam up, or be driven with extra
velocities in order to keep out of the way.

_Where the time table is so arranged as to call for speed nearly equal
to the full capacity of the engine, it is very obvious that the risks of
failure in “making time” must be much greater than at reduced rates; and
when they do occur, the efforts made to gain time must be
correspondingly greater and uncertain. A single example will be
sufficient to show this_:—

_A train whose prescribed rate of speed is thirty miles an hour, having
lost five minutes of time, and being required to gain it, in order to
meet and pass an opposing train at a station ten miles distant, must
necessarily increase its speed to forty miles an hour; and a train whose
prescribed rate of speed is forty miles an hour, under similar
circumstances, must increase its speed to sixty miles an hour; in the
former case it would probably be accomplished, whilst in the latter it
would more probably result in failure; or, if successful, it would be so
at a fearful risk of accident._

_But a failure in either case would have the effect of retarding the
movement of the opposing train, deranging the time of those of the same
and of an inferior class in both directions, involving, perhaps, on the
part of the latter, the necessity of similar struggles for time, and
thus may prove the primary cause of accident to all trains whose
movements may have been affected thereby._

The first cost of locomotives, (assuming the cost to increase with the
weight,) is thirty per cent. greater for express trains, than for those
of the second or third class.

The cost of repairs being assumed as the product of the weight by
distance run, and this distance being the same, is as the weight, or
increased thirty per cent. (This assumes the power to be equally well
adapted.)

The cost of cars does not (though it ought), differ much for express or
slow trains; the cost of repairs will certainly be increased.

The interest of construction capital to be charged to expresses, will
be, their mileage proportion plus any expense which may have been
incurred in reducing curves and grades; the proportion of repairs of
superstructure, charged to expresses, will depend on their weight. The
locomotive causes 25/29 of the wear of rails, and as the weight of the
engines is increased thirty per cent., the increased wear will be of
15/58.

The use of stations and of employees costs no more for express than for
accommodation trains.

The repairs of locomotives will be nearly, if not quite, as the product
of their weight by the distance run; and this, from the above, will be
thirty per cent. greater on an express than on an ordinary train, the
distance being the same.

The carriages for express trains ought to be at once stronger and more
convenient than those for the slower work, the shocks arising from
irregularities in the rails being very much greater as velocity
increases; and the runs being very long, passengers require easier
seats, even, in some cases, accommodation for sleeping. The cost for
repairs, therefore, of express cars, would be somewhat greater than for
any others.


                 COST AND MAINTENANCE OF WAY AND WORKS.

As the speed is increased, the relative effect of grade and curves is
lessened, but the absolute danger of passing curves is increased.
Express trains require larger radius of curvature, or greater elevation
of exterior rail than others, which extra elevation causes an
unnecessary resistance to all other trains. The rails to resist large
and heavy wheels must be heavier and more firmly fastened. All bridges
and viaducts (particularly if on grades or curves), will require more
strength to resist the increased shocks to which they will be subject.
The wear of rails is nearly as the weight passing over them; the wear of
rails consequent upon stopping and starting the trains depends upon the
momentum of the train which is to be imparted to them.

The proportion, in which the working expenses are distributed under the
several heads on the larger railways of Great Britain, is as follows:—

                     Direction and management,   7
                     Way and works,             16
                     Locomotive department,     35
                     Cars,                      38
                     Sundries,                   4
                                               ———
                                               100

And the percentage of increase due to fast travelling, to be applied to
the several items of expense, with the resulting increase in total
expense, is shown below.

                Direction and management,  7   0 =  0.0
                Way and works,            16  27 =  4.3
                Locomotive department,    35  30 = 10.5
                Cars,                     38  10 =  3.8
                Sundries,                  4   0 =  0.0
                                             ———   ————
                                             100   18.6

or 18 per cent. increase, nearly.

Express trains, as worked on many roads, run at an unnecessary speed, to
make up for frequent stops. Overcoming a long distance in a short time,
depends as much on decrease in the number of stops, as increase in the
speed.

The following figures show the effect of decreasing the number of stops.

A train running 400 miles, and stopping once in fifty miles, each stop
being five minutes, (including coming to rest and starting,) to pass
over the whole distance in eight hours, must run fifty-five miles per
hour.

Stopping once in twenty miles, sixty-three miles per hour.

Stopping once in ten miles, eighty-six miles per hour.

The following table shows the velocities of the different classes of
trains in England, France, and Belgium, including and excluding stops.


                           EXCLUDING STOPS.

               Express. 1st class. 2d class.      3d class.
      England,   43.9      32.8      32.8    25.2 miles per hour.
      France,     ——       27.5      24.3    28.1 miles per hour.
      Belgium,    ——       26.2      25.7    27.6 miles per hour.


                           INCLUDING STOPS.

               Express. 1st class. 2d class.      3d class.
      England,   36.5      24.8      24.8    17.5 miles per hour.
      France,     ——       22.1      17.9    19.9 miles per hour.
      Belgium,    ——       20.7      19.3    18.1 miles per hour.

The distances at which the different classes of trains stop in the
several countries, are as follows:—


                          TRAINS STOP ONCE IN

                  1st class.   2d class.    3d class.     Express.
    England,      8   miles,   8   miles,    5 miles,    24 miles.
    France,      10   miles,   6   miles,    6 miles,    —— miles.
    Belgium,      6.8 miles,   5.6 miles,    5 miles,    —— miles.


              OF THE INCREASED DANGER OF FAST TRAVELLING.

The causes of accident, beyond the control of passengers, are

              Collision by opposition.
              Collision by overtaking.
              Derailment by misplaced switches and draws.
              Derailment by obstacles upon the rails.
              Breakage of machinery.
              Failure of track or bridges.
              Fire.
              Boiler explosions.

Those _causes_ which are aggravated by fast travelling are the first,
second, fifth, and sixth; the _effects_ of all are worse at high speeds
than at low.

The proportion of accidents due to each of these causes, taken at random
from one hundred cases on English railways, are as follows:—

                       Collision,              56
                       Breaking of machinery,  18
                       Failure of the road,    14
                       Misplaced switches,      5
                       Obstacles on rails,      6
                       Boiler explosion,        1
                                              ———
                                              100

In collision by opposition, the engines, tenders, and baggage cars must
be demolished before the shock reaches the passengers; in collision by
overtaking, the engine of the rear train plunges at once into the last
passenger car of the leading train; the force in the last case is the
difference of the speeds, in the former the sum. The _increase_ of
danger from this cause, attendant upon express trains, is due, first, to
the longer time required in stopping, and second, in the greater shock
if collision occurs.

Breakage of machinery is more liable to take place while wheels are
revolving 25,000 times per hour, than when the speed is less.

Failure of the superstructure of bridges, (particularly when on curves
or grades,) is more liable to take place at high than at low velocities.

Accidents from obstacles upon the track, from fire, boiler explosions,
and misplaced switches, are no more attendant upon express than upon
other trains, but the consequences are worse with the high speeds.

From the analysis above, of one hundred accidents, it appears that
eighty-eight per cent. of the cases are due to the causes that are
aggravated by increase of speed, and if we assume the aggravation of
collision, and breakage of machinery, to be (speed being doubled) as two
to one, the danger of travelling a fixed distance, by express, is
eighty-eight per cent. greater than by a slow train.


          COMPARATIVE COST OF WORKING HEAVY AND LIGHT TRAINS.

414. The question is sometimes asked, if it would not be better to run a
greater number of trains and reduce the weight of engines. A comparison
of cost is easily made.

The cost of working trains consists of

                        Fuel, oil, and waste.
                        Engine-men’s wages.
                        Wear of rails.
                        Conductor and brakemen.
                        Wear of cars.

Suppose we have to move 1,000 tons per day over any road. If we do it by
one engine and 100 cars, the whole cost will be

                          One Engineer   $2.00
                          One Fireman     1.50
                          One Conductor   1.75
                          Four Brakemen   5.00
                                        ——————
                                        $10.25

And if we move 1,000 tons by _ten_ trains of one hundred tons each,

                      Ten Engine-men at $2 $20.00
                      Ten Firemen at    1½  15.00
                      Ten Conductors at 1¾  17.50
                      Ten Brakemen at   1¼  12.50
                                           ——————
                                           $65.00

Difference of salaries in favor of the heavy train, of $54.75.

As the whole weight upon the drivers must be the same to move a given
load by either method, the only difference in weights of engines will be
that upon the truck. To lead well a truck must have five tons upon it.
The whole weight upon _ten_ trucks is, then, fifty tons, and that upon
_one_, _five_ tons, which leaves an excess of forty tons to be daily
carried over the road by the small trains. The heaviest freight engine
will not cost over $15,000; the cost of an engine to draw one hundred
tons cannot be less than $5,000.

    10 × 5000 = 50000 less 15000 is $35000. 6/100 of 35000 is $2100.

Add to this five times as much fuel used in firing up and standing with
steam up, ten times as much oiling, cleaning, and repairing, ten times
as much engine house and shop accommodation; also that the cars in
frequent trains are much less loaded than in seldom ones, increased
delay and chance of accident from increased number of trains, and
estimating all of them at $170.00 per day, (the cost of the large engine
being assessed at $30 per day, and that of each of the small ones as
$20, the daily difference is $170,) and we have, as the whole daily
increased cost of working ten small over one large train,

    170.00 + 54.75 × (6/100 of 35000)/313 or 6.71 = $231.46 per day,

or $72,446.98 per annum, which employs a capital of $1,207,449.


                             BRANCH ROADS.

415. These lines, when belonging to the main road, are generally worked
at a loss; and when independent, are a poor investment. At a meeting of
the directors of the Boston and Worcester (Mass.) Railroad in February,
1855, it was declared that out of six branches, but one was profitable.
That four of them gave an income upon cost of from one and a quarter to
one and three quarter per cent.

Independent branch lines generally share a joint business by the mileage
standard; and here is where they lose, for if the branch trains do not
traverse the main line, and the tribute passengers help to fill a train
which runs at any rate upon the main, then the branch expense of
carrying the passengers is to that of the main, as (say ninety to ten),
and the branch should take 90/100 of the receipts. In this case the
branch is charged with using both the cars and road of the main. If it
runs its own cars over the main, (as when the branch is near the
terminus,) it should be charged only with the wear of the road.

In like manner several roads, forming a continuous line, should not
divide the receipts according to the mileage; but according to the cost
of working that mileage. Thus if we have the continuous line below,
column one shows the length; column two, the cost of building; column
three, that of maintaining; and column four, the division of receipts.

    Division.      Length.    Construction  Maintaining     Result.
                                Capital.      Capital.
        1             8            10            4       10 + 4  = 14
        2             9             6            3½       6 + 3½ =  9½
        3             6             7            2¾       7 + 2¾ =  9¾
        4            10             4            1¼       4 + 1¼ =  5¼


                    REPRODUCTION OF ROAD AND STOCK.

416. Besides the annual repairs necessary to maintain a road in proper
working order, there is needed a periodic expenditure for
_reproduction_. Evidently the time will come, upon all roads, when rails
and sleepers, buildings, bridges, etc., need to be replaced. Knowing the
life of rails, we also know the annual depreciation, and from that can
easily find what sum must annually be laid aside, which being properly
invested, shall, at the end of the life of the rail, together with its
interest, be equal to the cost of renewing.


                                 RAILS.

Suppose rails to last ten years, the annual depreciation is ten per
cent. At sixty lbs. per yard we have one hundred and five tons per mile,
which, at $60 per ton, amounts to $6,300. Let the cost of rerolling and
relaying be $30 per ton, the depreciation is then $30 per ton for ten
years, or $3 per ton per annum, or $315 per mile per annum.


