Transcriber’s Note

Variable spelling and hyphenation have been retained. Minor punctuation
inconsistencies have been silently repaired. The Errata of the original
edition have been corrected. Other changes made can be found at the end
of the book. Formatting and special characters are indicated as follows:

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                             PHILOSOPHICAL
                             TRANSACTIONS,
                              GIVING SOME
                                ACCOUNT
                                OF THE
             Present Undertakings, Studies, _and_ Labours,
                                OF THE
                              INGENIOUS,
                                IN MANY
                  Considerable Parts of the WORLD.


                  VOL. L. +PART II.+ For the Year 1758.

                               _LONDON_:

               Printed for +L. DAVIS+ and +C. REYMERS+,
                   Printers to the +ROYAL SOCIETY+,
               against _Gray’s-Inn Gate_, in _Holbourn_.

                              M.DCC.LIX.




                                 THE
                               CONTENTS
                                  TO
                          PART II. VOLUME L.


  LIX. _AN Account of the Effects of Electricity in paralytic Cases.
  In a Letter to_ John Pringle, _M. D. F.R.S. from_ Benjamin Franklin,
  _Esq; F.R.S._                                                  p. 481.

  LX. _Observations on the late Comet in_ September _and_ October
  _1757; made at the_ Hague _by Mr._ D. Klinkenberg: _In a Letter to
  the Rev._ James Bradley, _D. D. Astronomer Royal, and F.R.S. and
  Member of the Royal Academy of Sciences at_ Paris. _Translated from
  the_ Low Dutch.                                                p. 483.

  LXI. _Remarks on the different Temperature of the Air at_ Edystone,
  _from that observed at_ Plymouth, _between the 7th and 14th of_ July
  _1757. By Mr._ John Smeaton, _F.R.S._                          p. 488.

  LXII. _An Account of the Earthquake felt in the Island of_ Sumatra,
  _in the_ East Indies, _in_ November _and_ December _1756. In a
  Letter from Mr._ Perry _to the Rev. Dr._ Stukeley, _dated at_ Fort
  Marlborough, _in the Island of_ Sumatra, Feb. _20. 1757. Communicated
  by the Rev._ Wm. Stukeley, _M. D. F.R.S._                      p. 491.

  LXIII. _Concerning the Fall of Water under Bridges. By Mr._ J.
  Robertson, _F.R.S._                                            p. 492.

  LXIV. _An Account of the Earthquake in the West Parts of_ Cornwall,
  July _15th 1757. By the Rev._ William Borlase, _M. A. F.R.S.
  Communicated by the Rev._ Charles Lyttelton, _LL. D. Dean of_ Exeter,
  _F.R.S._                                                       p. 499.

  LXV. _Some Observations upon the Sleep of Plants; and an Account
  of that Faculty, which_ Linnæus _calls_ Vigiliæ Florum; _with an
  Enumeration of several Plants, which are subject to that Law.
  Communicated to_ Wm. Watson, _M. D. F.R.S. by Mr._ Richard Pulteney
  _of_ Leicester.                                                p. 506.

  LXVI. _An Account of the Case of a Boy troubled with convulsive Fits
  cured by the Discharge of Worms. By the Rev._ Richard Oram, _M. A.
  Chaplain to the Lord Bishop of_ Ely.                           p. 518.

  _An Account of the same Subject, in a Letter from Mr._ John Gaze,
  _of_ Walket, _in the County of_ Norfolk, _to Mr._ Wm. Arderon,
  _F.R.S. Communicated by Mr._ Henry Baker, _F.R.S._             p. 521.

  LXVII. _An Account of the extraordinary Heat of the Weather in_ July
  _1757, and of the Effects of it. In a Letter from_ John Huxham, _M.
  D. F.R.S. to_ Wm. Watson, _M. D. F.R.S._                       p. 523.

  LXVIII. _An Account of the fossile Thigh-bone of a large Animal, dug
  up at_ Stonesfield, _near_ Woodstock, _in Oxfordshire. In a Letter to
  Mr._ Peter Collinson, _F.R.S. from Mr._ Joshua Platt.          p. 524.

  LXIX. _A Discourse of the Usefulness of Inoculation of the horned
  Cattle to prevent the contagious Distemper among them. In a Letter
  to the Right Hon._ George _Earl of_ Macclesfield, _P. R. S. from_
  Daniel Peter Layard, _M. D. F.R.S._                            p. 528.

  LXX. _Trigonometry abridged. By the Rev._ Patrick Murdoch, _A. M.
  F.R.S._                                                        p. 538.

  LXXI. _An Account of Two extraordinary Cases of Gall-Stones. By_
  James Johnstone, _M. D. of_ Kidderminster. _Communicated by the Rev._
  Charles Lyttelton, _LL. D. Dean of_ Exeter.                    p. 543.

  LXXII. _A remarkable Case of Cohesions of all the intestines_, &c.
  _in a Man of about Thirty-four years of Age who died sometime last
  Summer, and afterwards fell under the Inspection of Mr._ Nicholas
  Jenty.                                                         p. 550.

  LXXIII. _Of the best Form of Geographical Maps. By the Rev._ Patrick
  Murdoch, _M. A. F.R.S._                                        p. 553.

  LXXIV. _A short Dissertation on Maps and Charts: In a Letter to the
  Rev._ Thomas Birch, _D. D. and Sec. R. S. By Mr._ William Mountaine,
  _F.R.S._                                                       p. 563.

  LXXV. _Cases of the remarkable Effects of Blisters in lessening the
  Quickness of the Pulse in Coughs, attended with Infarction of the
  Lungs and Fever: By_ Robert Whytt, _M. D. F.R.S. Fellow of the Royal
  College of Physicians, and Professor of Medicine in the University
  of_ Edinburgh.                                                 p. 569.

  LXXVI. _A remarkable Instance of Four rough Stones, that were
  discovered in an human urinary Bladder, contrary to the received
  Opinion; and successfully extracted by the lateral Method of Cutting
  for the Stone. By Mr._ Joseph Warner, _F.R.S. and Surgeon to_
  Guy’s-Hospital.                                                p. 579.

  LXXVII. _Observations on the_ Limax non cochleata Purpuram ferens,
  _The naked Snail producing Purple. By_ John Andrew Peyssonel, _M. D.
  F.R.S. Translated from the_ French. p. 585.

  LXXVIII. _New Observations upon the Worms that form Sponges. By_ John
  Andrew Peyssonel, _M. D. F.R.S. Translated from the_ French.   p. 590.

  LXXIX. _Account of an Experiment, by which it appears, that Salt of
  Steel does not enter the Lacteal Vessels; with Remarks. In a Letter
  to the Rev._ Thomas Birch, _D. D. Secret. R. S. By_ Edward Wright,
  _M. D._                                                        p. 594.

  LXXX. _A Dissertation on the Antiquity of Glass in Windows. In a
  Letter to the Rev._ Tho. Birch, _D. D. Secret. R. S. By the Rev._
  John Nixon, _M. A. F.R.S._                                     p. 601.

  LXXXI. _An Account of an extraordinary Case of the Efficacy of the
  Bark in the Delirium of a Fever. By_ Nicˢ. Munckley, _M. D. Physician
  to_ Guy’s-Hospital, _and F.R.S._                               p. 609.

  LXXXII. _An Account of an Earthquake felt at_ Lingfield _in_ Surrey,
  _and_ Edenbridge _in_ Kent, _on the 24th of_ January _1758. By_ James
  Burrow, _Esq; R. S. V. P._                                     p. 614.

  LXXXIII. _An Account of the Case of the First Joint of a Thumb torn
  off, with the Flexor Tendon in its whole Extent torn out. By_ Robert
  Home, _late Surgeon to the Thirtieth Regiment of Foot, and Surgeon
  at_ Kingston upon Hull. _In a Letter to_ John Pringle, _M. D. F.R.S._
                                                                 p. 617.

  LXXXIV. _An Account of the late Discoveries of Antiquities at_
  Herculaneum, _and of an Earthquake there; in a Letter from_ Camillo
  Paderni, _Keeper of the Museum at_ Herculaneum, _and F.R.S. to_ Tho.
  Hollis, _Esq; F.R.S. dated_ Portici, Feb. _1. 1758._           p. 619.

  LXXXV. _A further Attempt to facilitate the Resolution of
  Isoperimetrical Problems. By Mr._ Thomas Simpson, _F.R.S._     p. 623.

  LXXXVI. _Observations on the_ Alga Marina latifolia; _The Sea
  Alga with broad Leaves. By_ John Andrew Peyssonel, _M. D. F.R.S.
  Translated from the_ French.                                   p. 631.

  LXXXVII. _An Account of the distilling Water fresh from Sea-Water
  by Wood-Ashes. By Capt._ William Chapman: _In a Letter to_ John
  Fothergill, _M. D._                                            p. 635.

  LXXXVIII. _Observatio Eclipsis Lunaris facta_ Matriti _a Pª._ Joanne
  Wendlingen, _Societatis_ Jesu, _in Regali Observatorio Collegii
  Imperialis ejusdem Societatis, Die 30_ Julii _1757_.           p. 640.

  _Observatio Eclipsis Lunaris, facta ab eodem, eodem modo, eodem loco,
  iisdemque instrumentis, Die 24_ Januar. _Anni 1758._           p. 642.

  LXXXIX. _Observations upon a slight Earthquake, tho’ very particular,
  which may lead to the Knowlege of the Cause of great and violent
  ones, that ravage whole Countries, and overturn Cities. By_ John
  Andrew Peyssonel, _M. D. F.R.S. Translated from the_ French.   p. 645.

  XC. _A Catalogue of the_ Fifty Plants _from_ Chelsea Garden,
  _presented to the_ Royal Society _by the worshipful Company of
  Apothecaries, for the Year 1757, pursuant to the Direction of Sir_
  Hans Sloane, _Baronet, Med. Reg. & Soc. Reg. nuper Præses, by_ John
  Wilmer, _M. D. clariss. Societatis Pharmaceut._ Lond. _Socius,
  Hort._ Chelsean. _Præfectus & Prælector Botanic._              p. 648.

  XCI. _An Historical Memoir concerning a Genus of Plants called_
  Lichen _by_ Michelli, Haller, _and_ Linnæus; _and comprehended by_
  Dillenius _under the Terms_ Usnea, Coralloides, _and_ Lichenoides:
  _Tending principally to illustrate their several Uses. Communicated
  by_ William Watson, _M. D. F.R.S._                             p. 652.

  XCII. _An Account of the fossil Bones of an Allegator, found on
  the Sea-shore, near_ Whitby _in_ Yorkshire: _In a Letter to_ John
  Fothergill, _M. D. from Capt._ William Chapman.                p. 688.

  XCIII. _De rariori quadam_ Orthoceratitis _Specie, in_ Suecia
  _reperta, tractatus: in literis a_ Nicholao de Himsel, _M. D._ Riga
  Livono, _ad_ Gul. Watson, _M. D. R. S. S._                     p. 692.

  XCIV. _A further Account of the Effects of Electricity in the Cure of
  some Diseases: In a Letter from Mr._ Patrick Brydone _to Dr._ Robert
  Whytt, _Professor of Medicine in the University of_ Edinburgh, _and
  F.R.S._                                                        p. 695.

  XCV. _An Account of the Black Assize at_ Oxford, _from the Register
  of_ Merton College _in that University. Communicated by_ John Ward,
  _LL. D. With some additional Remarks._                         p. 699.

  XCVI. _A Description of the Plan of_ Peking, _the Capital of_ China;
  _sent to the Royal Society by Father_ Gaubil, è Societate Jesu.
  _Translated from the_ French.                                  p. 704.

  XCVII. _An Attempt to improve the Manner of working the Ventilators
  by the Help of the Fire-Engine. In a Letter to_ Tho. Birch, _D. D.
  Secret. R. S. from_ Keane Fitz-Gerald, _Esq; F.R.S._           p. 727.

  XCVIII. _An Account of some Experiments concerning the different
  Refrangibility of Light. By Mr._ John Dollond. _With a Letter from_
  James Short, _M. A. F.R.S. Acad. Reg. Suec. Soc._              p. 733.

  XCIX. _An Account of some extraordinary Effects arising from
  Convulsions; being Part of a Letter to_ John Huxham, _M. D. and
  F.R.S. from_ William Watson, _M. D. R. S. S._                  p. 743.

  C. _An Account of an extraordinary Storm of Hail in_ Virginia. _By_
  Francis Fauquier, _Esq; Lieutenant Governor of_ Virginia, _and F.R.S.
  Communicated by_ William Fauquier, _Esq; F.R.S._               p. 746.

  CI. _An Account of an extraordinary Case of a diseased Eye: In a
  Letter to_ Matthew Maty, _M. D. F.R.S. By_ Daniel Peter Layard, _M.
  D. F.R.S._                                                     p. 747.

  CII. _An Account of the Heat of the Weather in_ Georgia: _In a Letter
  from his Excellency_ Henry Ellis, _Esq; Governor of_ Georgia, _and
  F.R.S. to_ John Ellis, _Esq; F.R.S._                           p. 754.

  CIII. _The Invention of a General Method for determining the Sum of
  every 2d, 3d, 4th, or 5th_, &c. _Term of a Series, taken in order,
  the Sum of the whole Series being known. By_ Thomas Simpson, _F.R.S._
                                                                 p. 757.

  CIV. _Observatio Eclipsis Lunæ Die 30_ Julii _1757. habita_
  Olissipone _à_ Joanne Chevalier, _Congregationis Oratorii Presbytero,
  è Regiâ_ Londinensi _Societate. Communicated by_ Jacob de Castro
  Sarmiento, _M. D. F.R.S._                                      p. 769.

  CV. _Singular Observations upon the_ Manchenille Apple. _By_ John
  Andrew Peyssonel, _M. D. F.R.S. Translated from the_ French. p. 772.

  CVI. _Abstract of a Letter from Mr._ William Arderon, _F.R.S. to Mr._
  Henry Baker, _F.R.S. on the giving Magnetism and Polarity to Brass.
  Communicated by Mr._ Baker.                                    p. 774.

  CVII. _An Account of the_ Sea Polypus, _by Mr._ Henry Baker, _F.R.S._
                                                                 p. 777.

  CVIII. _A Description of the fossil Skeleton of an Animal found in
  the Alum Rock near_ Whitby. _By Mr._ Wooller. _Communicated by_
  Charles Morton, _M. D. F.R.S._                                 p. 786.

  CIX. _A Dissertation on the_ Phœnician _Numeral Characters antiently
  used at_ Sidon. _In a Letter to the Rev._ Tho. Birch, _D. D. Secret.
  R. S. from the Rev._ John Swinton, _M. A. of_ Christ-Church, Oxon.
  _F.R.S._                                                       p. 791.

  CX. _Of the Irregularities in the Motion of a Satellite arising from
  the Spheroidical Figure of its Primary Planet: In a Letter to the
  Rev._ James Bradley, _D. D. Astronomer Royal, F.R.S. and Member of
  the Royal Academy of Sciences at_ Paris; _by Mr._ Charles Walmesley,
  _F.R.S. and Member of the Royal Academy of Sciences at_ Berlin, _and
  of the Institute at_ Bologna.                                  p. 809.

  CXI. _Some Observations on the History of the_ Norfolk Boy. _By_ J.
  Wall, _M. D. In a Letter to the Rev._ Charles Lyttelton, _LL. D. Dean
  of_ Exeter.                                                    p. 836.

  CXII. _Observations upon the_ Corona Solis Marina Americana; _The_
  American Sea-Sun-Crown. _By_ John Andrew Peyssonel, _M. D. F.R.S._
                                                                 p. 843.

  CXIII. _An Account of several rare Species of Barnacles. In a Letter
  to Mr._ Isaac Romilly, _F.R.S. from_ John Ellis, _Esq; F.R.S._
                                                                 p. 845.

  CXIV. _A further Account of the poisonous Effects of the_ Oenanthe
  Aquatica Succo viroso crocante _of_ Lobel, _or Hemlock Dropwort. By_
  W. Watson, _M. D. F.R.S._ p. 856.

  CXV. _Extract of a Letter to_ John Eaton Dodsworth, _Esq; from Dr._
  George Forbes _of_ Bermuda, _relating to the_ Patella, _or_ Limpet
  Fish, _found there_.                                           p. 859.

  CXVI. _A Discourse on the_ Cinnamon, Cassia, _or_ Canella. _By_
  Taylor White, _Esq; F.R.S._                                    p. 860.




LIX. _An Account of the Effects of Electricity in paralytic Cases. In a
Letter to_ John Pringle, _M. D. F.R.S. from_ Benjamin Franklin, _Esq;
F.R.S._

[Read Jan. 12, 1758.]

SIR,

THE following is what I can at present recollect, relating to the
effects of electricity in paralytic cases, which have fallen under my
observation.

Some years since, when the news-papers made mention of great cures
performed in Italy or Germany, by means of electricity, a number of
paralytics were brought to me from different parts of Pensylvania, and
the neighbouring provinces, to be electrised; which I did for them at
their request. My method was, to place the patient first in a chair, on
an electric stool, and draw a number of large strong sparks from all
parts of the affected limb or side. Then I fully charged two six-gallon
glass jars, each of which had about three square feet of surface
coated; and I sent the united shock of these thro’ the affected limb or
limbs; repeating the stroke commonly three times each day. The first
thing observed was an immediate greater sensible warmth in the lame
limbs, that had received the stroke, than in the others: and the next
morning the patients usually related, that they had in the night felt
a pricking sensation in the flesh of the paralytic limbs; and would
sometimes shew a number of small red spots, which they supposed were
occasioned by those prickings. The limbs too were found more capable of
voluntary motion, and seemed to receive strength. A man, for instance,
who could not the first day lift the lame hand from off his knee, would
the next day raise it four or five inches, the third day higher; and
on the fifth day was able, but with a feeble languid motion, to take
off his hat. These appearances gave great spirits to the patients, and
made them hope a perfect cure; but I do not remember, that I ever saw
any amendment after the fifth day: which the patients perceiving, and
finding the shocks pretty severe, they became discouraged, went home,
and in a short time relapsed; so that I never knew any advantage from
electricity in palsies, that was permanent. And how far the apparent
temporary advantage might arise from the exercise in the patients
journey, and coming daily to my house, or from the spirits given by the
hope of success, enabling them to exert more strength in moving their
limbs, I will not pretend to say.

Perhaps some permanent advantage might have been obtained, if the
electric shocks had been accompanied with proper medicine and regimen,
under the direction of a skilful physician. It may be, too, that a few
great strokes, as given in my method, may not be so proper as many
small ones; since, by the account from Scotland of a case, in which two
hundred shocks from a phial were given daily, it seems, that a perfect
cure has been made. As to any uncommon strength supposed to be in the
machine used in that case, I imagine it could have no share in the
effect produced; since the strength of the shock from charged glass is
in proportion to the quantity of surface of the glass coated; so that
my shocks from those large jars must have been much greater than any,
that could be received from a phial held in the hand.

I am, with great respect,

                                 SIR,
                      Your most obedient Servant,
                             R. Franklin.

London, Dec. 21, 1757.




LX. _Observations on the late Comet in_ September _and_ October 1757;
_made at the_ Hague _by Mr._ D. Klinkenberg: _In a Letter to the Rev._
James Bradley, _D. D. Astronomer Royal, and F.R.S. and Member of the
Royal Academy of Sciences at_ Paris. _Translated from the_ Low Dutch.

[Read Jan. 12, 1758.]

SIR,

I Hope you will be pleased to excuse the liberty, which I take, of
troubling you with my observations on the comet, which made its
appearance here, and in other parts of Europe, in the months of
September and October last; and which, according to the news-papers,
was first observed the 11th September by Mr. Gartner, at Dorlkeurtz
near Dresden; then, by me, on the 16th of the said Month, here in the
Hague; and afterwards in different places. As I find, that you have
observed the comet, I doubt not but that you have done it in the most
accurate manner; and my great love for this science induces me to beg,
that I may have the happiness of knowing some of your observations.
My good friend Mr. Struyk at Amsterdam wrote me some time ago, that
he intended to ask the same favour of you; but I have not since heard
any further from him. I observed this comet from Septemb. 16th in
the morning, until Octob. the 11th in the morning; and found its
situations, according to my method, as follows:

                                           _Longit._   _Latit._
     1757.                                    °  ´       °  ´
  Sept. 16. at 4 h. ante mer. The comet in ♋ 10 15 with 10 10 North.
        17  -- 3      --  --  --  --  --   ♋ 14  7 ----  9 38
        18  -- 3¾     --  --  --  --  --   ♋ 18 10 ----  8 57
        19  -- 4      --  --  --  --  --   ♋ 22  1 ----  8 17
        22  -- 2¾     --  --  --  --  --   ♌  3 46 ----  6 15
        23  -- 4      --  --  --  --  --   ♌  7 36 ----  5 24
        25  -- 4¼     --  --  --  --  --   ♌ 14 50 ----  4  6
        28  -- 4      --  --  --  --  --   ♌ 24 22 ----  1 41
  Oct.   1  -- 4¾     --  --  --  --  --   ♍  2 46 ----  0 12 South.
         4  -- 4½     --  --  --  --  --   ♍  9 45 ----  1 30
         9  -- 4½     --  --  --  --  --   ♍ 20 20 ----  2 40
        11  -- 5      --  --  --  --  --   ♍ 24 46 ----  3  9

But the two last observations will, in my opinion, differ the most;
because, when I made them, I was in some doubt about the adjustment
of my instruments; and the comet was then far advanced into the
morning rays. I have, since the month of February last to the end of
May, made sundry observations on fixed stars, with a telescope of 16
inches, made by Mr. Short; and with a pendulum clock, made after the
manner of Mr. Graham, by Mr. Vryhthoff of this place. In the months
of February and March, by a medium of eight observations, I found,
that by the clock, the star Rigel, in every daily revolution, passed
4 min. 2⁴⁄₉ seconds of time earlier, in the telescope; and in the
latter end of May I found, by six observations, (the clock not in the
least changed or altered) on the star Spica Virginis, that that star,
in every revolution, passed 4 min. 5¹⁄₂₀ sec. earlier, in the same
telescope; which intervals differ pretty nearly 2⅗ seconds of time from
one another. Whether this difference arises from any defect in the
clock, or whether it proceeds from any small difference of velocity
of the earth’s motion round its axis, I would have been very glad to
have endeavoured to find out by farther inquiry, had not the death of
Mr. S. Koenig intervened, and I thereby hindered from continuing my
observations. The above observations were taken in the observatory of
his illustrious Highness the minor Prince of Orange and Nassau, _&c.
&c._ under the direction, and with the approbation of the aforesaid
Mr. Koenig. After the death of that gentleman, I petitioned her Royal
Highness the Princess Governess of these Provinces, _&c._ that I might
have leave to continue my astronomical observations; but as yet I have
not been able to obtain her Royal Highness’s permission: otherwise I
would have observed this last comet with more exactness. Had I been
able to pursue the above-mentioned observations, I would, for the
greater certainty in regard to the pendulum, have made use of a farther
precaution. By means of a stove, with the help of a thermometer, I
would have endeavoured to have kept the room (in which the clock stood)
in the winter, and at all times, in the same degree of heat it had at
the time I made the observations in the summer. I would also have daily
observed and noted the moon’s place, at the time of the observations.
Tho’ this is but a slight observation of mine; yet I make no doubt, but
that in case, by the different distances of the earth from the sun,
and the different distances and situations of the moon with respect
to the earth, and the respective effects produced by these causes,
any inequality arises in the velocity of the diurnal motion of the
earth on its axis, you (who have made the most sublime observations on
the aberration of the fixed stars, and more than any mortal ever did
before) must have discovered, and are well acquainted, with the same.

As my above-mentioned observations on the comet appeared too incorrect
to undertake a calculation for the ascertaining of its path from the
theory, I contented myself with effecting it by a construction. By this
means I found, on a figure, whose globular or spherical diameter was
13½ Rhineland inches, as follows:

That the comet was in its perihelion the 21st of October, at two of the
clock in the afternoon: the place of the perihelion 3 degrees in Leo.
The comet’s distance in the perihelion from the sun was about 34 parts,
whereof 100 make the mean distance between the sun and the earth. The
inclination of the comet’s orbit with the ecliptic 13 degrees; and the
southern latitude of the perihelion also 13 decrees: the ascending or
north node ☊ 4⅓ degrees in Scorpio; and the comet’s motion direct, or
according to the order of the signs of the zodiac. On this supposition
I have, for some of the times of observations, estimated the apparent
places of the comet, and found them as follows:

                                   _Long._  _Latit._
  Sept. 18, at 3¾ ante merid. In ♋ 18¹⁄₁₂ and 9 deg. North.
        19  -- 4   --  --     -- ♋ 22  ---- 8⅖
        22  -- 2¾  --  --     -- ♌  3⅝ ---- 6¼
        23  -- 4   --  --     -- ♌  7⅗ ---- 5½
        25  -- 4¼  --  --     -- ♌ 14⅔ ---- 4
        28  -- 4   --  --     -- ♌ 24⅓ ---- 1¾
  Oct.   4  -- 4½  --  --     -- ♍  9⅓ ---- 2 ---- South.
         9  -- 4¾  --  --     -- ♍ 19⅔ ---- 3⅖
        11  -- 5   --  --     -- ♍ 23⅛ ---- 3⅘

The observations, which I have taken, to ground the measurement on, are
those of the 16th and 23d of September, and of the 1st of October. It
appears very evident, not only from this rough calculation, but every
other circumstance of this comet, that it is not the same with that
in the year 1682: which, on certain accounts, is very desirable to be
known; for both here, and in other parts of the Netherlands, there
have been some people, who have published mere conjectures; and have
ventured (very minutely and exactly, as they pretended) about the time
that this comet first made its appearance, to predict the return of
the comet of the year 1682. But by the above, the weakness of their
pretensions is very evident to all the world: whereas, if this had
proved to be the expected comet, they would have assumed to themselves
much undue praise, and have pretended to knowlege even superior to the
every-where much celebrated Newton and Halley.

It appears also probable to me, that this comet is none of those
already calculated, or brought upon a list, by Messieurs Halley and
Struyk. It is somewhat remarkable, that the line of the nodes is
almost at right angles with the long axis of the ellipsis; which
corresponds nearly with the comets of the years 1580, 1683, and 1686:
but those had their perihelions northward of the ecliptic; whereas the
perihelion of the last, which we have lately seen, was to the southward
of the ecliptic.

I have the honour to subscribe myself, with the most perfect esteem for
you, and your sublime studies, very respectfully,

                                 SIR,
                Your very humble and obedient Servant,
                            D. Klinkenberg.

Hague, 13th Dec. 1757.




LXI. _Remarks on the different Temperature of the Air at_ Edystone,
_from that observed at_ Plymouth, _between the 7th and 14th of_ July
1757. _By Mr._ John Smeaton, _F.R.S._

[Read Jan. 12, 1758.]

SIR,

ON the reading of Dr. Huxham’s letter at the last meeting, some
observations occurred to me, concerning the different temperature of
the air, which I had observed at the Edystone, from what had been
observed by the Doctor at Plymouth, between the 7th and 14th of July
last: which having been desired by some members to be put into writing,
I beg leave to trouble you with the following.

Edystone is distant from Plymouth about 16 miles, and without the
head-lands of the Sound about 11.

The 7th and 8th were not remarkable at Edystone for heat or cold; the
weather was very moderate, with a light breeze at east; which allowed
us to work upon the rock both days, when the tide served.

About midnight, between the 8th and 9th, the wind being then fresh at
east, it was remarkably cold for the season, as I had more particular
occasion to observe, on account of a ship that was cast away upon the
rocks. The wind continued cold the 9th all day; which was complained
of by some of the shipwrecked seamen, who had not time to save their
cloaths; and so fresh at east, as prevented our going near the rocks,
or the wreck; and so continued till Sunday the 10th; when, seeing no
prospect of a sudden alteration of weather, I returned to Plymouth in
a sailing boat, wrapped up in my thick coat. As soon as we got within
the headlands, I could perceive the wind to blow considerably warmer;
but not so warm as to make my great coat uneasy. Having had a quick
passage, in this manner I went home, to the great astonishment of the
family to see me so wrapped up, when they were complaining of the
excessive heat: and indeed, it was not long before I had reason to join
in their opinion.

This heat I experienced till Tuesday the 12th, when I again went off to
sea, where I found the air very temperate, rather cool than warm; and
so continued till Thursday the 14th.

In my journal for Wednesday the 13th I find the following remarks,
_viz._ “This evening’s tide” (from 6 A. till 12 A.) “the wind at east,
but moderate, with frequent flashes of lightning to the southward. Soon
after we got on board the store-vessel, a squall of wind arose from the
south-west on a sudden, and continued for about a minute; part of which
time it blew so hard, we expected the masts to go by the board: after
which it was perfectly calm, and presently after a breeze returned from
the east.”

And in the journal of the 14th is entered, “This morning’s tide”
(_viz._ from 1 M. to 1 A.) “the air and sea quite calm.”

Hence it appears, how different the temper of the air may be in a
small distance; and to what small spaces squalls of wind are sometimes
confined.

It may not be amiss further to observe upon this head, that once, in
returning from Edystone, having got within about two miles of the
Ramhead, we were becalmed; and here we rolled about for at least four
hours; and yet at the same time saw vessels, not above a league from
us, going out of Plymouth Sound with a fresh of wind, whose direction
was towards us, as we could observe from the trim of their sails; and
as we ourselves experienced, after we got into it by tacking and rowing.

I am, Sir,

                       Your most humble Servant,
                              J. Smeaton.

Furnival’s-Inn Court, 12th Jan. 1758.




LXII. _An Account of the Earthquake felt in the Island of_ Sumatra, _in
the_ East-Indies, _in_ November _and_ December 1756. _In a Letter from
Mr._ Perry _to the Rev. Dr._ Stukeley, _dated at_ Fort Marlborough, _in
the Island of_ Sumatra, Feb. 20. 1757. _Communicated by the Rev._ Wm.
Stukeley, _M. D. F.R.S._

[Read Jan. 12, 1758.]

THE earthquake at Lisbon, which you gave me an account of, was
certainly the most awful tremendous calamity, that has ever happened
in the world. Its effects are extremely wonderful and amazing; and it
seems, as you observe, to have been felt in all parts of the globe.
On the 3d day of the same month the earthquake of Lisbon happened, I
felt at Manna[1] a violent shock myself; and from that time to the 3d
of December following I felt no less than twelve different shocks, all
which I took an exact account of in my pocket-bock. Since which we have
had two very severe earthquakes, felt, we believe, throughout this
island[2]. The walls of[3] Cumberland-house[4] were greatly damaged
by them. Salop-house[4], my own (formerly Mr. Massey’s), the houses
of Laye[5] and Manna, were all cracked by them; and the works at the
sugar-plantation[6] received considerable damage. The ground opened
near the _qualloe_[7] at Bencoolen, and up the River in several places;
and there issued therefrom sulphureous earth, and large quantities of
water, sending forth a most intolerable stench. Poblo Point[8] was much
cracked at the same time; and some _doosoons_[9] in-land at Manna were
destroyed, and many people in them.

These are all the ill effects, that have come to our knowlege; but, it
is reasonable to suppose, not all the damage, that has happened upon
the island.




LXIII. _Concerning the Fall of Water under Bridges. By Mr._ J.
Robertson, _F.R.S._

[Read Jan. 19, 1758.]

SOME time before the year 1740, the problem about the fall of water,
occasioned by the piers of bridges built across a river, was much
talked of at London, on account of the fall that it was supposed would
be at the new bridge to be built at Westminster. In Mr. Hawksmore’s
and Mr. Labelye’s pamphlets, the former published in 1736, and the
latter in 1739, the result of Mr. Labelye’s computations was given: but
neither the investigation of the problem, nor any rules, were at that
time exhibited to the public.

In the year 1742 was published Gardiner’s edition of Vlacq’s Tables;
in which, among the examples there prefixed to shew some of the
uses of those tables drawn up by the late William Jones, Esq; there
are two examples, one shewing how to compute the fall of water at
London-bridge, and the other applied to Westminster-bridge: but that
excellent mathematician’s investigation of the rule, by which those
examples were wrought, was not printed, altho’ he communicated to
several of his friends copies thereof. Since that time, it seems as
if the problem had in general been forgot, as it has not made its
appearance, to my knowlege, in any of the subsequent publications. As
it is a problem somewhat curious, tho’ not difficult, and its solution
not generally known (having seen four different solutions, one of them
very imperfect, extracted from the private books of an office in one of
the departments of engineering in a neighbouring nation), I thought it
might give some entertainment to the curious in these matters, if the
whole process were published. In the following investigation, much the
same with Mr. Jones’s, as the demonstrations of the principles therein
used appeared to be wanting, they are here attempted to be supplied.