                               SLEEPERS.

If sleepers last seven years, and cost forty cents apiece, their annual
depreciation per mile (at 2,400 per mile) will be $138 per mile
(nearly).


                                BRIDGES.

If wooden bridges cost $30 per lineal foot, and last twenty years, the
annual depreciation per foot will be $1.50, and if there is ten feet per
mile of road, $15 per annum per mile.


                                EXTRAS.

Allowing for the annual depreciation per mile of buildings, fences,
etc., $33, we have as the whole annual depreciation, $500 per mile; and
the amounts which yearly reserved and placed at compound interest for
each of the ten years, will pay for reproducing the road, are as
follows:—

                    At the end of the  1st year $298
                    At the end of the  2d  year  315
                    At the end of the  3d  year  333
                    At the end of the  4th year  354
                    At the end of the  5th year  373
                    At the end of the  6th year  397
                    At the end of the  7th year  417
                    At the end of the  8th year  446
                    At the end of the  9th year  472
                    At the end of the 10th year  500

which, at six per cent., gives, at the end of the tenth year, $500 each.

  NOTE.—Reproduction of rolling stock has been proved to be nothing
  more than repairs, as a locomotive may be fitted with one and
  another new part until none of the original machine remains. See
  Lardner’s Railroad Economy.

As the business upon a railroad increases, so does the amount of station
accommodation necessary, and also of rolling stock, which increase
should be debited to capital, and not to revenue.

The permanent investors in a railroad are in favor of having capital
maintained, even at the expense of revenue. The temporary shareholders,
and the speculators in stock, wish most to produce large dividends, even
at a sacrifice of capital, and would charge nothing to revenue.

The rights of both of the above classes are to be regarded, as the road
is often built mainly by the efforts of the temporary investors.


                     WORKING RAILROADS BY CONTRACT.

417. An experiment has lately been tried upon the working of railroads
which bids fair to reduce very considerably the cost of operating; and
to render the enterprises more profitable, namely, working the several
departments by contract; that is, paying certain persons a fixed price
for supplying the necessary amount of power, cars, or material per
annum, thus bringing into play _private interest_ and _individual
enterprise_. There is no doubt but that by a judicious system of this
kind, correctly applied, many roads which are now worthless could be
made to pay, while the value of good roads would be also increased.


                       CLASSIFICATION OF FREIGHT.

418. Freight is classified according to its nature, the commercial
nature of the country traversed by the road, and the direction of the
principal market. The distribution adopted upon some of the large roads
is as follows:—


                      CLASSIFICATION OF ARTICLES.

               [Articles marked thus * at owner’s risk.]


                         _Double First Class._

 Baskets, * Band Boxes;
 * Camphene;
 * Carboys, and contents;
 * Demijohns, and contents;
 * Eggs;
 Feathers, in bags;
 Furs;
 Hobby Horses;
 Musical Instruments;
 * Plaster of Paris, (ornaments);
 Pictures, in frames;
 Teazles, in casks;
 Wagons, (children’s);
 Willow Ware.

                             _First Class._

 * Ale, in glass;
 * Apples, green, _pre-paid_;
 Bacon, loose;
 Batting;
 Bells;
 * Berries, _pre-paid_;
 * Blinds, (window) in packages;
 Bonnets;
 * Books, in boxes;
 Boots;
 Bran, in bags;
 Brass, in sheets and pigs;
 Brass Castings;
 Brass Vessels;
 Bread and Biscuit;
 Brooms, in bales or bundles;
 Broom Handles, in boxes or bundles;
 Brushes;
 Buffalo Robes, packed;
 Buttons;
 * Candies and Confectionary, canvassed;
 Cane;
 Cards;
 Carpeting;
 Caps;
 China Ware;
 Chocolate;
 * Cigars, in boxes;
 Cinnamon;
 * Clocks, in boxes;
 Cocoa;
 Cassia;
 Coffee, ground;
 Collars;
 Combs;
 Copper, in sheets and pigs;
 Copper Vessels;
 Corks;
 * Cotton, in bales;
 * Cotton Waste;
 Covers and Sieves;
 * Cranberries;
 * Cutlery;
 Deer Skins, in bundles;
 Doors;
 Dry Goods;
 Fancy Goods;
 * Figs, in boxes;
 Fire-arms;
 * Fish, fresh, _pre-paid_;
 Flour, in bags;
 Forks, hay and manure;
 * Fruits, fresh, _pre-paid_;
 * Game, _pre-paid_;
 Garden Seeds;
 Ginger;
 * Glass, in boxes;
 * Glass Ware, in boxes or casks;
 Glue;
 * Grapes, _pre-paid_;
 Gun Stocks, in boxes or bundles;
 Hair, in sacks;
 Hams, loose;
 Harness;
 Hides, dry;
 Hoe Handles;
 * Hollow Ware;
 * Honey;
 Hops, pressed;
 * Ice, _pre-paid_;
 Indigo;
 Ink;
 Iron Castings, light;
 Ivory;
 Japan Ware;
 Joiners Work;
 * Lemons, in boxes, canvassed;
 * Looking-glasses, well boxed;
 * Machinery, boxed, light;
 Marble, wrought, at owner’s risk of breakage;
 Mats;
 Mattrasses, double, at 150 pounds each;
 Mattrasses, single, at 100 pounds each;
 Mill Stuffs, in bags or casks;
 Measures;
 * Meat, fresh, _pre-paid_;
 Meat, in bulk, salted;
 Medicines;
 * Melons, _pre-paid_;
 Moss, in sacks;
 Nuts, in sacks or casks;
 * Oranges, in boxes, canvassed, _pre-paid_;
 * Oysters, in cans or kegs;
 Palm Leaf, in bales;
 Paper, brown wrapping and straw, (light);
 Paper Hangings;
 Pelts;
 * Porter, in glass;
 * Poultry, dressed, _pre-paid_;
 * Prunes;
 Rags, (see second class);
 * Raisins;
 Rake Handles;
 Rattan;
 Rugs;
 Saddle Trees;
 Saddlery;
 * Sash, in packages;
 Scale Beams;
 Scythe Snaths;
 Shoes;
 Shovel Handles;
 Soap, fancy;
 Soda;
 Spices;
 * Spirits Turpentine;
 Stationery;
 Straw Goods;
 Teas, (see third class);
 Tin Ware, in crates or hhds.;
 Toys;
 Trunks, empty, 80 pounds each;
 Tubs;
 Turners’ Work;
 * Vegetables, _pre-paid_;
 Veneering;
 Wadding;
 Warp, on beams;
 Warp Beams;
 Waste, woollen;
 Wax;
 Whalebone;
 Wheelbarrows;
 Whips;
 Wicking;
 * Wines, in baskets or boxes;
 * Wooden Ware;
 Wool;
 Woollens.

                            _Second Class._

 Alcoholic Liquors;
 * Ale, in casks;
 Apples, dried;
 Alum;
 Anchors;
 Anvils;
 Ashes, pot or pearl;
 Axes, in boxes;
 Axles, iron;
 Bacon, packed;
 Bagging;
 Barilla;
 Bark, tanner’s, 1¼ cord per ton;
 Beans;
 * Beef, in casks or boxes;
 Beer, in casks;
 Bleaching Salts;
 Bones;
 * Bottles, packed, (empty);
 Brimstone;
 Burr Blocks;
 Burlaps, in original packages;
 * Butter, in firkins;
 * Candles, in boxes;
 Cannon;
 Canvas;
 Castings, heavy;
 Cement;
 Chains;
 Chalk;
 Chair and turned Stuff in bales or bdls.;
 Cider, in casks;
 Cheese, in boxes or casks;
 Clay, Coal, and Coke, in casks or boxes;
 Clover Seed;
 Coffee, in sacks;
 Copperas;
 Cordage;
 Crockery Ware, well packed;
 Domestics, in original packages;
 Dye Stuffs, in woods;
 Earthen Ware, well packed;
 * Fire Brick;
 Fish, dried or salted;
 Flax Seed;
 Flocks;
 Floor Cloth, painted;
 Flour, in barrels, 20 barrels or less;
 Furnaces;
 Grain, of all kinds;
 * Grindstones;
 Groceries, generally heavy, not otherwise specified;
 Gunnies, in bales;
 Hoes;
 Hams, shoulders or sides, in casks or boxes;
 Hardware, except Cutlery;
 * Hemp, in bales;
 Hemp Seed;
 * Hides, green;
 * High Wines;
 Hoops, shaved or split, 3,000 pounds per cord;
 India Rubber;
 Iron, pig, bloom, boiler, rod, and bar;
 Iron, hoop, sheet, or bolts;
 Iron, nuts, rivets, and spikes;
 Junk;
 Lard, in barrels or casks;
 Lead, sheet, pig, or pipe;
 Leather;
 Liquors, in barrels or casks;
 Lime, in barrels or casks;
 Marble, unwrought, at owner’s risk of breakage;
 Meal, in bags or casks;
 Molasses;
 Moss, pressed;
 Nails, in kegs;
 Oakum, in bales;
 Oil, owner’s risk of leakage;
 Oil Cake,
 Oil Cloth;
 * Oysters, in shell;
 Paints, dry or in oil;
 Paper, (white,) in boxes or bundles;
 Paper, (heavy brown and hardware);
 Pasteboard;
 Pepper;
 Peaches, dried;
 Peas, in sacks or casks;
 Pickles, in casks;
 * Pipes, in boxes;
 Pitch;
 Plaster, in casks or barrels;
 Ploughs;
 Pork, packed;
 * Porter, in casks;
 Potatoes, in casks or sacks;
 Rags, foreign, pressed;
 Rakes;
 Railroad Chairs and Spikes;
 Rice;
 Rope;
 Rosin;
 Saleratus;
 Salt, in bags or casks;
 Saltpetre;
 Scales, in boxes;
 Scythes, in bundles;
 Scythe Stones;
 Shot, in bags;
 Shovels and Spades;
 Sizing;
 Slate;
 Soap, (common,) in boxes;
 Soda:
 Spelter and Zinc;
 Spikes, in kegs;
 Spirits, domestic;
 Starch;
 Steel, in boxes or bundles;
 Steel Springs;
 Stone;
 * Stone Ware, well packed;
 Sugar;
 Sumac;
 Tallow, owner’s risk of heat;
 Tar;
 Tiles;
 Tin, metal and plate;
 Tobacco, in bales, boxes, or hhds.;
 Tow, pressed, (in bales,) owner’s risk of fire;
 Twine, in bales;
 Vegetable Roots, in sacks or casks;
 * Vinegar;
 Water, Mineral;
 Whiskey, in casks;
 White Lead;
 Whiting;
 * Wine, in casks;
 Wire, in rolls and casks;
 Woods, in shape, unfinished;
 Woods, of value, namely, Mahogany, Lignum Vitæ, Rosewood, Cherry,
    Cedar, Walnut, etc.;
 Wool, foreign, pressed, in bales;
 Yam, pressed;
 Zinc and Spelter.

                             _Third Class._

Includes the following articles in quantities of 8,000 pounds, and less
than 16,000 pounds, in any one shipment from one consignor to one
consignee. Same articles shipped in like manner, in quantities of 16,000
pounds and upwards, will be taken at special rates.

 Anchors;
 Anvils;
 Ashes, pot and pearl, in casks;
 Axes, iron;
 Bacon, packed;
 Bark, tanner’s, 1¼ cord per ton;
 Beans, in sacks or casks;
 Beef, packed;
 Burr Blocks;
 Cannon;
 Cement, in barrels or casks;
 Chain Cable;
 Cider;
 Clay;
 Coffee;
 Copper, in boxes;
 Flaxseed, in sacks or casks;
 Flour, in barrels;
 Grain, of all kinds;
 Grindstones;
 Hams, packed;
 High Wines;
 Iron, pig, bar, bloom, sheet, hoop, or rod;
 Iron Castings, heavy;
 Lard, in casks or barrels;
 Lead, sheet, pig, or pipe;
 Lime, in barrels;
 Marble, unwrought, at owner’s risk of breakage;
 Molasses;
 Nails, in kegs;
 Plaster, in barrels;
 Pork, packed;
 Potatoes, in sacks or casks;
 Railroad Iron, Chairs and Spikes;
 Salt, in sacks and barrels;
 Shot;
 Slate;
 Spikes, in kegs;
 Sugar, in casks;
 Teas;
 Tobacco, in boxes or hhds.;
 Vinegar, in barrels;
 Whiskey, in barrels.

Besides the above regular articles, are the following special objects of
transport:—

 Stores;
 Cabinet Ware;
 Brick;
 Charcoal;
 Pressed Hay;
 Broom Corn;
 Boxes of Cigars;
 Barrels;
 Bags;
 Corn in the Ear;
 Poultry;
 Looking-glasses;
 Trees and Shrubbery;
 Safes;
 Mill-stones;
 Steam-engines;
 Machinery;
 Agricultural Implements;
 Lumber;
 Live-Stock;
 Carriages;
 Coal and Coke.


                              TIME TABLES.

Fig. 158, (see end of volume).

419. The most complete graphic solution of an engineering problem, is
doubtless the time table of S. S. Post, Esq., chief engineer of the New
York and Erie Railroad. Let the vertical lines represent _time_ in
spaces of ten minutes each, and the horizontals, distances, the heavy
lines representing the several way stations. Suppose now that we leave
station A at six, A. M., and wish to arrive at K at two, P. M., stopping
ten minutes at each station; the number of way stations being eight, the
whole time consumed in stops will be 10 × 8 = 80 minutes. From two, P.
M., and on the line K, go back eighty minutes or to M, and from A draw A
B, in the direction A M, which cuts the line B B at B, which is four
miles, or thirteen minutes from A. Now, as we _wait_ ten minutes, pass
along _on the line_ B B one division (ten minutes) to B′ and start again
parallel to A B, arriving at C at one and a half hours from starting.
Proceeding thus, we arrive at K at the required time. The inclination of
the line shows the speed. Thus, if it passes twenty horizontal spaces in
six vertical divisions, we have twenty miles in sixty minutes, or twenty
miles per hour.

Suppose now we would start an express train at eight, A. M., from A to
arrive at K at one, P. M., (see line 8 F,) it will pass the first train
at station F, and will run at the rate of seventeen miles per hour from
A to F, at the same rate from F to G, and at _thirteen miles per hour_
from G to 1.

Suppose also that we start a train from K at six, A. M., to arrive at A
at eleven, A. M., we pass the before-mentioned trains at E and D.

Also a freight train which is required to pass the above named trains,
leaving K at eight, A. M., and arriving at A at one, P. M., will stop
ten minutes at G, ten minutes at M, pass the first train at L, wait ten
minutes on a siding at two and a half miles from L, and run to A at
nearly a uniform rate of speed.

So also may the motion of any train be laid down and traced through the
hours of the day upon the table. By plotting the profile of the road
upon the line A K, the places are shown at which grades will oblige us
to use a less speed. Curves also may be shown by increasing the
steepness of the grades; or by making a grade on the profile when the
road is level, steep enough to involve an amount of power equal to that
consumed by the curve.


                         LOCOMOTIVE REGISTERS.

420. American railroad reports are, as a general thing, quite destitute
of detailed accounts of the performance of the power. Some of the large
roads, indeed, are of late improving in this respect.

That fares and tolls may be properly applied to the different articles
of transport, the cost of moving each article should be known.

Such items as the salaries of employees, and repairs of machinery, are
easily distributed to the proper heads; but the correct amount of fuel,
oil, and waste, to be charged to any department, is not so evident. What
we require is, the exact amount of fuel, oil, and waste used, and work
done by each engine; to obtain which, some system of registering these
quantities must be adopted.

The following five blanks being filled, we have all that is required:—

Number 1 is the engineer’s weekly return to the master of machinery, and
gives, as seen, the times of arriving at, and departing from, each
station. The fuel should always be ready at each station for delivery,
in cords and half cords, or in tons and fractions, when coal or coke. It
may be delivered either from a small car placed on a pair of rails at
right angles to the track, or from a box hung upon a crane, which may be
at once swung over and lowered into the tender; the box which is already
in, being first removed. The latter method gives the most correct
results, as whatever fuel is left at the station may be credited to the
engine. The whole operation of wooding would not take longer than it
does to describe it, and would lead to a systematic and economical
method of working.

The tanks and pumps being charged to construction, we may, without
material error, charge the cost of the water supply to the trains
according to their mileage.

Number 2 is the wood register, showing the amount of fuel delivered to
the several engines from the different stations, and should be weekly
signed and returned by the station wood master to the fuel agent. The
engineer’s fuel receipts (No. 1) check these reports.

Number 3 is the conductor’s mileage account, giving the exact weight
left at, and taken from, each station; and, consequently, the load
carried between stations, which is checked by the station master’s
return.

Number 4 is the monthly account of the performance of engines, compiled
from the weekly return by the superintendent of machinery, and reported
to the superintendent.

Number 5 gives the annual performance of each and all of the engines
upon the road, and is obtained from the monthly reports, and from those
of the repair and transportation departments.

The work done by different classes of cars should be registered in like
manner.

Knowing the amount of material used, and also the work done, it is easy
to find the cost per mile of moving any article of transport, regard of
course being had to the character of the parts of the road traversed by
the several engines. An engine working a sixty feet grade should be
allowed more fuel than one which works a level only.


                               NUMBER 1.

A. and B. Railroad. Report of amount of material consumed, and of work
done by Engine No. 50, during the week ending July 4, 1856.

                                                     ————————, Engineer.

   ┌───────┬───────────────────────────────────────────────────────┐
   │MONDAY.│Name of train.                                         │
   ├───────┼──────────────────┬───┬───┬───┬───┬───┬───┬───┬───┬────┤
   │       │Name of station.  │   │   │   │   │   │   │   │   │    │
   ├───────┼──────────────────┼───┼───┼───┼───┼───┼───┼───┼───┼────┤
   │       │Time of arriving. │   │   │   │   │   │   │   │   │    │
   ├───────┼──────────────────┼───┼───┼───┼───┼───┼───┼───┼───┼────┤
   │       │Time of departing.│   │   │   │   │   │   │   │   │    │
   ├───────┼──────────────────┼───┼───┼───┼───┼───┼───┼───┼───┼────┤
   │       │Fuel taken.       │   │   │   │   │   │   │   │   │    │
   ├───────┼──────────────────┼───┴───┴───┴───┴───┴───┴───┴───┼────┤
   │       │                  │Whole cost fuel consumed       │————│
   │       │                  │Whole time under steam         │————│
   │       │                  │Whole time running             │————│
   └───────┴──────────────────┴───────────────────────────────┴────┘

And the same for each day of the week.


                           WEEKLY MEMORANDA.

                    Cords of wood used         ————
                    Gallons oil used           ————
                    Pounds tallow used         ————
                    Pounds waste used          ————
                    Miles run                  ————
                    Whole time running         ————
                    Whole time under steam     ————
                    Time under repairs         ————
                    Cost of repairs            ————
                         ————, Master of Machinery.


                               NUMBER 2.

 ┌───────────────────────────────────────────────────────────────────┐
 │ —— RAILROAD.  AMOUNT OF FUEL DELIVERED TO ENGINES FROM —— STATION │
 │                      DURING WEEK ENDING ——.                       │
 ├───────────────────────┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───────┤
 │    Name of Engine.    │A. │B. │C. │D. │E. │F. │G. │H. │K. │Total. │
 ├───────────┬───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │MONDAY.    │Morning.   │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │           │Afternoon. │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │TUESDAY.   │Morning.   │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │           │Afternoon. │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │WEDNESDAY. │Morning.   │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │           │Afternoon. │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │THURSDAY.  │Morning.   │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │           │Afternoon. │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │FRIDAY.    │Morning.   │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │           │Afternoon. │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │SATURDAY.  │Morning.   │   │   │   │   │   │   │   │   │   │       │
 ├───────────┼───────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───────┤
 │           │Afternoon. │   │   │   │   │   │   │   │   │   │       │
 ├───────────┴───────────┴───┴───┴───┴───┼───┴───┴───┴───┴───┴───────┤
 │Total to each engine.                  │    Wood Station Master ——.│
 └───────────────────────────────────────┴───────────────────────────┘


                               NUMBER 3.

A. and B. Railroad. Conductor’s mileage return, for week ending July 4,
1856, showing work done by Engine No. 54.

 ┌───────────┬─────────────────────────────────────────────────────────┐
 │MONDAY.    │Train.                                                   │
 ├───────────┼─────────────────────┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┤
 │           │Station.             │  │  │  │  │  │  │  │  │  │  │  │  │
 ├───────────┼─────────────────────┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤
 │           │Cars taken.          │  │  │  │  │  │  │  │  │  │  │  │  │
 ├───────────┼─────────────────────┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤
 │           │Cars left.           │  │  │  │  │  │  │  │  │  │  │  │  │
 ├───────────┼─────────────────────┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤
 │           │Cars in train.       │  │  │  │  │  │  │  │  │  │  │  │  │
 ├───────────┼─────────────────────┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤
 │           │Weight of train.     │  │  │  │  │  │  │  │  │  │  │  │  │
 ├───────────┼─────────────────────┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤
 │           │Eq’d distance.       │  │  │  │  │  │  │  │  │  │  │  │  │
 ├───────────┼─────────────────────┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┤
 │           │Eq’d mileage.        │  │  │  │  │  │  │  │  │  │  │  │  │
 ├───────────┼─────────────────────┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┼──┤
 │           │Total equated mileage                                 │——│
 ├───────────┴──────────────────────────────────────────────────────┴──┤
 │And the same for each day of the week.                               │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 │                                                                     │
 └─────────────────────────────────────────────────────────────────────┘


                               NUMBER 4.