PRINCIPLES.

I. _A heavy body, that in the first second of time has fallen the
height of a feet, has acquired such a velocity, that, moving uniformly
therewith, will in the next second of time move the length of 2 a feet._

II. _The spaces run thro’ by falling bodies are proportional to one
another as the squares of their last or acquired velocities._

 These two principles are demonstrated by the writers on mechanics.

III. _Water forced out of a larger chanel thro’ one or more smaller
passages, will have the streams thro’ those passages contracted in the
ratio of 25 to 21._

 This is shewn in the 36th prop. of the 2d book of Newton’s Principia.

IV. _In any stream of water, the velocity is such, as would be acquired
by the fall of a body from a height above the surface of that stream._

 This is evident from the nature of motion.

V. _The velocities of water thro’ different passages of the same
height, are reciprocally proportional to their breadths._

  For, at some time, the water must be delivered as fast as it comes;
  otherwise the bounds would be overflowed.

  At that time, the same quantity, which in any time flows thro’ a
  section in the open chanel, is delivered in equal time thro’ the
  narrower passages; or the momentum in the narrow passages must be
  equal to the momentum in the open chanel; or the rectangle under the
  section of the narrow passages, by their mean velocity, must be equal
  to the rectangle under the section of the open chanel by its mean
  velocity.

  Therefore the velocity in the open chanel is to the velocity in the
  narrower passages, as the section of those passages is to the section
  of the open chanel.

  But the heights in both sections being equal, the sections are
  directly as the breadths;

  Consequently the velocities are reciprocally as the breadths.

VI. _In a running stream, the water above any obstacles put therein
will rise to such a height, that by its fall the stream may be
discharged as fast as it comes._

  For the same body of water, which flowed in the open chanel, must
  pass thro’ the passages made by the obstacles:

  And the narrower the passages, the swifter will be the velocity of
  the water:

  But the swifter the velocity of the water, the greater is the height,
  from whence it has descended:

  Consequently the obstacles, which contract the chanel, cause the
  water to rise against them.

  But the rise will cease, when the water can run off as fast as it
  comes:

  And this must happen, when, by the fall between the obstacles, the
  water will acquire a velocity in a reciprocal proportion to that in
  the open chanel as the breadth of the open chanel is to the breadth
  of the narrow passages.

VII. _The quantity of the fall caused by an obstacle in a running
stream is measured by the difference between the heights fallen from
to acquire the velocities in the narrow passages and open chanel._

  For just above the fall, the velocity of the stream is such, as would
  be acquired by a body falling from a height higher than the surface
  of the water:

  And at the fall, the velocity of the stream is such, as would be
  acquired by the fall of a body from a height more elevated than the
  top of the falling stream; and consequently the real fall is less
  than this height.

  Now as the stream comes to the fall with a velocity belonging to a
  fall above its surface;

  Consequently the height belonging to the velocity at the fall must be
  diminished by the height belonging to the velocity, with which the
  stream arrives at the fall.


PROBLEM.

_In a chanel of running water, whose breadth is contracted by one or
more obstacles; the breadth of the chanel, the mean velocity of the
whole stream, and the breadth of the water-way between the obstacles
being given; To find the quantity of the fall occasioned by those
obstacles._

  Let _b_ = breadth of the chanel in feet.
      _v_ = mean velocity of the water in feet per sec.
      _c_ = breadth of the water-way between the obstacles.

Now 25: 21∷ _c_: 21 ⁄ 25 _c_ the water-way contracted. _Principle III._

And 21 ⁄ 25 _c_: _b_∷ _v_: 25_b_ ⁄ 21_c_ _v_ the veloc. _per_ sec. in
the water-way between the obstacles. _Princip. V._

Also (2_a_)²: _vv_∷ _a_: _vv_ ⁄ 4_a_ the height fallen to acquire the
vel. v. I. & II.

And (2_a_)²: (25_b_ ⁄ 21_c_)² × _vv_∷ _a_: (25_b_ ⁄ 21_c_)² × _vv_ ⁄
4_a_ the height fallen to acquire the vel. 25_b_ ⁄ 21_c_ _v_. I. & II.

Then (25_b_ ⁄ 21_c_)² x (_vv_ ⁄ 4_a_) - (_vv_ ⁄ 4_a_) is the measure of
the fall required. VII.

Or ((25_b_ ⁄ 21_c_)² - 1) × _vv_ ⁄ 4_a_ is a rule, by which the fall
may be readily computed.

Here _a_ = 16,0899 feet and 4_a_ = 64,3596.


EXAMPLE I. _For London-Bridge._

By the observations made by Mr. Labelye in 1746,

The breadth of the Thames at London-bridge is 926 feet;

The sum of the water-ways at the time of the greatest fall is 236 feet;

The mean velocity of the stream taken at its surface just above bridge
is 3⅙ feet _per_ second.

Under almost all the arches there are great numbers of drip-shot piles,
or piles driven into the bed of the water-way, to prevent it from being
washed away by the fall. These drip-shot piles considerably contract
the water-ways, at least ⅙ of their measured breadth, or about 39⅓ feet
in the whole.

So that the water-way will be reduced to 196⅔ feet.

Now _b_ = 926; _c_ = 196⅔; _v_ = 3⅙; 4_a_ = 64,3596.

Then 25_b_ ⁄ 21_c_ = 23150 ⁄ 4130 = 5,60532.

And 5,60532² = 31,4196; and 31,4196 - 1 = 30,4196 = (25_b_ ⁄ 21_c_)² -
1.

Also _vv_ = (19 ⁄ 6)² = 361 ⁄ 36; And _vv_ ⁄ 4_a_ = 361 ⁄ (36 ×
64,3596) = 0,15581.

Then 30,4196 × 0,15581 = 4,739 feet, the fall sought after.

By the most exact observations made about the year 1736, the measure of
the fall was 4 feet 9 inches.


EXAMPLE II. _For Westminster-Bridge._

Altho’ the breadth of the river at Westminster-bridge is 1220 feet;
yet, at the time of the greatest fall, there is water thro’ only the
thirteen large arches, which amount to 820 feet: to which adding the
breadth of the twelve intermediate piers, equal to 174 feet, gives 994
for the breadth of the river at that time: and the velocity of the
water just above bridge (from many experiments) is not greater than 2¼
feet _per_ second.

Here _b_ = 994; _c_ = 820; _v_ = 2¼; 4_a_ = 64,3596.

Now 25_b_ ⁄ 21_c_ = 24850 ⁄ 17220 = 1,443.

And 1,443² = 2,082; And 2,082 - 1 = 1,082 = (25_b_ ⁄ 21_c_)² - 1.

Also _vv_ = (⁹⁄₄)² = ⁸¹⁄₁₆; And _vv_ ⁄ 48 = 81 ⁄ (16 × 64,3696) =
0,0786.

Then 1,082 × 0,0786 = 0,084 feet, the fall sought.

Which is about 1 inch; and is about half an inch more than the greatest
fall observed by Mr. Labelye.




LXIV. _An Account of the Earthquake in the West Parts of_ Cornwall,
July _15th 1757. By the Rev._ William Borlase, _M. A. F.R.S.
Communicated by the Rev._ Charles Lyttelton, _LL.D. Dean of_ Exeter,
_F.R.S._

[Read Jan. 26, 1758.]

ON Friday the 15th of July, 1757. a violent shock of an earthquake was
felt in the western parts of Cornwall.

The thermometer had been higher than usual, and the weather hot, or
calm, or both, for eight days before; wind east and north-east. On the
14th in the morning, the wind shifting to the south-west, the weather
calm and hazy, there was a shower. The afternoon hazy and fair, wind
north-west. The barometer moderately high, but the mercury remarkably
variable.

On the 15th in the morning, the wind fresh at north-west, the
atmosphere hazy. Being on the sands, half a mile east of Penzance, at
10 A. M. near low water, I perceived on the surface of the sands a
very unusual inequality: for whereas there are seldom any unevennesses
there, but what are made by the rippling of the water, I found the
sands, for above 100 yards square, all full of little tubercles (each
as large as a moderate mole-hill), and in the middle a black speck on
the top, as if something had issued thence. Between these convexities
were hollow basons of an equal diameter. From one of these hollows
there issued a strong rush of water, about the bigness of a man’s
wrist, never observed there before nor since.

About a quarter after six, P. M. the sky dusky, the wind being at west
north-west, it fell quite calm. At half past six, being then in the
summer-house at Keneggy, the seat of the Hon. J. Harris, Esq; near
Penzance, with some company, we were suddenly alarmed with a rumbling
noise, as if a coach or waggon had passed near us over an uneven
pavement; but the noise was as loud in the beginning and at the end,
as in the middle; which neither the sound of thunder, or of carriages,
ever is. The sash-casements jarred: one gentleman thought his chair
moved under him; and the gardener, then in the dwelling house (about an
hundred yards distant from us) felt the stone pavement of the room he
was in move very sensibly.

In what place the shock began, and whether progressive or instantaneous
in the several places where it was felt, is uncertain, for want of
accurately determining the precise point of time in distant places.

The shock was not equally loud or violent. Its extent was from the
isles of Scilly eastward as far as Liskerd, and towards the north as
far as Camelford; thro’ which district I shall trace it, according to
the best informations I could procure.

In the island of St. Mary, Scilly, the shock was violent. On the
shores of Cornwall, opposite to Scilly (in the parish of Senan, near
the Land’s-end) the noise was heard like that of a spinning-wheel on
a chamber-floor. Below stairs there was a cry, that the house was
shaking; and the brass pans and pewter rattled one against another
in several houses in the same parish. In the adjoining parish of
St. Just, two young men being then swimming, felt a strong and very
unusual agitation of the sea. In the town of Penzance, in one house
the chamber-bell rung; in another the pewter plates, placed edgeways
on a shelf, shifted, and slid to one end of the shelf: and it was
every-where perceived more or less, according as people’s attention was
engaged.

At Trevailer, the seat of William Veale, Esquire, about two miles from
Penzance, the noise was heard, and thought at first to be thunder:
the windows shook, and the walls of the parlour, where Mr. Veale
sat, visibly moved. The jarring of the windows continued near half a
minute; but the motion of the walls not quite so long: and some masons,
being at work on a contiguous new building, the upright poles of the
scaffolds shook so violently, that, for fear of falling, they laid
hold on the walls, which, to their still greater surprize, they found
agitated in the same manner. And a person present, who was at London
at the time of the two shocks in the year 1751, thought this shock to
resemble the second, both in degree and duration[10].

At Marazion, the next market-town east of Penzance, the houses of
several persons shook to that degree, that people ran out into the
street, lest the houses should fall upon them.

In the borough of St. Ives, on the north sea, six miles north of
Penzance, the shock was so violent, that a gentleman, who had been at
Lisbon during several shocks, said, that this exceeded all he had met
with, except that on the 1st of November 1755, so fatal to that city.

At Tehidy, the seat of Francis Basset, Esq; the rooms shook, and
the grounds without doors were observed to move. The shock was felt
sensibly at Redruth, St. Columb, Bodman, _&c._ along to Camelford,
which is about 90 miles from the isle of Scilly. From Marazion eastward
it was felt at several places in like manner, as far as Lostwythyel;
but at Liskerd, about ten miles east of Lostwythyel, it was but faintly
perceived, and that by a few persons. It was still less sensible at Loo
and Plymouth, “scarcely sufficient to excite curiosity or fear”[11].

The times of its duration were various. At Keneggy we thought the noise
could not have lasted above six seconds; at Trevailer, not two miles
distant to the west, it was thought to have lasted near half a minute;
in the parish of Gwynier half a minute; at Ludgvan, three miles east
of Penzance, the noise was rather longer than half a minute; but the
shaking felt in the garden, and observed in the houses, short and
momentary. In Germo great Pinwork, seven miles east of Penzance, it
lasted only a few seconds; but in the isles of Scilly it was computed
at 40 seconds.

Thus was this earthquake felt in towns, houses, and grounds adjacent;
but still more particularly alarming in our mines, where there is less
refuge, and consequently a greater dread from the tremors of the earth.

In Carnorth adit, in the parish of St. Just, the shock was sensibly
felt 18 fathom deep; in the mine called Boscadzhill-downs, more than 30
fathom.

At Huel-rith mine, in the parish of Lannant, people saw the earth
move under them, first quick, then in a slower wavy tremor; and
the stage-boards of the little winds or shafts 20 fathom deep were
perceived to move.

In Herland mine, commonly called the Manor, in the parish of Gwynier,
the noise was heard 55 and 60 fathom deep, as if a studdle[12] had
broke, and the deads[13] were set a running. It was nothing like the
noise of thunder.

In Chace-water mine the same noise was heard, at least 70 fathom under
the surface.

At Huel-rith mine, near Godolphin, the noise was seemingly underneath.
I felt (says the director of the mine) the earth move under me with a
prodigious swift, and apparently horizontal tremor: its continuance was
but for a few seconds of time, not like thunder, but rather a dull
rumbling even sound, like deads running under ground. In the smith’s
shop the window-leaves shook, and the slating of the house cracked.
The whim-house shook so terribly, that a man there at work ran out of
it, concluding it to be falling. Several persons then in the mine,
working 60 fathom deep, thought they found the earth about them to
move, and heard an uncommon noise: some heard the noise, and felt no
tremor; others, working in a mine adjoining called Huel-breag, were
so frightened, that they called to their companions above to be drawn
up from the bottoms. Their moor-house was shaken, and the padlock of
their candle-chest was heard to strike against the staples. To shew,
that this noise proceeded from below, and not from any concussion in
the atmosphere above, this very intelligent captain of the mine[14]
observes, from his own experience, that thunder was never known to
affect the air at 60 fathoms deep, even in a single shaft pierced into
the hardest stone; much less could it continue the sound thro’ such
workings as there are in this mine, impeded in all parts with deads,
great quantities of timber, various noises, such as the rattling of
chains, friction of wheels and ropes, and dashing of waters; all which
must contribute to break the vibrations of the air as they descend: and
I intirely agree with this gentleman’s conclusion, that thunder, or any
other noises from above in the atmosphere, could not be heard at half
the depth of this mine. This therefore could be no other than a real
tremor of the earth, attended with a noise, owing to a current of air
and vapour proceeding upwards from the earth.

I do not hear of any person in those parts, who was so fortunate as to
be near any pool or lake, and had recollection enough to attend to the
motion of the waters; but it may be taken for granted, that during the
tremors of the earth the fluids must be more affected than the solids:
nay, the waters will apparently be agitated, when there is no motion
of the earth perceptible, as was the case of our ponds and lake-waters
in most parts of Britain on the 1st of November 1755. Whence this
happens is difficult to say: whether the earth’s bosom undergoes at
such times a kind of respiration, and alternately emits and withdraws
a vapour thro’ its most porous parts sufficient to agitate the waters,
yet not sufficient to shake the earth; or whether the earth, during the
agitation of the waters, does rock and vacillate, tho’ not so as to be
sensible to man; is what I shall leave to future inquiry.

Earthquakes are very rare in Cornwall. This was but of short duration,
and did no harm any-where, as far as I can learn; and it is to be hoped
not the sooner forgotten for that reason; but rather remembered with
all the impressions of gratitude suitable to an incident so alarming
and dangerous, and yet so inoffensive.




LXV. _Some Observations upon the Sleep of Plants; and an Account
of that Faculty, which_ Linnæus _calls_ Vigiliæ Florum; _with an
Enumeration of several Plants, which are subject to that Law.
Communicated to_ Wm. Watson, _M. D. F.R.S. by Mr._ Richard Pultney _of_
Leicester.

[Read Jan. 26, 1758.]

ACosta and Prosper Alpinus, who both wrote near the conclusion of the
XVIth century, are, I believe, the first, who recorded that nocturnal
change in the leaves of plants, which has since been called _somnus_.
It is an observation indeed as old as Pliny’s time, that the leaves of
trefoil assume an erect situation[15] upon the coming of storms. The
same is observable of our wood-sorrel; and Linnæus adds, of almost all
plants with declinated stamina[16]. In the _Trifolium pratense album
C. B._ or common white-flowered meadow trefoil, it is so obvious, that
the common people in Sweden remark, and prognosticate the coming of
tempests and rain from it.

The examples of sleeping plants instanced by Alpinus are but few.
That author says, it was common to several Egyptian species[17];
but specifies only the Acaciæ, Abrus, Absus, Sesban, and the
Tamarindtree. Cornutus some time afterwards remarked this property
in the Pseudo-acacia Americana. From that time it has remained almost
unnoticed, till Linnæus, ever attentive to nature’s works, discovered
that the same affair was transacted in many other plants; and his
observations have furnished us with numerous and obvious examples
thereof. Mr. Miller mentions it in the _Medicago arborea Lin. Sp. Pl.
778_. and we may add to the list two other common plants not mentioned
by Linnæus: these are the _Phaseolus vulgaris_, common kidney-bean;
and the _Trifolium pratense purpureum majus_, or clover-grass: in both
which this nocturnal change is remarkably displayed. Doubtless the same
property exists in numberless other species; and future observation
will very probably confirm Dr. Hill’s sentiment, that no “plant or tree
is wholly unaffected by it.”

It is now more than twenty years since Linnæus first attended to this
quality in plants. In his _Flora Lapponica_, when speaking of the
_Trifolium pratense album_, as above-mentioned, he remarks, that the
leaves of the Mimosa, Cassia, Bauhinia, Parkinsonia, Guilandina, and
others in affinity with them, were subject to this change in the night
time: and he had then carried his observations so far, as to find, that
heat and cold were not the cause of this quality; since they were alike
influenced by it when placed in stoves, where the temperature of the
air was always the same.

The merit of reviving this subject is therefore due to the illustrious
Swede; and the naturalist is greatly indebted to him for so far
extending his observations thereon.

The subject of the _somnus plantarum_ cannot but be highly entertaining
to the lovers of natural knowlege: and such, I apprehend, cannot be
less entertained with that faculty, which Linnæus calls _vigiliæ
florum_; of which we shall give a brief account.

Previous to our explanation of this affair it is proper to observe,
that the flowers of most plants, after they are once opened, continue
so night and day, until they drop off, or die away. Several others,
which shut in the night-time, open in the morning either sooner or
later, according to their respective situation in the sun or shade,
or as they are influenced by the manifest changes of the atmosphere.
There are however another class of flowers, which make the subject of
these observations, which observe a more constant and uniform law in
this particular. These open and shut duly and constantly at certain and
determinate hours, exclusive of any manifest changes in the atmosphere;
and this with so little variation in point of time, as to render the
phænomenon well worth the observation of all, whose taste leads them
this way.

This faculty in the flowers of plants is not altogether a new
discovery; but we are indebted to the same hand for additional
observations upon this head likewise. It is so manifest in one of our
common English plants, the _Tragopogon luteum_, that our country people
long since called it _John-go-to-bed-at-noon_. Linnæus’s observations
have extended to near fifty species, which are subject to this law.
What we find principally upon this subject is in the _Philosophia
Botanica_, p. 273. We will enumerate these plants, and mention the
time when the flowers open and shut, that those, who have opportunity
and inclination, may gratify themselves, and probably at the same time
extend this branch of botanic knowlege still farther.

It is proper to observe, that as these observations were made by
Linnæus in the academical garden at Upsal, whoever repeats them in
this country will very probably find, that the difference of climate
will occasion a variation in point of time: at least this will obtain
in some species, as our own observations have taught us; in others the
time has corresponded very exactly with the account he has given us.

Whether this faculty hath any connexion with the great article of
fecundation in the oeconomy of flowers, I cannot determine: in the
mean time it is not improbable. Future and repeated observations, and
well-adapted experiments, will tend to illustrate this matter, and it
may be lead the way to a full explanation of the cause.


1. Anagallis flore phœniceo C. B. pin. 252. Raii Syn. p. 282. Anagallis
arvensis Lin. Spec. plant. p. 148. _The Male Pimpernel._ The flowers
of this plant open about eight o’clock in the morning, and never
close till past noon. This plant is common in kitchen-gardens and in
corn-fields, and flowers in June, and continues in flower three months.

2. The Anagallis cærulea foliis binis ternisve ex adverso nascentibus
C. B. pin. p. 252. Raii Hist. Plant. p. 1024. Anagallis Monelli Sp.
plant. 148. _Blue-flowered Pimpernel with narrow leaves._ The flowers
of this plant observe nearly the same time in opening and shutting as
the foregoing.

3. Convolvulus peregrinus cæruleus folio oblongo C. B. pin. 295.
Convolvulus tricolor Sp. plant. 158. _Little blue Convolvulus, or
Bindweed._ This opens its flowers between the hours of five and six in
the morning, and shuts them in the afternoon.

4. Phalangium parvo flore ramosum C. B. pin. 29. Raii Hist. Pl. 1193.
_Branched Spiderwort with a small flower._ These open about seven in
the morning, and close between the hours of three and four in the
afternoon.

5. Lilium rubrum Asphodeli radice C. B. pin. 80. Hemerocallis fulvus
Sp. pl. 324. _The Day Lily._ The flowers open about five in the
morning, and shut at seven or eight in the evening.

6. Plantago aquatica minor. Park. 1245. Raii Syn. 257. Alisma
ranunculoides Sp. pl. 343. Fl. Suec. 2. Nº. 325. _The lesser
Water-Plantain_, during its flowering-time, only opens its flowers each
day about noon.

7. Caryophyllus sylvestris prolifer C. B. pin. 209. Raii Syn. 337.
Dianthus prolifer Sp. pl. 410. _Proliferous Pink._ The flowers expand
about eight in the morning, and close again about one in the afternoon.

8. Spergula purpurea J. B. III. 722. Raii Syn. p. 351. Arenaria rubra.
Sp. pl. 423. _Purple Spurrey._ These expand between nine and ten in the
morning, and close between two and three in the afternoon. This little
plant is common among the corn in sandy soils, and flowers in June.

9. Portulaca latifolia sativa C. B. pin. 288. Portulaca oleracea Sp.
pl. p. 445. _Common Purslain_, opens its flowers about nine or ten in
the morning, and closes them again in about an hour’s time.

10. Ficoides Africana, folio plantaginis undulato micis argenteis
adsperso Boerh. Ludg. I. p. 291. Mesembryanthemum chrystallinum Sp. pl.
480. _Diamond Ficoides._ The flowers of this plant open at nine or ten,
and close at three or four in the afternoon.

11. Ficoides Africana folio tereti in villos radiatos abeunte. Tourn.
Mesembryanthemum barbatum Sp. pl. 482. The flowers of this species
expand at seven or eight in the morning, and close about two in the
afternoon.

12. Ficoides folio tereti Neapolitana flore candido Herm. Ludg.
252. Kali Crassulæ minoris foliis C. B. pin. 289. Mesembryanthemum
nodiflorum Sp. pl. 480. The flowers of this plant open at ten or eleven
in the morning, and close at three in the afternoon.

13. Mesembryanthemum folio linguiformi latiore Dillen. Hort.
Elth. Mesembryanthemum linguiforme Sp. pl. 488. _Ficoides with a
tongue-shaped leaf._ These open at seven or eight in the morning, and
are closed about three in the afternoon.

14. Nymphæa alba J. B. III. 770. Raii Syn. 368. Nymphæa alba Sp. pl.
510. Fl. Suec. 2. Nº. 470. _White Water Lily._ This plant grows in
rivers, ponds, and ditches, and the flowers lie upon the surface of the
water. At their time of expansion, which is about seven in the morning,
the stalk is erected, and the flower more elevated above the surface.
In this situation it continues till about four in the afternoon, when
the flower sinks to the surface of the water, and closes again.

15. Papaver erraticum nudicaule flore flavo odorato Dillen. Hort. Elth.
302. Papaver nudicaule Sp. pl. p. 507. _Wild Poppy with a naked stalk
and a yellow sweet-smelling flower._ The flower of this plant opens at
five in the morning, and closes at seven in the evening.

16. Alyssoides incanum, foliis sinuatis Tourn. Inst. 213. Alyssum
sinuatum Sp. pl. 651. _Hoary Madwort with sinuated leaves._ The flowers
of this plant expand between the hours of six and eight in the morning,
and close at four in the afternoon.

17. Abutilon repens alceæ foliis, flore helvolo Dillen. Hort. Elth. 5.
Malva Caroliniana Sp. pl. 688. _Creeping Indian Mallow with leaves like
Vervain Mallow, and a flesh-coloured flower._ These open at nine or ten
in the morning, and close at one in the afternoon.

18. Tragopogon luteum Ger. 595. Raii Syn. 171. Tragopogon pratense
Sp. pl. 789. _Yellow Goats Beard_, or _Go-to-bed-at-noon_. The latter
of these names was given to this plant long since, on account of this
remarkable property. The flowers open in general about three or four
o’clock, and close again about nine or ten, in the morning. These
flowers will perform their _vigiliæ_, if set in a phial of water,
within doors for several mornings successively; and I have sometimes
observed them to be quite closed, from their utmost state of expansion,
in less than a quarter of an hour. It flowers in June.

19. Tragopogon gramineis foliis, hirsutis. C. B. pin. 275. Raii. Hist.
Plant. 253. _Rose-coloured Goats Beard._ These open between five and
six in the morning, and close about eleven. Tragopog. hybridum Sp.
plant. 789.

20. Tragopogon, calycibus corolla brevioribus inermibus, foliis
lyrato-sinuatis. Hort. Ups. 244. Sp. pl. 790. Hall. Hort. Gotting. 2.
p. 419. The flowers of this plant open at six or seven in the morning,
and shut between the hours of twelve and four in the afternoon.

21. Sonchus Tingitanus papaveris folio. Tourn. Raii Suppl. 137.
Scorzonera Tingitana Sp. pl. 791. _African Sowthistle with a poppy
leaf._ This plant opens its flowers between four and six in the
morning, and closes them in about three hours.

22. Sonchus repens, multis hieracium majus J. B. II. 1017. Raii Syn.
163. Sonchus arvensis Sp. pl. 793. _Tree Sowthistle._ These flowers
expand about six or seven, and close between eleven and twelve in the
forenoon. This is common in corn-fields, and flowers in June, July, and
August.

23. Sonchus lævis Ger. Raii Syn. 161. Sonchus oleraceus Sp. pl. 794.
_Smooth or unprickly Sowthistle, Hares Lettuce._ These open about five
in the morning, and close again at eleven or twelve.

24. Sonchus lævis laciniatus cæruleus C. B. pin. 124. Raii Hist. pl.
225. Sonchus alpinus Sp. pl. 794. _Blue-flowered Mountain Sowthistle._
These open about seven, and close about noon.

25. Sonchus tricubitalis, folio cuspidato Merr. pin. Raii Syn. 163.
Sonchus asper arborescens C. B. pin. 124. Sonchus palustris Sp. pl.
793. _The greatest Marsh tree Sowthistle._ It expands its flowers about
six or seven, and closes them about two in the afternoon.

26. Lactuca sativa C. B. pin. 122. Sp. pl. 795. _Garden Lettuce_, opens
its flowers about seven, and closes them about ten, in the forenoon.

27. Dens leonis Ger. 228. Raii Syn. 170. Leontodon Taraxacum Sp. pl.
798. _Dandelion._ It expands at five or six, and closes at eight or
nine, in the forenoon. This flowers early in the spring, and again in
the autumn.

28. Dens leonis hirsutus leptocaulos, Hieracium dictus. Raii Syn.
171. Leontodon hispidum Sp. pl. 799. _Rough Dandelion_, or _Dandelion
Hawkweed_. This plant opens its flower about four in the morning, and
keeps it expanded till three in the afternoon. In May.

29. Hieracium minus præmorsa radice. Park. 794. Raii Syn. 164.
Leontodon autumnale. Sp. pl. 799. _Hawkweed with bitten roots_, or
_Yellow Devil’s-bit_. The flowers open about seven, and keep in an
expanded state till about three in the afternoon. It flowers in July
and August.

30. Pilosella repens Ger. 573. Raii Syn. 170. Hieracium Pilosella Sp.
pl. 800. _Common creeping Mouse-ear._ It opens about eight in the
morning, and closes about two in the afternoon. Very common on dry
pastures, flowering in June and July.

31. Hieracium murorum folio pilosissimo C. B. pin. 129. Raii Syn. 168.
Hieracium murorum Sp. pl. 802. The flowers of this plant expand about
six or seven, and close about two in the afternoon. Upon old walls,
flowering in June and July. This is called in English, _French_ or
_Golden Lungwort_.

32. Hieracium fruticosum angustifolium majus. C. B. pin. 129. Hieracium
umbellatum Sp. pl. 804. _Narrow-leaved bushy Hawkweed._ The flowers of
this species expand about six in the morning, and remain open till five
in the afternoon.

33. Hieracium fruticosum latifolium hirsutum C. B. pin. 129. Raii
Syn. p. 167. Hieracium sabaudum Sp. pl. 804. _Bushy Hawkweed with
broad rough leaves._ These flowers are in their expanded state from
about seven in the morning till one or two in the afternoon. In woods,
flowering in June and July.

34. Hieracium montanum cichorii folio. Raii. Syn. p. 166. Hieracium
paludosum Sp. pl. 638. Fl. Suec. 2. Nº. 702. _Succory-leaved Mountain
Hawkweed._ The flowers expand about six in the morning, and close about
five in the afternoon.

35. Hieracium hortense floribus atro-purpurascentibus C. B. pin.
128. Hieracium aurantiacum Sp. pl. 801. _Garden Hawkweed with deep
purple flowers_, or _Sweet Indian Mouse-ear_. The flowers are in their
expanded state from six or seven in the morning till three or four in
the afternoon.

36. Hieracium luteum glabrum, sive minus hirsutum. J. B. Raii Syn. 165.
Crepis tectorum Sp. pl. 807. _Smooth Succory Hawkweed._ The flowers of
this plant expand about four in the morning, and close about noon.

37. Hieracium Alpinum Scorzoneræ folio Tourn. Inst. 472. Crepis Alpina
Sp. pl. 806. _Mountain Hawkweed with a vipers-grass leaf._ These open
about five or six, and close at eleven in the forenoon.

38. Hieracium dentis leonis folio, flore suave-rubente, C. B. pin. 127.
Raii hist. pl. 231. Crepis rubra Sp. pl. 806. _Hawkweed of Apulia with
a flesh-coloured flower._ The flowers remain in their expanded state
from six or seven in the morning till one or two in the afternoon.

39. Hieracium echioides, capitulis cardui benedicti C. B. pin. 128.
Raii Syn. 166. Picris echioides Sp. pl. 792. _Lang de bœuf._ On banks
about hedges, and about the borders of fields, flowering in August.
These expand about four or five in the morning, and never close before
noon: sometimes they remain open till nine at night.

40. Hieracium Alpinum latifolium hirsutie incanum flore magno. C.
B. pin. 128. Raii Syn. p. 167. Hypochæris maculata Sp. pl. 810.
_Broad-leaved Hungarian Hawkweed._ These flowers are in their
vigilating state from six in the morning till four in the afternoon.

41. Hieracium ramosum, floribus amplis, calycibus valde hirsutis,
foliis oblongis obtusis: dentibus majoribus inæqualibus incisis Raii
Suppl. 144. 76. Hypochæris Achyrophorus Sp. pl. 810. This plant opens
its flowers about seven or eight in the morning, and closes them about
two in the afternoon.

42. Hieracium minus dentis leonis folio, oblongo glabro C. B. pin. 127.
Hypochæris glabra Sp. pl. 811. These expand about nine in the morning,
and close about twelve or one o’clock.

43. Hieracium falcatum alterum Raii Hist. 256. Lapsana calycibus
fructus undique patentibus, radiis subulatis, foliis lyratis Hort. Ups.
245. Sp. pl. 812. The flowers open at five or six, and close between
the hours of ten and one.

44. Hedypnois annua Tourn. Inst. 478. Hyoseris hedypnois Sp. pl. 809.
The flowers open at seven or eight, and close again at two in the
afternoon.