 ┌───────────────────────────────────────────────────────────────────┐
 │  A. AND B. RAILROAD. PERFORMANCE OF LOCOMOTIVE ENGINES FOR MONTH  │
 │                           ENDING ——.                            │
 ├───────┬────┬─────┬───────────────────────┬───────────┬────────────┤
 │       │    │Miles│                       │           │            │
 │Number.│Use.│run. │         Time.         │  Wages.   │   Fuel.    │
 │       │    │     │                       │           │            │
 ├───────┼────┼─────┼────────┬─────┬────────┼─────┬─────┼──────┬─────┤
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │ At  │ Under  │     │Cost │      │Miles│
 │       │    │     │Working.│rest.│repairs.│Cost.│ per │Cords.│ per │
 │       │    │     │        │     │        │     │mile.│      │cord.│
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 ├───────┼────┼─────┼────────┼─────┼────────┼─────┼─────┼──────┼─────┤
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 ├───────┼────┼─────┼────────┼─────┼────────┼─────┼─────┼──────┼─────┤
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 │       │    │     │        │     │        │     │     │      │     │
 ├───────┴────┴─────┴────────┴─────┴────────┴─────┴─────┴──────┴─────┤
 │                                                                   │
 └───────────────────────────────────────────────────────────────────┘

 ┌────────────────────────────────────────────────────────────────────┐
 │  A. AND B. RAILROAD. PERFORMANCE OF LOCOMOTIVE ENGINES FOR MONTH   │
 │                            ENDING ——.                            │
 ├────────────────────────────────────────────┬───────────┬───────────┤
 │                                            │           │           │
 │          Oil, waste, and tallow.           │ Repairs.  │  Totals.  │
 │                                            │           │           │
 ├───────┬─────┬──────┬───────┬───────┬───────┼─────┬─────┼─────┬─────┤
 │       │     │      │       │       │ Cost  │     │     │     │     │
 │       │     │      │       │Cost of│  per  │     │     │     │     │
 │Gallons│Miles│Pounds│Pounds │ oil,  │mile of│     │Cost │     │Cost │
 │  oil  │ per │  of  │  of   │waste, │ oil,  │Cost.│ per │Cost.│ per │
 │ used. │pint.│waste.│tallow.│  and  │waste, │     │mile.│     │mile.│
 │       │     │      │       │tallow.│  and  │     │     │     │     │
 │       │     │      │       │       │tallow.│     │     │     │     │
 ├───────┼─────┼──────┼───────┼───────┼───────┼─────┼─────┼─────┼─────┤
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 ├───────┼─────┼──────┼───────┼───────┼───────┼─────┼─────┼─────┼─────┤
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 │       │     │      │       │       │       │     │     │     │     │
 ├───────┴─────┴──────┴───────┴───────┴───────┴─────┴─────┴─────┴─────┤
 │                                                                    │
 └────────────────────────────────────────────────────────────────────┘

 ┌────────────────────────────────────────┐
 │   A. AND B. RAILROAD. PERFORMANCE OF   │
 │LOCOMOTIVE ENGINES FOR MONTH ENDING ——.│
 ├──────────────────────────────────┬─────┤
 │                                  │Comp,│
 │            Work done.            │work │
 │                                  │done.│
 ├────────────────┬─────────────────┼─────┤
 │                │                 │     │
 │                │                 │     │
 │                │                 │     │
 │    Freight.    │   Passenger.    │     │
 │                │                 │     │
 │                │                 │     │
 │                │                 │     │
 ├────────┬───────┼─────────┬───────┼─────┤
 │        │ Cost  │         │ Cost  │     │
 │Equated │per ton│ Equated │per ton│     │
 │freight │  per  │passenger│  per  │     │
 │mileage.│equated│mileage. │equated│     │
 │        │ mile. │         │ mile. │     │
 ├────────┼───────┼─────────┼───────┼─────┤
 │        │       │         │       │     │
 │        │       │         │       │     │
 │        │       │         │       │     │
 │        │       │         │       │     │
 │        │       │         │       │     │
 │        │       │         │       │     │
 ├────────┴───────┴─────────┴───────┴─────┤
 │           ——, General Superintendent.│
 └────────────────────────────────────────┘


                               NUMBER 5.

 ┌────────────────────────────────────┐
 │A. AND B. RAILROAD. ANNUAL REPORT OF│
 │  COST OF MAINTENANCE OF, AND WORK  │
 │ DONE BY THE LOCOMOTIVE POWER, ALSO │
 │ THE COST PER TON AND PASSENGER PER │
 │ MILE, TOGETHER WITH THE NATURE AND │
 │ AMOUNT OF REPAIRS, THE DIMENSIONS, │
 │ & THE PRESENT STATE OF THE STOCK,  │
 │               1856.                │
 ├───────┬───────────┬────────┬───────┤
 │       │Name of the│        │Date of│
 │Name or│builder or │ Use to │commc’g│
 │Number │manufactory│which it│ work  │
 │of the │from whence│   is   │ upon  │
 │engine.│  bought.  │applied.│  the  │
 │       │           │        │ road. │
 ├───────┼───────────┼────────┼───────┤
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 ├───────┼───────────┼────────┼───────┤
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 ├───────┼───────────┼────────┼───────┤
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 │       │           │        │       │
 ├───────┴───────────┴────────┴───────┤
 │       RECAPITULATION, NO. 1.       │
 │                                    │
 │ Cost per equated mile, per ton, of │
 │working freight engines.            │
 │                                    │
 │  Engineer and fireman. Fuel. Oil,  │
 │tallow, and waste. Repairs.│ Total. │
 │                           │        │
 └───────────────────────────┴────────┘

 ┌───────────────────────────────────────────────────────────┐
 │ A. AND B. RAILROAD. ANNUAL REPORT OF COST OF MAINTENANCE  │
 │ OF, AND WORK DONE BY THE LOCOMOTIVE POWER, ALSO THE COST  │
 │ PER TON AND PASSENGER PER MILE, TOGETHER WITH THE NATURE  │
 │AND AMOUNT OF REPAIRS, THE DIMENSIONS, & THE PRESENT STATE │
 │                    OF THE STOCK, 1856.                    │
 ├───────────────────────────────────────────────────────────┤
 │                                                           │
 │                                                           │
 │GENERAL CHARACTER AND PRINCIPAL DIMENSIONS OF THE ENGINES. │
 │                                                           │
 │                                                           │
 │                                                           │
 ├─────────────────────┬────────┬────────────────┬───────────┤
 │                     │        │                │           │
 │                     │        │                │           │
 │                     │Capacity│                │           │
 │                     │   of   │                │           │
 │      Weights.       │ tender │   Cylind’rs.   │  Mode of  │
 │                     │   in   │                │connection.│
 │                     │gallons.│                │           │
 │                     │        │                │           │
 │                     │        │                │           │
 │                     │        │                │           │
 ├──────┬───────┬──────┼────────┼────────┬───────┼───────────┤
 │Whole │       │      │        │        │       │           │
 │weight│Weight │Weight│        │        │       │           │
 │  of  │ upon  │of the│        │        │       │           │
 │engine│  the  │tender│        │Diameter│Stroke.│           │
 │ with │driving│ with │        │of bore.│       │           │
 │ fuel │wheels.│feed. │        │        │       │           │
 │ and  │       │      │        │        │       │           │
 │water.│       │      │        │        │       │           │
 ├──────┼───────┼──────┼────────┼────────┼───────┼───────────┤
 │      │       │      │        │        │       │           │
 │      │       │      │        │        │       │           │
 │      │       │      │        │        │       │           │
 │      │       │      │        │        │       │           │
 │      │       │      │        │        │       │           │
 │      │       │      │        │        │       │           │
 ├──────┴───────┴──────┴────────┼────────┴───────┴───────────┤
 │                  RECAPITULATION, NO. 2.                   │
 │                                                           │
 │ Cost per equated mile, per passenger, of working engines. │
 │                                                           │
 │Engineer and fireman. Fuel. Oil, tallow, and waste.        │
 │                     Repairs.                     │ Total. │
 │                                                  │        │
 └──────────────────────────────────────────────────┴────────┘

 ┌─────────────────────────────────────────────────────────┐
 │A. AND B. RAILROAD. ANNUAL REPORT OF COST OF MAINTENANCE │
 │OF, AND WORK DONE BY THE LOCOMOTIVE POWER, ALSO THE COST │
 │PER TON AND PASSENGER PER MILE, TOGETHER WITH THE NATURE │
 │  AND AMOUNT OF REPAIRS, THE DIMENSIONS, & THE PRESENT   │
 │                STATE OF THE STOCK, 1856.                │
 ├──────────────────────────────────────────────────┬──────┤
 │                                                  │      │
 │                                                  │Number│
 │GENERAL CHARACTER AND PRINCIPAL DIMENSIONS OF THE │  of  │
 │                   ENGINES.                       │miles │
 │                                                  │ run  │
 │                                                  │      │
 ├─────────────────┬────────┬───────────────────────┼──────┤
 │                 │Relative│                       │      │
 │                 │ power, │                       │      │
 │                 │   or   │                       │      │
 │                 │traction│                       │      │
 │ Driv’g wheels.  │  at a  │        Boiler         │      │
 │                 │  mean  │                       │      │
 │                 │cylinder│                       │      │
 │                 │pressure│                       │      │
 │                 │ of 75  │                       │      │
 │                 │  lbs.  │                       │      │
 ├───────┬─────────┼────────┼─────┬────────┬────────┼──────┤
 │       │         │        │     │        │        │      │
 │       │         │        │     │        │        │      │
 │       │         │        │     │ Whole  │Area of │      │
 │Number.│Diameter.│        │Grate│heating │ blast  │      │
 │       │         │        │area.│surface.│orifice.│      │
 │       │         │        │     │        │        │      │
 │       │         │        │     │        │        │      │
 │       │         │        │     │        │        │      │
 ├───────┼─────────┼────────┼─────┼────────┼────────┼──────┤
 │       │         │        │     │        │        │      │
 │       │         │        │     │        │        │      │
 │       │         │        │     │        │        │      │
 │       │         │        │     │        │        │      │
 │       │         │        │     │        │        │      │
 │       │         │        │     │        │        │      │
 ├───────┴─────────┴────────┴─────┴────────┴────────┴──────┤
 │                                                         │
 │                                                         │
 │                                                         │
 │                                                         │
 │                                                         │
 │                                                         │
 │                                                         │
 └─────────────────────────────────────────────────────────┘

 ┌─────────────────────────────────────────────────────┐
 │    A. AND B. RAILROAD. ANNUAL REPORT OF COST OF     │
 │   MAINTENANCE OF, AND WORK DONE BY THE LOCOMOTIVE   │
 │POWER, ALSO THE COST PER TON AND PASSENGER PER MILE, │
 │ TOGETHER WITH THE NATURE AND AMOUNT OF REPAIRS, THE │
 │ DIMENSIONS, & THE PRESENT STATE OF THE STOCK, 1856. │
 ├─────────────────────────────────────────────────────┤
 │                                                     │
 │                                                     │
 │   WHOLE EXPENSE OF WORKING AND OF MAINTAINING THE   │
 │         LOCOMOTIVES, AND EXPENSE PER MILE.          │
 │                                                     │
 │                                                     │
 │                                                     │
 ├─────────┬───────────────────────────────────────────┤
 │         │                                           │
 │         │                                           │
 │         │                                           │
 │ Cost of │                                           │
 │enginemen│      Cost of oil, waste, and tallow.      │
 │   and   │                                           │
 │firemen. │                                           │
 │         │                                           │
 │         │                                           │
 │         │                                           │
 ├─────────┼───────┬─────┬──────┬──────┬───────┬───────┤
 │         │       │Miles│      │      │       │ Cost  │
 │         │       │ run │      │      │ Cost  │  per  │
 │         │Gallons│ to  │Pounds│Pounds│for oil│ mile  │
 │         │of oil │ one │  of  │  of  │waste, │run for│
 │         │ used. │pint │waste │tallow│  and  │ oil,  │
 │         │       │ of  │used. │ used │tallow.│waste, │
 │         │       │oil. │      │      │       │  and  │
 │         │       │     │      │      │       │tallow.│
 ├─────────┼───────┼─────┼──────┼──────┼───────┼───────┤
 │         │       │     │      │      │       │       │
 │         │       │     │      │      │       │       │
 │         │       │     │      │      │       │       │
 │         │       │     │      │      │       │       │
 │         │       │     │      │      │       │       │
 │         │       │     │      │      │       │       │
 ├─────────┴───────┴─────┴──────┴──────┴───────┴───────┤
 │               RECAPITULATION, NO. 3.                │
 │  Of —— freight engines —— are in working order, or  │
 │    —— per cent. of the whole. Average work of an    │
 │  engine is —— days per annum, and for each day at   │
 │       work —— days repairing and —— at rest.        │
 │                                                     │
 │                                                     │
 └─────────────────────────────────────────────────────┘

 ┌───────────────────────────────────────────────────────────────────┐
 │ A. AND B. RAILROAD. ANNUAL REPORT OF COST OF MAINTENANCE OF, AND  │
 │   WORK DONE BY THE LOCOMOTIVE POWER, ALSO THE COST PER TON AND    │
 │PASSENGER PER MILE, TOGETHER WITH THE NATURE AND AMOUNT OF REPAIRS,│
 │      THE DIMENSIONS, & THE PRESENT STATE OF THE STOCK, 1856.      │
 ├─────────────────────────────────────────────┬─────────────────────┤
 │                                             │                     │
 │                                             │                     │
 │ WHOLE EXPENSE OF WORKING AND OF MAINTAINING │  TIME OF SERVICE.   │
 │    THE LOCOMOTIVES, AND EXPENSE PER MILE.   │                     │
 │                                             │                     │
 │                                             │                     │
 ├─────────────────┬───────────────┬───────────┼───────┬─────┬───────┤
 │                 │               │           │       │     │       │
 │                 │               │           │       │     │       │
 │                 │               │           │ Time, │Time,│       │
 │                 │               │           │  in   │ in  │ Time  │
 │  Cost of fuel.  │   Repairs.    │  Total.   │ days, │days,│ while │
 │                 │               │           │  of   │ at  │ under │
 │                 │               │           │active │rest.│repair.│
 │                 │               │           │s'vice.│     │       │
 │                 │               │           │       │     │       │
 │                 │               │           │       │     │       │
 ├─────┬─────┬─────┼───────┬───────┼─────┬─────┼───────┼─────┼───────┤
 │     │     │     │       │ Cost  │     │     │       │     │       │
 │     │     │Cost │       │  per  │     │Total│       │     │       │
 │Cords│Cost │ per │Cost of│ mile  │     │cost │       │     │       │
 │ of  │ of  │mile │repairs│run for│Total│ per │       │     │       │
 │fuel │fuel.│ run │  of   │repairs│cost.│mile │       │     │       │
 │used.│     │ for │engine.│  of   │     │run. │       │     │       │
 │     │     │fuel.│       │engine │     │     │       │     │       │
 │     │     │     │       │       │     │     │       │     │       │
 ├─────┼─────┼─────┼───────┼───────┼─────┼─────┼───────┼─────┼───────┤
 │     │     │     │       │       │     │     │       │     │       │
 │     │     │     │       │       │     │     │       │     │       │
 │     │     │     │       │       │     │     │       │     │       │
 │     │     │     │       │       │     │     │       │     │       │
 │     │     │     │       │       │     │     │       │     │       │
 │     │     │     │       │       │     │     │       │     │       │
 ├─────┴─────┴─────┴───────┴───────┴─────┴─────┴───────┴─────┴───────┤
 │                      RECAPITULATION, NO. 4.                       │
 │                                                                   │
 │      Same as 3; for passenger, in place of freight engines.       │
 │                                                                   │
 │                                                                   │
 │                                                                   │
 │                                                                   │
 └───────────────────────────────────────────────────────────────────┘

 ┌──────────────────────────────────────────────────────────────┐
 │ A. AND B. RAILROAD. ANNUAL REPORT OF COST OF MAINTENANCE OF, │
 │ AND WORK DONE BY THE LOCOMOTIVE POWER, ALSO THE COST PER TON │
 │AND PASSENGER PER MILE, TOGETHER WITH THE NATURE AND AMOUNT OF│
 │  REPAIRS, THE DIMENSIONS, & THE PRESENT STATE OF THE STOCK,  │
 │                            1856.                             │
 ├──────────────────────────────────────────────────────────────┤
 │                                                              │
 │                                                              │
 │       RECEIPTS, OR AMOUNT OF WORK DONE BY LOCOMOTIVES.       │
 │                                                              │
 │                                                              │
 │                                                              │
 ├─────────────┬────────────────────────────────┬───────────────┤
 │             │                                │               │
 │             │                                │               │
 │             │                                │               │
 │             │                                │               │
 │ Passenger.  │          Merchandise.          │ Mixed trains. │
 │             │                                │               │
 │             │                                │               │
 │             │                                │               │
 │             │                                │               │
 │             │                                │               │
 ├───────┬─────┼───────┬───────┬───────┬────────┼───────┬───────┤
 │       │     │       │       │       │        │       │ Cost  │
 │       │Cost │Freight│ Cost  │Tons of│        │       │per ton│
 │ Cars  │ per │ cars  │  per  │freight│Cost per│Mileage│(gross)│
 │carried│ car │carried│ mile  │carried│ton per │  of   │  per  │
 │  one  │ per │  one  │  for  │  one  │mile for│ mixed │ mile  │
 │ mile. │mile.│ mile. │freight│ mile  │freight.│trains.│  for  │
 │       │     │       │ cars. │       │        │       │ mixed │
 │       │     │       │       │       │        │       │trains.│
 ├───────┼─────┼───────┼───────┼───────┼────────┼───────┼───────┤
 │       │     │       │       │       │        │       │       │
 │       │     │       │       │       │        │       │       │
 │       │     │       │       │       │        │       │       │
 │       │     │       │       │       │        │       │       │
 │       │     │       │       │       │        │       │       │
 │       │     │       │       │       │        │       │       │
 ├───────┴─────┴───────┴───────┴───────┴────────┴───────┼───────┤
 │                    RECAPITULATION, NO. 5.                    │
 │Relative cost per equated mile of gross to net tons of freight│
 │ carried. Relative cost per equated mile of gross to net tons │
 │                    of passengers carried.                    │
 │                                                              │
 │                                                              │
 │                                                              │
 └──────────────────────────────────────────────────────────────┘

 ┌────────────────────────────────────────┐
 │  A. AND B. RAILROAD. ANNUAL REPORT OF  │
 │COST OF MAINTENANCE OF, AND WORK DONE BY│
 │THE LOCOMOTIVE POWER, ALSO THE COST PER │
 │  TON AND PASSENGER PER MILE, TOGETHER  │
 │ WITH THE NATURE AND AMOUNT OF REPAIRS, │
 │ THE DIMENSIONS, & THE PRESENT STATE OF │
 │            THE STOCK, 1856.            │
 ├────────┬───────────┬────────┬──────────┤
 │ Total  │           │        │          │
 │equated │Comparative│ Nature │ Present  │
 │mileage │ effect of │   of   │condition │
 │   of   │ engines.  │repairs.│    of    │
 │engines.│           │        │machinery.│
 │        │           │        │          │
 ├────────┼───────────┼────────┼──────────┤
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 ├────────┼───────────┼────────┼──────────┤
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 ├────────┼───────────┼────────┼──────────┤
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 │        │           │        │          │
 ├────────┴───────────┴────────┴──────────┤
 │                                        │
 │                                        │
 │___________________                     │
 │                                        │
 │                                        │
 │                   Gen’l Superintendent.│
 │                                        │
 └────────────────────────────────────────┘


                               TELEGRAPH.

421. The magnetic telegraph has lately come into use as a means of
communication along the lines of long railroads, and nothing serves
better the purposes of adjusting the movement of trains, of transmitting
orders, and of keeping the general superintendent informed at all hours,
of the exact condition in detail of the whole road, and of all its
trains. The following is extracted from Mr. McCallum’s Report, before
referred to:—

“A single track railroad may be rendered more safe and efficient, by a
proper use of the telegraph, than a double track railroad without its
aid,—as the double track can only obviate collisions which occur between
trains _moving in opposite directions_, whilst the telegraph may be used
effectually in preventing them, either from trains moving in an
_opposite, or the same direction_; and it is a well established fact
deduced from the history of railroads, both in Europe and in this
country, that collisions between trains moving in the same direction
have proved by far the most fatal and disastrous, and should be the most
carefully guarded against. I have no hesitation in asserting, that a
single track railroad, having judiciously located turnouts, equal, in
the aggregate, to one quarter of its entire length, and a well-conducted
telegraph, will prove to be a more safe and profitable investment than a
much larger sum expended in the construction of a _continuous_ double
track, operated without a telegraph.

“Collisions between fast and slow trains, moving in the same direction,
are prevented by the application of the following rule:—‘The conductor
of a slow train will report himself to the superintendent of the
division, immediately on arrival at a station where by the time table he
should be overtaken by a faster train; and he shall not leave that
station until the fast train passes, without special orders from the
superintendent of the division.’ A slow train under such circumstances,
may, at the discretion of the division superintendent, be directed to
proceed. He, being fully apprised of the position of the delayed train,
can readily form an opinion as to the propriety of doing so, and thus,
whilst the delayed train is permitted to run without regard to the slow
train, the latter can be kept entirely out of its way.

  “NOTE.—In moving trains by telegraph, nothing is left to chance.
  Orders are communicated to the conductors and engineers of the
  opposing trains, and their answers returned giving their
  understanding of the order before either is allowed to proceed.

“Their passing place is fixed and determined, with orders _positive_ and
_defined_ that neither shall proceed beyond that point until after the
arrival of the other; whereas, in the absence of a telegraph, conductors
are governed by general rules and their individual understanding of the
same; which rules are generally to the effect, that in cases of
detention, the train arriving first at the regular passing place, shall,
after waiting a few minutes, proceed cautiously, ‘expecting to meet the
other train,’ until they have met and passed, the one failing to reach
the ‘half way post’ between stations being required to back (always a
dangerous expedient), and the other permitted to proceed; the delayed
train being subjected to the same rule in regard to all other trains of
the same class it may meet, thus pursuing its hazardous and uncertain
progress during the entire trip. The history of such a system furnishes
a serious commentary on the imperfection of railroad regulations.

“The liability to collision under the system referred to has prompted
the invention of various expedients for suddenly arresting the progress
of trains; and which seem to have been conceived under the impression,
more imaginary than real, that the difficulties they were designed to
obviate, are unavoidable in their character; but which may, by the
exercise of ordinary care and the use of the telegraph, be subjected to
perfect control. Some of these inventions undoubtedly possess sufficient
merit to entitle them to adoption under any circumstances, whilst
others, for the above reasons, are entirely valueless—indeed it is
questionable whether a reliance on their use may not in many cases lead
to danger, _by producing recklessness, and thus increase instead of
diminish the evils sought to be avoided_.”


                      NEW YORK AND ERIE RAILROAD.

422. As a fine specimen of American railroad engineering, and American
railroad management, stands the above-named line, extending from Jersey
City to Lake Erie, at Dunkirk; embracing with its branches 496 miles of
road, employing over 1,000,000 dollars worth of labor per annum, upwards
of 200 locomotive engines, and about 3,000 cars; earning annually over
5,000,000, and expending 2,680,000 dollars.

The whole cost of the road up to September 30, 1855, was, with the
equipment, nearly $33,750,000. There are 129 truss bridges, amounting in
all to 15,692 feet in length; 64 trestle, stringer, and pile bridges, of
5,489 feet total length; 3 viaducts, of length 1,274 feet in all; 167
arch culverts, of from 3 to 30 feet span; 527 box culverts, from 1 to 12
feet span; 92 wood sheds, 14,200 feet total length; 435 buildings; 433
switches, of 387,914 feet available length, and 504,205 feet total
length.

Notwithstanding the immense amount of business transacted by such a
road, so complete is the organization and management of employees, that
the general superintendent, sitting in his New York office, can at any
moment tell, within one mile, where each car or engine is, what it is
doing, with what loaded, the consignor and consignee, and the time of
arriving and departing the several stations, and other trains; and thus
at any moment may perceive and correct faults and remissness, and in
reality _control_ the whole road.




                               APPENDIX.