45. Hieracium montanum alterum leptomacrocaulon Col. Raii Hist. 234.
Lapsana chondrilloides Sp. pl. 812. _Mountain Hawkweed with long
slender stalks and small flowers._ The flowers are in their expanded or
vigilating state from five or six in the morning till about ten.

46. Cichoreum sylvestre Ger. em. 284. Raii Syn. 172. Cichorium Intybus
Sp. pl. 813. _Wild Succory._ On the borders of fields, flowering in
August and September. The flowers open about eight in the forenoon, and
keep expanded till about four in the afternoon.

47. Calendula arvensis C. B. pin. 275. Raii Hist. 338. Calendula
officinalis Sp. pl. 921. _Wild Marigold._ The flowers expand from nine
in the morning till three in the afternoon.

48. Calendula foliis dentatis Roy. Ludg. 177. Miller, p. 50. Tab. 75.
f. 1. Calendula pluvialis Sp. pl. 921. _Marigold with indented leaves._
The flowers expand from seven in the morning till three or four in the
afternoon. Linnæus observes of this plant, that if its flowers do not
expand about their usual time in the morning, it will almost assuredly
rain that day; with this restriction indeed, that the plant is not
affected by thunder showers. Phil. Bot. 275.

49. Sonchus pedunculis squamatis, foliis lanceolatis indivisis
sessilibus. Hort. Upsal. 244. Flor. Suec. 2. Nº. 690. Lactuca Salicis
folio, flore cæruleo. Amman. ruth. 211. Of this plant it is remarked,
that whenever the flowers are in the expanded state in the night-time,
the following day generally proves rainy.




LXVI. _An Account of the Case of a Boy troubled with convulsive Fits
cured by the Discharge of Worms. By the Rev._ Richard Oram, _M. A.
Chaplain to the Lord Bishop of_ Ely.

[Read Jan. 26, 1758.]

JOseph, son of John and Mary Postle, of Ingham in the county of
Norfolk, was subject to convulsive fits from his infancy; which were
common and tolerable till he was about seven years of age. About
that time they began to attack him in all the varieties that can be
conceived. Sometimes he was thrown upon the ground; sometimes he was
twirled round like a top by them; at others he would spring upwards
to a considerable height, _&c._ and once he leaped over an iron bar,
that was placed purposely before the fire to prevent his falling into
it. He was much burned; but was rendered so habitually stupid by his
fits, that he never expressed the least sense of pain after this
accident. His intellect was so much impaired, and almost destroyed,
by the frequency and violence of his fits, that he scarce seemed
to be conscious of any thing. He did not acknowlege his father or
mother by any expressions or signs; nor seemed to distinguish them
from other people. If at any time he escaped out of the house without
the observation of the family, he had not understanding to find and
return to it; but would pursue the direction or road he first took,
and sometimes lose himself. Once he was missing for a whole night; and
found the next morning in the middle of a fen, stuck fast in mud as
deep as his breast. He was very voracious, and would frequently call
for something to eat; which was the only indication he gave of his
knowing any thing. No kind of filth or nastiness can be conceived,
which he would not eat or drink without distinction. He appeared to be
as ill as he really was; for he was become a most shocking spectacle.
He was so much emaciated, that he seemed to have no flesh upon his
bones; and his body so distorted, that he was rendered quite a cripple.
His parents consulted a physician at Norwich, who very judiciously (as
it will appear) considered his disorder as a worm-case, and prescribed
for it accordingly; but (being afraid, I presume, to give too violent
medicines to the boy) without success. In short, he was so singularly
afflicted, that his parents told me they could not help thinking him
under some evil influence.

It was observed, that his disorder varied, and grew worse, at certain
periods of the moon.

In these miserable circumstances the poor boy continued to languish,
till he was about eleven years of age (July 1757), when he accidentally
found a mixture of white lead[18] and oil, which had some time before
been prepared for some purpose of painting, set by on a shelf, and
placed, as it was thought, out of his reach. There was near half a pint
of this mixture when he found it; and, as he did not leave much, it is
thought he swallowed about a quarter of a pint of it. There was also
some lamp-black in the composition; which was added to give it a proper
colour for the particular use it was intended for in painting. It was,
as I suppose it usually is, linseed oil, which had been mixed with the
lead and lamp-black.

The draught began to operate very soon, by vomiting and purging him for
near 24 hours in the most violent manner. A large quantity of black
inky matter was discharged; and an infinite number of worms, almost
as small as threads, were voided. These operations were so intense,
that his life was despaired of. But he has not only survived them, but
experienced a most wonderful change and improvement after them: for his
parents assured me in November 1757, when I saw him, that he had daily
grown better from the time of his drinking the mixture, both in body
and mind. Instead of a skeleton, as he almost was before, he is become
fat, and rather corpulent: and his appetite is no longer ravenous, but
moderate and common. His body too is become straight and erect. His
understanding is at least as much benefited by this peculiar remedy. It
cannot be expected, that he should already have attained much knowlege,
as he seemed, before he was so wonderfully relieved, to be almost
destitute of ideas. But he appeared, when I saw him, to have acquired
nearly as much knowlege in four months, as children usually do in four
years; and to reason pretty well on those things, which he knew. He is
now capable of being employed on many occasions; is often sent a mile
or two on errands, which he discharges as carefully, and then returns
as safely, as any person.

It is farther remarkable, that the boy’s mother, her father, and
sister, are frequently infested with worms. Her father, tho’ about 60
years of age, is still much troubled with them: the worms, which he
voids, appear flat, and much larger than those, which his children have
observed. Her sister is often exceedingly disordered by them. About
three months since they threw her into violent convulsions, and for
some time deprived her of her senses. But the mother of the boy has
been affected in a more extraordinary manner than the rest. About 20
years ago she voided some worms, which forced their way thro’ the pores
of the skin, as it is supposed; for they were found in small clusters
under her arms. As she was very young then, she does not remember
how she was particularly affected; only, that she suffered violent
struggles and convulsions. She is still, about five or six times in a
year, seized with fainting fits, which usually attack her in bed, and
last three or four minutes; but she cannot certainly say, tho’ there is
very little reason to doubt, that they are occasioned by worms.


_An Account of the same Subject, in a Letter from Mr._ John Gaze, _of_
Walket, _in the County of_ Norfolk, _to Mr._ Wm. Arderon, _F.R.S.
Communicated by Mr._ Henry Baker, _F.R.S._

[Read Jan. 26, 1758.]

JOseph Postle, son of John Postle, of Ingham in Norfolk, until about
the age of seven years was an healthy well-looking child; but about
that age was afflicted with stoppages, which often threw him into
convulsive fits, and at last rendered him quite an idiot. He continued
in this condition for about four years, eating and drinking all that
time any thing that came in his way, even his own excrements, if
not narrowly watched. His father took the advice of several eminent
physicians, both at Norwich and elsewhere; but all their prescriptions
proved of no service.

About the beginning of August last he happened to get at a
painting-pot, wherein there was about a pound of white lead and
lamp-black mixed up with linseed oil. This he eat almost all up
before he was discovered. It vomited and purged him, and brought away
prodigious numbers of small worms. In a few days he grew well, his
senses returned, and he is now able to give as rational answers as can
be expected from a boy of his age. His appetite is good, he is very
brisk, and has not had the least return of his former disorder.

I heard of the above by several people; but not being satisfied, got
my friend to go to Mr. Postle’s house, of whom he had the foregoing
account.

January 12th, 1758.




LXVII. _An Account of the extraordinary Heat of the Weather in_ July
1757, _and of the Effects of it. In a Letter from_ John Huxham, _M. D.
F.R.S. to_ Wm. Watson, _M. D. F.R.S._

[Read Feb. 2, 1758.]

I Find by your letter, that the heat at London was not so great in
the beginning of July 1757, as at Plymouth by two or three degrees of
Fahrenheit’s thermometer. We had again, after much rain at the close
of the month, and in the beginning of August, excessive heat; _viz._
on the 8th, 9th, and 10th of August; which mounted the mercury in that
thermometer to 85; nay, on the 9th, to near 86. I never before remember
the mercury in that thermometer to exceed 84; and that is even here a
very extraordinary degree of heat.

The consequences of this extremely hot season were hæmorrhages from
several parts of the body; the nose especially in men and children,
and the uterus in women. Sudden and violent pains of the head, and
vertigo, profuse sweats, great debility and oppression of the spirits,
affected many. There were putrid fevers in great abundance; and a vast
quantity of fluxes of the belly both bilious and bloody, with which the
fevers also were commonly attended. These fevers were always ushered
in by severe pains of the head, back, and stomach; vomitings of green
and sometimes of black bile, with vast oppression of the _præcordia_,
continual anxiety, and want of sleep. These were soon succeeded by
_tremores tendinum_, _subsultus_, delirium, or stupor. The pulse was
commonly very quick, but seldom tense or strong; was sometimes heavy
and undose. The blood oftentimes florid, but loose; sometimes livid,
very rarely sizy: in some however, at the very attack, it was pretty
dense and florid. The tongue was generally foul, brown, and sometimes
blackish; and towards the crisis often dry. The urine was commonly high
coloured, and in small quantity; frequently turbid, and towards the end
deposed a great deal of lateritious sediment. A vast number were seized
with this fever, during, and soon after, the excessive heats; tho’ but
few died in proportion. Long and great heats always very much exalt the
acrimony of the bilious humours; of which we had this summer abundant
instances.

Bleeding early was generally beneficial; profuse, always hurtful,
especially near the state of the fever.




LXVIII. _An Account of the fossile Thigh-bone of a large Animal, dug up
at_ Stonesfield, _near_ Woodstock, _in_ Oxfordshire. _In a Letter to
Mr._ Peter Collinson, _F.R.S. from Mr._ Joshua Platt.

[Read Feb. 2, 1758.]

Dear Sir,

ABOUT three years ago I sent you some _vertebræ_ of an enormous size,
which were found in the slate-stone pit at Stonesfield, near Woodstock,
in this county.

[Illustration: _Philos. Trans. Vol. L._ TAB. XIX. _p. 525_.

_J. Mynde sc._]

I have lately been so lucky as to procure from the same place the
thigh-bone of a large animal, which probably belonged to the same
creature, or one of the same genus, with the _vertebræ_ above-mentioned.

As the bone, and the stone, in which it is bedded, weigh no less than
two hundred pounds, I have sent you a drawing of it (_See_ TAB. XIX.);
from which, and the following short description, you may, I hope, form
some idea of this wonderful fossile.

The bone is 29 inches in length; its diameter, at the extremity of
the two trochanters, is 8 inches; at the lower extremity the condyles
form a surface of 6 inches. The lesser trochanter is so well expressed
in the drawing, that you cannot mistake it; and both the extremities
appear to be a little rubbed by the fluctuating water, in which I
apprehend it lay some time before the great jumble obtained, which
brought it to this place; and from whence I imagine it to have been
part of a skeleton before the flood. For if it had been corroded by any
menstruum in the earth, or during the great conflux of water before the
draining of the earth, it must have suffered in other parts as well as
at each end: but as the extremities only are injured, we can attribute
such a partial effect to the motion of the water only, which caused it
to rub and strike against the sand, _&c._

The small trochanter was broken in lifting it out of the hamper, in
which it was brought to me; but not unhappily; since all the _cancelli_
were by that means discovered to be filled with a sparry matter, that
fixed the stone of the stratum, in which it lay. The outward coat or
cortex is smooth, and of a dusky brown colour, resembling that of the
stone, in which it is bedded.

One half of the bone is buried in the stone; yet enough of it is
exposed to shew, that it is the thigh-bone of an animal of greater bulk
than the largest ox. I have compared it with the recent thigh-bone of
an elephant; but could observe little or no resemblance between them.
If I may be allowed to assume the liberty, in which fossilists are
often indulged, and to hazard a vague conjecture of my own, I would say
it may probably have belonged to the hippopotamus, to the rhinoceros,
or some such large animal, of whose anatomy we have not yet a competent
knowlege.

The slate-pit, in which this bone was found, is about a quarter of
a mile north-west from Stonesfield, upon the declivity of a rising
ground, the upper stratum of which is a vegetable mould about eight
or ten inches thick: under this is a bed of rubble, with a mixture of
sand and clay, very coarse, about six feet deep, in which are a great
number of _anomiæ_ both plain and striated, and many small oblong
oysters, which the workmen call the sickle-oyster, some of them being
found crooked, and bearing some resemblance to that instrument; but all
differing from the _curvi-rostra_[19] of Moreton.

Immediately under this stratum of rubble is a bed of soft grey stone,
of no use; but containing the _echini ovarii_, with great _mamillæ_,
the _clypeati_ of different sizes, all well preserved; and also many
_anomiæ_ and _pectines_. This bed, which is about seven or eight feet
in depth, lies immediately above the stratum of stone, in which the
bone was found.

This stratum is never wrought by the workmen, being arenarious, and too
soft for their use. It is about four or five feet thick, and forms a
kind of roof to them, as they dig out the stone, of which the slates
are formed; for they work these pits in the same manner as they do the
coal-pits, leaving pillars at proper distances to keep their roof from
falling in.

This last bed of slate-stone is about five feet depth, and lower than
this they never dig. So that the whole depth of the pit amounts to
about 24 or 25 feet.

It was by working out the slate-stone, that this bone was discovered
sticking to the roof of the pit, where the men were pursuing their
work; and with a great deal of caution, and no less pains, they got it
down intire, but attached to a large piece of stone; and in this state
it now remains in my possession.

There is no water in the works, but such as descends from the surface
thro’ perpendicular fissures; and the whole is spent in forming the
stalactites and stalagmites, of which there is great variety, and whose
dimensions are constantly increasing. One of the workmen has been so
curious, as to mark the time of the growth of some of them for several
years past.

I am, with the greatest esteem,

                               Dear Sir,
                          Your ever obedient,
                       and most humble Servant,
                             Joshua Platt.

Oxon, Jan. 20. 1758.




LXIX. _A Discourse on the Usefulness of Inoculation of the horned
Cattle to prevent the contagious Distemper among them. In a Letter to
the Right Hon._ George _Earl of_ Macclesfield, _P. R. S. from_ Daniel
Peter Layard, _M. D. F.R.S._

[Read Feb. 2, 1758.]

My Lord,

THE honour you have done me, in condescending to peruse my Essay on the
contagious Distemper among the horned Cattle, claims my most respectful
thanks; and I am no less obliged to your Lordship for the just remark
you made, “That before inoculation could be practised on the horned
Cattle, it is necessary to bring proofs, that this disease is not
susceptible more than once; and also assurances, that a recovery from
the distemper by inoculation guards the beast from a second infection.”

An intire conviction of the analogy between this disease and the
small-pox would not permit me to omit mentioning the great advantages,
which must arise from inoculation; and therefore, my Lord, I recommend
its use: nor do I find any reason to alter my opinion, after having
carefully read over what has been published, and made the strictest
inquiry I was able in several parts of Great Britain.

I shall, in the concisest manner possible, submit the following
particulars to your Lordship’s consideration, and the learned Society,
over which you so deservedly preside.

The Marquis de Courtivron, in two memoirs read before the Royal
Academy of Sciences in the year 1748, and published by that learned
body, relates the observations he, together with Monsieur Pelversier
de Gombeau, formerly surgeon to the regiment de la Sarre, made on
the rise, progress, and fatality, of the contagious distemper at
Issurtille, a town in Burgundy; to which are added experiments they
made, by application, digestion, and inoculation, towards communicating
the disease; and concludes from the failure of these attempts, that the
distemper can only be communicated from one beast to another. Besides,
notwithstanding the Marquis observes[20] the regularity of the illness,
the critical days, on the seventh and ninth, and particularly that all
such as recovered had more or fewer pustules broke out in different
parts of the body; yet[21] he will not allow of Rammazzini’s opinion,
of the analogy between this distemper and the small-pox, nor that it is
an eruptive fever; but ranks it as a plague.

But the Marquis goes still farther. He positively say,[22] “That in
the preceding years, in the provinces of Bresse, Maconnois, and Bugey,
some private persons had suffered by buying cattle recovered from the
distemper, which had, at that time, the pustules remaining on them:
which cattle had the distemper afterwards.” Nay, he adds that “even
after recovering twice, a third infection has seized and killed many.”

No wonder, my Lord, that such positive assertions should stagger, and
cause the practice of inoculation not to be received, till the nature
of the disease be absolutely determined, and facts prove the contrary
of what has been asserted.

In a matter of so great importance to every nation, it were to
be wished, that the Marquis de Courtivron had produced attested
observations of these second and third infections: for tho’ a nobleman
of his rank, character, and great abilities, would not willingly impose
upon the world; yet it may happen, that he may have received wrong
informations.

As to the nature, rise, progress, and fatality, of this distemper
at Issurtille, it appears to be the same disease as raged in these
kingdoms. All the symptoms agree, as described by Rammazzini, Lancisi,
the Marquis, and in my Essay. A distempered beast gave rise to the
three infections. The illness was every-where the same in Italy,
France, and Britain; and either terminated _fatally_ on the fourth or
fifth day, when a scouring prevented the salutary eruptions, or in
some cases by abortion; and on the seventh or ninth _favourably_, when
the pustules had regularly taken their course. Tho’ the Marquis did
not observe, that any particular medicines were of use, he says, that
in general acids were beneficial, especially poor thin wines somewhat
sour; and that the distempered beasts were all fond of these acids[23].

The fatality was likewise the same, as will appear from the Marquis’s
tables. Of 192 head of cattle, 176 died. The mortality was chiefly
among the fat cattle, cows with calf, and young sucking or yearling
calves; and of the surviving sixteen, only two calves out of
seventy-seven lived, and these two, with seven other beasts of the
sixteen, escaped the infection, tho’ constantly among the diseased: so
that it is plain,

  Of 192 beasts, 176 died
                   7 recovered
                   9 escaped the infection.
                 ---
                 192

The mortality was as considerable in these kingdoms.

Whoever will compare the appearances, progress, and fatality, of the
small-pox, with what is remarked by authors of authority, as Rammazzini
and Lancisi, and other observers, relative to the contagious distemper
among the horned cattle, will not be at a loss one moment to determine,
whether this disease be an eruptive fever, like unto the small-pox, or
not.

Now if, as the Marquis has granted in both his memoirs[24], it be a
general observation, that an eruption of pustules on some parts of the
body, regularly thrown out, digested, and dried, is the means used by
nature to effect the cure; and that in general the morbid matter does
not affect the parotid, inguinal, or other glands, nor produce large
carbuncles and abscesses, as the plague does: Nay more, since it is
observed by the Marquis, that the difference between the contagious
distemper of 1745 and 1746, and of 1747 and 1748, was, that in the
former the salutary eruptions appeared, but in the latter were, as he
justly apprehends, checked by the excessive cold weather; and should
it appear, that by inoculation the same regular eruptive fever has
been produced, with every stage, and the same symptoms as arise in the
small-pox; the nature of this distemper will then be ascertained.

I shall now proceed, my Lord, to lay before your Lordship and the
Society the accounts I have received relating to the infection
and inoculation of the cattle, and make some observations on the
experiments made at Issurtille.

So long, my Lord, as the distemper has raged in Great Britain, not
one attested proof has been brought of any beast having this disease
regularly more than once. I make no doubt but these creatures may be
liable to eruptions of different kinds; but as all sorts of eruptions,
says Dr. Mead[25], are not the small-pox, nor measles, so every pustule
is not a sign of the plague. Thro’ ignorance, or fraud, persons may
have been deceived in purchasing cattle, and have lost them, as well
in England as in the provinces of France mentioned by the Marquis; but
until a second infection be proved, the general opinion must prevail in
this case, as in the small-pox: for tho’ many have insisted on the same
thing with regard to the small-pox, yet a single instance, properly
vouched and attested, has never been produced, either after recovery
from the natural way, or from inoculation; unless what is frequently
the case with nurses and others attending the small-pox, that is,
pustules breaking out in their arms and face, be allowed as the signs
of a second infection.

The farmers and graziers in Huntingdonshire, Cambridgeshire,
Lincolnshire, Kent, and Yorkshire, from whence I have written
testimonies, all agree, that they never knew of a beast having the
contagious distemper more than once. In this county particularly, Mr.
J. Mehew, the farmer mentioned in my Essay, has now among his stock
at Godmanchester _eight cows_, which had the contagious distemper the
first time it appeared in Godmanchester in 1746. It returned in 1749,
1755, and 1756; the two last not so generally over the town as the two
former years. All these four times Mr. Mehew suffered by the loss of
his cattle; yet those _eight cows_, which recovered in 1746, remained
all the while the distemper was in the farm the three years it raged,
were in the midst of the sick cattle, lay with them in the same barns,
eat of the same fodder, nay of such as the distempered beasts had left
and slabbered upon, drank after them, and constantly received their
breath and steams, without ever being in the least affected. Is not
this a convincing proof? If in general the cattle be susceptible of a
second infection, how comes it, that not one of these _eight_ cows were
affected?

In the years abovementioned the distemper spared no beast, but such as
had recovered from that disease: and this is confirmed to me by Mr.
Mehew’s father and brother, all the chief farmers of Godmanchester, and
is the opinion of all the farmers and graziers in Huntingdonshire, who
are so thoroughly convinced of there being no second infection, that
they are always ready to give an advanced price for such cattle as have
recovered from the contagious distemper.

The Rev. Mr. Scaife, assistant to the Rev. Dr. Greene, Dean of
Salisbury, in his parish of Cottenham, Cambridgeshire, acquaints me,
that the farmers in that neighbourhood lost, in 1746 and 1747, twelve
hundred head of cattle, in 1751 four hundred and seventy; and tells me,
that Mr. Ivett, Sayers, Moor, Dent, Lawson, chief farmers at Cottenham,
Mr. Taylor, Sumpter, and Matthews, of his own parish of Histon, and
the farmers of Wivelingham alias Willingham, unanimously declare, they
never had one instance of a beast having the distemper twice.

Mr. Thorpe, a farmer and grazier near Gainsborough in Lincolnshire, has
had beasts recovered from the distemper, which have herded with cattle
fallen ill afterwards, and never met with a single instance of a second
infection.

Mr. Lostie, an eminent surgeon at Canterbury, has inquired for me of
the farmers and graziers in that part of Kent, and about Romney-Marsh;
and from whence no belief of a second infection can be had.

The Rev. Dr. Fountayne, Dean of York, writes me word, that no beast has
been known, in his neighbourhood, to have had the distemper twice. And
several persons from that county, and others, have told me the same
thing.

If the above testimony of persons of character and veracity, together
with the concurrent persuasion of farmers in general, be allowed of, it
must be determined, that there is no instance of a second infection.
Supposing now it should appear, that this distemper is regularly, as
in the natural way, tho’ in a milder manner, produced by inoculation,
and that inoculation secures a beast also from a second infection; then
undoubtedly inoculation will be recommendable.

The very few trials made in England, and those not with the greatest
exactness or propriety, will yet serve to put this matter out of all
doubt.

The Rev. Dean of York had five beasts inoculated, by means of a skein
of cotton dipped in the matter, and passed thro’ a hole, like a seaton,
in the dew-lap. Of these five, one cow near the time of calving died:
the other four, after going thro’ the several stages of this contagious
disease, recovered; two of which, being cows young with calf, did not
slip their calves. All four have herded with distempered cattle a long
while, and never had the least symptom of a second infection.

Mr. Bewley, a surgeon of reputation in Lincolnshire, inoculated three
beasts two years old, for Mr. Wigglesworth of Manton, in the dew-lap,
and with _mucus_ from the nostrils. All three had the regular symptoms
of the contagious distemper in a mild manner, recovered, and tho’ they
herded a twelvemonth after with five or six distempered beasts, they
never were the least affected. Mr. Bewley also declared to Mr. Thorpe,
that there never was one instance produced, that he knew of, of a
second infection.

Since it is plain, that notwithstanding neither well-digested _pus_ was
made use of, nor incisions made in the properest places, and it may be
supposed few medicines were given; yet inoculation succeeded so as to
bring on the distemper in a regular and mild manner, as appears by the
cows with calf not slipping their calves. One may fairly conclude, that
in this contagious distemper, like unto the small-pox, the practice of
inoculation is not only warrantable, but much to be recommended.

But how comes it then, that neither by application, digestion, nor
inoculation, the distemper was not communicated in France?

The Marquis says, that this distemper is not communicated but from
one beast to another immediately. I must beg leave to say, that to my
knowlege the distemper in February 1756 was carried from the farm-yard,
where I visited some distempered cattle, to two other farm-yards, each
at a considerable distance, without any communication of the cattle
with each other, and merely by the means of servants going to and fro,
or of dogs.

The experiments made on four beasts, by tying over their heads part of
distempered hides, or pieces of linen and woollen cloth or silk, which
had received the breath and steams of dying cattle, serve to shew, by
the bullock’s forcing off the cloth tied about him, that the putrid
stench was disagreeable to him; but that neither his blood, nor that of
the other three beasts, was then in a state to receive the infection.

With regard to the pustules, which the Marquis relates were mixed
with oats and bran, or dissolved in white wine; the distempered bile,
which was mixed with milk; milk taken from diseased cows; water, in
which part of a distempered hide had been steeped; and the precaution
taken to force these mixtures into the paunch of calves, by means of
a funnel, whose end was covered with a piece of raw distempered skin,
that the beast might both swallow and suck in the disease. All these
experiments could have no other effect than what followed; which was,
that the acrimony of the distempered bile created first a _nausea_, and
then produced a violent scouring, which killed the beast, leaving marks
of its irritation on the intestines.

The practice of inoculation is but lately followed, and even now but
little known, in the provinces of France. Its advantages have not long
since been strangely disputed at Paris. In the case of inoculating
cattle, instead of a slip of raw hide taken from a beast just dead, or
putting a pustule into the neck, they should either have passed in the
dewlap cotton or silk dipped in well-digested _pus_, or have inserted
in proper incisions cotton-thread or silk soaked with _pus_ either on
the shoulders or buttocks; the true way of inoculating in the English
manner. Some persons have indeed thought, that to inoculate with the
blood of the infected would answer the intention; but most of the
modern practitioners chuse to depend on digested matter.

Several constitutions will not receive infection, let them be
inoculated ever so judiciously. A Ranby, a Hawkins, a Middleton, and
other inoculators, will tell us, that the incisions have sometimes
suppurated so much, and pustules have appeared round the edges of the
wound, without any other particular marks of the disease; and yet the
patient has never had the small-pox afterwards. The Marquis mentions an
instance somewhat of the same kind in his first Memoir, p. 147.

The examination of these very important and interesting particulars
has, I observe, drawn me into a prolixity, which I fear may prove
tedious to your Lordship: but should I have removed all doubts,
and brought convincing proofs of the absurdity of fearing a second
infection; should I have shewn inoculation to be a necessary practice,
and that the contagious distemper may be communicated more ways than
one; I hope your Lordship will excuse the length of this letter.
I shall only add my earnest wishes, that the legislature may, by
effectual means, prevent the importation of distempered cattle
and hides into these kingdoms; the only means of naturalizing and
perpetuating a dreadful distemper, now, thank God! much decreased among
us.

I am, with the greatest respect,

                               My Lord,
                            Your Lordship’s
                Most humble and most obedient Servant,
                         Daniel Peter Layard.

Huntingdon, 26 Nov. 1757.




LXX. _Trigonometry abridged. By the Rev._ Patrick Murdoch, _A. M.
F.R.S._

[Read Feb. 2, 1758.]

THE cases in trigonometry, that can properly be called different from
one another are no more than _four_; which may be resolved by _three_
general rules or theorems, expressed in the sines of arcs only; using
the supplemental triangle as there is occasion.

[Illustration: _Philos. Trans. Vol. L._ TAB. XX. _p. 539_.

_J. Mynde sc._]

CASE I.

_When of three given parts two stand opposite to each other, and the
third stands opposite to the part required._


THEOREM I.

_The sines of the sides are proportional to the sines of angles
opposite to them._


DEMONSTRATION.

Let QR (TAB. XX. _Fig._ 1.) be the base of a spherical triangle; its
sides PQ, PR, whose planes cut that of the base in the diameters QC_q_,
RC_r_. And if, from the angle P, the line PL is perpendicular to the
plane of the base, meeting it in L, all planes drawn through PL will
be perpendicular to the same, by 18. _el._ 11. Let two such planes be
perpendicular likewise to the semicircles of the sides, cutting them in
the straight lines PG, PH; and the plane of the base in the lines LG,
LH.

Then the plane of the triangle PGL being perpendicular to the two
planes, whose intersection is QGC_q_, the angles PGQ LGQ will be right
angles, by 19. _el._ 11. PG likewise subtends a right angle PLG, and
the angle PGL measures the inclination of the semicircle QP_q_ to the
plane of the base (_def._ 6. _el._ 11.) that is (by 16 _el._ 3. and 10
_el._ 11.) it is equal to the spherical angle PQR: whence PG is to PL
as the radius to the sine of PQR. The same way PL is to PH as the sine
of PRQ is to the radius: and therefore, _ex æquo_. PG the sine of the
side PQ is to PH the sine of PR, as the sine of PRQ is to the sine of
PQR.


CASES II. _and_ III.

_When the three parts are of the same name._

And,

_When two given parts include between them a given part of a different
name, the part required standing opposite to this middle part._


THEOREM II.

_Let_ S _and_ s _be the sines of two sides of a spherical triangle_,
d _the sine of half the difference of the same sides_, a _the sine of
half the included angle_, b _the sine of half the base; and writing
unity for the radius, we have_ Ssa² + d² - b² = 0; _in which_ a _or_ b
_may be made the unknown quantity, as the case requires_.


DEMONSTRATION.

Let PQR (_Fig._ 2.) be a spherical triangle, whose sides are PQ PR,
the angle included QPR, the base QR, PC the semiaxis of the sphere, in
which the planes of the sides intersect.

To the pole P, draw the great circle AB, cutting the sides (produced,
if needful) in M and N; and thro’ Q and R, the lesser circles Q_q_,
_r_R, cutting off the arcs Q_r_ _q_R equal to the difference of the
sides; join MN, Q_q_, _r_R, QR, _qr_.

Then the planes of the circles described being parallel (_Theod.
sphæric._ 2. 2.), and the axis PC perpendicular to them (_10. 1. of
the same_), their intersections with the planes of the sides, as QT,
and R_t_, will make right angles with PC; that is, QT and R_t_ are the
sines (S, _s_.) of the sides PQ PR, and MC NC are whole sines. Now the
isosceles triangles MCN, QT_q_, _rt_R, being manifestly similar; as
also MN, the subtense of the arc which measures the angle QPR, being
equal to (2_a_) twice the sine of half that angle; we shall have MN:
MC∷ Q_q_: QT∷ _r_R: R_t_; or, in the notation of the theorem, Q_q_ =
2S_a_, _r_R = 2_sa_. And further, the chords Q_r_ _q_R being equal, and
equally distant from the center of the sphere, as also equally inclined
to the axis PC, will, if produced, meet the axis produced, in one point
Z. Whence the points Q, _q_, R, _r_, are in one plane (2. _el._ 11.),
and in the circumference in which that plane cuts the surface of the
sphere: the quadrilateral Q_q_R_r_ is also a segment of the isosceles
triangle ZQ_q_, cut off by a line parallel to its base, making the
diagonals QR, _qr_, equal. And therefore, by a known property of the
circle, Q_q_ × _r_R + (_q_R)² = (QR)²; which, substituting for Q_q_ and
R_r_ the values found above, 2_d_ for Q_r_, 2_b_ for QR, and taking the
fourth part of the whole, becomes S_sa_² + _d_² = _b_² the proposition
that was to be demonstrated.

  _Note_ 1. If this, or the preceding, is applied to a plane triangle,
  the sines of the sides become the sides themselves; the triangle
  being conceived to lie in the surface of a sphere greater than any
  that can be assigned.

   _Note_ 2. If the two sides are equal, _d_ vanishing, the operation
  is shorter: as it likewise is when one or both sides are quadrants.

  _Note_ 3. By comparing this proposition with that of the Lord
  Neper[26], which makes the 39th of Keill’s Trigonometry, it appears,
  that if AC, AM, are two arcs, then sin. (AC + AM) ⁄ 2 × sin. (AC -
  AM) ⁄ 2 = ((_b_ + _d_) × (_b_ - _d_) =) (sin. ½ AC + sin. ½ AM) ×
  (sin. ½ AC - sin. ½ AM). And in the solution of Case II. the first of
  these products will be the most readily computed.