                                   A.
                          DECIMAL ARITHMETIC.

The advantage of a Decimal system of Arithmetic and of mensuration, as
applied to engineering, can hardly be overstated. Civil and mechanical
engineers both use “per force” some decimal expressions, as 0.7854,
3.1416, etc., etc. Why not adopt the system entirely? All calculations
are much easier made decimally, and measurements made with more
exactness. The most perfect system of weights and measures is doubtless
that of the French. All lengths are based upon the _meter_ as a unit,
and whether the mechanic is making a watch or a locomotive his scale is
metrical. The meter is exactly 1/10000000 of the distance from the pole
to the equator, and was found, by measuring a meridian line from Rhodes
to Dunkirk (France), 570 miles long. The metrical scale is thus,

                      Millimetre  .001  or 1/1000
                      Centimetre  .01   or 1/100
                      Decimetre    .1   or ⅒
                      Metre        1.
                      Decametre   10.
                      Hectometre  100.
                      Kilometre  1000.
                      Myriametre 10000.

The metre is 3.280899 ft., or 39.370788 English inches. The English and
American foot is ⅓ of the yard; the yard is 35000/351393 of a pendulum
vibrating seconds at the latitude of London, at the level of the sea, in
a vacuum. The standard American scale is an eighty-two inch bar made by
Troughton of London for the United States Coast Survey. In civil
engineering the decimal division is almost entirely adopted; indeed, any
other would lead to almost endless calculation. The chain is one hundred
feet long and divided into one hundred links. The tape is graduated to
feet, tenths, and hundredths. The levelling rod to feet, tenths,
hundredths, and thousandths. As the English foot is so universally
adopted, and as it may at any time be got from a pendulum, it might not
be best to attempt to introduce the metre, but the foot should certainly
be divided decimally. The division should be thus,

                            .001  or 1/1000
                             .01  or 1/100
                             .1   or ⅒
                             1.
                             10.
                            100.
                            1000.

thus preserving a constant ratio, and not changing the proportion at
each increase or decrease as follows:—

                          8/8 = 1 inch.
                          12 inches = 1 foot.
                          16½ feet = 1 rod.
                          40 rods = 1 furlong.
                          8 furlongs = 1 mile.
                          3 feet = 1 yard.
                          6 feet = 1 fathom.


                                   B.
                           ALGEBRAIC FORMULÆ.

As this work may come into the hands of those who are unacquainted with
the solution of algebraic problems, it was thought best to give the
following:—

  _a_ + _a_, signifies _a_ added to _a_, or 2 _a_.

  _a_ – _a_, denotes _a_ less _a_, or 0.

  _a_ × _a_, _a_ multiplied by _a_, or _a_ square, _a^2_ (see below).

                 _a_ ÷ _a_,}
                           } _a_ divided by _a_, or 1.
                 or _a_/_a_}

  _a^2_, the square of _a_, or _a_ × _a_

  _a^3_, the third _power_ of _a_, or _a_ × _a_ × _a_.

  √(_a_), the square root of _a_, or _a_^½

  ∛(_a_), the cube or third root of _a_, or _a_^⅓

  (_a_ + _b_ + _c_)/_d_, shows that the sum of _a_, _b_, and _c_, is
  to be divided by _d_.

  (_a_ + _b_ + _c_) _d_ or (_a_ + _b_ + _c_) × _d_, denotes that the
  _sum_ of _a_, _b_, and _c_, is to be multiplied by _d_.

  Generally in place of writing _a_ × _b_ to express multiplication,
  we put simply _a b_.

The above signs may be compounded in any manner; thus,

                   ∜([[((_a_ + _b_)_c_)/_d_]/_m_]¾).

Here we have, first, the product of _c_ by the sum of _a_ and _b_; this
is divided by _d_, and three quarters of the quotient is divided by _m_;
and, finally, the fourth root of the last result is extracted, which is
the value of the expression.

The following examples show the use of formulæ. See Chapter VI., on
Earthwork, art. _Average Haul_:—

Required the average haul of several masses of earth. Let _m m′ m″ m^n_
represent the several masses, and _d d′ d″ d^n_ the respective hauls;
_S_ the sum of the masses, _D_ the average haul, and we have

           _D_ = (_m d_ + _m′ d′_ + _m″ d″_ + _m^n d^n_)/_S_.

           If we make the values _m_   = 100 also _d_   = 100
                                 _m′_  = 200      _d′_  =  50
                                 _m″_  = 300      _d″_  =  75
                                 _m^n_ = 400      _d^n_ = 200

the sum is 1000, and we have

  _D_ = (100 × 100 + 200 × 50 + 300 × 75 + 400 × 200)/1000 = 122.5 ft.

In Chapter VIII., _Wooden Bridging_, we have the expression

                        _S_ = (4_b_ _d^2_)/_l_;

                            and if _b_ = 10
                                   _d_ = 12
                               and _l_ = 20

_S_ becomes

                        (4 × 10 × 144)/20 = 288.

In Chapter IX., _Iron Bridges_, we have

                 _T_ = (_ph_)/(2_f_)√(_h^2_ + 4_f^2_);

                         and making _p_ = 4000
                                    _h_ =  500
                                    _f_ =   80

we have

        ((4000 × 500)/(2 × 80))√(500^2 + (4 × 80^2)) = 6562202.

In Chapter XIII., _Elevation of Exterior Rail_,

                    _E_ = ((_WV^2_)/(32_R_)/_W_)_g_,

                          and when _W_ =   50
                                   _V_ =   20
                                   _g_ =    5
                                   _R_ = 2000

we have

               _E_ = ((50 × 400)/(32 × 2000)/50)5 = 0.03

And finally, in the latter part of Chapter XIV., we have the formula

              _D_ = √(([_n_(_d_ + _c_)^2])/0.7854)_A_/_B_,

                          and making _n_ = 200
                                     _d_ =   1
                                     _c_ =  1½
                                     _A_ =   4
                                     _B_ =   3

we have

                  _D_ = √([200(2 + 1½)^2]/0.7854)4/3,

                 Now 1 + 1½ = 5/2 and (5/2)^2 is 25/4,

                 also, 200 × 25/4 = 1250,

                 1250 × 4/3 = 1666,

                 1666 ÷ 0.7854 = 2121,

                 finally, √(2121) = 446 very nearly.


                                   C.
                         WEIGHTS AND MEASURES.

    Name of material.             Weight per cubic foot.
    Air                           0.077 lbs.
    Earth                       112.    lbs.
    Water                        62.5   lbs.
    Ice                          58.0   lbs.
    Sand                        132.0   lbs.
    Clay                        120.0   lbs.
    Chalk                       155.0   lbs.
    Brick                       110.0   lbs. See Chap. XI., masonry.
    Brickwork                    95.0   lbs.
    Dry mortar                   96.0   lbs.
    Sandstone                   140.0   lbs.
    Limestone                   142.0   lbs. Average 86 to 198.
    Granite                     175.0   lbs.
    Coal, Bituminous       60 to 80.0   lbs.
    Coal, Anthracite       85 to 95.0   lbs.
    Coke                   50 to 65.0   lbs.
    Coal, Cannel           75 to 80.0   lbs.
    Wrought Iron                480.0   lbs.
    Cast-Iron                   450.0   lbs.
    Steel                       487.0   lbs.

                  _Hard Wood._

    Green                          62.0 lbs.
    Air dried                      46.0 lbs.
    Kiln dried                     40.0 lbs.

                  _Soft Wood._

    Green                          53.0 lbs.
    Air dried                      30.0 lbs.
    Kiln dried                     28.0 lbs.

                        Weight per bushel.
    Wheat                            60 lbs.
    Corn on the cob                  70 lbs.
    Corn, shelled                    56 lbs.
    Rye                              56 lbs.
    Oats                             35 lbs.
    Barley                           47 lbs.
    Potatoes, Irish                  60 lbs.
    Potatoes, Sweet                  55 lbs.
    Beans, White                     60 lbs.
    Beans, Castor                    46 lbs.
    Bran                             20 lbs.
    Clover Seed                      60 lbs.
    Timothy                          45 lbs.
    Hemp                             44 lbs.
    Flax                             56 lbs.
    Buckwheat                        52 lbs.
    Peaches, Dried                   33 lbs.
    Apples, Dried                    24 lbs.
    Onions                           57 lbs.
    Salt, Coarse                     50 lbs.
    Malt                             38 lbs.
    Corn Meal                        48 lbs.
    Salt, Fine                       55 lbs.


                                   D.
                    VALUE OF THE BIRMINGHAM GAUGES.

                        Number. Size in inches.
                              0           0.340
                              1            .300
                              2            .284
                              3            .259
                              4            .238
                              5            .220
                              6            .203
                              7            .180
                              8            .105
                              9            .148
                             10            .134
                             11            .120
                             12            .100
                             13            .095
                             14            .083
                             15            .072
                             16            .065
                             17            .058
                             18            .049
                             19            .042
                             20            .035
                             21            .032
                             22            .028
                             23            .025
                             24            .022
                             25            .020
                             26            .018
                             27            .016
                             28            .014
                             29            .013
                             30            .012


                                   E.
                          LOCOMOTIVE BOILERS.

If the ideas of Clark and Overman are correct, the value of _vertical
flues_ with the _water inside_, as compared with _horizontal flues_ with
_water outside_, is comparatively as follows: One half of the surface of
the horizontal tube (the upper half) is available, but this half
generates steam twice as fast as the same area of upright tube surface.
Thus the amount of evaporation will be the same in either position, for
the same absolute tube surface, not considering the increased diameter
by applying the heat to the outside, or the advantage, so highly
estimated by Overman, of applying the heat to the convex surface.

The following application of Montgomery’s vertical flue boiler to the
locomotive engine for heat generation and application, seems to satisfy
nearly all requirements. Retaining the original furnace shell, produce
it forwards so that it shall just clear the driving axle, let the sides
drop to within two feet of the rail, and close up the bottom. Next,
inside of this place a rectangular box which shall be a continuation of
the inner box, the top being about nine inches above the diametric chord
of the semicircular crown, leaving a water space of three or four inches
between the sides and bottom of the two boxes. Fill the inner box with
vertical tubes, the top and bottom being flue plates, the tubes being
screwed in at one end and fitted with a screw thimble at the other, may
be removed for cleaning at any time and will effectually stay the inner
box against the enormous pressure upon the top and bottom. The pressure
being inside of the tubes will tend to keep the end joints tight, where,
in the common boiler, the reverse is the case.

That the burning gases may retain sufficient heat to burn until they are
discharged, there should be less tube surface at the back than at the
front end, a requirement which is easily satisfied by decreasing the
number and increasing the size of tubes from the front to the back end.
In the common boiler the ferrule area being less than the flue area, a
stronger blast is used than is really necessary to draw the hot gases
through the tubes, while in the vertical tube boiler the gas area may be
equally large at all points.

Again, any amount of oxygen may be applied to the gases at any point of
their passage from the furnace to the smoke box, by the admission of
fresh air to any part of the barrel. Thus the advantage of a combustion
chamber (if there is any) is obtained without the sacrifice of a single
inch of heating surface, as we only require to admit air _between_ the
tubes and not _into_ them; this may be done either by hollow stay bolts
or by larger openings, to be open or shut at pleasure.

If the gases in passing through the boiler are left to themselves, we
get, without an effort, the effect produced by Montgomery’s third claim,
namely, the application of the heat to the upper half of the tubes; and,
however we wish to apply the passing heat to the flues, complete control
over the motion of the gases may be had by the use of a Venetian blind
damper in the smoke box, in two parts; the upper and the lower parts
moving independently, allow us to throw the heat upon any part of the
length of the tubes. Of course, by heating most the upper part of the
flues, we stand a better chance of getting circulation.