CASE IV.

_When the part required stands opposite to a part, which is likewise
unknown_: Having from the _data_ of Case I. found a fourth part, let
the sines of the given sides be S, _s_; those of the given angles Σ,
σ; and the sines of half the unknown parts _a_ and _b_; and we shall
have, as before, S_sa_² + _d_² - _b_² = 0; and if the equation of the
supplements be (Σσα² + δ²) - β² = 0; then, because α² = 1 - _b_² = 1 -
(S_sa_² + _d_²), and β² = 1 - _a_², substituting these values in the
second equation, we get

THEOREM III.

(1 - Σσ × (1 - _d_²) - δ²) ⁄ (1 - S_s_Σσ) = _a_²; in words thus:

_Multiply the product of the sines of the two known angles by the
square of the cosine of half the difference of the sides: add the
square of the sine of half the difference of the angles; and divide the
complement of this sum to unity, by the like complement of the product
of the four sines of the sides and angles; and the square root of the
quotient shall be the sine of half the unknown angle._

If we work by logarithms, the operation will not be very
troublesome; but the rule needs not be used, unless when a table
of the trigonometrical analogies is wanting. To supply which, the
foregoing theorems will be found sufficient, and of ready use; being
either committed to memory, or noted down on the blank leaf of the
trigonometrical tables.

  _Note_, The schemes may be better, raised in card-paper, or with bent
  wires and threads.




LXXI. _An Account of Two extraordinary Cases of Gall-Stones._ By James
Johnstone, _M. D. of_ Kidderminster. _Communicated by the Rev._ Charles
Lyttelton, _L. L. D. Dean of_ Exeter.

                         _To the Rev. Dr._ Lyttelton, _Dean of_ Exeter.
[Read Feb. 9, 1758.]

Rev. Sir,

ACcording to promise I send you a short account of the two
extraordinary cases we talked of, the last time I had the pleasure of
seeing you at Kidderminster.

The truth of the first narrated case you are already a sufficient judge
of; and if it is at all necessary to ascertain the second in like
manner, I can at any time produce the poor woman and her husband before
you, who will attest the truth of sufferings, which will not easily
escape their memory.

You are at liberty to dispose of this paper as you shall think proper.
I am,

                             Reverend Sir,
               Your respectful and most humble Servant,
                             J. Johnstone.

Kidderminster, Sept. 11. 1757.


THO’ it is now pretty well known, that colicky and icteric diseases
often arise from gall-stones generated in the bilious receptacle, and
obstructing its canals; yet an example of one, of such enormous size,
voided into the _duodenum_ from the _ductus communis_, as happened in
the first of the following cases, is a very rare, if not intirely an
unexampled occurrence. It will encourage us not too easily to despair
of the expulsion of the largest _calculi_ from the gall-bladder; and
will teach us, that all violent attacks of pain about the stomach
are not owing to gout reflected upon that organ: it will make us
more cautious of giving drastic cathartics, heating and inflaming
medicines, upon such a vague presumption; and ought to dispose those,
who are trusted with the lives of their fellow-creatures, to a nicer
observation of even the minutest symptoms and circumstances, which may
occur in diseases.

The second case points out, under certain circumstances, the
practibility of extracting, by incision into the gall-bladder itself,
those _calculi_, which, from their figure, or other impediments, cannot
be voided in the natural way. The method of performing this unusual
operation, and some instances of its success, have already been made
public in the Memoires de l’Acad. de Chirurg.


1. Mrs. F----, a sedentary corpulent old lady, had been much subject
to colicky complaints, without jaundice, in the vigour of life. The
seat of the pain was chiefly under the right _hypochondrium_, as high
as the stomach. She had been tolerably free from it for at least eight
years past. December 5, 1753, about eleven o’clock in the evening, she
was suddenly seized with a violent pain, extending from that part of
the stomach lying under the right side, thro’ to her back. She compared
it to a sword driven in that direction. This pain continued not only
with unremitted violence, but even increased, till seven o’clock in the
morning: all this time she vomited and strained almost incessantly;
but after her stomach was emptied of its contents, nothing came up
besides clear slime, streaked with blood. About seven o’clock in the
morning she felt her pain fall or move lower, as she expressed it,
and from that time became remarkably easier. Soon after this change,
she became extremely sick, and vomited up, for the first time, a
prodigious quantity of greenish yellow bile. She had not before this
seizure been remarkably costive; and in her pain had a free motion
to stool with effect; but during the remainder of the (6th) day had
none, tho’ all this time emollient clysters were injected; and she
took regularly every two hours a powder of _magnes. alb. terr. fol.
tartar. tart. vitriol. ana_ ℈j. _ol. nuc. mosch. gutt._ j. with a
draught of the _succ. limon. & sal. absinth_. But in the middle of the
night, and all day (the 7th), she had an abundant discharge of loose
bilious stools. She had continued free from excessive pain since the
morning of the former day, only now and then complained of uneasiness
sometimes in one, sometimes in another, part of her bowels. About
twenty-four hours after her first seizure, she felt a great pain
striking towards the bottom of her back, and one hour after voided
the extraordinary _calculus_, of which the figure and description are
subjoined. Some time after pieces of skins were voided by stool, which
were evidently of the texture and appearance of the internal villous
coat of the intestines and gall-bladder. The above medicines were the
only ones she used, by my direction, under her painful complaint,
excepting an external fomentation, and bleeding, which the hardness and
contractedness of her pulse seemed to require. She was ordered to drink
plentifully of thin broths, and other soft diluent liquors. During the
course of her disorder she had no appearance of jaundice, nor since;
and, considering her years, enjoys at present (Sept. 1757) very good
health.

This _calculus_, as appears by the figure, was of a pyriform shape,
resembling the form of the _cystis fellea_ itself. Its surface was
quite smooth and polished, excepting towards the base, at that part
marked A, where it was scabrous, as if some other substance had lain
contiguous to it. When broken through, it was composed of concentrical
laminæ, which were alternately white and ochre-coloured. In length it
measured one inch and three tenths; its transverse section measured at
least seven tenths of an inch. It had a saponaceous smoothness, like
other gall-stones, and floated upon water. It weighed only about 126
grains.

Tho’ it be difficult to conceive, how so bulky a substance, generated
in the gall-bladder, could be conveyed along so narrow a passage as
the common biliary duct, especially considering the obliquity of its
insertion for near half an inch of length betwixt the coats of the
_duodenum_; yet there seem sufficient _data_ in the above case to
prove, that this animal stone was not formed in the alimentary tube,
but (large as it was) had come into it from the _ductus communis
choledochus_.

The shape and saponaceous smoothness, and colour of the laminæ, of this
substance, shew it was moulded in the gall-bladder, and formed from
bilious particles. The severe pain and torture, and enormous vomiting,
she underwent, for seven hours after her first seizure, argue, that it
must then be lodged in some canal much narrower and straighter than the
alimentary canal; for so soon as it dropped into that, the severe pain
in a great measure ceased.

But that straight canal, in which it was situated during those
seven hours of torture, could be no other than the _ductus communis
choledochus_; for, during this space of time, no bile was emptied
into the bowels, nor thrown up by the strongest efforts of vomiting.
But no sooner had she perceived the cause of her pain to move or drop
downwards (a sensation, which points out the precise moment the stone
must have dropped into the _duodenum_), than she began to sicken,
and instantly after vomited up a vast quantity of bilious matter;
which now, from the de-obstructed duct, began to flow freely into
the _duodenum_. The obstruction of the _ductus choledochus_ was of
too short a duration (only three hours) to occasion any observable
jaundice. And it appears by the bloody flesh-like knots, thrown up
with phlegm by vomiting, that the passage of the substance was not
effected without considerable laceration of the small bilious ducts.
And this easily accounts for the separation of the villous coat, which
afterwards appeared in this patient’s stools.

[Illustration: This coarse delineation represents the figure and true
bulk of the _calculus_; which, I believe, is still in my patient’s
custody.]

2. In February 1752. I was called to relieve a poor woman of this
place, Sarah Ewdall, aged 30 years and upwards, and the mother of
several children. She laboured under the jaundice, and complained of
a severe acute pain striking thro’ from the right _hypochondrium_
to her back, with frequent vomitings. A præternatural hardness, of
a compass not exceeding the hollow of the hand, was then plainly to
be felt at the pit of the stomach, or a little nearer to the right
_hypochondrium_. When that particular part was pressed, she complained
of great pain. The pain at this part was always increased by attempting
to lie upon the left side. She was blooded, fomented externally,
had emollient saponaceous clysters injected, and a nitrous apozem,
and pills composed of _galban. & sap. Castillens._ and soon after
recovered. She had frequent returns of the same complaint after this;
but I saw her not again till Jan. 1755, when she lay insensible in a
fit, which for several days deprived her of the use of her speech and
of all her senses, only she tossed her limbs about. About a quarter of
a year after she had recovered from this fit, Mr. Cooper of this place,
her apothecary, informed me, that from a small sore at the pit of her
stomach, which came since her last illness, she had voided several
gall-stones. Curiosity prompted me to inquire into the matter of fact
from herself. She shewed me the sore, which was now almost cicatrized.
She said, that soon after her last illness a little pimple arose upon
that part of the pit of the stomach, which had been hard ever since she
had been subject to the jaundice. This pimple broke, ran matter, and at
different times the _calculi_, which she shewed me, had come out with
the matter. Her stomach had been somewhat painful before it broke, but
was now easy. The _calculi_, which she shewed me, had the appearance
of being fragments of larger ones, and some were almost dust; tho’ she
assured me they all came from the sore in that condition. Of these
fragments I have two or three of the largest now in my custody: they
are light, swim on water, smooth like soap; are of a yellow colour, and
in some parts brown like snuff; and consist of similar concentrical
layers. The poor woman has since then been troubled with returns of
pain and jaundice, in the intervals of which her skin is perfectly
clear and white. She is still alive, and ready to attest the truth of
this narrative.

                                                          J. Johnstone.

Kidderminster, Sept. 11th, 1757.



LXXII. _A remarkable Case of Cohesions of all the Intestines_, &c.
_in a Man of about Thirty-four Years of Age, who died some time last
Summer, and afterwards fell under the Inspection of Mr._ Nicholas Jenty.

[Read Feb. 9, 1758.]

THE subject was tall, and partly emaciated. I found nothing externally
but a wound in the left side, which seemed to me to have been
degenerated into an ulcer. As I did not know the man when he was alive,
and had him two days after his decease, I cannot give an immediate
account of the cause of his death. But in opening his abdomen, I found
the epiploon adhering close to the intestines, in such a manner, that I
could not part it without tearing it. It felt rough and dry. And as I
was going to remove the intestines, to examine the mesentery, I found
them so coherent one with the other, that it was impossible for me to
divide them without laceration. Then I inflated the intestinal tube,
for the inspection of this extraordinary phænomenon; but, to my great
surprize, all the external parts of the intestines appeared smooth;
very few of the circumvolutions were seen, occasioned by the strong
lateral cohesions of their sides with each other. The substance of the
intestines was rough, and a great many pimples, as big as the head of
a pin, appeared in them, and were almost free from any moisture. It is
proper to observe, that these pimples have been taken for glands by the
late Dr. James Douglas, and others; whereas they are in reality nothing
else but the orifices of the exhaling vessels obstructed, and are not
to be met with except in morbid cases.

After having made incisions in that part of the _colon_ next to
the _rectum_, I found the _peritonæum_, or external membrane which
invests the intestines, and the _viscera_ of the _abdomen_, to be of
the thickness of a six-pence; and I fairly drew all the intestines
from their external membrane without separating their cohesions;
the _peritonæum_, or external membrane, afterwards appearing like
another set of intestines. I found a fluid in the intestines; and I
will not take upon me to say, how the peristaltic motion must have
been performed. And afterwards I parted the stomach from its external
tunic, as I had done the intestines. I found no obstruction in the
mesenteric glands; but every evolution of the mesentery firmly cohered
together. The liver also adhered closely to the diaphragm, and its
adjacent parts: and in the _vesicula fellis_ I found the bile pretty
thick, neither too green nor too yellow, but a tint between both. I
met with nothing remarkable in the other parts of the _abdomen_. In
opening the _thorax_, I found the lungs closely adhering to the ribs
laterally, and posteriorly and interiorly close to the _pericardium_.
In making an incision to open the _pericardium_, I found it so closely
adhering to the heart, that I could not avoid wounding that organ, and
with much difficulty could part it from it. I met with no fluid in the
_pericardium_. The heart was small; and in the internal side the pores
of the _pericardium_ appeared so large, that one might have insinuated
the head of a middling pin into them. They have been described by some
anatomists, who have met with cases somewhat similar to this, but
without such universal adhesions; and they have been supposed to have
been glands. The same pores likewise appeared on the heart; which, in
my opinion, are nothing but the extremities of the exhaling vessels. In
removing the heart, I found the _dorsal_, and other lymphatic glands
above the lungs, quite large, indurated, and of a dark greyish colour.
Nothing remarkable appeared in the lungs; only, that the portion of
the _pleura_, which invests the lungs, and is generally thin, was here
thick and rough; and thro’ a glass it appeared as if covered with
grains of sand; and might in several places have been easily torn from
the lungs.

The _aorta_ was pretty large; and in that part of it, which runs on the
tenth _dorsal vertebra_, I found a _cystis_, as big as an olive, full
of _pus_; and lower down, immediately before that vessel perforates the
diaphragm, I found another, something less, full of matter likewise;
both which portions I have by me. That portion of the _aorta_, where
the _cystis_ appeared, was rather thicker than the other, and osseous.
In opening the _cranium_, I found in that part of the _cerebrum_, which
lies over the _cerebellum_, a table spoonfull of _pus_, of a greenish
colour; and examining it thro’ a glass, there was an appearance of
_animalcula_ in it.




LXXIII. _Of the best Form of Geographical Maps. By the Rev._ Patrick
Murdoch, _M. A. F.R.S._

[Read Feb. 9, 1758.]

I. WHEN any portion of the earth’s surface is projected on a plane,
or transferred to it by whatever method of description, the real
dimensions, and very often the figure and position of countries, are
much altered and misrepresented. In the common projection of the
two hemispheres, the meridians and parallels of latitude do indeed
intersect at right angles, as on the globe; but the linear distances
are every-where diminished, excepting only at the extremity of the
projection: at the center they are but half their just quantity, and
thence the superficial dimensions but one-fourth part: and in less
general maps this inconvenience will always, in some degree, attend the
_stereographic_ projection.

The _orthographic_, by parallel lines, would be still less exact,
those lines falling altogether oblique on the extreme parts of the
hemisphere. It is useful, however, in describing the circum-polar
regions: and the rules of both projections, for their elegance, as well
as for their uses in astronomy, ought to be retained, and carefully
studied. As to Wright’s, or Mercator’s, nautical chart, it does not
here fall under our consideration: it is perfect in its kind; and will
always be reckoned among the chief inventions of the last age. If it
has been misunderstood, or misapplied, by geographers, they only are to
blame.


II. The particular methods of description proposed or used by
geographers are so various, that we might, on that very account,
suspect them to be faulty; but in most of their works we actually
find these two blemishes, _the linear distances visibly false_, and
_the intersections of the circles oblique_: so that a quadrilateral
rectangular space shall often be represented by an oblique-angled
rhomboid figure, whose diagonals are very far from equal; and yet,
by a strange contradiction, you shall see a fixed scale of distances
inserted in such a map.


III. The only maps I remember to have seen, in which the last of these
blemishes is removed, and the other lessened, are some of P. Schenk’s
of Amsterdam, a map of the Russian empire, the Germania Critica of the
famous Professor Meyer, and a few more[27]. In these the meridians are
straight lines converging to a point; from which, as a center, the
parallels of latitude are described: and a rule has been published for
the drawing of such maps[28]. But as that rule appears to be only an
easy and convenient approximation, it remains still to be inquired,
_What is the construction of a particular map, that shall exhibit the
superficial and linear measures in their truest proportions?_ In order
to which,


IV. Let E_l_LP, in this figure (_See_ TAB. XXI.) be the quadrant of
a meridian of a given sphere, whose center is C, and its pole P; EL,
E_l_, the latitudes of two places in that meridian, EM their middle
latitude. Draw LN, _ln_, cosines of the latitudes, the sine of the
middle latitude MF, and its cotangent MT. Then writing unity for the
radius, if in CM we take C_x_ = N_n_ ⁄ (L_l_ × MF × MT), and thro’ _x_
we draw _x_R, _xr_, equal each to half the arc L_l_, and perpendicular
to CM; the conical surface generated by the line R_r_, while the figure
revolves on the axis of the sphere, will be equal to the surface of
the zone that is to be described in the same time by the arc L_l_; as
will easily appear by comparing that conical surface with the zone, as
measured by _Archimedes_.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXI. _p. 554_.

_J. Mynde sc._]

And, lastly, If from the point _t_, in which _r_R produced meets the
axis, we take the angle C_t_V in proportion to the longitude of the
proposed map, as MF the sine of the middle latitude is to radius, and
draw the parallels and meridians as in the figure, the whole space
SOQV will be the proposed part of the conical surface expanded into a
plane; in which the places may now be inserted according to their known
longitudes and latitudes.


EXAMPLE.

V. Let L_l_, the breadth of the zone, be 50°, lying between 10° and 60°
north latitude; its longitude 110°, from 20° east of the Canaries to
the center of the western hemisphere; comprehending the western parts
of Europe and Africa, the more known parts of North America, and the
ocean that separates it from the old continent.

And because C_x_ = N_n_ ⁄ (L_l_ × MF × MT), add these three logarithms.

    Log. 0.8726650 (= 50° to radius 1)            -1.9408476
    Log. MF (sin. 35°)                            -1.7585913
    Log. MT (tang. 55°)                            0.1547732
                                                  ----------
  Take the sum                                    -1.8542121
  from log. N_n_ (= .6923772)                     -1.8403427
                                                  ----------
  the remainder                                   -1.9861306
  is the logarithm of C_x_. And because 1:
  C_x_ ∷ MT : _xt_, to this adding the log. MT 0.1547732
                                                  ----------
    The sum                                        0.1409038

is the log. of _xt_ = 1.383260; and _x_R (= _xr_ = ½ L_l_) being
.4363325, R_t_ will be 0.9469275, _rt_ = 1.8195925. Whence having fixed
upon any convenient size for our map, the center _t_ is easily found.
As, allowing an inch to a degree of a great circle, or 50 inches to the
line R_r_, R_t_ the semidiameter of the least parallel will be 54.255
inches, and that of the greatest parallel 104.255 inches.

Again, making as radius to MF so the longitude 110° to the angle S_t_V,
that angle will be 63° 5´ ⅗. Divide the meridians and parallels, and
finish the map as usual.

  _Note_, The log. MT being repeated in this computation with a
  contrary sign, we may find _xt_ immediately by subtracting the sum of
  the logarithms of L_l_ and MF from the log. of N_n_.


VI. A map drawn by this rule will have the following properties:

1. The intersections of the meridians and parallels will be
rectangular.

2. The distances north and south will be exact; and any meridian will
serve as a scale.

3. The parallels thro’ _z_ and _y_, where the line R_r_ cuts the arc
L_l_, or any small distances of places that lie in those parallels,
will be of their just quantity. At the extreme latitudes they will
exceed, and in mean latitudes, from _x_ towards _z_ or _y_, they will
fall short of it. But unless the zone is very broad, neither the excess
nor the defect will be any-where considerable.

4. The latitudes and the superficies of the map being exact, by the
construction, it follows, that the excesses and defects of distance,
now mentioned, compensate each other; and are, in general, of the least
quantity they can have in the map designed.

5. If a thread is extended on a plane, and fixed to it at its two
extremities, and afterwards the plane is formed into a pyramidal or
conical surface, it may be easily shewn, that the thread will pass
thro’ the same points of the surface as before; and that, _conversely_,
the shortest distance between two points in a conical surface is
the right line which joins them, when that surface is expanded into
a plane. Now, in the present case, the shortest distances on the
conical surface will be, if not equal, always nearly equal, to the
correspondent distances on the sphere: and therefore, all rectilinear
distances on the map, applied to the meridian as a scale, will, nearly
at least, shew the true distances of the places represented.

6. In maps, whose breadth exceeds not 10° or 15°, the rectilinear
distances may be taken for sufficiently exact. But we have chosen our
example of a greater breadth than can often be required, on purpose
to shew how high the errors can ever arise; and how they may, if it is
thought needful, be nearly estimated and corrected.


Write down, in a vacant space at the bottom of the map, a table of the
errors of equidistant parallels, as from five degrees to five degrees
of the whole latitude; and having taken the mean errors, and diminished
them in the ratio of radius to the sine of the mean inclination of
the line of distance to the meridian, you shall find the correction
required; remembering only to distinguish the distance into its parts
that lie _within_ and _without_ the sphere, and taking the difference
of the correspondent errors, in _defect_ and in _excess_.

But it was thought needless to add any examples; as, from what has been
said, the intelligent reader will readily see the use of such a table;
and chiefly as, whenever exactness is required, it will be more proper,
and indeed more expeditious, to compute the distances of places by the
following canon.

_Multiply the product of the cosines of the two given latitudes by
the square of the sine of half the difference of longitude; and to
this product add the square of the sine of half the difference of the
latitudes; the square root of the sum shall be the sine of half the arc
of a great circle between the two places given._

Thus, if we are to find the true distance from one angle of our map to
the opposite, that is, from S to Q, the operation will be as follows:

        L. sin. 30° = -1.6989700
        L. sin. 80° = -1.9933515
      2 L. sin. 55° = -1.8267290
                      ----------
                      -1.5190505 = log. of 0.330408
  and 2 L. sin. 25° = -1.2518966 = log. of 0.178606
                      ----------           --------
                       Log. of the sum     0.509014 is -1.7067297
                                         Whose half is -1.8533648
  the L. sin. of 45° 31´, the double of which is 91° 2´, or 5462
  geographical miles.

And seeing the lines TS, TQ, reduced to minutes of a degree, are
6255.189 and 3255.189 respectively, and the angle STV is 63° 5´⅗, the
right line SQ on the map will be 5594´, exceeding its just value by
132´ or ¹⁄₄₂ of the whole.

7. The errors on the parallels increasing fast towards the north,
and the line SQ having, at last, nearly the same direction, it is not
to be wondered that the errors in our example should amount to ¹⁄₄₂.
Greater still would happen, if we measured the distance from O to Q
by a straight line joining those points: for that line, on the conic
surface, lying every-where at a greater distance from the sphere than
the points O and Q, must plainly be a very improper measure of the
distance of their correspondent points on the sphere. And therefore, to
prevent all errors of that kind, and confine the other errors in this
part of our map to narrower bounds, it will be best to terminate it
towards the pole by a straight line KI touching the parallel OQ in the
middle point K, and on the east and west by lines, as HI, parallel to
the meridian thro’ K, and meeting the tangent at the middle point of
the parallel SV in H. By this means too we shall gain more space than
we lose, while the map takes the usual rectangular form, and the spaces
GHV remain for the _title_, and other inscriptions.


VII. Another, and not the least considerable, property of our map
is, that it may, without sensible error, be used as a sea-chart; the
rumb-lines on it being logarithmic spirals to their common pole _t_,
as is partly represented in the figure: and the arithmetical solutions
thence derived will be found as accurate as is necessary in the art of
sailing.

Thus if it were required to find the course a ship is to steer between
two ports, whose longitudes and latitudes are known, we may use the
following

RULE.

_To the logarithm of the number of minutes in the difference of
longitude add the constant logarithm[29] -4.1015105, and to their sum
the logarithm sine of the mean latitude, and let this last sum be_ S.

_The cotangent of the mean latitude being_ T, _and an arithmetical mean
between half the difference of latitude and its tangent being called_
m, _from the logarithm of_ T + m _take the logarithm of_ T - m, _and
let the logarithm of their difference be_ D; _then shall_ S - D _be
nearly the logarithm tangent of the angle, in which the ship’s course
cuts the meridians_.

  _Note_, We ought, in strictness, to use the ratio of _tx_ + _x_R to
  _tx_ - _x_R instead of T + _m_ to T - _m_; but we substitute this
  last as more easily computed, and very little different.


EXAMPLE 1.

Let the latitudes, on the same side of the equator, be 10° and 60°;
then the middle latitude and its complement are 35° and 55°, and half
the difference of the latitudes is 25°: and the difference of longitude
being 110°, the operation will stand as below.

  Log. 6600´ (in 110°)   3.8195439
  Constant log.         -4.1015105
                        ----------
                        -1.9210544
  Log. sin. 35°         -1.7585913
                        ----------
                            S = ... -1.6796457
        Again T = 1.4281480
            _m_ =  .4513202
                  ---------
  Log. (T + _m_) (= 1.8794682)  0.2740350
  Log. (T - _m_) (= 0.9768278) -1.9898180
                             ----------
                         Log. 0.2842170 = D = -1.4536500
                                              ----------
  S - D (= log. tangent 59° 16´)            =  0.2259957
  agreeing to a minute with the solution by a table of meridional
  parts.


EXAMPLE 2.

The rest remaining, let the difference of longitude be only 40°; then

  Log. 2400´ (in 40°)     3.3802112
  Constant log.          -4.1015105
                         ----------
                         -1.4817217
  Log. sin. 35°          -1.7585913
                         ----------
                     S =             -1.2403130
                     D (as before) = -1.4536500
                                     ----------
  S - D (= log. tang. 31° 27´ ½)   -1.7866630


EXAMPLE 3.

Let the difference of longitude be 40°; but the latitudes 56° and 80°;

    And log. 2400´  }
    + log. constant }     = -1.4817217
    Log. sin. 68°         = -1.9671659
                            ----------
                                S =     -1.4488876
  T (tang. 22°) =        .4040262
  _m_ =             .2109980
                         --------
  Log. (T + _m_) (= .6150242) -1.7888921
  Log. (T - _m_) (= .1830282) -1.2625181
                                   ----------
                    Log.           0.5263740 = D = -1.7212944
                                                   ----------
  S - D (= log. tangent 28° 6´)                  = -1.7275932
  wanting of the true answer no more than 1° 4´.

And in all cases that can occur, the error of this rule will be
inconsiderable.

It is not meant, however, that it ought to take place of the easier and
better computation by a table of meridional parts: but it was thought
proper to shew, by some examples, how safely the map itself may be
depended on in the longest voyages; provided it is sufficiently large,
and the necessary rumb-lines are exactly drawn[30].




LXXIV. _A short Dissertation on Maps and Charts: In a Letter to the
Rev._ Thomas Birch, _D. D. and Secret. R. S. By Mr._ Wm. Mountaine,
_F.R.S._

[Read April 6, 1758.]

                                               London, March 21. 1758.

SIR,

AMONG the several improvements made in arts and sciences by ingenious
men, the construction of _globes_, _maps_, or _charts_, deserves a
place: not only on account of the pleasure and satisfaction that
arises to speculative minds, in surveying the extent and divisions of
this terraqueous globe, but also for their real use and service to
navigation, trade, and commerce.

_Globes_ perhaps were first invented, as bearing the nearest semblance
to the natural form of the earth and sea, with proper circles thereon
described, and the several empires and kingdoms, according to their
extent, latitudes, and longitudes, as far as geography and history
would admit.

But tho’ these convey the most general and truest ideas of the position
and situation of places; yet, as containing but a small surface, they
were found not extensive enough to take in particular kingdoms or
states, with their subdivisions, cities, and rivers, so as to convey
an adequate and sufficient representation. Besides, they were not so
portable and commodious in voyages or travels.

_Maps_ and _Charts_ were therefore thought of, as being most convenient
for both the purposes above-mentioned; the accuracy of which depends
on representing the meridians and parallels in such manner, that when
places are laid thereon, according to their latitudes and longitudes,
they may have such respect to each other, as they have on the globe
itself; and those are either _globular_ or _rectilinear_.

_Globular_, or _curvilinear_, are either general or particular.

_General_, are the hemispheres; for the most part constructed
stereographically.

_Particular_, contain only some part of the terraqueous globe; and of
this sort there are sundry modes of construction, which for the most
part are defective, so as not to be applied with accuracy and facility
to the purposes intended, in determining the courses or bearings of
places, their distances, or both.

_Rectilinear_ were therefore very early adopted, on which the meridians
were described parallel to each other, and the degrees of latitude and
longitude every-where equal; the rumbs were consequently right lines;
and hereby it was thought, that the courses or bearings of places would
be more easily determined.

But these were found also insufficient and erroneous, the meridians
being parallel, which ought to converge; and no method or device used
to accommodate that parallelism.

Notwithstanding the great deficiency in this plane map or chart, it was
preferred, especially in nautical business; and hath its uses at this
day in topographic constructions, as in bays, harbours, and very narrow
zones.

However, the errors herein were sooner discovered than corrected, both
by mathematicians and mariners, as by Martin Cortese, Petrus Nonius,
Coigniet, and some say by Ptolemy himself.

The first step towards the improvement of this chart was made by
Gerardus Mercator, who published a map about the year 1550, wherein the
degrees of latitude were increased from the equator towards each pole;
but upon what principles this was constructed, he did not exhibit.

About the year 1590, Mr. Edward Wright, an Englishman, discovered
the true principles upon which such a chart should be constructed;
and communicated the same to one Jodocus Hondius, an engraver, who,
contrary to his honest faith and engagement, published the same as
his own invention: This occasioned Mr. Wright, in the year 1599, to
exhibit his method of construction, in his book, intitled, _Correction
of Errors in Navigation_; in the preface of which book may be seen
his charge and proof against Hondius; and also how far Mercator has
any right to share in the honour due for this great improvement in
geography and navigation.

Blundevill, in his Exercises, page 327, published anno 1594, gives a
table of meridional parts answering to even degrees, from 1° to 80°
of latitude, with the sketch of a chart constructed therefrom; but
this table he acknowledged to have received from Mr. Wright, in the
following words, page 326, _viz._ “In the mean time to reform the saide
faults,” (in the plane chart) “Mercator hath in his universal chard or
mappe made the spaces of the parallels of latitude to bee wider everie
one than other from the equinoctial towards either of the poles, by
what rule I know not, unless it be by such a table as my friend Maister
Wright of Caius-college in Cambridge at my request sent me (I thank
him) not long since for that purpose, which table with his consent, I
have plainlie set down,” _&c._

About the year 1720, a globular chart was published, said to be
constructed by Mr. Henry Wilson; the errors in which were obviated
by Mr. Thomas Haselden, in a letter to Dr. Halley; who at the same
time exhibited a new scale, whereby distances on a given course may
be measured, or laid off, at one extent of the compasses, on Wright’s
projection; and was intended to render the same as easy in practice as
the plane chart.

The above chart was published in opposition to Mr. Wright’s, which that
author charged with imperfections and errors, and that it represented
places bigger than they are upon the globe.

It is true, the surface is apparently enlarged; but the position of
places, in respect to one another, are in no wise distorted; and it may
be asserted, with the same parity of reason, that the lines of sines,
tangents, and secants, are false, because the degrees of the circle,
which are equal among themselves, are thereupon represented unequal.

Yet if a map or chart was so constructed, as to shew the situation and
true extent of countries, _&c. primâ facie_ (if I may be allowed the
expression), and yet retain all the properties, uses, and simplicity,
of Wright’s construction, it would be a truly great improvement; but
this seems to be impossible.

The method exhibited by the Rev. Mr. Murdoch, in his paper, read before
the Royal Society on the 9th of February last, shews the situation of
places, and seems better calculated for determining superficial and
linear measures, than any other that has occurred to me.

This Gentleman illustrates his theory with examples justly intended to
point out the quantity of error, that will happen in a large extent.

For instance; Between latitudes 10° and 60° N. and containing 110
degrees difference of longitude, Mr. Murdoch computes the distance at
5594 miles; which, upon the arc of a great circle, is found to be 5477,
or by other methods 5462; so that the difference is only 117, or at
most 132 miles in so great an extent, and to an high latitude; and the
higher the latitude the greater the error is like to be, where-ever
middle latitude is concerned.

His courses also agree very nearly with computations made from the
tables of meridional parts.

In example the first they are the very same:

In example the 2d they agree to half a minute:

In example the 3d they vary 1° 4´, on account of the high latitudes,
which extend from 56° to 80° N.

However, I do not esteem this method so simple, easy, and concise, in
the practice of navigation, as Mr. Wright’s construction, especially in
determining the bearings or courses from place to place: nor will it (I
presume) admit of a zone containing both north and south latitude.

Of these inconveniences Mr. Murdoch seems to be extremely well
acquainted, when he expresses himself in the following very candid and
ingenuous terms, _viz._ “As to Wright’s or Mercator’s nautical chart,
it does not here fall under our consideration: it is perfect in its
kind; and will always be reckoned among the chief inventions of the
last age. If it has been misunderstood or misapplied by geographers,
they only are to blame.”--And again, at the end of his nautical
examples, he concludes thus, _viz._ “It is not meant, however, that it
ought to take place of the easier and better computation by a table of
meridional parts.”

I have the honour to be, with the greatest respect,

                                 SIR,
                       The ROYAL SOCIETY’S, and
                     _Your_ most obedient Servant,
                          William Mountaine.


ADDENDA _to Mr._ Murdoch_’s Paper_, Nº. LXXIII.

  IF it is required “to draw a map, in which the superficies of a given
  zone shall be equal to the zone on the sphere, while at the same time
  the projection from the center is strictly geometrical;” _Take_ Cx
  _to_ CM _as a geometrical mean between_ CM _and_ Nn, _is to the like
  mean between the cosine of the middle latitude, and twice the tangent
  of the semidifference of latitudes_; and project on the conic surface
  generated by _xt_. But here the degrees of latitude towards the
  middle will fall short of their just quantity, and at the extremities
  exceed it: which hurts the eye. Artists may use either rule: or, in
  most cases, they need only make C_x_ to CM as the arc ML is to its
  tangent, and finish the map; either by a projection, or, as in the
  first method, by dividing that part of _xt_ which is intercepted by
  the secants thro’ L and _l_, into equal degrees of latitude.

   Mr. Mountaine justly observes, “that my rule does not admit of a
  zone containing N. and S. latitudes.” But the remedy is, _to extend
  the lesser latitudes to an equality with the greater; that the cone
  may be changed into a cylinder, and the rumbs into straight lines_.




LXXV. _Cases of the remarkable Effects of Blisters in lessening the
Quickness of the Pulse in Coughs, attended with Infarction of the
Lungs and Fever: By_ Robert Whytt, _M. D. F.R.S. Fellow of the Royal
College of Physicians, and Professor of Medicine in the University of_
Edinburgh.

[Read Feb. 16, 1758.]

ONE of the most natural effects of blistering plaisters, when applied
to the human body, is to quicken the pulse, and increase the force
of the circulation. This effect they produce, not only by means of
the pain and inflammation they raise in the parts to which they are
applied, but also because the finer particles of the _cantharides_,
which enter the blood, render it more apt to stimulate the heart and
vascular system.

The apprehension, that blisters must in every case accelerate the
motion of the blood, seems to have been the reason, why some eminent
physicians have been unwilling to use them in feverish and inflammatory
disorders, till after the force of the disease was a good deal abated,
and the pulse beginning to sink. However, an attentive observation
of the effects, which follow the application of blisters in those
diseases, will shew, that instead of increasing, they often remarkably
lessen the frequency of the pulse. This I had occasion formerly to take
notice of[31], and shall now evince more fully by the following cases.


I. A widow lady, aged about 50, was seized (December 1755) with a bad
cough, oppression about her stomach and breast, and a pain in her
right side, tho’ not very acute. Her pulse being quick, and skin hot,
some blood was taken away, which was a good deal sizy: attenuating and
expectorating medicines were also prescribed. But as her complaints
did not yield to these remedies, I was called on December 26th, after
she had been ill about ten days; at which time her pulse beat from 96
to 100 times in a minute, but was not fuller than natural. I ordered
her to lose seven or eight ounces more of blood, which, like the
former, was sizy; and next day, finding no abatement of her complaints,
I advised a blister to be applied, in the evening, to that part of
her right side which was pained. Next morning, when the blister was
removed, the pain of her side was gone, and her pulse beat only 88
times in a minute, and in two days more it came down to 78. However,
after the blistered part became dry, the pulse rose in one day’s time
to 96, and continued between that number and 90 for four days; after
which I ordered a large blister to be put between her shoulders. When
this plaister was taken off, her pulse beat under 90 times in a minute;
and next day it fell to 76, and the day after to 72. The cough and
other symptoms, which were relieved by the first blister, were quite
cured by the second.


II. John Graham, bookbinder, in Edinburgh, aged 37, of a thin habit
of body, formerly subject to coughs, and thought to be in danger of
a _phthisis pulmonalis_, having exposed himself unwarily to cold
in the night time, was, about the end of January 1756, seized with
a bad cough and feverishness; for which he was blooded, and had a
diaphoretic julep, a pectoral decoction, and a mixture with _gum.
ammoniacum_ and _acetum scilliticum_, given him by Mr. James Russell,
surgeon-apothecary in this place. On the 12th of February, after he
had been ill above a fortnight, I was desired to visit him. He seemed
to be a good deal emaciated; his eyes were hollow, and cheeks fallen
in: he was almost constantly in a sweat; coughed frequently, and spit
up a great quantity of tough phlegm, somewhat resembling _pus_: his
pulse beat from 112 to 116 times in a minute. In this condition I
ordered immediately a blister to be applied between his shoulders,
which lessened in some degree his cough and spitting, as well as the
frequency of his pulse; but the blistered part no sooner began to
heal, than he became as ill as before, and continued in this bad way
nine or ten days, gradually wasting, with continued sweats, and a
great spitting of a thick _mucus_. During this time he used _tinctura
rosarum_, and the mixture with _gum. ammon._ and _acet. scillit._
without any sensible benefit, and had six ounces of blood taken away,
which was very watery, and the _crassamentum_ was of a lax texture.
In this almost desperate condition, another blister, larger than the
former, was put between his shoulders, which remarkably lessened his
cough and spitting, and in two or three days reduced his pulse to
96 strokes in a minute. After this he continued to recover slowly,
without the assistance of any other medicine, except the _tinctura
rosarum_ and the mixture with _gum. ammon._ and _acet. scillit._ and at
present he enjoys good health.


III. Mrs.----, aged upwards of 40, who had for several years been
subject to a cough and spitting in the winter months, was, in October
1756, seized with those complaints in a much greater degree than
usual; to remove which, she was blooded, and got some attenuating and
pectoral medicines from Mr. John Balfour, surgeon-apothecary in Leith.
I was called on November 11th, after she had been ill several weeks,
and found her in a very unpromising condition. She had a frequent
and severe cough, with great shortness of breath and a wheezing; her
lungs seemed to be quite stuffed with phlegm, of which she spit a vast
quantity every day, and of such an appearance, that I was apprehensive
it was, in part at least, truly purulent. When she sat up in a chair,
her pulse beat above 130 times in a minute. She had a considerable
thirst, and her tongue was of a deep red colour, with a beginning
aphthous crust on some parts of it. She was so weak, and her pulse so
feeble, that there was no place for further bleeding: a blister was
therefore applied to her back, November 11th, which somewhat lowered
her pulse, and lessened the shortness of breathing and quantity of
phlegm in her lungs. November 16th, a second blister was laid to her
side, which gave her still more sensible relief than the former, and
reduced her pulse to 114 strokes in a minute. November 25th, a third
blister was applied to her back; by which her cough and wheezing were
rendered considerably easier, and the phlegm, which she spit up, lost
its purulent appearance, became thinner, more frothy, and was much
less in quantity. Her pulse beat now only 104 times in a minute. After
this, her cough and spitting increasing again, she had, on the 20th of
December, a fourth blister applied to her back, which, like the former,
did her great service. Her stomach being extremely delicate, I scarce
ordered any medicines for her all this time, except a cordial julep,
with _spir. volat. oleos._ tincture of rhubarb as a laxative, and a
julep of _aqu. rosar. acet. vin. alb._ and _syr. balsam._ of which last
she took two table spoonfuls twice or thrice a day in a quarter of a
pint of lintseed tea. After the fourth blister, she drank for some time
a cupful of _infusum amarum_ twice a day, and continued to recover
slowly: and tho’ during the remaining part of the winter she was, as
usually, a good deal troubled with a cough, yet in the spring she got
free from it, and is now in her ordinary health.


IV. Christian Mʿewen, aged 21, had laboured under a cough, thick
spitting, pain of her breast, and pains in her sides affecting her
breathing, for about a twelvemonth: and after getting, by proper
remedies, in a good measure free from those complaints, her cough, from
catching a fresh cold, increased to a greater degree than ever, became
hard and dry, and was attended with a constant difficulty of breathing,
pain in her left side, and head-ach. After having been seven or eight
days in this condition, she was admitted into the Royal Infirmary,
January 9th, 1757. As her pulse was small, tho’ very quick, _viz._
beating 130 in a minute, I thought it unnecessary to bleed her, as
from former experience I did not doubt but that blistering alone would
relieve her: I ordered, therefore, a large blister to be applied to her
left side, where she complained of pain, and prescribed for her the
following julep:

  ℞ _Aqu. menth. simp. spirit. Minderer. ana_ ℥ iij. _acet. scillit._ ℥
  i. _sacchar. alb._ ℥ ij. _misce; cap. coch._ ij. _ter in die_.

She was also desired to breathe frequently over the steam of hot water,
and to drink lintseed tea.

January 10th. Her pulse beat only 112 times in a minute, and was
somewhat fuller than on the 9th. The blister was not removed till late
in the evening, and made a plentiful discharge. The cough having been
so severe last night, as to keep her from sleep, I ordered her the
following anodyne draught:

  ℞ _Spirit. Minderer._ ℥ ss. _acet. scillit._ ȝ i. _syr. papav. alb._
  ȝ vi. _misce; cap. hor. somni._

Jan. 11th. The cough easier last night; difficulty of breathing less;
pulse 108 in a minute. Ordered the anodyne draught to be repeated, and
the use of the julep, with _acet. scillit._ to be continued.

Jan. 12th. Pulse slower; cough and pain of the side easier; but still
complains of a head-ach.

Jan. 13th. Pulse 94 in a minute; cough continues easier in the night,
but is troublesome in the day-time.

Jan. 14th. Every way better; pulse only 80 in a minute. As her cough
is still bound, ordered her, besides the medicines above-mentioned, a
pectoral decoction of _rad. alth._ &c.

Jan. 15th. Cough and other complaints in a great measure removed; pulse
65 in a minute.

From this time her cough gave her little trouble; but on the 18th she
complained of a pain in the _epigastrium_, with sickness at stomach,
want of apetite, and a giddiness in her head, which were considerably
relieved by a vomit, _infusum amarum_, and stomachic purges; and were
almost wholly cured by the return of her menses on the 5th of February,
after an interval of eight weeks.


V. A girl 21 months old, who had (December 1756) a great load of
the small-pox, and not of a good kind, with a cough and obstructed
breathing, was, on the seventh day from the eruption, blistered on the
back; by which the pulse was lessened from 200 to 156 strokes in a
minute. Next day her legs were also blistered, and the pulse thereby
fell to 136. But the child’s lungs being much oppressed, and her throat
being so full of pustules that she could scarce swallow any thing, she
died towards the end of the ninth day.


I could add several other cases of the remarkable effects of blisters
in lessening the quickness of the pulse in coughs attended with fever,
pain in the side, and pituitous infarction of the lungs: but those
above may be sufficient to put this matter out of doubt, as well as to
remove any prejudice, that may still remain against the free use of so
efficacious a remedy.

In a true peripneumony, especially where the inflammation is great,
repeated bleeding is the principal remedy, and blisters early applied
are not so proper. But when the peripneumony is of a mixed kind;
when the lungs are not so much inflamed as loaded with a pituitous
matter; when bleeding gives but little relief; when the pulse, tho’
quick, is small; when the patient is little able to bear evacuations,
and the disease has continued for a considerable time; in all these
cases blistering will produce remarkable good effects, and, far from
increasing, will generally lessen the frequency of the pulse, and
fever, more speedily than any other remedy.

On the other hand, when the fever and frequency of the pulse proceed
from a true inflammation of the lungs, from large obstructions tending
to suppuration, or from an open ulcer in them, blisters will be of less
use, nay, sometimes will do harm, except in the last case, where they,
as well as issues and setons, are often beneficial, tho’ seldom able
to compleat a cure. But as in pituitous infarctions of the lungs, with
cough and fever, repeated blisters applied to the back and sides are
far preferable to issues or setons, so these last seem most proper in
an open ulcer of the lungs. The former make a greater and more sudden
derivation, and are therefore adapted to acute cases; the latter act
more slowly, but for a much longer time, and are therefore best suited
to chronic diseases. Further, while blisters evacuate chiefly the
serous humours, issues and setons generally discharge true purulent
matter, and on this account may be of greatest service in internal
ulcers.

In what manner blisters may lessen the fever and frequency of the
pulse attending internal inflammations, I have elsewhere endeavoured
to explain[32]; and shall only add here, that in the cases above
recited, where the quick pulse and feverishness proceeded more from a
pituitous infarction than a true inflammation of the lungs, blisters,
by relieving this organ, in some measure, of the load of humours
oppressing it, would render the circulation through its vessels freer,
and consequently lessen the quickness of the pulse, and other feverish
symptoms.

It may not, however, be improper briefly to point out the reason,
why blisters, which have been observed to be remarkably efficacious,
even when early applied, in pleurisies[33], are less so in true
peripneumonies. This difference, I imagine, may be accounted for from
there being no immediate communication between the pulmonary vessels
and those of the sides and back, to which the blisters are applied;
whereas the _pleura_, and intercostal muscles, are furnished with
blood-vessels from the intercostal arteries, which also supply the
teguments of the _thorax_: so that while a greater flow of serous
humours, and also indeed of red blood, is derived into the vessels of
the external parts, to which the vesicatories are applied, the force
of the fluids in the vessels of the inflamed _pleura_, or intercostal
muscles, must be considerably lessened. Further, as the intercostal
muscles and _pleura_ are, as well as the teguments of the _thorax_,
supplied with nerves from the _true_ intercostals, blisters applied to
the back and sides may perhaps, on this account also, have a greater
effect in relieving inflammations there than in the lungs, which have
nerves from the eighth pair, and from the _intercostals_ improperly so
called.

Edinburgh, May 23d, 1757.


_Extract of a Letter from Dr._ Whytt, _Professor of Medicine in the
University of_ Edinburgh, _and F. R. S. to Dr._ Pringle, _F.R.S._

                                               Edinburgh, 10 Nov. 1757.

WHAT you remark with regard to blisters being freely used by the
physicians at London, in the cases mentioned in the paper I last sent
you, is very just, and indeed what I knew; but altho’ their efficacy
in such circumstances is now generally acknowleged both in England
and Scotland, yet I do not remember that their remarkable quality in
lessening the quickness of the pulse has been particularly attended to.
This, therefore, I thought it might not be amiss to ascertain by a few
careful observations.

I agree intirely with you, as to the use of blisters in fevers; being
of opinion, that when there is no particular part obstructed or
inflamed, they are of little service, and sometimes hurtful, unless
perhaps towards the end, when the pulse begins to sink. Nay, in fevers,
where the substance of the brain is affected, and not its membranes,
I have never found any sensible benefit from blisters: and I always
suspect the brain itself affected, when a fever and delirium come on
without any preceding head-ach, or redness in the _tunica albuginea_ of
the eyes. This kind of fever I have met with several times, and have
observed it to be generally fatal.




LXXVI. _A remarkable Instance of Four rough Stones, that were
discovered in an human urinary Bladder, contrary to the received
Opinion; and successfully extracted by the lateral Method of Cutting
for the Stone. By Mr._ Joseph Warner, _F. R. S. and Surgeon to_
Guy’s-Hospital.

[Read Feb. 23, 1758.]

THE favourable reception those few papers have met with from the Royal
Society, which I have done myself the honour of addressing to them,
encourages me to take the liberty of offering the following account to
their consideration: and I am the more immediately induced to submit
this paper to their perusal, as the fact hereafter related may possibly
be not esteemed a matter of mere curiosity; since it is probable,
that the inferences deduced from the history of the subsequent case,
when attended to, may prove of the greatest consequence to the future
ease and welfare of the patient, as well as be a means of preventing
the operator from falling into such errors, as cannot fail of drawing
an imputation upon his character, in the practice of one of the most
capital and difficult undertakings in his profession.

It is a maxim laid down by the most judicious and best received writers
upon operations in surgery, that when the surface of a stone, which
has been extracted from the bladder, appears to be totally rough, it
amounts to a proof of its having been there alone. But notwithstanding
I admit it is from experience found, that the observation is in general
well grounded, it may nevertheless appear, from the following case,
that this rule is not unexceptionable: for which reason perhaps it may
be thought right, that we should not be determined from circumstances
only; but, on the contrary, that it is necessary for every surgeon to
take such methods during the operation, as will enable him to judge
with that degree of certainty, without which he cannot be enabled to do
so.

The methods I would recommend are these: That after the extraction of
a stone from the bladder, tho’ the whole of its surface be rough, the
operator should nevertheless introduce the forefinger of his left or
right hand thro’ the wound into the cavity of the bladder; by which
means, if the subject be under twelve years of age, he will be enabled
to come in contact with every internal part of the bladder with his
finger: but if the subject be an adult, and of a corpulent habit of
body, the finger, under these circumstances, not being found to be
sufficiently long for the purpose, he must have recourse to a female
catheter, or some other instrument that is nearly strait, quite smooth
and polished, and of about nine or ten inches long; which will serve
the purpose equally well, if of a proper form and thickness. This is
the method I have made use of upon the like occasions of late years,
without giving any great degree of pain to the patient, or considerably
retarding the operation.

Since I have had the opportunity of making the following observation,
as well as a prior observation something similar to this, where two
rough stones were extracted by me a few years ago from a young man’s
bladder of 15 years of age, I cannot help suspecting, that there may
have been instances of one or more stones being left behind in the
bladder at the time of operating, merely from the operator’s putting
too great a confidence in this general rule. Which suspicion I am led
into from having known people, who have undergone the operation of
cutting for the stone, relapse into the like disorder in a short time
after the healing of their wounds, attended with such symptoms, as have
obliged them to submit to a second operation; when the stone, upon
being extracted, has appeared of so considerable a size, as to make it
suspicious, that this stone must probably have been of a much longer
growth, than the short time betwixt the two operations could admit of.
The maxim laid down to us by authors, of a smooth and polished stone
in the bladder being never there alone, but always accompanied with
one or more stones of the same kind, I know no exception to. But if
this phænomenon should ever occur, the strict observance of that rule
(delivered to us by judicious writers in surgery) of always searching
the bladder under the like appearances, on presumption of one or more
stones being left behind, cannot be attended with any future mischief
to the patient, when carefully executed by the methods recommended
above, and undoubtedly should always be strictly attended to. The
smooth and polished appearances of the surfaces of human _calculi_ are
universally supposed to arise from their rubbing one against the other;
which may with reason be supposed to be the case: but I confess this
inference is not satisfactory to me; since it is probable, if this was
the sole cause of their smoothness, the same effect would probably be
always produced, when attended with the same degree of friction. But
as this may be considered as a matter of mere speculation, I refer the
decision of this point to those of superior abilities.


CASE.

Mr. William Woodhams, a gentleman farmer, of a corpulent habit of body,
in the 46th year of his age, now living in the parish of Udimore,
within three miles of Rye in Sussex, was attacked about eight years ago
with severe complaints in his loins, accompanied with an incapacity of
voiding his urine without the assistance of proper medicines, which
were administered to him by a neighbouring apothecary for that purpose.
These medicines had the desired effect: they promoted a secretion, and
an evacuation of urine; which appeared to be loaded with a considerable
quantity of gravelly particles mixed with a _mucus_ of a whitish
colour. In the space of three weeks he had perfectly recovered from
this attack, and continued well for near five years afterwards, without
any return of his complaint, except when he rode hard on horseback, or
drank more freely of strong liquors than usual. At the expiration of
five years he was seized with an acute fever, of which he recovered in
a few weeks.

Very soon after his recovery from this illness, he began to complain
of excessive pain in voiding his urine, or upon going to stool;
which symptoms were so greatly increased for many months before he
submitted to the operation, as to quite disable him from riding, from
walking, or from using any kind of exercise. His urine, of late, was
continually and involuntarily flowing from him in small quantities. He
complained of great pain and soreness in his fundament, attended with
a _tenesmus_. This account he delivered to me on the second day after
the operation; and at the same time he very feelingly told me, that he
had enjoyed but very few and short intervals of ease for the three last
years, till since the operation.

On the 30th of January 1758, I cut him, at his own house in Sussex,
having first prepared him for the operation in the manner, that is
usual upon the like occasion. In the operation, I extracted the four
stones, which I now have the honour of laying before the Royal Society.
The whole surfaces of these stones appear to be rough, not having the
least marks of ever having rubbed against each other during their
confinement in the bladder: but yet I conjecture this must frequently
have been the case, as there was no difficulty in embracing these
_calculi_ with the forceps: for had they been contained in different
cells or pouches in the bladder, which sometimes have been observed
from dissections, this circumstance would, in all probability, have
rendered it impracticable for me to have so immediately got at them, if
at all.

The forceps was introduced only three times into the bladder for
effecting the extraction of the three first stones, and only twice for
the extraction of the fourth stone. Besides these four stones, which
I have presented to the Society for their inspection, I thought it
not improper to produce, at the same time, some other human _calculi_,
for their further satisfaction, each of which was found single in the
urinary bladders of different subjects. The surfaces of these stones
may be observed to be much smoother than the surface of either of the
four stones, that were extracted from Mr. Woodhams’s bladder in the
operation I have just now recited; and therefore it was more reasonable
to expect to find each of these stones accompanied with one or more
stones in the same bladder (according to the received opinion), than it
was to find more stones than one in the case of Mr. Woodhams’s, which
has given rise to these observations.

But as the fact before us does of itself shew the impropriety and
danger of determining from the surfaces of such extraneous bodies,
perhaps it may be thought needless to enlarge upon this subject, to
strengthen those precautions so reasonable to be observed in this
operation. However, as I have already taken notice of the smooth and
polished appearances of the surfaces of such stones, as are probably
never found single in the bladder; I have produced two stones of this
kind, that were extracted from the same bladder, to shew, that these
stones do no more resemble those stones of Mr. Woodhams’s, than a piece
of polished marble can be said to resemble a rough block of the same
species.

 _P. S._ I am informed, by a letter from Sussex, dated the 18th
 instant, that Mr. Woodhams is perfectly well in health; that the whole
 of his urine had passed through the urethra for the last five or six
 days; and that his wound will, in all probability, be soon healed.

                                                         Joseph Warner.

Hatton-Garden, February 22. 1758.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXII.(a) _p. 584_.

Plate _is an exact representation of the sizes and external appearances
of the four rough stones described in the preceding paper_

_J. Mynde sc._]




LXXVII. _Observations on the_ Limax non cochleata Purpur ferens, _The
naked Snail producing Purple. By_ John Andrew Peyssonel, _M. D. F.R.S.
Translated from the_ French.

[Read Feb. 23, 1758.]

AMONG the fish we meet with in the seas of the Antilles of America,
we find, that this I am going to describe will appear precious, from
the beautiful purple colour it produces, in the same manner, that the
cuttle-fish produces its ink, if a means could be found to procure this
liquor in a sufficient quantity to render it an article of commerce.
These fishes are soft, viscous, without shells, scales, or bones; are
of the nature of the _polypi_, and such other kinds, without feet,
fins, or any thing to supply their places. Their motion is vermicular;
and, like the slugs, they wreath themselves up, and when touched make
themselves quite round.

They fill up certain membranes of the body with water. Their local
motion; _antennæ_, which they lengthen and contract; and a great many
other properties, which they have in common with snails, slugs, and
turbinated shell-fish, made me call them naked snails: and altho’ they
have not the most essential qualities of snails, I thought I might
give them the name; for they have no particular appellation in this
country. Some call them piss-a beds, some sea-cats, and others a less
modest name, _tapecon_, taken from Pliny. The Negroes and country
people disagree upon this subject; and therefore I thought all their
names ought to be rejected, in order to adopt a more significant one,
which I have given them; and that altho’ they are without shells, a
quality essential to snails, they had a right to that class by their
other properties and qualities.

This fish is commonly four inches long, and two thick; of a greenish
colour, spotted with black, each of which forms a circle. The under
part is like that of snails, flat, with kinds of _mamillæ_, or
rugosities, which are adhesive; by means of which they advance in a
vermicular motion; and when touched become round, by retracting their
neck and head; and afterwards protrude them considerably, according to
their motion and progression, crawling upon rocks to seek their food.

The head of this animal has a flatness, or is inclinable to a square or
parallelogram. On each side there are membranes or skins, which form
kinds of ears; and under them others, which at times fill with water,
and are then transparent. Under this thick skin there is a _cranium_,
of a kind of coriaceous or cartilaginous matter; and in the _cranium_
we find the brain, which is a white substance, and very firm. At the
basis of the head its oval wide mouth is placed, being above two lines
long, which often discovers a white hard edge, with which he crops the
fucus’s, and other sea-plants, for his nourishment.

About half an inch from the ears there are two horns, or _antennæ_,
like those of some testaceous animals, which serve them for eyes; and
these _antennæ_ extend and contract at will, turning to either side
also. The _oesophagus_ begins at the upper and inner part of the mouth,
which is a delicate long tube; near which there is another thick one,
and made nearly like the colon, which leads to a bag, or the first
stomach, which may be likened to the craw of a fowl: it is always
filled with fucus mixed with sand. Sometimes this stomach is double, or
at least lengthens itself considerably, and the aliment parts it, as it
were, into two portions. After this craw, or stomach, we find another,
which performs the same office with the gizzard of fowls. The membranes
are thick, and are set with twelve stones, or horny pieces, of a bright
yellow colour, and as transparent as fine yellow amber, ending in
points like a diamond; so that the great side, or basis, is set into
the membrane of the gizzard as a diamond in its socket: others differ
in size, having different figures, that in acting all together they may
be able to break and grind the herbs the animal feeds upon, as well by
the strength of the muscle or gizzard, which puts them into action, as
by the situation of these stones, assisted by grains of sand found in
it, turning the whole by this trituration into a liquor. Afterwards,
what was thus triturated by the power of the gizzard passes into a
third belly or stomach, which is covered by a purple body, resembling
the _parenchyma_ of the liver, and nearly of the same consistence: then
this belly turns into a long tube, which surrounds this _parenchyma_,
and is covered in like manner by a very fine membrane: it is full
of a white liquor, like chyle, and goes to discharge itself into
another reservoir, at the side of which is a yellowish gland, like
a _pancreas_. From these two bodies or glands one of which may be
called hepatic, and the other pancreatic, two conduits pass out; that
of the _pancreas_ is white, the other of a blackish purple: the first
conducts its chyle, condensed, into a reservoir or bladder, which may
be resembled to the _receptaculum chyli_ of Pequet, and from thence
passes to the fecal matter: the other conducts to a body made like the
mesentery, but which is always found out of the common capacity or
cavity, in which all the _viscera_ are contained; which I thus describe:

This common capacity is very large, beginning at the head and ending
at the tail of the fish: it is sometimes filled with a yellowish
water, and is formed by the fleshy body of the animal; which is only a
membrane composed of fibres every way interwoven together, open at the
top, where the organs are situated, which contain the purple juice.

There is a hollow upon the back of the animal, where the canal, filled
with a reddish juice, passes out, carrying it to a fringed body like a
mesentery; and it is there the purple juice is brought to perfection;
and afterwards goes to a long sack lying under a kind of horny plate,
not like the bone of the cuttle-fish, but like the bone of the _sepia_,
or little cuttle-fish, which we call _le couteau_. This bone, or
horny substance, is transparent; and is of a triangular figure, or
approaching the form of a bivalve shell. On the right side it is
fastened by a strong cartilaginous muscle, which binds it to the body
of the animal; and on the left it is open and detached, and easy to be
pulled up: then it is easy to see underneath both the mesenteric body,
and the tube or reservoir of the purple juice. This bone, or horny
plate, is covered by a loose membrane, which is by no means attached to
it, but capable of being filled and inflated with water or wind.

The whole is covered with two membranes, which are continuations of the
flesh of the fish’s body: the membranes are loose, and larger than are
necessary to the bone: they are wrinkled or rumpled over one another,
to cover the whole, and to defend the bone and _viscera_ from all kinds
of pressure; but they are ready to stretch one from the other, and
leave the parts destined for the purple juice uncovered. They begin a
little under the neck, and extend, in the female animal, to the tail,
which is flat; and in the male they do not go so low, but end at some
distance from the tail.

The females are oviparous; for eggs are found in the grand cavity, at
the side of the pancreatic body.

I have already said, that when the animal is touched, he makes himself
round, and throws out his purple juice, as the cuttle-fish does his
ink. This juice is of a beautiful deep colour: it tinges linen, and the
tincture is difficult to get out. It remains at present to try if we
can collect a sufficient quantity of this juice, and to find a means of
preserving the tincture; which would then be certainly of great value:
to which purpose I may apply myself.

When the fish is boiled, or put into spirits, it shrinks up, and
loses two thirds of its size; because all the water, which is in
the interstices of the fibres, is dissipated, and the dried fibres
contract: which clearly appears from dissecting them.

Dated at Guadaloupe, 20 Mar. 1757.

                                                             Peyssonel.




LXXVIII. _New Observations upon the Worms that form Sponges. By_ John
Andrew Peyssonel, _M. D. F.R.S. Translated from the_ French.

[Read Feb. 23, 1758.]

THE existence of the nests of corallines and lithophyta, and the
mechanism of their polypi, made me conjecture, that it was the same
with respect to sponges; that animals, nested in the interstices of
their fibres, gave them their origin and growth: but I had not yet seen
nor discovered the insects, nor observed their work. Sponges appeared
to me only as skeletons: but I at length discovered these worms, which
form sponges, in the four following species:

1. _Spongia Americana tubo similis_; The tube-like sponge of Plumier.

2. _Spongia Americana longissima funiculo similis_; The cord-like
sponge of Plumier.

3. _Spongia Americana capitata et digitata_; The fingered sponge of
Plumier.

4. _Spongia Americana favo similis_; The honeycomb sponge of Plumier.

These four kinds only differ in form: they have the same qualities, are
made by the same kinds of worm, and what may be said of the one agrees
exactly with all the rest; for I made the same observations upon them
all.

They may be classed among the _spongiæ hyrcinæ_, so called by J.
Bauhin, because of the roughness of their fibres, by a metaphor, from
pieces covered with mud; or among those called by Pliny _tragos_, or
_aphysiæ_, being foul, and difficult to cleanse; and may take the name,
which Father Plumier has given them, drawn from their figure.

These four kinds of sponges are composed of hard, firm, dirty fibres,
sometimes brittle; separated one from another, having large hollows,
or cylindrical tubes, dispersed thro’ their substance. These tubes
are smooth within. The interstices of their fibres are filled with a
mucilaginous gluey matter, when the sponge is just taken out of the
sea. The mucilage is of a blackish colour, soon putrifies in the water,
or falls into dust when dried in the sun.

When a fresh sponge is squeezed, this mucilage comes out frothy, by
the mixture of the windings of its fibres: it always issues forth with
sand, or little parcels of shells crushed by the sea. These fibres,
which consist of the twisted doubles of the sponge, form as it were a
labyrinth filled with worms, which are easily crushed, and their juice
is confused with the mucilage; but having carefully torn the sponges,
and their gross fibres, I discovered the living worms, such as I shall
mention hereafter.

These species of sponge commonly grow upon sandy bottoms. At their
origins we perceive, as it were, a nodule of sand, or other matter,
almost petrified, round which the worms begin to work, and round which
they retire, as to their last seat or refuge; where I had the pleasure
of seeing them play, exercise themselves, and retire, by examining them
with the microscope; and I have even made my observations without its
assistance.


_A Description of the Worms which form the Sponges._

The worms I found in these kinds of sponges are about one-third of a
line thick, and two or three lines in length. They are so transparent,
that one may discern their _viscera_ thro’ their coverings and
substance: the blood may be seen to circulate, and all their parts to
act. They have a conic figure, with a small black head furnished with
two pincers: the other extremity is almost square, and much larger than
the head. Upon the back may be seen two white streaks or fillets, as if
they contained the chyle: these two canals are parallel to each other
from the head to the other extremity, where they come together. In the
middle, where the belly and _viscera_ ought to be placed, a blackish
matter is perceivable, which has a kind of circulation: sometimes
it fills all the body of the worm, sometimes it gathers towards the
head, or at the other end, and sometimes it follows the motion of the
animal. This vermicular motion or progression begins at the posterior
extremity, and ends at the head, which is pushed, and consequently
advances forward. I kept these worms alive out of the sponge, quite
detached from it, more than an hour, having examined them thoroughly
with a middling magnifier; for a great magnifier would be the grave of
the insect.