It might be objected that so much flat boiler surface would give a form
more liable to explosion than the circular barrel. Experiments lately
made by William Fairbairn, (England,) induced by the bursting of a
locomotive fire box, show that the flat surfaces are the strongest forms
of the boiler, or, to use his own words, “are conclusive as to the
superior strength of flat surfaces as compared with the top, or even the
cylindrical parts of the boiler.” His experiments show that two plates
one fourth and three eighths inch thick, connected by screw stay bolts
four inches from centre to centre, will resist over one thousand lbs.
per square inch.

By such a plan of engine we may always have any amount of heating
surface with a moderate sized boiler, and a low centre of gravity.

The _excess_ of cost of the engine, above described, over the common
form would be about $500, the annual interest of which is $30, which
must be saved by the new plan, (say ten cords of wood).

Any saving beyond this is pure gain.


                                   F.
           EFFECT OF GRADES ON THE COST OF WORKING RAILROADS.

The cost of working a railroad will be increased by augmenting the
steepness of grades. First, because of the mechanical effect of the
inclines; second, on account of decreased capacity of the road. The cost
of maintaining and working a road consists of items, a few of which are
functions of grades and many which are not. The chief items which are
affected by grades are, fuel consumption, first cost of locomotives, and
perhaps wear of rails, where grades are so steep as to require sand
ascending, and application of brakes descending, the rails will be
somewhat more worn. When not so steep as this the repair of
superstructure will not be much increased. Steeper inclines involve the
use of heavier engines, or more of them. Heavy engines generally have no
more weight on one pair of wheels, and often not so much, as lighter
ones; and though there is more abrasive power on increased total rolling
weight, there is less deflection of rails, by means of less concentrated
loads. It would seem, therefore, that the effect of grades upon the wear
of superstructure was but little, if not inconsiderable. The first cost
of engines may be increased from $1,000 to $2,500 to enable them to work
steep grades. If the wheels are the same size in both engines, we should
require greater steam pressure, consequently (see Chapter XIV.) more
fuel; and if the steam power was the same, smaller wheels or larger
cylinders, also requiring (Chapter XIV.) more fuel.

In doubling the work done by the engine we by no means double the amount
of fuel consumed, (see Chapter XIV.,) but increase it by about ninety
per cent.

The division of expenses upon five of the largest English railroads was
for a certain time as follows:—

                    Salaries                   $6.83
                    Way and works              15.76
                    Locomotives                35.15
                    Cars                       38.14
                    Sundries                    3.69
                                             ———————
                                             $100.00
                      Percentage for engines   35.00

Upon the roads of Belgium,

                    Salaries                   $5.47
                    Way and works              26.62
                    Locomotives                49.96
                    Cars                       14.80
                    Sundries                    3.15
                                             ———————
                                             $100.00
                      Locomotive percentage    50.00

Upon the railroads of New York State (2,200 miles) (State Engineer’s
Report, 1854),

                    Salaries                  $10.00
                    Way and works              15.00
                    Locomotives                40.00
                    Cars                       20.00
                    Sundries                   15.00
                                             ———————
                                             $100.00
                    Locomotive percentage      40.00

Average percentage of all of the above charged to locomotives 41⅔ of the
whole locomotive expense; fuel absorbs 62½ percent.; and as a double
amount of work requires ninety per cent. more fuel, we have, as the cost
of working a grade causing a double resistance (say twenty-five feet per
mile), 90/100 of 62/100 of 42/100, or very nearly 22 per cent. of the
cost of working the train; to which add ⅒ more, interest on locomotive
capital, and we have, as the bad effect of a twenty-five feet grade,
when

                     _C_ = locomotive capital,
                     _D_ = annual cost of working,

                       ⅒ of 6/100_C_ + 22/100_D_.

                               _Example._

 Locomotive capital                                $1,000,000
 Cost of working                                      200,000
 Annual expense of a level road (at six per cent.)              $60,000
                                                              + 200,000
                                                               ————————
                                                               $260,000

 And upon a road with continuous 25 feet grades                 $60,000
                                                                + 6,000
                                                              + 200,000
 + 200,000 × 22/100, or                                          44,000
                                                               ————————
 Total                                                         $310,000

or 120 per cent. of the cost of working the level road, the increase
being twenty per cent., or allowing five per cent. for other
contingencies, twenty-five per cent.; also the increase due to a fifty
feet grade, fifty per cent.; and so on as long as only one engine is
required to draw the full train, (its power being increased by varying
its dimensions). When the train has to be broken and two or more engines
are needed, the percentage will of course increase. The point at which
the train ought to be broken may be found easily, either as depending
upon the load or the grade, by a comparison of working expenses.


                                   G.
   SPECIFICATION FOR A PASSENGER LOCOMOTIVE ENGINE FOR THE A. AND B.
                               RAILROAD.


                             _Requirement._

Speed 20 miles per hour, including stops; fuel, wood; weight of train
150 tons; maximum grade 60 feet per mile; sharpest curve 3° or 1,910
feet radius; rail 60 lbs. per yard on ties 2 feet from centre to centre.


                     _General Plan and Dimensions._

Outside connections; four five feet driving wheels with best Ames’s
tire, all tires being flanged; level cylinders 15 inches diameter of
bore and 20 inch stroke. Centre-bearing truck, with inside and outside
bearings, and Lightener boxes. Square wrought iron frame well braced,
4–30 inch Whitney and Sons’ cast-iron truck wheels, spread 60 inches
centre to centre. Lifting link motion working through rockers, valves
described hereafter. Truck supplied with fore and aft safety chains, and
safety beams beneath axles. Weight on drivers 30,000 lbs., on truck
10,000 lbs. Tender to be mounted on two trucks, each of 4–30 inch
Whitney and Sons’ wheels, spread 54 inches from centre to centre. To
have square iron frames well braced with outside Lightener boxes; tank
to hold 1,600 gallons.


                       _Detailed Specifications._

_Boiler._—Grate 38 inches wide, 54 inches long, surface 20″ above rail,
grate bars cast solid for 6 inches of the front end, to be 4 inches
deep, and ¾ inch thick, placed ¾ inch apart in the clear; lower edges
chamfered on each side by a chamfer of ½ inch deep and ¼ inch wide;
centre of grate bars to be supported by a wrought iron bar 1 inch thick
and 4 inches deep, attached as in drawing. _Fire-box._—Outer sides of
furnace shell 51 inches wide by 62 inches long; crown 8 feet above rail,
to be made of ⅜ inch iron plates with a 16 inch necking of angle iron to
carry the rear dome; corners to be joined by flanges rounded to a 4 inch
radius. The crown of the shell to be raised 9 inches above the barrel
crown, the connection being made by a sloping offset 20 inches long on
top. End plates lap jointed to sides and top; the seams joining the
fire-box to the waist, to be double riveted. Furnace to be made of ½
inch copper plates, ¾ inch at tubes, lap jointed, 42¼ inches wide, and
51½ inches long inside; side water spaces to be 3 inches clear at the
bottom, widening (by sloping inwards the sides of the furnace) to 4
inches at the top of inner box; front spaces 4 inches, rear spaces 4
inches at bottom and 5 inches at top. Doorway made with a wrought iron
ring fastened with ⅝ inch rivets, door of ⅜ inch plate with ¼ inch
shield. Furnace joined to shell with ⅞ inch copper stay bolts, screwed
and riveted at both ends, placed 44 inches from centre to centre. Eight
roof-ribs laid widthwise of the crown of the furnace, being each 6
inches deep and ¾ inch thick, double welded at the ends and riveted at
the centre, held down by T head bolts 5 inches between centres, bars to
be raised above the crown sheet by ⅜ inch thimbles. Dome opening,
neckling to be made of angle iron which shall be connected with the
roof-ribs by 4–1⅛ inch stays, connected and placed as in the drawing.
The back and tube sheets of the furnace are flanged over on top; the
crown is flanged downwards on the sides, but not on the back and front.
One dome is placed on the crown of fire-box shell 26 inches diameter and
24 inches high; opening of dome into boiler 16 inches diameter. Lower
part of dome of wrought, top of cast-iron, put on with a ground joint.
Furnace and shell to be connected at bottom by a wrought iron bar 3
inches wide, 2½ inches deep. The whole boiler to be thoroughly caulked
inside and out. Barrel of ¼ inch best Philadelphia stamped charcoal
iron, 44 inches diameter outside of main crown next the fire-box, and 43
inches next the smoke box end, 10 feet long with 3 inch angle irons at
ends. Front dome of ½ inch plate worked in one piece, 23 inches
diameter. End plates of boiler stayed with six 1 inch rods, cottered
into blocks, riveted to plates; barrel plates riveted with ¾ inch
rivets, and 1¾ inch pitch. _Smoke box_, 2′ 4″ long, same diameter as
barrel, of 3/16 inch plates well riveted, bolted to the angle iron so as
to be easily removed for inside repairs; front tube sheet 6/8 inch.
_Tubes_, 140 two inch (outside) diameter No. 9 thickness at fire end,
No. 14 at smoke end 10 feet long, placed ½ inch apart. The smoke box end
of tubes to be closed at pleasure by a venetian blind damper. Chimney of
¼ inch iron outside, diameter 16 inches, top 6′ 6″ above crown of
barrel, fitted with proper stack, cone, and sparker. Ash pan of ¼ inch
plate made with 1½ inch angle iron, and band on upper edge, fitted with
doors both before and behind, 7 inches deep and riding 6 inches clear of
the rail. _Steam pipes_, 6 inch pipes of No. 10 copper running the whole
length of the boiler, connected at the domes with 5 inch cast-iron stand
pipes. Cast-iron branch pipes in smoke box leading to valve chests, 5
inches diameter. Throttle to be in a cast-iron chest in smoke box, as
shown in drawing, having an area at least as large as the steam port.
Changes of direction in pipes to be made by curves and not by angles.
Exhaust pipe of No. 10 copper, 5 inches diameter at lower end, fitted
with a variable blast orifice, ranging from eight to four square inches
area, to be inclosed in a petticoat pipe.

_Cylinders_, 15 inches bore, and long enough for a 20 inch stroke, or
28¾ inches from outside to outside of ground faces, casting ⅞ inch
thick, covers 1⅛ inch thick, placed level and firmly bolted to main
frame and to horizontal truss brace, as shown in drawing; heads to go on
with ground joint. Valve seat to have steam ports 14 × 1⅜ inches;
exhaust port 14 × 2½ inches; outside lap of valve ⅝ inch, inside
nothing; 1/16 inch lead on 4¾ inch throw of valve, gradually increasing
as the throw is reduced, to scant 5/16. Steam chests bolted to a level
face, ground joint with ¾ inch bolts pitched 4 inches.

_Valve motion._—Shifting link with lifting shaft, sector, lever, rocker,
etc., of the most approved form; four solid eccentrics of 5¼ inches
throw, fastened to axle by four square ended set screws pressing
hardened steel dies, cut with sharp grooves on their ends, against the
axle; the friction of the dies against the axle holding the eccentric in
place. Eccentric straps of cast-iron, with oil caps cast on, and grooved
out inside so as to shut over the eccentric and exclude dust. Link
forged solid and case hardened, 17 inches by 2¼ inches inside the slot;
thickness of iron all around the slot 1½ inches, whole lateral thickness
2 inches. Eccentric rods of ⅞ iron 3 inches deep, 5½ feet between
centres, fastened to link and to eccentric, as shown in the drawing.
Link curved to a radius 6 inches less than the distance between the
centre of driving axle and centre of link at mid gear. The links, boxes,
stack, etc., to be of wrought iron, case hardened. _Pistons_ with one
outside composition ring and two circumferential grooves filled with
Babbitt metal, and one inside ring of wrought iron; outside ring cut
obliquely at one place with a small wrought iron flap on each edge to
prevent leakage of steam at the point of division. Glands of piston and
valve rod stuff boxes of cast-iron with tight brass or composition
bushings.