I was surprised, after having finished my observations, when I put them
near a piece of the fresh sponge, where the nests were moist, and from
which I had pulled them, to see them enter into them, and disappear,
being lost in the windings of the tubes. I thought to have found them
again; but it was a difficult task to search for them. I crushed them,
or they were themselves mashed in the tubes, which I pressed, and of
which I had consequently spoiled the texture; but I could not find
them; and this happened several times.

These worms have no particular lodge: they walk indifferently into
the tubular labyrinth. So that, without offence to Pliny and other
naturalists, I do not see, that it is in their power to dilate and
contract the bodies of the sponges; which always remain in the same
state of magnitude, without being any way sensible to the touch, or
any other motion of the sea, nor to any other accident whatsoever,
being an inanimate body; for the animal sensitive life, or whatever
you will have it, belongs only to the worms, that form these bodies,
and which are their dwelling-places; and which, by the slaver or juice
they deposit, make the sponge increase or grow, as bees, wasps, and
especially the wood-lice of America, increase their nests or cells.

These sponges, nests, or cells, are attached to some solid body in the
sea. Some kinds are fixed to rocks; others, as those I am speaking of,
are fastened to heaps of sand, or to pieces of petrified matter, and
even upon sandy bottoms; and the sea putting in motion the sand, and
the little parcels of broken shells, forces them into the holes of the
sponge: there the sand binds and mixes with mucilaginous juice, and
never is loosed from it but when the sponge is well dried, or with
the mucilage when putrified, or in powder; and yet some part will
remain, which it is very difficult to take out from the twisted canals,
especially in those sponges of the _tragos_ kind, so hard to cleanse.
In a word, the blood or humours, which the ancients have observed, is
no other than the mucilage or juice of the substance of these worms.

Dated at Guadaloupe, 1 March, 1757.




LXXIX. _Account of an Experiment, by which it appears, that Salt of
Steel does not enter the Lacteal Vessels; with Remarks. In a Letter to
the Rev._ Tho. Birch, _D. D. Secr. R. S. By_ Edward Wright, _M. D._

[Read Mar. 2, 1758.]

SIR,

THO’ iron is universally allowed to be one of the most powerful
medicines now in use, yet many physicians observing, that the _fæces_
of patients, who used it either in a metallic or saline form, were
tinged of a black colour, have been led to think, that, in a metallic
state, it could not be reduced into particles fine enough to be
received by the lacteal vessels; and if taken in a saline form, that
it underwent a precipitation in the intestines, by which, being
reduced to an earth or calx, it was in like manner rendered incapable
of making its way into the blood. But the accurate experiments, with
which Signor Menghini has favoured the public in the Memoirs of the
Bononian Academy[34], sufficiently prove, that the ore and filings of
iron, finely levigated, enter the blood in considerable quantity; as
does also the _crocus_, _calx_, or earthy part of the metal, tho’ in
less proportion than the two former, which were found to act with a
violent _stimulus_ on the vessels, and to have dissolved and broke the
_crasis_ of the blood of different animals, that had used them for some
weeks in large doses mixed with their ordinary food. Tho’ it must be
allowed, that these experiments are very curious, yet the subject seems
to require a further inquiry, viz. _Whether iron is capable of entering
the blood in a state of solution, or under a saline form_: for, from
the violent _stimulus_, as well as from the dissolution of the blood,
and other symptoms brought on by the use of the ore and filings, these
substances (not being properly dissolved) appear to have acted in a
manner so grossly mechanical, that, whatever Signor Menghini may think,
very little is to be concluded from them, with regard to the action of
iron on the human body, in such cases, as indicate its use, and where a
rational physician would think proper to prescribe it as a medicine.

Having read Signor Menghini’s memoir, I recollected, that in the year
1753 I had, with the assistance of two friends, made the following
experiment, in order to discover, whether iron, in a saline form, is
capable of entering the lacteals.

An ounce and a half of salt of steel dissolved in a sufficient quantity
of water, filtrated and mixed with about a pound of bread and milk,
were forced down the throat of a dog, that had been kept fasting for
36 hours. An hour after he had swallowed this mixture, having secured
him in a supine posture, as is usual in such experiments, we opened the
abdomen, and observed the lacteal vessels, like white threads, running
along the mesentery in a very beautiful manner. Upon slitting open part
of the small guts, we there found a good deal of the mixture, which
appeared frothy, but without any black colour, or the least sign of the
salt being precipitated; and struck a deep inky colour with infusion
of galls. Tho’ the white colour of the lacteals convinced us, that
they were full of chyle, yet, as it would have been impossible to have
collected a sufficient quantity of it from them, we found it necessary
to open the thorax, and tie the thoracic duct a little above the
receptacle, which, from the ligature, soon became turgid, the animal
being alive and warm, and the chyle still continuing its course towards
the thoracic duct. Having cut open the receptacle, we easily collected
a sufficient quantity of chyle, and immediately mixed therewith, drop
by drop, infusion of galls; a very simple and easy method, by which an
incredibly small quantity of salt of steel may be discovered in most
liquors: but not the smallest change of colour was observed, tho’ they
were rubbed together for some time, and allowed to stand several hours.
Now had there been a single atom (so to speak) of the salt in so small
a portion of chyle, as that used in this experiment, which was, as near
as I could guess, some what less than half an ounce, it is not to be
imagined, that it could have failed to discover itself by this method
of trial; for upon adding one fourth of a grain of the salt, this
mixture instantly became of a bright purple: and I have found, by other
experiments, that the smallest quantity of salt of steel shews itself
as readily in the chyle by galls, as in any other liquor of the same
consistence.

This experiment (which was as fair as could have been desired),
together with another observation I have made, _viz._ that neither the
blood nor urine of patients, during the use of salt of steel, in the
least change colour with galls, renders it more than probable, that
this salt _does not enter the blood_.

As the salt was found to have undergone no change in the small guts,
it appears, that it is not prevented from entering the lacteals by its
being decomposed or precipitated, as has been imagined; but, on the
contrary, that what renders it incapable of being received by these
vessels, is its _astringency_: for the lacteals seem to be endowed with
that admirable faculty of admitting such particles of pure chyle as
they happen to be in contact with, and of accommodating their diameters
to them, at the same time that by their natural irritability, and
power of constriction they obstinately exclude such as are astringent;
which, were they to enter the lacteals, would either produce dangerous
obstructions in these vessels, or, if they got into the blood, would
occasion polypous concretions in the larger vessels, or coagulations
incapable of being transmitted thro’ the minute vessels of the lungs;
the effects of which would be either sudden death, or at least
inflammations and suppurations from obstructions in the pulmonary
vessels; inconveniences, which nature, by precluding astringents from
entering the lacteals, has carefully and wisely avoided.

Salt of steel, taken internally, must retain its astringency until it
be precipitated; which can scarce ever fail to happen in the great
guts, from the putrid _fæces_ they contain, which are always observed
to be tinged of a black colour from the metallic basis of the salt,
part of which, as it has little or no astringency, may, no doubt,
enter the blood, as Signor Menghini observed of the _crocus_, which
is the same substance; and we know, from the experiments of Lister
and Musgrave[35], that particles much grosser than those of the white
chyle, provided they be not astringent, or very acrid, are conveyed by
the lacteals. But the metallic basis being separated from its acid, and
thus reduced to a mere calx or earth, can scarce be supposed to have
any medicinal quality whatsoever, or at least to have any share in the
virtues justly attributed to salt of steel.

As this salt is not only astringent, and consequently a strengthener,
but at the same time acts with a gentle _stimulus_, all its virtues
(which are known to be very great in diseases, where the fluids are
either viscid, cold, and phlegmatic, or dissolved and watery, from a
laxity of the solids) may be accounted for from its immediate effects
on the stomach and _primæ viæ_, and on the system of the solids in
general by consent; which it would be needless to illustrate by similar
examples, because well known to every one the least versed in medical
studies. I shall therefore only beg leave, from the obvious qualities
of this medicine, and from what has been observed above, to deduce the
following corollaries.

1. That salt of steel has no deobstruent or aperient virtue by any
immediate action, that it can possibly have on the blood, or other
animal fluids, as some have imagined; but that, on the contrary, it
owes this quality to its _not entering the blood_, which it would
otherwise coagulate, and to _its action on the solids alone_.

2. That in diseases proceeding from a laxity of the solids, great care
ought to be taken to restore and invigorate the _primæ viæ_; since a
medicine (and this we may presume not the only one) whose immediate
action is confined to those parts, is yet found by experience to
produce so salutary effects in such diseases.

3. That as this salt does not enter the blood, and consequently cannot
be in danger of too much stimulating or constricting the vessels, on
which it only acts by consent, it may, in small doses, be successfully
used in many cases, where it has been imagined to be hurtful,
particularly in consumptions of the lungs, so frequent and fatal in
this island; which are commonly attended with too great a laxity of
the _primæ viæ_, and of the solids in general, tho’ they seem more
immediately to proceed from a laxity and weakness of the pulmonary
vessels; in which circumstances it must be of the utmost consequence
to restore the tone of those principal organs of chylification, the
_primæ viæ_; as good chyle not only corrects the acrimony of the blood,
which in the advanced stages of consumptions so much prevails, but
likewise saves a great deal of labour, which the lungs (already too
much oppressed) must otherwise undergo from a crude and ill-concocted
chyle. Agreeably to this we find, in the _Essays Physical and Literary_
of Edinburgh[36], two well-vouched histories of patients far gone in
consumptions, with the usual symptoms of pain in the breast, cough,
gross spitting of fetid matter, difficulty of breathing, hectic fits,
and morning sweats, perfectly cured in a few weeks, by the use of the
Hartfell-Spaw near Moffat; which, contrary to what is observed in most
natural chalybeat waters, contains a fixed vitriol of iron.


These, Sir, are the few observations I had to make at present on this
subject. I have taken the liberty to address them to you, in order, if
you shall think proper, to be communicated to your illustrious Society;
which, I hope, will continue to latest posterity those interesting
researches for the advancement of every branch of natural knowlege, by
which it has already acquired so much and so deserved honour; and am,
with the greatest respect,

                                 SIR,
                  Your most obedient humble Servant,
                            Edward Wright.

Strand, Feb. 28. 1758.




LXXX. _A Dissertation on the Antiquity of Glass in Windows. In a Letter
to the Rev._ Tho. Birch, _D. D. Secret. R. S. By the Rev._ John Nixon,
_M. A. F.R.S._

[Read Mar. 2, 1758.]

                                                 London, March 2. 1758.

Dear Sir,

I Had the honour last winter to lay before the Royal Society a few
observations upon some of the curiosities found at Herculaneum,
_&c._[37]. Among other articles, I just mentioned a piece of a plate
of white glass; and now beg leave to inquire into the uses, to which
such plates might be applied in the early age, to which this fragment
undoubtedly belongs.

And here a person, who forms his ideas of ancient customs by what
he sees practised in later times, may be ready to offer several
conjectures; in some of which he will, probably, be mistaken; as in
others he may be justified by the genuine evidences of antiquity.

And, first, It is obvious to imagine, that such plates might serve
for _specula_, or looking-glasses. And, indeed, that _specula_ were
anciently made, not only of metals, and some stones, as the[38]
phengites, _&c._ but also of glass, may, I think, be collected from
Pliny, who, having mentioned the city of Sidon as formerly famous for
glass-houses, adds immediately afterwards, _Siquidem etiam specula
excogitaverat_[39]. But then it is to be observed, that before the
application of quicksilver in the constructing of these glasses (which,
I presume, is of no great antiquity), the reflection of images by such
_specula_ must have been effected by their being besmeared _behind_,
or tinged _thro’_ with some dark colour, especially black, which would
obstruct the refraction of the rays of light[40]. Upon these hypotheses
(supposing the tincture to be given after fusion) the _lamina_ before
us may be allowed to be capable of answering the purpose here assigned.

It may further be suggested, that plates of this kind might be intended
to be wrought into lens’s, or convex glasses, either for burning, or
magnifying objects placed in their focus. But this designation cannot
be supported by proper vouchers from antiquity. On the contrary, we
are informed, that the ancients used either _specula_[41] of metal, or
balls[42] of glass for the former of these purposes; as it is well
known, that glass was not applied to the latter, in optical uses, till
the beginning of the XIIIth century[43].

However, we may with greater probability propose another use, for
which the ancients might employ such plates of glass, as are now under
consideration, _viz._ the adorning the walls of their apartments by
way of wainscot. This I take to be the meaning of the _vitreæ cameræ_
mentioned by Pliny[44]; who intimates, that this fashion took its rise
from glass being used by M. Scaurus[45] for embellishing the scene
of that magnificent theatre, which he erected for exhibiting shows
to the Roman people in his ædileship[46]. And we may collect from
the same author[47] (what is further confirmed by his contemporary
[48]Seneca), that this kind of ornament had been admitted, in his
time, into chambers in houses, baths, _&c._ Whether the plates used for
this purpose were stained with various colours (as mentioned above),
or had tints of divers kinds applied to the back part of them, I shall
not pretend to determine: but in either way they would have a very
agreeable effect.

The last destination, which the obvious congruity of the thing itself,
countenanced by the practice of many ages past, as well as of the
present time, would induce one to ascribe to such plates of glass, is
that of windows for houses, baths, portico’s, _&c._ But I am sensible,
that whoever should be hardy enough to advance such an hypothesis,
would be censured as an innovator, in opposing the general opinion of
the connoisseurs in antiquity. These gentlemen are almost unanimous in
asserting, that whenever we meet with mention made of _specularia_ in
ancient writers (especially those _of_, or near _to_, the age, to which
we must refer this fragment), we are to understand by that term nothing
but fences made of _laminæ_, either of a certain stone called from its
transparent quality _lapis specularis_[49], brought first from Hispania
Citerior, and afterwards found in Cyprus, Cappadocia, Sicily, and
Africa; or of another stone of the same nature, _viz._ the phengites.
These, tho’ expressly distinguished from each other by Pliny[50],
are yet reckoned by some moderns[51] as one and the same thing; and
thought to have been nothing but a kind of white transparent talc, of
which (according to Mons.[52] Valois) there is found a great quantity
in Moscovy at this day.

Now that this _lapis specularis_, or phengites, was really used for
windows by the ancient Romans in their houses, _&c._ cannot be denied;
since (according to the opinion of the learned[53] in antiquity) this
usage is mentioned by Seneca[54] among other improvements in luxury
introduced in his time. But whether it was so used exclusive of other
materials (particularly glass), may, I think, admit a doubt. Salmasius
is of opinion[55], that nothing can be determined upon this point from
the word _specular_ itself, which seems to be a generical term, equally
applicable to windows of all kinds, whether consisting of the _lapis
specularis_, or any other transparent substance.

And as (according to this learned writer) there is nothing in the term
_specular_ itself, which hinders it from being extended to windows made
of other materials besides those above-mentioned; so others imagine,
that there are some intimations in ancient authors, which require, that
it should actually be so extended. Thus Mr. Castells, the ingenious
illustrator of the villa’s of the ancients, thinks[56], that “if this
had not been the case, Palladius would not have given directions to his
husbandman to make _specularia_ in the _olearium_[57], or store-room,
where the olives were preserved. For it appears (says this author) from
Pliny’s describing a temple[58] built of the _lapis specularis_, or
phengites, as the greatest rarity in his time, and the mention Plutarch
makes of a room in Domitian’s palace lined with it, that it was not
common enough for husbandmen to purchase;” _viz._ in such quantities,
as were required for the purposes mentioned above.

I shall not take upon me to decide upon the weight of this argument of
Mr. Castells; but only observe, that if any one should be induced by
it to think, that the use of glass for windows may be of much greater
antiquity than is commonly allowed, or even as old as the fragment,
which occasions these remarks, he may find other probable reasons to
corroborate his opinion. As, first, that there seems to have been a
natural and obvious transition from the practice of using glass plates
for the ornamenting the walls of apartments to that of introducing
light into those apartments, (as we find the _lapis specularis_
was in fact employed at the same time for both those purposes) and
consequently it seems reasonable to suppose, that the latter of these
applications could not be long in point of time after the former.
But it appears from the authorities produced above, that the former
of these usages did actually subsist in the age[59] of Pliny; and
therefore before the destruction of Herculaneum, where he lost his
life[60]. From whence we may draw no improbable conclusion, that the
latter destination of plates of glass, (_viz._ for window-fences) did
likewise precede the same event.

Give me leave to add further, that this presumptive argument in
favour of the antiquity of windows made of plates of glass receives
an additional force from the close relation, which must be allowed to
subsist between them, and those composed of the _lapis specularis_. The
former must be looked upon as an improvement upon the other, as they
answered all the purposes of convenience, and at the same time were
more beautiful; and being the manufacture[61] of Italy, might probably
be purchased at a less expence. Upon all which accounts it seems
reasonable to conclude, that one of these inventions would naturally be
introductory to the other: and consequently, that as window-lights of
the _lapis specularis_ began to be used within the memory of Seneca,
who died[62] under Nero, about _anno Christi_ 68. (_Helvic._), the
original of those of glass may have fair pretensions to a place within
the period assigned in the foregoing paragraph, _viz._ some years
before the destruction[63] of Herculaneum, in whose ruins the plate
before us was buried.


To conclude: I need not observe to you, that all the evidence here
produced to prove the usage of glass-windows to have been coæval
with the fragment we are now considering, is of the conjectural kind
only: for, I must confess, I have not been able to trace it up by any
positive authority higher than about 200 years short of the epocha last
mentioned, _viz._ to the latter end of the third century[64], when
it is expresly mentioned by Lactantius in these words:--_Manifestius
est, mentem esse, quæ per oculos ea, quæ sunt opposita, transpiciat,
quasi per fenestras lucente vitro aut speculari lapide obductas._--De
opificio Dei, cap. v.

I am,

                                 SIR,
                  Your most obedient humble Servant,
                               J. Nixon.




LXXXI. _An Account of an extraordinary Case of the Efficacy of the Bark
in the Delirium of a Fever. By_ Nicˢ. Munckley, _M. D. Physician to_
Guy’s-Hospital, _and F.R.S._

[Read April 6, 1758.]

AS the following case contains some circumstances, which are curious in
themselves, and which may be of service to be known, I have thought it
proper to be laid before the Society.

On Sunday the 5th of March I was sent for to a gentleman, of about 30
years of age, who had been for some days ill of a fever. I found him
with a degree of heat considerably above what was natural, and with a
pulse rather low, but quick, and beating, as measured by a stop-watch,
about a hundred strokes in a minute. In this situation he continued,
without any remarkable alteration, for the two following days; and,
from the appearance of this disease, I imagined, that it would not be
speedily terminated. On Wednesday, the third day of my seeing him, I
found him however much better; his heat being considerably abated, and
his pulse being more than twenty strokes in a minute slower than it
had been the day before. On this alteration, so much in his favour,
it might have been thought he was growing well, had it not been, that
there was no appearance either by sweat or urine, or on the skin, by
which it could be imagined the disease was perfectly judged. On this
account no alteration was made in his treatment that day: but finding,
the next morning, that he had slept well the preceding night, and that
his pulse continued quiet, being no more than 74 strokes in a minute,
he was allowed to get up in the evening, to have his bed made; and I
should have thought him well, had not every appearance of a critical
separation been still wanting. On this account, I thought him to be
very liable to a return of his fever; and therefore, when early the
next morning I was informed, that he had been without any sleep,
and quite delirious, the whole night, I was not greatly alarmed, as
thinking he had a feverish paroxysm, to which the bark would probably
put an end. When I saw him that morning, I found him very delirious;
but, to my great surprise, quite free from all kind of fever whatever;
his pulse being then as calm as it had been the preceding day. In this
condition he remained all that day, and the following night; nothing,
that was attempted to relieve him, having done him the least service:
on the contrary, his delirium increased so much, as to make it very
difficult for the attendants to keep him in bed. The next morning he
was much as he had been the day before; his imagination continuing
greatly disturbed, and he at times laughing, and playing antic tricks,
and using gestures the most opposite to his common demeanour when
well; and which, tho’ the pulse had not been so perfectly quiet, had
more the appearance of a _mania_, than of the delirium of a fever. In
this unhappy situation, there was but one thing, which seemed likely
to bring the affair to a speedy determination: this it was proper to
attempt, tho’ the indications for it were very obscure, and the event
perfectly uncertain. On recollecting the time of this delirium’s
coming on, which was about 36 hours after the pulse had grown quiet;
and perceiving, that one glass of the water, which had been made in
the night, was thick, and seemed disposed to drop a sediment; there
was some reason to suspect, and indeed to hope, that tho’ the pulse
had been perfectly calm during the whole time of the delirium, there
was something of the fever still at the bottom of this complaint.
From these indications, obscure as they were, it was judged proper to
make a trial of the bark; which was accordingly ordered to be taken
immediately, and to be repeated every two hours. This method succeeded
beyond what could have been imagined; insomuch that it was observable,
even by the attendants on this gentleman, that his mind came evidently
more and more to itself after every dose: and in the evening, after he
had taken six drachms, his urine grew thick, and dropt a lateritious
sediment; and, excepting the weakness naturally consequent on such
violent emotions as he had undergone, both of mind and body, he was
as well as ever he had been in his life. He hath repeated the bark at
proper intervals, as is usual after intermittent fevers, and continues
to this day perfectly well.

The use of the bark, in the most irregular intermittent disorders, is
very happily so well known in this island, that it might perhaps have
been thought needless to have recited any case merely in confirmation
of this practice: and I am too well aware of the insufficiency of
every thing, but a number of facts on which to found any philosophical
truth, to presume to rest any thing on one single instance only. But
the case above related is of so very extraordinary a kind, as to make
it worthy of being mentioned, both on its own account, and for that
analogy, which being found by experience to subsist between diseases,
affords the surest method of reasoning on practical subjects. The two
remarkable circumstances of this case are, the delirium’s coming on,
and continuing, without any exacerbation of the pulse; and the bark’s
proving so speedy and effectual a remedy, tho’ given at a time, when
there was no appearance of any remission of the symptom, which it
was intended to remove. It hath been thought, that a quick pulse is
so essential to the definition of a fever, as to be a pathognomonic
symptom of it. But experience is against this notion: perhaps the
present case is a proof of the contrary; however this be, there have
not been wanting instances, in which, towards the end of a fever, the
pulse has grown quiet, without the abatement of any other symptom, and
the patient hath generally lain comatose, and with the appearance of
one, who hath taken a large quantity of opium. Galen, in the third book
of the Presages of the Pulse, mentions this symptom, and pronounces
it to be almost a fatal sign: and the same thing hath happened in
more instances than one, which have come to my knowlege. May not then
the above-recited case lead to this useful inquiry, Whether in fevers
of every kind, when the pulse is quiet, the bark is not proper to be
given, and likely to prove a remedy? In this case it proved absolutely
such: and that it is at least a safe medicine in all such cases, in
which any practitioner of experience or judgment would ever think
of giving it, is now certainly known. For my own part, I can safely
declare, that in near ten years experience of it in Guy’s-Hospital,
during which time I find I have given it, on different occasions, to
above five hundred patients in that house only, I never, from the
most accurate observation I could make, saw it do any harm, or bring
on any bad symptom, even in cases where it did not succeed according
to the intention for which it was ordered; and (which I have thought
worth remarking) in chronical cases, even in those, where the bark
hath been by many thought the most prejudicial, when, on the coming on
of an intermittent fever, the bark hath been necessary to cure this
secondary disease, the original distemper hath gone on, according to
the best judgment I could form of it, exactly in the same manner, as it
would have done had the bark never been given.




LXXXII. _An Account of an Earthquake felt at_ Lingfield _in_ Surrey,
_and_ Edenbridge _in_ Kent, _on the 24th of_ January 1758. _By_ James
Burrow, _Esq., R. S. V. P._

[Read April 6, 1758.]

IN the London Chronicle, Nº. 181, published on the 25th of February
1758, in page 185, is the following article: “We hear, that about
two o’clock in the morning of the 24th of last month” (which was the
month of January), “an Earthquake was felt in the parishes of Worthe,
and East-Grinsted, in Sussex; Lingfield, in Surrey; and Edenbridge,
in Kent; and other adjacent places: which alarmed several of the
inhabitants very much; but no damage ensued.”

Mr. Burrow, having some connection with these two last parishes of
Lingfield and Edenbridge, immediately wrote to the Rev. Mr. Goodricke
of Lingfield, to inquire into the truth of this report: and Mr.
Goodricke’s answer confirmed the fact of its being felt there, and at
other adjacent places; and added, “that it shook the beds and windows,
and made the plates rattle; and went off with a noise, like a small
gust of wind.”

However, Mr. Burrow did not then judge it to be either regular or
proper to trouble the Society with this account; because Mr. Goodricke
only received it from hearsay and report, he himself happening to be
absent from Lingfield at that time.

But Mr. Burrow having passed some days, during the late recess of
the Society, at a place called Starborough-castle, which lies nearly
_between_ the two churches of Lingfield and Edenbridge (scarce four
miles distant from each other), he has had an opportunity of being
more particularly and circumstantially informed of the fact, as far
as relates to those two parishes: and he is now assured, that it was
certainly and undoubtedly felt and observed by _some_ persons in each
of those two parishes; tho’ (as it happened in the dead of the night,
when most people were fast asleep) it was not _generally_ perceived:
nor was it much spoken of, even by those, who were sure they felt it.

The persons, from whose own mouths he can authenticate the fact, are
James Martin, Adam Killick, Mrs. Jewell, and Mr. Chapman: and he has
no less doubt as to Mr. Orgles and Mrs. Pigott (who was waked and much
frighted by it), tho’ he did not indeed personally converse with either
of the two last.

These two, and Mrs. Jewell, all inhabit quite close to Lingfield
church-yard, on different sides of it: and Chapman lives within a
quarter of a mile of it, to the south-west.

James Martin lives within a bow-shot of Starborough-castle, at the
eastern edge of the parish of Lingfield, where it joins to that of
Edenbridge; and Adam Killick’s habitation is three miles north-east of
Starborough, at the north-western point of the parish of Edenbridge.

All these four, with whom Mr. Burrow personally conversed, agreed
as to the _time_ of the concussion; _viz._ between one and two in
the morning: and they all agreed as to the _shaking_ of their beds
and windows; and all of them described the _continuance_ of the
shock as not much more than instantaneous: but they did _not_ all
hear the _noise_, which _some_ of them observed it to conclude with;
particularly Adam Killick heard NO _noise_ at all; and yet, he says,
he was broad awake when it first began: and it shook his house and
bed, and made his windows rattle so much, that he was apprehensive of
their being broken; and even caused one pane of glass (which was indeed
loose before) actually to drop out. But James Martin, who was likewise
fully awake (as was his wife too), _did hear_ the noise distinctly. He
says, he felt his house and bed shake, heard his windows rattle, and
some earthen ware clatter upon a chest of drawers; and also heard a
noise, like the distant discharge of a cannon: whereupon he immediately
said to his wife, “Lord! what is _that_?” but she happening, at that
very instant, either to cough or sneeze (she cannot recollect which of
the two), did not, tho’ quite awake, perceive any thing at all of the
matter. However, she confirmed her husband’s asking her this question
under an apparent surprize.

Mr. Burrow had a very particular conversation with these two
separately: and he had also a very minute detail from Adam Killick
(who works for him as a sort of gardener at Starborough); who further
added, “that the shock waked and frighted his wife, tho’ she was fast
asleep before.”

6th April, 1758.

                                                          James Burrow.




LXXXIII. _An Account of the Case of the First Joint of the Thumb torn
off, with the Flexor Tendon in its whole Extent torn out. By_ Robert
Home, _late Surgeon to the Thirtieth Regiment of Foot, and Surgeon at_
Kingston upon Hull. _In a Letter to_ John Pringle, _M. D. F.R.S._

[Read April 6, 1758.]

SIR,

I Take the liberty of inclosing to you a case in surgery, which I
imagine is not very common. Marchetis indeed has an observation of the
same kind; and there are several others collected together by Mons.
Morand, in the second volume of the Memoires of the Royal Academy
of Surgery at Paris: but as I have not heard of that volume’s being
translated into English, and believe there is no observation of a
similar nature in the Philosophical Transactions, I beg the favour of
you to communicate it to the Royal Society, of which you are a Fellow;
and at the same time to make them an offer of the joint of the thumb,
with its adherent tendon, which you will receive at the same time with
this; hoping they will do me the honour of accepting it, as a testimony
(tho’ trifling) of my great esteem and respect for the most learned
Society in Europe. Your Friend Dr. Knox saw the patient dressed oftener
than once; and Mr. Thornhill, late Surgeon and Manmidwife in Bristol,
saw it when near healed.

I beg you will believe me to be, with great truth,

                                 SIR,
                          Your most obedient,
                       and most humble Servant,
                             Robert Home.

Hull, March 17th, 1758.


JAnuary 2d, 1758, William Taylor, 17 years of age, an apprentice to a
white-smith in this place, in endeavouring to make his escape from one,
who was going to correct him, opened the door of a cellar, and threw
himself into it; but in his hurry so intangled his right thumb with the
latch, that the whole weight of his body was suspended by it, until it
gave way, and was torn off at the first articulation; the flexor tendon
being at the same time pulled out in its whole length, having broke
when it became muscular. I was immediately sent for, found little or no
hæmorrhage, and the bone of the second phalanx safe, and covered with
its cartilage, but protruding considerably, occasioned by part of the
skin belonging to it being irregularly torn off with the first joint.

I was doubtful, whether or not I should be obliged, at last, to make a
circular incision, and saw the bone even with the skin; but thought it
proper to give him a chance for the use of the whole phalanx.

He complained only for the first day of a pretty sharp pain in the
course of the tendon; to which compresses, wrung out of warm brandy,
were applied: but his arm was never swelled; there was no _ecchymosis_;
nor had he so much fever, as to require bleeding even once. The cure
proceeded happily, no symptoms arising from the extracted tendon. At
the third dressing the bone was covered; and no other application but
dry lint was necessary during the whole time. No exfoliation happened;
yet it was twelve weeks before it was intirely cicatrised, owing to the
loss of skin: and he seems to enjoy the use of the stump as completely,
as if that tendon was not lost.




LXXXIV. _An Account of the late Discoveries of Antiquities at_
Herculaneum, _and of an Earthquake there; in a Letter from_ Camillo
Paderni, _Keeper of the Museum at_ Herculaneum, _and F.R.S. to_ Tho.
Hollis, _Esq; F.R.S. dated_ Portici, Feb. 1. 1758.

[Read April 6, 1758.]

WE have been working continually at Herculaneum, Pompeii, and Stabiæ,
since my last of Dec. 16, 1756. The most remarkable discoveries made
there are these, which follow.

February 1757, was found a small and most beautiful figure of a naked
Venus in bronze, the height of which is six Neapolitan inches. She has
silver eyes, bracelets of gold on her arms, and chains of the same
metal above her feet; and appears in the attitude of loosening one of
her sandals. The base is of bronze inlaid with foliage of silver, on
one side of which is placed a dolphin.

In July we met with an inscription, about twelve Neapolitan palms in
length, which I have here copied.

                 IMP·CAESAR·VESPASIANVS·AVG·PONTIF·MAX

           TRIB·POT·̅VĪĪ·IMP·X̅VĪĪ·P·P·COS·̅VĪĪ·DESIGN·̅VĪĪĪ

          TEMPLVM·MATRIS·DEVM·TERRAE·MOTV·CONLAPSVM·RESTITVIT

After having found a great number of volumes of papirus in Herculaneum;
many pugillaries, styles, and stands with ink in them, as formerly
mentioned; at length, in the month of August, upon opening a small box,
we also found, to our exceeding great joy, the instrument, with which
they used to write their manuscripts. It is made of wood, of an oblong
form, but petrified, and broke into two pieces. There is no slit in it,
that being unnecessary, as the ancients did not join their letters in
the manner we do, but wrote them separate.

In September were discovered eight marble busts, in the form of terms.
One of these represents Vitellius, another Archimedes; and both are
of the finest workmanship. The following characters, in a black tint,
are still legible on the latter, namely, ΑΡΧΙΜΕΔ which is all the
inscription that now remains.

In October was dug up a curious bust of a young person, who has a
helmet on his head, adorned with a civic crown, and cheek-pieces
fastened under his chin. Also another very fine bust of a philosopher,
with a beard, and short thick hair, having a slight drapery on his left
shoulder. Likewise two female busts; one unknown, in a veil; the other
Minerva, with a helmet; both of middling workmanship.

In November we met with two busts of philosophers, of excellent
workmanship, and, as may be easily perceived, of the same artist; but
unfortunately, like many others, without names.

In January was found a small, but most beautiful eagle, in bronze.
It hath silver eyes, perches on a _praefericulum_, and holds a fawn
between its talons.

In the same month we discovered, at Stabiæ, a term six palms high, on
which is a head of Plato, in the finest preservation, and performed in
a very masterly manner. Also divers vases, instruments for sacrificing,
scales, balances, weights, and other implements for domestic uses, all
in bronze.

At length I have finished, with much labour, the examination and
arrangement of the scales, balances, and weights, which are very
numerous in this museum; and, what is remarkable, many of the former,
with all the weights, exactly answer those now in use at Naples.
At present I am considering the liquid measures; and also engaged
in disposing the paintings in the new apartment allotted for them.
These affairs, with my usual province of inspecting the workmen, who
are busied in digging; my being obliged to keep an exact register of
every thing, that is discovered; besides other daily and accidental
occurrences; employ my time so intirely, that I have not a moment’s
repose, but in my bed.

The square belonging to the palace, in which the museum is deposited,
will be finished, and completely ornamented, by Easter. In the center
of it I have placed the bronze horse, which was broken in many pieces,
and restored by me, as mentioned in my last. In the walls of the
colonades are affixed all the inscriptions hitherto discovered: and I
shall yet adorn them with altars, curule chairs, and other antiquities
proper for such places. The principal entrance into the museum hath
been made to correspond with the grand stair-case. On the right side
of it stands the consular statue of Marcus Nonius Balbus, the father;
and on the left, that of Marcus Nonius Balbus, the son; with two
inscriptions relating to, and found near them. Upon the stair-case
are placed eight antique statues in bronze, on beautiful pedestals
of polished marble. In an opening in the center of the right hand
colonade is fixed the statue of the wife of the elder Balbus, with the
antique inscription belonging to it. At the entrance of the square,
a magnificent pair of iron gates, with palisades, are just put up,
ornamented with many bronzes, which are gilt; and on the sides of these
gates are two other consular statues of persons unknown.


The whole day and night of the 24th of last month it seemed as if Mount
Vesuvius would again have swallowed up this country. On that day it
suffered two internal fractures, which intirely changed its appearance
within the crater, destroying the little mountain, that had been
forming within it for some years, and was risen above the sides; and
throwing up, by violent explosions, immense quantities of stones, lava,
ashes, and fire. At night the flames burst out with greater vehemence,
the explosions were more frequent and horrible, and our houses shook
continually. Many fled to Naples, and the boldest persons trembled.
For my own part, I resolved to abide the event here at Portici, on
account of my family, consisting of eight children, and a very weak
and aged mother, whose life must have been lost by a removal in such
circumstances, and so rigorous a season. But it pleased God to preserve
us; for the mountain having vented itself that night and the succeeding
day, is since become calm, and throws out only a few ashes.




LXXXV. _A further Attempt to facilitate the Resolution of
Isoperimetrical Problems. By Mr._ Thomas Simpson, _F.R.S._

[Read April 13, 1758.]

ABOUT three years ago I had the honour to lay before the Royal
Society the investigation of a general rule for the resolution of
isoperimetrical problems of that kind, wherein one, only, of the two
indeterminate quantities enters along with the fluxions, into the
equations expressing the conditions of the problem. Under which kind
are included the determination of the greatest figures under given
bounds, lines of the swiftest descent, solids of the least resistance,
with innumerable other cases. But altho’ cases of this sort do, indeed,
most frequently occur, and have therefore been chiefly attended to by
mathematicians, others may nevertheless be proposed, such as actually
arise in inquiries into nature, wherein _both_ the flowing quantities,
together with their fluxions, are jointly concerned. The investigation
of a _rule_ for the resolution of these, is what I shall in this paper
attempt, by means of the following

GENERAL PROPOSITION.

_Let_ Q, R, S, T, &c. _represent any variable quantities, expressed in
terms of_ x _and_ y (_with given coefficients_), _and let_ q, r, s, t,
&c. _denote as many other quantities, expressed in terms of_ ẋ _and_ ẏ;
_It is proposed to find an equation for the relation of_ x _and_ y, _so
that the fluent of_ Qq + Rr + Ss + Tt, &c. _corresponding to a given
value of_ x (_or_ y), _may be a_ maximum _or_ minimum.

[Illustration]

Let _A E_, _A F_, and _A G_, denote any three values of the quantity
_x_, having indefinitely small _equi-differences E F_, _F G_; and let
_E L_, _F M_, and _G N_, (perpendicular to _A G_) be the respective
values of _y_, corresponding thereto; and, supposing _EF_ (= _FG_ =
_ẋ_) to be denoted by _e_, let _c M_ and _d N_ (the successive values
of _ẏ_) be represented by _u_ and _w_. Moreover, supposing _P´p´_
and _P´´p´´_ to be ordinates at the middle points _P´ P´´_, between
_E_, _F_ and _F_, _G_, let the former (_P´p´_) be denoted α, and the
latter (_P´´p´´_) by β; putting _A P´_ = _a_ and _A P´´_ = _b_. Then,
if _a_ and α (the mean values of _x_ and _y_, between the ordinates
_E L_ and _F M_) be supposed to be substituted for _x_ and _y_, in
the given quantity _Qq_ + _Rr_ + _Ss_ + _Tt_, _&c._ and if, instead
of _ẋ_ and _ẏ_, their equals _e_ and _u_ be also substituted, and the
said (given) quantity, after such substitution, be denoted by _Q´q´_ +
_R´r´_ + _S´s´_ + _T´t´_, _&c._ it is then evident, that this quantity
_Q´q´_ + _R´r´_ + _S´s´_ + _T´t´_, _&c._ will express so much of the
whole required fluent, as is comprehended between the ordinates _E L_
and _F M_, or as answers to an increase of _E F_ in the value of _x_.
And thus, if _b_ and β be conceived to be wrote for _x_ and _y_, _e_
for _ẋ_, and _w_ for _ẏ_, and the quantity resulting be denoted by
_Q´´q´´_ + _R´´r´´_ + _S´´s´´_ + _T´´t´´_, _&c._ this quantity will,
in like manner, express the part of the required fluent corresponding
to the interval _F G_. Whence that part answering to the interval _E
G_ will consequently be equal to _Q´q´_ + _R´r´ &c._ + _Q´´q´´_ +
_R´´r´´ &c._ But it is manifest, that the whole required fluent cannot
be a _maximum_ or _minimum_, unless this part, supposing the bounding
ordinates _E L_, _G N_ to remain the same, is also a _maximum_ or
_minimum_. Hence, in order to determine the fluxion of this expression
(_Q´q´_ + _R´r´ &c. Q´´q´´_ + _R´´r´´ &c._) which must, of consequence,
be equal to nothing, let the fluxions of _Q´_ and _q´_ (taking α and
_u_ as variable) be denoted by _̅Q_̇α and _̅qu⋅_; also let _̅R_̇α and
_̅ru⋅_ denote the respective fluxions of _R´_ and _r´_; and let, in
like manner, the fluxions of _Q´´, q´´, R´´, r´´, &c._ be represented
by _̿Q_̇β, _̿q͘w_, _̿R_͘͘β͘ _̿rẇ_, _&c._ respectively. Then, by the
common rule for finding the fluxion of a rectangle, the fluxion of our
whole expression (_Q´q´_ + _R´r´ &c._ + _Q´´q´´_ + _R´´r´´ &c._) will
be given equal to _Q´ ̅qu⋅_ + _q´ ̅Q_̇α + _R´ ̅ru⋅_ + _r´ ̅R_̇α _&c._
+ _Q´´̿qẇ_ + _q´´ ̿Q_̇͘͘͘β + _R´´ ̿r͘w_ + _r´´ ̿R_̇β _&c._ = 0.

But _u_ + _w_ being = _GN_ - _EL_, and β - α = (_GN_ - _EL_) ⁄ 2 (a
constant quantity), we therefore have _ẇ_ = -_u͘_, and ̇β = ̇α: also
_u_ being (= 2_rp´_) = 2α - 2_EL_, thence will _u͘_ = 2̇α: which values
being substituted above, our equation, after the whole is divided by
̇α, will become

    2_Q´ ̅q_ + _q´ ̅Q_ + 2_R´ ̅r_ + _r´ ̅R, &c._ - 2_Q´´ ̿q_ + _q´´
    ̿Q_ - 2_R´´ ̿r_ + _r´ ̿R, &c._ = 0;

    or, _Q´´ ̿q_ - _Q´ ̅q_ + _R´´ ̿r_ - _R´ ̅r &c._ = (_q´ ̅Q_ + _q´´
    ̿Q_) ⁄ 2 + (_r´ ̅R_ + _r´´ ̿R_) ⁄ 2, _&c._

But _Q´´ ̿q_ - _Q´ ̅q_, the excess of _Q´´ ̿q_ above _Q´ ̅q_, is
the increment or fluxion (answering to the increment, or fluxion,
_ẋ_) arising by substituting _b_ for _a_, β for α, and _w_ for _u_.
Moreover, with regard to the quantities on the other side of the
equation, it is plain, seeing the difference of _q´ ̅Q_ and _q´´ ̿Q_
is indefinitely little in comparison of their sum, that _q´ ̅Q_ may be
substituted in the room of (_q´ ̅Q_ + _q´´ ̿Q_) ⁄ 2, _&c._ which being
done, our equation will stand thus:

  _Flux. Q´ ̅q_ + _R´ ̅r &c._ = _q´ ̅Q_ + _r´ ̅R &c._

But _q´ ̅Q_ + _r´ ̅R &c._ represents (by the preceding notation) the
fluxion of _q´Q´_ + _r´R´ &c._ (or of _Qq_ + _Rr &c._) arising by
substituting α for _y_, making α alone variable, and casting off ̇α.
If, therefore, that fluxion be denoted by ̇υ, we shall have _flux. Q´
̅q_ + _R´ ̅r &c._ = ̇υ, and consequently _Q´ ̅q_ + _R´ ̅r &c._ = υ. But
_Q´ ̅q_ + _R´ ̅r &c._ (by the same notation) appears to be the fluxion
of _Q´q´_ + _R´r´ &c._ (or of _Qq_ + _Rr &c._) arising by substituting
_u_ for _ẏ_, making _u_ alone variable, and casting off _̇u_. Whence
the following


GENERAL RULE.

_Take the fluxion of the given expression_ (_whose fluent is required
to be a_ maximum _or_ minimum) _making_ ẏ _alone variable; and, having
divided by_ ÿ, _let the quotient be denoted by_ υ: _Then take, again,
the fluxion of the same expression, making_ y _alone variable, which
divide by_ ẏ; _and then this last quotient will be_ = ̇υ.

When _ẏ_ is not found in the quantity given, υ will then be = 0; and,
consequently, the expression for ̇υ, equal to nothing also. But if
_y_ be absent, then will ̇υ = 0, and consequently the value of υ = a
constant quantity. It is also easy to comprehend, that, instead of _ẏ_
and _y, ẋ_ and _x_ may be made successively variable. Moreover, should
the case to be resolved be confined to other restrictions, besides that
of the _maximum_ or _minimum_, such as, having a certain number of
other fluents, at the same time, equal to given quantities, still the
same method of solution may be applied, and that with equal advantage,
if from the particular expressions exhibiting all the several
conditions, one general expression composed of them all, with unknown
(but determinate) coefficients, be made use of.

In order to render this matter quite clear, let _A, B, C, D, &c._ be
supposed to represent any quantities expressed in terms of _x, y_, and
their fluxions, and let it be required to determine the relation of _x_
and _y_, so that the fluent of _Aẋ_ shall be a _maximum_, or _minimum_,
when the cotemporary fluents of _Bẋ, Cẋ, Dẋ, &c._ are, all of them,
equal to given quantities.

It is evident, in the first place, that the fluent of _Aẋ_ + _bBẋ_
+ _cCẋ_ + _dDẋ, &c._ (_b, c, d, &c._ being any constant quantities
whatever) must be a _maximum_, or _minimum_, in the proposed
circumstance: and, if the relation of _x_ and _y_ be determined (_by
the rule_), so as to answer this single condition (under all possible
values of _b, c, d, &c._) it will also appear evident, that such
relation will likewise answer and include all the other conditions
propounded. For, there being in the general expression, thus derived,
as many unknown quantities _b, c, d, &c._ (to be determined) as there
are equations, by making the fluents of _Bẋ, Cẋ, Dẋ, &c._ equal to the
values given; those quantities may be so assigned, or conceived to be
such, as to answer all the conditions of the said equations. And then,
to see clearly that the fluent of the first expression, _Aẋ_, cannot
be greater than arises from hence (other things remaining the same)
let there be supposed some other different relation of _x_ and _y_,
whereby the conditions of all the other fluents of _Bẋ, Cẋ, Dẋ, &c._
can be fulfilled; and let, _if possible_, this new relation give a
greater fluent of _Aẋ_ than the relation above assigned. Then, because
the fluents _bBẋ, cCẋ, dDẋ, &c._ are given, and the same in both cases,
it follows, according to this supposition, that this new relation must
give a greater fluent of _Aẋ_ + _bBẋ_ + _cCẋ_ + _dDẋ, &c._ (under all
possible values of _b, c, d, &c._) than the former relation gives:
_which is impossible_; because (whatever values are assigned to _b,
c, d, &c._) _that_ fluent will, it is demonstrated, be the greatest
possible, when the relation of _x_ and _y_ is that above determined, by
the General Rule.

To exemplify, now, by a particular case, the method of operation above
pointed out, let there be proposed the fluxionary quantity (_xⁿ yᵐ
ẏᵖ_) ⁄ _ẋ⁽ᵖ ⁻ ¹⁾_; wherein the relation of _x_ and _y_ is so required,
that the fluent, corresponding to given values of _x_ and _y_, shall
be a _maximum_, or _minimum_. Here, by taking the fluxion, making _ẏ_
alone variable (_according to the rule_) and dividing by _ÿ_, we shall
have (_pxⁿ yᵐ ẏ⁽ᵖ ⁻ ¹⁾_) ⁄ _ẋ⁽ᵖ ⁻ ¹⁾_ = υ. And, by taking the fluxion
a second time, making _y_ alone variable, and dividing by _ẏ_, will be
had (_mxⁿ y⁽ᵐ ⁻ ¹⁾ ẏᵖ_) ⁄ _ẋ⁽ᵖ ⁻ ¹⁾_ = ̇υ. Now from these equations to
exterminate υ, let the latter be divided by the former; so shall _mẏ_
⁄ _py_ = ̇υ ⁄ υ; and therefore _ay⁽ᵐ ⁄ ᵖ⁾_ = υ (_a_ being a constant
quantity). From whence _y⁽ᵐ ⁄ ᵖ⁾ẏ_ = _(a ⁄ p)⁽¹ ⁄ ⁽ᵖ ⁻ ¹⁾⁾_ × _ẋx⁽⁻⁽ⁿ ⁄
⁽ᵖ ⁻ ¹⁾⁾⁾_; and consequently (_p_ ⁄ (_m + p_)) × _y⁽⁽ᵐ + ᵖ⁾ ⁄ ᵖ⁾_ = _(a
⁄ p)⁽¹ ⁄ ⁽ᵖ ⁻ ¹⁾⁾_ × (_p_ - 1) ⁄ (_p_ - _n_ - 1) × _x_⁽⁽_ᵖ_ ⁻ _ⁿ_ ⁻ ¹⁾
⁄ ⁽_ᵖ_ ⁻ ¹⁾⁾.

Let there be now proposed the two fluxions _xⁿyᵐẋ_ and _xᵖy⒬ẏ_, the
fluent of the former being required to be a _maximum_, or _minimum_,
and that of the latter, at the same time, equal to a given quantity.
Then the latter, with the general coefficient _b_ prefixed, being
joined to the former, we shall here have _xⁿyᵐẋ_ + _bxᵖy⒬ẏ_. From
whence, by proceeding as before, _bxᵖy⒬_ = υ, and _mxⁿy⁽ᵐ ⁻ ¹⁾ẋ_ +
_qbxᵖy⁽ᵖ ⁻¹⁾ẏ_ = ̇υ. From the former of which equations, by taking the
fluxions on both sides, will be had _pbx⁽ᵖ ⁻¹⁾y⒬ẋ_ + _qbxᵖy⁽⒬ ⁻ ¹⁾ẏ_ (=
̇υ) = _mxⁿy⁽ᵐ ⁻ ¹⁾ẋ_ + _qbxᵖy⁽⒬ ⁻ ¹⁾ẏ_. Whence _pbx⁽ᵖ ⁻ ¹⁾y⒬_ = _mxⁿy⁽ᵐ
⁻ ¹⁾_; and therefore _pby⁽⒬ ⁻ ᵐ ⁺ ¹⁾_ = _mx⁽ⁿ ⁻ ᵖ ⁺ ¹⁾_. And in the
same manner proper equations, to express the relation of _x_ and _y_,
may be derived, in any other case, and under any number of limitations.




LXXXVI. _Observations on the_ Alga Marina latifolia; _The Sea Alga with
broad Leaves. By_ John Andrew Peyssonel, _M.D. F.R.S. Translated from
the_ French.

[Read April 13, 1758.]

HAVING cast anchor at Verdun, the road at the entrance of the river of
Bourdeaux, I was fishing with a kind of drag-net upon a bank of sand,
which was very fine and muddy. We collected a number of sea-plants,
and among them the great broad-leaved Alga, which I did not know: and
as the root or pedicle of this plant appeared to be very particular, I
observed it with attention. The following is its description, and the
detail of my observations.

From a pedicle, which is sometimes flat, and sometimes round (for they
vary in these plants, and might be about three lines in diameter,
and an inch high, of a blackish colour, and coriaceous substance,
approaching to the nature of the bodies of lithophyta), a single
flat leaf arises, about an inch or an inch and half broad, thick in
its middle to about three lines, ending at the sides in a kind of
edge, like a two-edged sabre, almost like the common Alga, formed of
longitudinal fibres interlaced with other very delicates ones, and the
whole filled with a thick juice, like the _parenchyma_ of succulent
plants, such as the Sedum, Aloes, and the like, of a clear yellowish
green, and transparent. This first leaf is always single, and serves
instead of a trunk or stem to the whole plant.

When it rises to about a foot high, more or less, it throws out at the
sides other leaves formed of a continuation of the longitudinal fibres;
and these second leaves are of the same thickness and substance with
the first: they are two or three feet long, and the whole plant is
five or six, or more (for one can hardly tell the length); and is not
capable of supporting itself, but is sustained by the strength of the
waters, in which it floats.

The substance of the plant is not so solid as that of the common Alga,
which is capable of drying as it fades, and of being kept: whereas
the leaves of this great Alga shrink and wither in the air, become
of a blackish colour, and very friable, or indeed soon fall into
putrifaction. I never observed, that they bore any fruit: perhaps this
was not the season.

But what we find particular in this plant is its root or foot: First,
this pedicle extends in ribs, like what we call the thighs of certain
trees: these thighs are in right lines: perhaps they run in the same
direction or situation, that is, placed north and south, or east and
west; but this I could not observe. They are about three or four
lines high towards the pedicle, and, ending, are lost. They flourish
and spread at the bottom, forming an elliptical bladder, like an egg,
flattened above and below, and rounded at the sides, being intirely
empty: it is rough without, and very smooth within. This egg, or oval
bladder, is exactly round at the ends of the great diameter, but varies
a little in the lesser diameter, and forms itself like the body of a
fiddle. The under part is a little flattened; and there is a hole,
which is very considerable, in the center of the two diameters. This
hole is about an inch wide, and is quite round: it gives passage to
the root, or pivot, which I shall by and by mention: the edges appear
to turn a little inward: and it is by this hole that the egg fills
with sea-water. The whole substance of this bladder or egg is of a
coriaceous matter, firm and transparent, and of a clear green; nor can
there be any fibres, either longitudinal or transverse, observed upon
it.

The vault at the top, surmounted by the thighs, is as it were
granulated; but at the rounding of the egg it produces a kind of
_mammæ_, or little elevations, very round and cylindrical, intirely
full; of the same nature and substance with the egg.

In examining the under part of the egg, we found a second rank of these
_mamellæ_, somewhat longer than the first, and at equal distances
from one another, in a circular line; then a third yet longer; then a
fourth, which at the extremities were bifurcated; and at last a fifth
rank, which divided into three, and sometimes into five, branches:
these last, placed round the hole, were wreathed inwards, and several
were joined together, and only formed a small body; and in wreathing
themselves thus they close and embrace the pivot mentioned below.
None of these _mamellæ_ have any apparent opening: their substance is
compact, of the same nature with the bladder or egg, that produces them.

Below the trunk and thighs the plant protrudes a pivot, of a like
substance with that of the bladder. This pivot, which is large at its
origin, proceeding thus from the trunk and thighs, forms something like
the knot of the sea-tree: it descends perpendicularly to the trunk,
diminishing as it lengthens, and as it grows round; and then divides
into a number of _mamellæ_, branched and wreathed inwards so firmly, as
not to be retracted; of a coriaceous nature, blackish, forming a bunch
like what we call the Rose of Jericho. I cannot recollect the name of
this plant or flower.

This bunch, or wreathed rose, incloses a heap of gravel, as if
petrified or hardened, and ends upon a level with the hole of the egg,
exactly as high as the last rank of _mamellæ_, which wreath upon,
embrace, and sustain it, leaving always an empty space to let the
sea-water pass in, which should fill the inside of the egg or bladder,
and even to let in little fishes and shells.

I was surprised to find in one little living muscles, as they always
are attached to some solid body by their beards. Now by what means
could they enter into this egg? I conjectured, that they had their
beginning there, by the seminal matter of muscles carried in by the
sea-water. I also found some small star-fish, whose rays might be about
four or five lines long.

If my stay here had been longer, I had continued my observations;
and perhaps should have made some discoveries. It belongs to the
academicians of Bourdeaux to push these observations further, if they
think proper.

From the Entrance of the river of Bourdeaux, the 4th of August, 1756.

                                                             Peyssonel.




LXXXVII. _An Account of the distilling Water fresh from Sea-water
by Wood-ashes. By Capt._ William Chapman: _In a Letter to_ John
Fothergill, _M. D._

[Read April 13, 1758.]

                                         Whitby, 10th 2d mo. Feb. 1758.

THY kind acceptance of my last emboldens me to inform thee, how, on
my return from a voyage to the north part of Russia, I procured a
sufficient quantity of fresh water from sea-water, without taking with
me either instruments or ingredients expressly for the purpose.

Some time in September last, when I had been ten days at sea, by an
accident (off the north cape of Finland) we lost the greatest part of
our water. We had a hard gale of wind at south-west, which continued
three weeks, and drove us into 73° lat. During this time I was very
uneasy, as knowing, if our passage should hold out long, we must be
reduced to great straits; for we had no rains, but frequent fogs, which
yielded water in very small quantities. I now blamed myself for not
having a still along with me (as I had often thought no ship should be
without one). But it was now too late; and there was a necessity to
contrive some means for our preservation.

I was not a stranger to Appleby’s method: I had also a pamphlet wrote
by Dr. Butler, intituled, _An easy Method of procuring of fresh Water
at Sea_. And I imagined, that soap might supply the place of capital
lees, mentioned by him. I now set myself at work, to contrive a still;
and ordered an old pitch-pot, that held about ten quarts, to be made
clean: my carpenter, by my direction, fitted to it a cover of fir deal,
about two inches thick, very close; so that it was easily made tight by
luting it with paste. We had a hole thro’ the cover, in which was fixed
a wooden pipe nearly perpendicular. This I call the still-head: it was
bored with an augre of 1½ inch diameter, to within three inches of the
top or extremity, where it was left solid. We made a hole in this,
towards the upper part of its cavity (with a proper angle) to receive
a long wooden pipe, which we fixed therein, to descend to the tub in
which the worm should be placed. Here again I was at a loss; for we
had no lead pipe, nor any sheet-lead, on board. I thought, if I could
contrive a strait pipe to go thro’ a large cask of cold water, it might
answer the end of a worm. We then cut a pewter dish, and made a pipe
two feet long; and at three or four trials (for we did not let a little
discourage us) we made it quite tight. We bored a hole thro’ a cask,
with a proper descent, in which we fixed the pewter pipe, and made
both holes in the cask tight, and filled it with sea-water: the pipe
stuck without the cask three inches on each side. Having now got my
apparatus in readiness, I put seven quarts of sea-water, and an ounce
of soap, into my pot, and set it on the fire. The cover was kept from
rising by a prop of wood to the bow. We fixed on the head, and into it
the long wooden pipe above-mentioned, which was wide enough to receive
the end of the pewter one into its cavity. We easily made the joint
tight.

I need not tell thee with what anxiety I waited for success: but I
was soon relieved; for, as soon as the pot boiled, the water began
to run; and in twenty-eight minutes I got a quart of fresh water. I
tried it with an hydrometer I had on board, and found it as light as
river-water; but it had a rank oily taste, which I imagine was given it
by the soap. This taste diminished considerably in two or three days,
but not so much as to make it quite palateable. Our sheep and fowls
drank this water very greedily without any ill effects. We constantly
kept our still at work, and got a gallon of water every two hours;
which, if there had been a necessity to drink it, would have been
sufficient for our ship’s crew.

I now thought of trying to get water more palateable; and often perused
the pamphlet above-mentioned, especially the quotation from Sir R.
Hawkins’s voyage, who “with four billets distilled a hogshead of water
wholsome and nourishing.” I concluded he had delivered this account
under a veil, lest his method should be discovered: for it is plain,
that by four billets he could not mean the fuel, as they would scarce
_warm_ a hogshead of water. When, ruminating on this, it came into my
head, that he burnt his four billets to ashes, and with the mixture
of those ashes with sea-water he distilled a hogshead of fresh water
wholsome and nourishing. Pleased with this discovery, I cut a billet
small, and burnt it to ashes; and after cleaning my pot, I put into
it a spoonful of those ashes, with the usual quantity of sea-water.
The result answered my expectations: the water came off bright and
transparent, with an agreeable pungent taste, which at first I thought
was occasioned by the ashes, but afterwards was convinced it received
it from the resin or turpentine in the pot, or pipes annexed to it.
I was now relieved from my fears of being distressed thro’ want of
water; yet thought it necessary to advise my people not to be too free
in the use of this, whilst we had any of our old stock remaining; and
told them, I would make the experiment first myself; which I did, by
drinking a few glasses every day without any ill effect whatever. This
water was equally light with the other, and lathered very well with
soap. We had expended our old stock of water before we reached England;
but had reserved a good quantity of that which we distilled. After my
arrival at Shields, I invited several of my acquaintance on board to
taste the water: they drank several glasses, and thought it nothing
inferior to spring-water. I made them a bowl of punch of it, which was
highly commended.

I have not the convenience of a still here, or should have repeated the
experiment for the conviction of some of my friends: for as to myself,
I am firmly persuaded, that wood-ashes mixed with sea-water will yield,
when distilled, as good fresh water as can be wished for. And I think,
if every ship bound a long voyage was to take a small still with Dr.
Hales’s improvements, they need never want fresh water. Wood-ashes
may easily be made, whilst there is any wood in the ship; and the
extraordinary expence of fuel will be trifling, if they contrive so
that the still may stand on the fire along with the ship’s boiler.

I shall think myself sufficiently recompensed, if any hints here may
tend to the relief of my brother sailors from the dismal extremity of
want of water; an extremity too little regarded by those, who have
never experienced it.

  _P. S._ During my passage from Russia we very rarely had any _aurora
  borealis_; and those few we saw were faint, and of short continuance:
  at which I was much surprised; for about ten years ago, being in a
  high north latitude, we had very beautiful ones almost every night in
  the month of September; which exceeded any I have seen described in
  the _Philosophical Transactions_, or _Memoires de l’Academie Royale_.

                                                           Wm. Chapman.




LXXXVIII. _Observatio Eclipsis Lunaris facta_ Matriti _a Pª._ Joanne
Wendlingen, _Societatis_ Jesu, _in Regali Observatorio Collegii
Imperialis ejusdem Societatis, Die_ 30 Julii 1757.

  _Quælibet observatio bis instituta fuit, semel interjecto oculum
  inter lentemque ocularem vitri clari, cærulei, plani, ac bene tersi,
  fragmento. Hæ observationes notantur hac voce_ cerul. _Telescopium,
  quo usus sum, est_ Gregorianum _trium pedum_ Anglicanorum, _omnino
  præclarum_.

_Communicated by_ Matthew Maty, _M. D. F.R.S._

[Read April 20, 1758.]

  IMMERSIONES.                  |Tempus verum| Differentia
                                |  h  ´  ´´  |
  PRincipium eclipsis, _clar._  |   9 47 34  |
  Mare Humorum,        _clar._  |  -- 52 47  |
                       { _cær._ |  -- 54 28  |   ´´
  Grimaldus            { _clar._|  -- 55 27  |  ---- 59
                       {_cær._  |  10  1 21  |  ---- 13
  Bullialdus           {----    |  10  1 34  |
                       {----    |  --  9 35  |  ---- 10
  Keplerus             {----    |  --  9 45  |
                       {----    |  -- 16 15  |  ---- 12
  Copernicus           {----    |  -- 16 28  |
                       {----    |  -- 18 14  |  ---- 10
  Heraclides           {----    |  -- 18 24  |

  Manilius             {_clar._ |  10 30 43  |     ´´
                       {_cær._  |  10 30 54  |  ---- 11
  Menelaus             {----    |  -- 34 11  |  ----  9
                       {----    |  -- 34 20  |
  Promontorium         {----    |  -- 44 49  |  ----  9
                       {----    |  -- 44 58  |
  Mare Crisium         {----    |  -- 45 33  |  ---- 11
                       {----    |  -- 45 44  |
  Proclus, _clar._              |  -- 46 54  |
                       {----    |  -- 54 48  |  ---- 14
  Plato                {----    |  -- 55  2  |
                       {----    |  11  7  3  |
  Langrenus            {----    |  11  7 23  |  ---- 20

  EMERSIONES.                   |Tempus verum| Differentia
                                |  h  ´  ´´  |
  Plato                {_clar._ |  11 40 34  |   ´´
                       {_cær._  |  11 40 48  |  ---- 14
  Heraclides           {----    |  -- 41 27  |  ---- 12
                       {----    |  -- 41 39  |
  Grimaldus            {----    |  -- 47 57  |  ----  7
                       {----    |  -- 48  4  |
  Keplerus             {----    |  -- 52 58  |  ---- 10
                       {----    |  -- 53  8  |
  Copernicus           {----    |  12  1 36  |  ---- 12
                       {----    |  12  1 48  |
  Menelaus             {----    |  -- 17 18  |  ---- 10
                       {----    |  -- 17 28  |
  Finis eclipseos, _clar._      |  -- 52 15  |


_Observatio Eclipsis Lunaris, facta ab eodem, eodem modo, eodem loco,
iisdemque instrumentis Die_ 24 Januar. _Anni_ 1758.