_Frame_ forged from good scrap 4×2 inches, the main bar being straight
from end to end with pedestals welded on; the rear end piece to be a
heavy forged foot plate, the front end an oak beam 7×14 inches placed on
the flat side. All the pedestals on one side having adjustable keys.
Flat boiler braces averaging 4½ × ⅞ inches with broad palms riveted to
the boiler; the attachment at the furnace to be made by the Rogers
expansion brace, details of the frame as in the drawing; frame to be
placed true wherever needed to receive the working parts of the engine.

_Wheels, axles, and springs._—Four cast-iron driving wheels tired with
best flanged Ames’s tires 2 inches thick, diameter with tire five feet,
tires to be turned to a true cone of .072 inches per wheel, wheels to be
truly balanced. Rest scrap or bloom axles, front 7 and rear 6 inches in
diameter, bearings 8 inches long, collars of cast-iron held by set
screws, axles to be cylindrical and not smaller at the centre than at
the end. Four springs of seventeen steel plates, each 4 × ⅜ × 40 inches;
equalizing lever between springs. Inside bearing springs of truck hung
from equalizer, which latter bears upon the axle boxes.

_Slides, pumps, connecting rods, etc., etc._—Slides, flat wrought iron
bars 3 × 1¼ inches, case hardened. Cross head bearing of cast-iron 16
inches long and 2 inches thick. Pumps, full stroke brass pumps 5/16 inch
thick with 1⅞ inch plungers, ram of wrought iron with an eye fixed on
cross head and worked by it. Waterways in body 2 inches, in valves 1¾
inches. Three ball valves with 2¼ inch hollow balls, one for suction and
two for delivery; pipes ⅛ inch thick, 2 inches diameter, suction of
iron, delivery of copper, cock of brass on delivery pipe worked by rod
at cab. Air chamber on forcing side of pump equal to capacity of barrel;
on suction side half the same. Flat connecting rods forged from solid
piles without welds. Babbett lined boxes upon all stub ends. Straps held
on each by two bolts, one key to each bearing. Safety-valves, one to be
3½ inches diameter, placed on the rear dome, and one forward, 4 inches
diameter, both to be well fitted and supplied with the proper beams and
spring balances. Barrel to be covered with hair felting ½ inch thick, to
be furnished with a Russia iron jacket. Cylinders to be protected by an
½ inch felt coat and cased in brass.

The engine to have all the usual fixtures, bell, whistle, gauges,
heater, pet, blow-off, and other cocks, name plates, oil cups, sandbox,
tools, oil cans, etc., etc. Pilot to be 5 feet long, of flat horizontal
wooden bars 2½ × 4 inches with a heavy centre piece, the whole to be
well hung and firmly braced. Cab to be neatly built, with a projecting
cornice, and windows, doors, etc., to be furnished in the best manner.
The whole engine to be well painted and varnished. The draw bar to be
strongly attached to the frame of the engine at 30 inches above the
rail, and connected by a double elliptical spring to the centre beam of
the tender.

_Tender._—Tank to hold 1,600 gallons, top and side plates ⅛ inch, and
bottom plate ¾ inch well riveted and caulked inside and out. Brakes to
apply from a single wheel to each side of all of the wheels, that is, at
sixteen points; brake blocks hung with safety chains and springs to
carry them away from the wheels. One spring 26 inches long, of ten
levers 3 × 5/16 inches over each wheel. Frame of seasoned oak 10 × 4
inches, centre beam 5 × 20 inches. The whole to be thoroughly painted
and varnished.


                          _General Provision._

All of the material, both of engine and tender, to be of the very best
quality, and all of the construction done in the most thorough and
workmanlike manner. The engine and tender being in every respect equal
to the best that has heretofore been sent from the —— shops. For more
detailed information, see plans accompanying.


                                   H.
          RELATIVE COST OF TRANSPORT BY RAILROAD AND BY STAGE.

Too great a reduction of the cost of travel was both expected of and
given by railroad companies at the commencement of the system, as the
following will show:—

_Voted_, “That the directors are hereby earnestly and urgently requested
forthwith to increase the rates of transportation, both for passengers
and freight, in all cases in which, in their opinion, they are now too
low, and hereafter to decline all business that will not give to the
corporation a full remuneration for expenses and a fair profit for its
transportation.”

Why the railroad rates should have been placed so low, it would be hard
to show.

The cost of moving eight passengers by stage one hundred miles, would be
somewhat as follows. Let a common road cost one thousand dollars per
mile, and suppose the stage travel to use one tenth of the capital
expended; the daily interest for one trip is

              (100 × 1000 × 6/100)/365 ÷ 10 or                     $1.64

 Ten horses and one stage,

                 (1500 + 500 × 6/100)/365 or                        0.33

 Daily salary of driver and stable hands,                           5.00

 Daily interest on stable cost, repairs, &c., &c.,                  1.03

                                                                   —————

 Whole cost of moving 8 passengers 100 miles,                      $8.00

 Cost of moving one passenger one mile,                              .01

 Again. Let a railroad cost $25,000 per mile, one hundred miles cost
   $2,500,000, and if we run ten trains per day the daily interest, at
   six per cent., for one train is

                (2500000 × 6/100)/365 ÷ 10 =                      $41.10

 A locomotive costs      $10,000,

 Two cars cost             4,000,

                 and (14000 × 6/100)/365 is                         2.30

 And the daily cost of road and equipment,                        $43.40

 divide by 100, for the cent per mile,                              0.43

 The average number of passengers carried in one car, (see
   New York State Engineer’s Report,) is 17; two cars, 34,
   whence 43/34 =                                               1⅓ cents

 The daily cost per mile, per passenger, is then, for the
   use of the road and equipment,                               1⅓ cents

 The cost of maintaining and working is, per passenger, per
   mile, (see New York State Engineer’s Report for 1854.)       1¼ cents

 Whence the whole cost of carrying one passenger one mile
   upon a railroad will be                                   27/12 cents

 The relative cost of transport is, then, thus,

     By stage,                                                    1 cent

     By railroad,                                            27/12 cents

 and the relative charge thus,

     By stage,                                                   5 cents

     By railroad,                                                3 cents

And the comparative profit as 5 less 1, or 4; to 3 less 27/12, or 5/12;
or as 1 to 9.6.


                                   I.
 FORM FOR RECORDING THE RESULTS OF EXPERIMENTAL TRIPS WITH LOCOMOTIVES.

In comparing the work done by different locomotives, we must know not
only the relative amounts of material consumed, but also the exact
nature of the work done, as depending upon speed, load, curves, and
grades. The following blank, when filled, has been found to give
complete information, for comparison.

     Station,                                                    ——
     Time of arriving,                                           ——
     Time of departing,                                          ——
     Time running,                                               ——
     Time standing,                                              ——
     Distance,                                                   ——
     Rise,                                                       ——
     Fall,                                                       ——
     Degrees of curvature,                                       ——
     Equated distance,                                           ——
     Cars taken,                                                 ——
     Cars left,                                                  ——
     Load between stations,                                      ——
     Equated mileage of train,                                   ——
     Gauge pressure,                                             ——
     Notch of sector,                                            ——
     Fuel used,                                                  ——
     Water used,                                                 ——
     Lbs. of fuel per gallon of water,                           ——
     Lbs. of fuel per equated mileage, per ton or per passenger, ——
     Comparative effect,                                         ——


                                   K.
                     PROPER WEIGHT OF LOCOMOTIVES.

To move a given load the engine requires a certain amount of power; to
exert such power there is needed load enough on the drivers to prevent
slipping on the rail. This load varies from three times the tractive
power, (in the best state of the rails,) to ten times the tractive
power, and even more, (in the worst state). A fair working average
(without sand), being one sixth; with sand, much less. Sand must be used
upon grades and upon bad rails. To find then the proper weight, we have
only to estimate the tractive power upon the hardest point of the road,
and multiply it by six.


                              _Examples._

How heavy an engine is needed to draw two hundred tons (including engine
and tender) at twenty miles per hour over sixty feet grades?

The resistance on a level is

               200 ×((20 × 20)/171 + 8) =     2,060 pounds.

             The resistance due to the grade

                200 × (60/5280 × 2240) =      5,200 pounds.

             The resistance due to curves

                        200 × 5=              1,000 pounds.
                                             ——————
             And the whole resistance,        8,260 pounds.
             which multiplied by 6, is       49,560 pounds.

or 22.1 tons, to which add 5 tons as the necessary load upon the truck,
and the whole weight is 27.1 tons, which is the necessary weight of an
engine to draw 200 tons over 60 feet grades, at 20 miles per hour.

Or, generally,

 Let _W_     = Weight of engine, tender, and train, in tons,
 Let _V_     = Speed in miles per hour,
 Let _a_/_b_ = Fraction expressing the grade,
 Let _c_     = Resistance, in pounds per ton due to the sharpest curve,
                 which, assume as 5 lbs., as we have no reliable data,

and we have, as the weight of the engine,

           [_W_(_V^2_/171 + 8) + _a_/_b_ × 2240 + 5]6/2240 =

weight of engine exclusive of weight on truck.

If we assume the adhesion as one fourth of the weight on the drivers,
and load 150 tons, speed twenty miles per hour, and grade forty feet per
mile, the above formula becomes,

          [150((20 × 20)/171 + 8) + (40/52802240) + 5]4/2240 =

nine tons nearly.

To which add five tons, and we have as the whole weight, fourteen tons.

[Illustration: Fig. 158.]

------------------------------------------------------------------------




                          TRANSCRIBER’S NOTES


 1. Made corrections listed in Errata beginning on p. xv.
 2. Did not correct the error for page 32 line 2 as it referred to the
      cut rather than the text.
 3. Changed “area 2,827 miles” to “area 2,827 square miles” on p. 4.
 4. Added “GENERAL TOPOGRAPHY” subheading on p. 12.
 5. Changed “11480.667” to “11,480,667” on p. 40.
 6. Changed “+ 5,297.334 + 4,437.334” to “+ 5,297,334 + 4,437,334” on p.
      54.
 7. Added “SLOPES” subheading on p. 89.
 8. Added “FORM OF RAILROAD SECTIONS” subheading on p. 97.
 9. Added “ROCK EXCAVATION” and “BLASTING AND QUARRYING” subheadings on
      p. 115.
10. Added “SIDINGS AND CROSSINGS” subheading on p. 298.
11. Changed “18.24 cubic feet per hour” to “18.24 cubic feet per hour of
      water” on p. 304.
12. Changed all commas to decimals in the table's right-hand column
      titled “Resistance in lbs. per ton” on p. 314 to agree with the
      previous expression.
13. Added “RETARDING OF TRAINS” subheading on p. 401.
14. Added “CLASSIFICATION OF BUILDINGS”, “LOCATION OF BUILDINGS”, and
      “TERMINAL PASSENGER HOUSE” subheadings on p. 403.
15. Added “TERMINAL FREIGHT HOUSE” and “ENGINE HOUSE AND APPURTENANCES”
      subheadings on p. 405.
16. Added “WOOD SHED AND TANK” subheading on p. 407.
17. Silently corrected typographical errors.
18. Retained anachronistic and non-standard spellings as printed.
19. Enclosed italics font in _underscores_.
20. Enclosed bold font in ¶pilcrow signs¶.
21. Superscripts are denoted by a caret before a single superscript
      character or a series of superscripted characters enclosed in
      curly braces, e.g. M^r. or M^{ister}.