_Ab hora 5ᵗᵃ usque ad finem observationis tantum commovebatur
imprægnata plurimum vaporibus athmosphæra, ut tota lunæ illuminatæ
portio præter morem undulare videretur. Flabat boreas, indicante
thermometro Reaumuriano. 1. grandem infra aquæ congelationem._

  IMMERSIONES.                       |Tempus verum| Differentia
                                     |  h  ´ ´´   |
  Principium                         |   4  7 42  |    ´´
  Grimaldus                 {_cær._  |  --  9 55  |  ---- 38
                            {_clar._ |  -- 10 33  |
  Aristarchus               {----    |  -- 15 37  |  ---- 34
                            {----    |  -- 16 11  |
  Mare Humorum              {----    |  -- 20 48  |  ---- 24
                            {----    |  -- 21 12  |
  Copernicus                {----    |  -- 26 45  |  ---- 13
                            {----    |  -- 26 58  |
  Plato                     {----    |  -- 35 41  |  ---- 41
                            {----    |  -- 36 22  |
  Tycho                     {----    |  -- 39 31  |  ---- 38
                            {----    |  -- 40  9  |
  Menelaus                  {----    |  -- 45 43  |  ---- 39
                            {----    |  -- 46 22  |
  Plinius                   {----    |  -- 50 17  |  ---- 27
                            {----    |  -- 50 44  |
  Promontorium Somni        {----    |  -- 58 15  |  ---- 27
                            {----    |  -- 58 42  |
  Cleomedes                 {----    |   5  0 22  |  ---- 14
                            {----    |   5  0 36  |

  Proclus                   {_cær._  |   5  2  9  |
                            {_clar._ |   5  2 15  |  ----  6
  Princip. Maris Crisii     {----    |  --  3  6  |  ---- 25
                            {----    |  --  3 31  |
  Langrenus                 {----    |  --  7 40  |  ---- 14
                            {----    |  --  7 54  |
  Immers. tot. Maris Crisii {----    |  --  8 19  |  ---- 11
                            {----    |  --  8 30  |
  Immersio totalis Lunæ     {----    |  -- 12 50  |  ---- 40
                            {----    |  -- 13 30  |

In fine cœlum serenum, & athmosphæra quieta.


REFLEXIO.

Notabilis appulsus umbræ terrestris ad faculas maculasque lunares
differentia, dum partim vitro colore cæruleo tincto, partim absque
eo, observationes instituuntur, inventa a Dº. de Barros, & tum in
observatorio Parisino tum alibi sæpius confirmata, ad me duplicem
hanc lunæ eclipsim, ea qua vel licuit circumspectione, instituendam
determinavit, spe fretus; me phænomeni hujus causas, si non veras,
veritati saltem proximas, inventurum; unde in tempore de vitris planis
bene tersis, diametri mediæ lineæ, partim colore cæruleo claro, partim
flavo tinctis mihi provideram, his tamen ultimis uti non licuit ob
nimiam umbræ penumbræque confusionem.

Interjecto oculum inter, lentemque ocularem vitri cærulei fragmento,
sequentia observavi. 1. Umbra terrestris in immersione citius maculam
aut faculam lunarem attigit, & in emersione tardius deseruit, quam dum
absque eo observationem institui. 2. Claritas lunæ, alioquin offendens
oculum, suavior apparebat. 3. Limites umbræ perfecte terminabantur
excepta secunda eclipsi, in qua (flante borea) ab hora quinta
illuminata lunæ pars undulare videbatur.

Suppositis his phænomenis, uti et athmosphæra lunari, de qua vix
dubio locus, sequentia intuli: 1. Quo densior dicta athmosphæra
fuerit, major radiorum portio ab hac in immersam umbræ terrestri lunæ
portionem, limitibus saltem proximam, reflectetur, eosque reddet
dubios, quod quidem contingit, dum absque adminiculo per nudum
telescopium observatio instituitur, secus vero dum oculum inter,
lentemque ocularem, vitrum cæruleo colore tinctum interjicitur. Addito
secundo, ac tertio phænomeno, nempe per vitrum cæruleum lumen multum
apparere suavius, infertur, si color cæruleus sufficit ad mitigandam
tantopere eam lunæ illuminatæ portionem, quæ extra omnem umbram
conspicitur, quanto magis sufficit, ad tollendam omnem claritatem, quæ
ab athmosphæra lunari in hoc corpus reflectitur? & ecce tibi secundam
illationem, nempe limites umbræ facilius determinari. 3. Diametrum
umbræ majorem videri debere, & vel ideo immersiones macularum aut
facularum lunarium citius, emersiones vero tardius succedere debere;
quæ quidem omnia cum observationibus congruunt.

Dixi in prima illatione, reflecti aliquam luminis portionem a lunæ
athmosphæra in ipsam eclipsatam corporis hujus portionem, non secus,
ac in globo hoc terraqeno accidit, qui post solis occasum aliquo adhuc
tempore illuminatur. Hæc lucis reflexio tanto erit major, quanto
athmosphæra fuerit densior, & quia supponere licat, hanc in luna non
semper esse æqualem, infertur, differentiam temporis appulsus umbræ non
in omni eclipsi lunari posse esse æqualem, quod demum convenire videtur
duplici meæ observationi, ut ex adnotatis temporum differentiis liquet.
Hæc mea est circa propositum phænomenon opinandi ratio.




LXXXIX. _Observations upon a slight Earthquake, tho’ very particular,
which may lead to the Knowlege of the Cause of great and violent ones,
that ravage whole Countries, and overturn Cities. By_ John Andrew
Peyssonel, _M. D. F.R.S. Translated from the_ French.

[Read April. 20, 1758.]

I Went to make my observations upon the natural history of the sea;
and when I arrived at a place called the Cauldrons of Lance Caraibe,
near Lancebertrand, a part of the island of Grande Terre Guadaloupe,
in which place the coast runs north-east and south-west, the sea being
much agitated that day flowed from the north-west. There the coast is
furnished with hollow rocks, and vaults underneath, with chinks and
crevices: and the sea, pushed into these deep caverns by the force
and agitation of the waves, compresses the air, which, recovering its
spring, forces the water back in the form of the most magnificent
fountains; which cease, and begin again at every great pressure. This
phænomenon is common to many places in this island. The explanation of
it is easy; but the following is what I particularly observed.

As I walked within about forty paces from the brink of the sea, where
the waves broke, I perceived, in one place, the plants were much
agitated by some cause, that was not yet apparent. I drew near, and
discovered a hole about six feet deep, and half a foot diameter;
and stopping to consider it, I perceived the earth tremble under my
feet. This increased my attention; and I heard a dull kind of noise
underground, like that which precedes common earthquakes; which I have
observed many a time. It was followed by a quivering of the earth; and
after this a wind issued out of the hole, which agitated the plants
round about. I watched to see whether the motion extended to any
distance; but was sensible it did not reach above three or four paces
from the hole, and that no motion was perceived farther off.

I further observed, that this phænomenon never happens till after the
seventh wave rolls in; for it is a common thing in this country to find
the sea appear calm for some time, and then to produce seven waves,
which break upon the coast one after another: the first is not very
considerable; the second is somewhat stronger; and thus they go on
increasing to the seventh, after which the sea grows calm again, and
retires. This phænomenon of the seven waves is observed by navigators
with great attention, especially at low water, in order to be the
better able to go in or come out at the very time that the sea grows
quiet. These seven waves successively fill the caverns, which are all
along the coast; and when the seventh comes to open itself, the air
at the bottom of the caverns being greatly compressed, acted by its
elasticity, and immediately made those fountains and gushings I have
mentioned; and the waters continuing in the caverns, up to the very
place of the hole, began to produce that dull noise, caused the emotion
or earthquake, and finished with the violent wind forced up thro’ the
hole; after which the water retired into the sea, and having no further
impelling cause, on account of the waves, rendered every thing quiet
again.

I observed, that this phænomenon happened at no limited time, but
according to the approach of the waves, being strongly put in motion
after the seventh. I remained near half an hour to observe it; and
nearly followed the course of the cavern to its entrance, directed by
the disposition of the coast. I made my negroes go down where the water
broke; for they doubted the report of the greatness of these caverns;
and when the sea was calm one of them ventured in, but returned very
quickly, or he must have perished. Therefore I conclude, that these
small earthquakes round the hole, about forty paces from the wave, were
only caused by the compressed air in some great vault about this place,
and that by its force was driven up the hole that appeared: that this
air in the caverns, compressed to a certain degree, first caused the
dull noise, by the rolling of the waters, which resisted in the cavern;
then acting more violently, caused the small earthquake, which ceased
when the wind passed out of the hole, and that the sea retired, and
gave liberty to the air, which was contained and compressed.

Such are the observations I have made; from which the learned, who are
endeavouring to find the cause of earthquakes, since that dreadful one,
which destroyed the city of Lisbon, may make such conclusions as they
shall think proper.

At Guadaloupe, Jan. 6. 1757.

                                                             Peyssonel.




XC. _A Catalogue of the_ Fifty Plants _from_ Chelsea Garden, _presented
to the_ Royal Society _by the worshipful Company of Apothecaries, for
the Year 1757, pursuant to the Direction of Sir_ Hans Sloane, _Baronet,
Med. Reg. & Soc. Reg. nuper Præses, by_ John Wilmer, _M. D. clariss.
Societatis Pharmaceut._ Lond. _Socius, Hort._ Chelsean. _Præfectus &
Prælector Botanic._

[Read April 20, 1758.]

  1751  ALlium sylvestre latifolium. C. B. P. 74.
        Allium ursin. bifolium vernum sylvatic. J. B. 2. 565.
  1752  Anacampseros flavo flore Amman. Ruth. 96.
  1753  Anchusa strigosa, foliis linearibus dentatis, pedicellis
          bractea minoribus, calycibus fructiferis inflatis.
          Lefl. Linn. Sp. Plant. 133.
  1754  Asplenium sive Ceterach. J. B. 3. 749. Offic. 121.
  1755  Bidens calyce oblongo squamoso, feminibus radii corolla non
          decidua coronatis, Miller. Icon.
  1756  Cactus repens decemangularis Lin. Sp. Pl. 467.
  1757  Cerasus pumila Canadensis, oblongo angusto folio, fructu parvo,
          Du Hamel. Mill. Icons.
  1758  Ceratocarpus Amæn. Acad. 1. p. 412. Hort. Ups. 281.
  1759  Cotula flore luteo, radiato. Tourn. 495. Buphthalmum Cotulæ
          folio C. B. P. 134.
  1760  Cracca minor Rivini. Vicia segetum cum filiquis plurimis
          hirsutis C. B. P. 345.
  1761  Cucubalus calycibus subglobosis glabris reticulato-venosis,
          capsulis trilocularibus, corollis subnudis, Flor. suec. 360.
  1762  Cucubalus calycibus subglobosis, caule ramoso patulo, foliis
          linearibus acutis, Mill. Dict.
        Lychnis sylvestris quæ Been album vulgo, foliis
          angustioribus et acutioribus C. B. P. 205.
  1763  Cunonia floribus sessilibus, spathis maximis.
          Butner Cunonia, tab. 1.
  1764  Cupressus foliis imbricatis frondibus ancipitibus. Linn. Spec.
          Plant. 1003.
        Cupressus nana Mariana fructu cæruleo parvo. Pluk. Mantiss. 61.
  1765  Cyclamen Hederæ folio C. B. P. 308. Offic. 162.
  1766  Diosma foliis lineari-lanceolatis subtus convexis, bifariam
          imbricatis. Linn. Sp. Plant. 198.
  1767  Euonymoides Canadensis Saraz. Boerh. Ind. Alt. 237.
  1768  Filipendula foliis ternatis Hort. Cliff. 191.
  1769  Filipendula vulgaris, an Molon Plinii C. B. 163. Offic. 197.
  1770  Heliotropium foliis ovato-lanceolatis, spicis plurimis
          confertis, caule fruticoso. Miller’s Icons.
  1771  Hieracium fruticosum latifolium hirsutum C. B. P. 129.
  1772  Hyoscyamus rubello flore. C. B. P. 169.
        Hyoscyamus Syriacus. Cam. Icon. 21. J. B. 3. 628.
  1773  Hypericum floribus monogynis staminibus corolla longioribus,
          calycibus coloratis caule fruticoso. Miller’s Icons.
  1774  Hypericum floribus trigynis, calycibus acutis, staminibus
          corolla brevioribus, caule fruticoso. Linn. Hort. Cliff. 380.
          Miller’s Icons.
  1775  Iris corollis barbatis, germinibus trigonis, foliis ensiformibus
          longissimis, caule foliis longiore bifloro. Miller’s Icons.
  1776  Isatis sativa, sive latifolia. C. B. P. 113. Glastum sativum. J.
          B. 2. 909.
  1777  Juniperus vulgaris fruticosa C. B. 488. Off. 252.
  1778  Ixia foliis gladiolatis linearibus caule bulbifero.
          Miller’s Icons.
  1779  Ixia foliis gladiolatis glabris, floribus corymbosis
          terminalibus. Miller’s Icons.
  1780  Larix C. B. 493. Officin. 264.
  1781  Laserpitium foliis amplioribus, semine crispo. Tourn. 324.
  1782  Linum calycibus capsulisque obtusis. _Sibirian Flax._ Miller’s
          Icons.
  1783  Liriodendrum. Hort. Cliff. 223.
        Tulipifera arbor Virginiana. Hort. Lugd. Bat. 612.
  1784  Oenanthe Apii folio C. B. P. 162.
  1785  Passerina foliis linearibus. Hort. Cliff. 146. Sp. 1.
  1786  Platanus Orientalis verus. Park. 1427.
  1787  Platanus Occidentalis aut Virginiensis. Park. 1427.
  1788  Platanus Orientalis Aceris folio. T. Cor. 41.
  1789  Prenanthes foliis integris serratis scabris, radice repente,
          flore purpureo cæruleo. Mill. Dict.
  1790  Ruta sylvestris linifolia; Hispanica Boccon. Barrel Icon. 1186
          H. Mus. p. 2. 82. tab. 73.
  1791  Saxifraga muscosa; trifido folio. Tourn.
  1792  Scabiosa Virgæ Pastoris folio. C. B. P. 270.
        Scabiosa latifolia peregrina. Tabern. Icon. 160.
  1793  Thalictrum majus, siliqua angulosa aut striata, C. B. P. 336.
  1794  Thalictrum majus non striatum. C. B. P. 336.
  1795  Thalictrum Canadense majus caulibus viridantibus. Boerhaav.
  1796  Thalictrum Alpinum Aquilegiæ foliis. Tourn.
  1797  Thalictrum minus Asphodeli radice magno flore. Tourn. 271.
  1798  Thuya strobilis squarrosis squamis acuminatis reflexis. Hort.
          Upsal. 289.
  1799  Tordylium Narbonense minus. Tourn. 320.
  1800  Tridax. Hort. Cliff. 418. After American. procumbens, foliis
          laciniatis et hirsutis. Houston.




XCI. _An Historical Memoir concerning a Genus of Plants called_ Lichen,
_by_ Micheli, Haller, _and_ Linnæus; _and comprehended by_ Dillenius
_under the Terms_ Usnea, Coralloides, _and_ Lichenoides: _Tending
principally to illustrate their several Uses. Communicated by_ Wm.
Watson, _M. D. F.R.S._

  ----_Natura nihil frustra creaverit, posteros tamen tot inventuros
  utilitates ex_ Muscis _auguror, quot ex reliquis vegetabilibus_.

  Cui bono? Amæn. Acad. III. p. 241.

[Read Apr. 27 & May 4, 1758.]

THE whole class of mosses were taken but very little notice of by
the revivers of botany in the sixteenth century: they indeed took
some pains to distinguish the particular species that the ancients
had mentioned, but disregarded almost all the rest. Modern botanists
however suppose, that they were but little successful in general in
their application of the ancient names to plants: nor is a failure in
such attempts to be wondered at, considering the too great conciseness,
and frequent obscurity, of their descriptions. In the class of mosses,
as in many others, the accounts transmitted to us are little more than
a scene of uncertainty and confusion.

It is to the moderns we are indebted for the discovery of the far
greater number of the plants of this class. In this branch of
botany our own countrymen Mr. Ray, Buddle, Dale, Doody, Petiver, and
Dr. Morison, Sherard, Richardson, and others, have distinguished
themselves: and amongst foreigners M. Vaillant, Sig. Micheli, and
the very eminent Dr. Haller: but, beyond all, the late learned and
indefatigable professor at Oxford, Dr. Dillenius, has herein made the
most ample discoveries and improvements, of which his elaborate history
will ever remain a standing proof.

The word _lichen_ occurs in the writings of Dioscorides and Pliny;
and tho’ it may be doubtful, there is nevertheless good reason to
apprehend, that Dioscorides meant to describe under that name the very
plant, or at least one of the same genus, to which the commentators
agreed to affix his description. Since then the name has been variously
applied by different authors; on which account it is necessary to
premise, that the _lichen sive hepatica Off._ or liverwort of the
shops, does not fall under this generical term, as it is now formed by
the three above-named authors. They comprehend under the term _Lichen_,
and Dillenius under those of _Usnea_, _Coralloides_, and _Lichenoides_,
the hairy tree-moss or _usnea_ of the shops; the _muscus pulmonarius_,
tree-lungwort, or oak-lungs; the _lichen terrestris cinereus_, or
ash-coloured ground liverwort; the coralline-mosses; the cup-mosses;
horned mosses; the _orchel_, or Canary-weed; the _muscus islandicus_ of
Bartholine; and a multitude of others found upon trees, walls, rocks,
and stones, in all parts of the world, and in many parts thereof in
very great abundance.

Caspar Bauhine in his _Pinax_, John Bauhine, and countrymen Gerard
and Parkinson, and their cotemporaries, as they wrote before the time
that generical characters in botany were in use, included these lichens
among the other herbaceous mosses, under the general name of _muscus_;
adding to the name in general some epithet descriptive of its form,
place of growth, or supposed virtue.

Mr. Ray, both in his History of Plants, and in the Supplement, as
he was usually averse to the forming of new names, has interspersed
them among other mosses, under the character of _musci steriles seu
aspermi_, retaining the synonyms of the two Bauhines, Gerard, and
Parkinson, to the general species.

Dr. Morison seems to have been the first, who separated them intirely
from the herbaceous mosses; and, from the analogy he supposed they had
with the fungus tribe, formed them into a genus, under the name of
_musco-fungus_. He enumerates fifty species and upwards under this term
in the _Historia Oxoniensis_, and has divided them into five orders,
according to their different appearances, as follows:

  1. _Musco-fungi e terra prominentes, latiores._ 5.
  2. _Musco-fungi pixidati._ 11.
  3. _Musco-fungi corniculati._ 26.
  4. _Musco-fungi crustæ modo adnascentes._ 37.
  5. _Musco-fungi corticibus arborum dependentes._ 53.

Table the 7th of his 15th section exhibits several good figures of some
of these lichens.

Tournefort was the first, who adapted the generical term _lichen_ to
them; but it was in consequence of his joining them to the lichen
of the shops. He has however excluded the coralline-mosses, and
forms them into a genus, by the name of _coralloides_; to which he
has connected some plants, properly of the fungus tribe. In this
distinction he is followed by Dr. Boerhaave in his _Index alter
Plantarum_.

Dr. Dillenius first called them _lichenoides_, in the catalogue of
plants growing about Giessen, chusing to retain the word _lichen_ to
the liverwort of the shops. Under this name however, in this work, he
does not comprehend the _usneæ_, or hairy tree-mosses, but refers them
to the _conservæ_, adding the epithet _arborea_ to each species, to
distinguish them from the water kinds. He enumerates upwards of sixty
species of _lichenoides_, but has applied few or no synonyms to them.

Under the same generic term he has introduced them into the third
edition of Ray’s Synopsis of British Plants, taking in the _usneæ_, and
recounting upwards of ninety species, all found spontaneously growing
in England. Many of these are undoubtedly only varieties. They are in
this work very naturally divided into several orders and subdivisions,
for the greater ease of distinguishing them, as follows:

_Lichenoides_

  _caulifera_
    1. _Capillacea et non tubulosa scutellata._
    2. _Coralliformia tuberculosa plerumque._
      a. _Solida et non tubulosa._
      b. _Tubulosa._
    3. _Pyxidata._
    4. _Fungiformia._

  _cauliculis destituta_
    1. _Mere crustacea._
    2. _Crusta foliosa scutellata seu foliis scutellatis arcte
    adnascentibus_ -
      a. _Substantiæ gelatinosæ._
      b. _Substantiæ durioris._
    3. _Foliis magis liberis nec tam arcte adnascentibus_
      a. _Scutellatis et tuberculatis._
      b. _Peltatis._

M. Vaillant, in the _Botanicon Parisiense_, retains Tournefort’s
names. Many of these lichens, as well as other mosses, are accurately
represented in the elegant tables, which adorn that work. Dr. Haller
tells us he learnt to distinguish almost all the mosses solely by the
help of these tables, so well are they expressed. The lovers of botanic
science are greatly indebted to Boerhaave for his publication of that
work.

Micheli, after Tournefort, adopts the term _lichen_, and comprehends
all the species under it, except one or two, which he calls
_lichenoides_. This author however does not take into this genus the
liverwort of the _materia medica_; he describes the species of that
genus under the name of _marchantiæ_. Near twenty of the plates in his
_Nova Plantarum Genera_ are taken up in representing various species
of this genus. In this work they are divided into thirty-eight orders
or subdivisions; a circumstance very necessary indeed, considering
how greatly he has multiplied the number of the species. It is to
be regretted, that so indefatigable an author, one whose genius
particularly led him to scrutinize the minuter subjects of the science,
should have been so solicitous to increase the number of species under
all his genera: an error this, which tends to great confusion and
embarassment, and must retard the progress and real improvement of the
botanic science.

Dr. Haller retains Micheli’s term, and enumerates 160 kinds in his
_Enumeratio Stirpium Helvetiæ_: he divides them into seven orders,
according to the following titles:

  1. _Lichenes corniculati & pixidati._
  2. _Lichenes coralloidei._
  3. _Lichenes fruticosi alii._
  4. _Lichenes pulmonarii._
  5. _Lichenes crustacei scutis floralibus ornati._
  6. _Lichenes scutellis ornati._
  7. _Lichenes crustacei non scutati._

The extensive number of the species, and the difficulty of
distinguishing them with a tolerable degree of certainty, has deterred
Dr. Haller from adding so full and complete a list of synonyms to the
plants of this genus as he has elsewhere done in that splendid work.
Plate the 2d exhibits several elegant sorts of these lichens.

Linnæus, and the followers of his method, who seem to have established
their generical character from Micheli’s discoveries, retain also his
generical title. Micheli’s passion for the multiplication of species
is no-where more conspicuous than in the plants of this genus, which
he has most enormously augmented to the number of 298 species. The
Swedish professor cannot be charged with this foible: it is one of the
excellencies of his writings, that they inculcate the reverse. He has
so far retrenched this genus, that in his general enumeration of plants
he recounts only eighty species belonging to it. They are in this work
divided into eight orders, according to the difference of appearance
which they form by their _facies externa_, little or no regard being
had to what are usually called the parts of fructification.

  1. _Lichenes leprosi tuberculati._
  2. _Lichenes leprosi scutellati._
  3. _Lichenes imbricati._
  4. _Lichenes foliacei._
  5. _Lichenes coriacei._
  6. _Lichenes scyphiferi._
  7. _Lichenes fructiculosi._
  8. _Lichenes filamentosi._

Dr. Dillenius, in his most elaborate work, intituled, _Historia
Muscorum_, has divided this Michelian genus into three, under the names
of _usnea_, _coralloides_, and _lichenoides_. Under the word _usnea_
he comprehends the hairy tree-mosses, among which are the _usnea_ of
the shops, and the true _usnea_ of the Arabians. Of these he describes
sixteen species. Under _coralloides_ he describes thirty-nine species,
among which are the cup-mosses, and many others, disposed according to
the following scheme:

Ordo I. _Fungiformia, non tubulosa, nec ramosa._ 5.

Ordo II. _Scyphiformia, tubulosa, simplicia et prolifera._

  Series 1. _Scyphis perfectioribus._ 13. Cup-mosses.
  Series 2. _Scyphis imperfectis._ 20. Horned mosses.

Ordo III. _Ramosa fruticuli specie summitatibus acutis multifariam
divisis._

  Series 1. _Species tubulosæ._ 30. Tubulous coralline mosses.
  Series 2. _Species solidæ._ 39. Solid coralline mosses; among which is
    the _orchel_.

The genus of _lichenoides_ contains 135 species, disposed according to
the following scheme:

  Ordo I. _Species aphyllæ mere crustaceæ._ {1. _Tuberculosæ._ 8.
                                            {2. _Scutellatæ._ 18.

                              {1. _Gelatinosæ tuberculosæ et
                                   scutellatæ._ 35.
  Ordo II. _Species foliosæ._ {2. _Aridiores et exsuccæ,
                                   scutellatæ._ 100.
                              {3. _Aridiores peltatæ et clypeatæ._ 121.

These plants are not only largely described, and accompanied with the
most perfect assemblage of synonyms; but every species is accurately
figured, and many of them in various views, and at different ages of
their growth; by which this laborious work, notwithstanding it is
conversant upon the minutest, and consequently the most abstruse
parts of botany, may nevertheless be justly esteemed, without any
exaggeration, one of the most complete works extant of the kind.

Dr. Hill, in his History of Plants, has disposed them into five
genera, under the following names: 1. _Usnea_, comprehending the hairy
tree-mosses; 2. _Platysma_, flat-branched tree-mosses, the lungwort,
and others; 3. _Cladonia_, containing the orchel and coralline-mosses;
4. _Pyxidium_, the cup-mosses; 5. _Placodium_, the crustaceous mosses.

The plants of this extensive genus are very different in their form,
manner of growing, and general appearance: on which account those
authors, who preserve them under the same name, saw the propriety and
necessity of arranging them into different orders and subdivisions,
that the species might be distinguished with greater facility. Upon the
same principle Dr. Dillenius and Dr. Hill have formed them into several
genera.

So far as the parts of fructification are distinguishable in these
plants, they appear in different forms upon different species: on some,
in the form of tubercles; on others, in the form of little concave
dishes, called _scutellæ_; on others, of oblong flat shields or pelts.
All these are conceived by Micheli and Linnæus to be receptacles of
male flowers. The female flowers and seeds are suspected by the same
authors to be dispersed in the form of farina or dust upon the same
plants, and in some instances on separate ones. Dillenius has not
dared to determine any thing positively with regard to the real parts
of fructification in these lichens: time will hereafter, it is to be
hoped, throw more light upon the subject.

In order to convey a more distinct idea of the several plants of this
genus, which enter into œconomical or medical uses in the various parts
of the world, we shall distribute them into several orders, according
to the custom of former writers: and as is not consistent with our plan
to describe each of these species, we shall refer to the page of the
more modern authors, where they may be found.


1. Lichenes filamentosi.

_Such as consist of mere solid filaments, of a firm and solid but
flexible texture, having the appearance of fructification in the
form of_ scutellæ, _or flat round bodies growing from the sides or
extremities of these filaments_.

This order or division comprehends the hairy tree-mosses, or _usnea_
of Dillenius and Hill; several of the species of the fifth order of
lichens of Micheli; and the _lichenes filamentosi_ of Linnæus.

Dr. Dillenius describes sixteen species under the term _usnea_, several
of which are found in England, tho’ some of them, as the common _usnea_
of the shops, but very sparingly, and none of them in any considerable
plenty. The thick woods in many other parts of Europe, and the rest of
the globe, afford them in great plenty. They hang from the branches of
various kinds of trees, like large tufts of hair, to a considerable
length: some species grow several feet long. The rocks on the tops
of high mountains afford several kinds. They are of various colours;
some whitish, ash-coloured, others grey or blackish, and two or three
species have a yellow or orange hue.

The commentators in general agreed in making the _bryon_ of[65]
Dioscorides one of these hairy tree-mosses, which they called _usnea_.
No wonder, therefore, that at the restoration of letters it became a
matter of controversy, which of them was the _usnea_ of the ancients.
Dioscorides recommends his as an astringent; and tells us, that
“the best grew upon the cedar; but that from whatever tree it was
gathered, the whitest and most fragrant was preferable to the black.”
The several _usneæ_ would undoubtedly in different countries be found
upon different trees. In Italy, that of the larch-tree was the most
odoriferous; and on that account Matthiolus[66] preferred it to all
others. That kind, which at length obtained a place in the shops as the
_usnea_ of the ancients, was a species commonly found in our countries
on old oaks and other trees, and is called by Dillenius[67] stringy
tree-moss, or _usnea_ of the shops. Many excellent virtues have been
ascribed to it, on a supposition of its being the true _usnea_; but it
does not appear to have deserved them: and the present practice, at
least in England, has quite expunged it, and that perhaps very justly.

Dr. Dillenius is evidently of opinion however, that this common
_usnea_, tho’ it obtained a place in the shops as such, is not the
_bryon_ of Dioscorides and Pliny, or the _phaseon_ of Theophrastus,
since he has applied these names from those fathers of botany to
another species, which he calls the _beard usnea_[68]. Nor does either
of these species appear to be the true _usnea_ of the Arabians,
whatever title they may seem to have to it, either from their colour
or smell. Bellonius, as he is quoted by Dr. Dillenius, tells us, “that
the true _usnea_, or _bryon_, as he calls it, is sold at Constantinople
under the name of _usnech_; and tells us we are deceived in believing
ours to be the true _usnea_.” Dillenius has therefore described another
species[69], which he received from the East Indies, from Madagascar,
and St. Helen’s, as the _Usnea Arabum_. This plant the Indians call
_saliaga_; and Camelli assures us, that, while fresh, it has a very
fragrant musk-smell. He adds, that he had himself experienced what
Serapio says of it; _viz._ that a vinous infusion of it restrains
fluxes, stops vomiting, strengthens the stomach, and induces sleep.

The common _usnea_ of the shops was said to be the basis of that fine
perfumed powder, which the French called _corps de cypre gris_, and
which formerly made a great article of trade at Montpelier. Dr. Brown
hints[70], that the perfumers use it still; but he does not add, where.
John Bauhine gives us the whole process[71] for making that power,
which was vended in great quantities to all parts of France. It is
nevertheless true, that other of the lichens had as great a share in
the competition as the _usnea_; as the demand for that powder could
not have been answered, if the makers had confined themselves to the
_usnea_ alone. It was necessary too, inasmuch as other species are
equally well adapted to the same uses[72].

This _usnea_ is abundantly plentiful in the woods of Lapland; and
Linnæus[73] relates, that the inhabitants apply it to their feet,
when they are sore and excoriated with much walking. The benefit they
receive from it in this case is undoubtedly owing to its styptic
quality, which is remarked by Matthiolus, and by Mr. Ray[74] from the
German Ephemerides.

The _beard usnea_ before mentioned, which is abundantly common upon
the trees both in the northern regions of Europe and America, as well
as in the eastern kingdoms, and is described by Mr. Ray as hanging
to the length of two feet, the filaments of which are not thicker
than a common thread, and of a greenish white colour, is used by
the inhabitants of Pensylvania to dye an orange colour with. This
information Dillenius received from Mr. Bartram.

The black _mane usnea_, which grows in vast quantities in the Lapland
woods, in a defect of the common coralline moss makes part of the
fodder, and is equally acceptable to the rein-deer in the winter
time[75].

The long beaded _usnea_, or necklace-moss[76], enters into the
like œconomical uses in Virginia, where it is very plentiful. The
inhabitants find it a very agreeable fodder in the winter season to
both sheep and cows[77].

The Norwegians appropriate one of these _usnea_ to a singular use.
Pontoppidan tells us[78], “they have a certain kind of yellow moss
hanging on the branches of trees of the firs and pines, which is very
venomous, yet applied to a necessary use; for being mixed in pottage,
or with flesh, as a bait for the wolves, they infallibly die of it.”
That the species here referred to is the brass-wired _usnea_ of
Dillenius[79], or the _lichen vulpinus_ of Linnæus, cannot be doubted,
since this last author mentions[80] the same application of it with
very little variation. In England it is very rare; in Sweden plentiful,
especially in the province of Smoland, where the natives dye woollen
goods yellow with it.

John Bauhine describes a very beautiful species, under the name of
_laricus muscus_[81], which gives a very elegant citron colour upon
chewing, or upon maceration in water. Dillenius is doubtful, whether
this is what he has described under the name of the orange-coloured
forked _usnea_[82].

We may here observe by the bye, that the _usnea cranii humani_, which
thro’ the influence of superstition formerly obtained a place in the
catalogues of the _materia medica_, does not belong to this division
of the lichens. The writers of those times distinguished two kinds of
_usnea humana_, under the names of _crustacea_ and _villosa_. Any of
the crustaceous lichens, but more properly the common grey-blue pitted
_lichenoides_ of Dillenius, was used for the former of these; and, as
Dale tells us, was held in most esteem. The _villosa_ was a species of
the genus of _hypnum_. Indeed it does not appear, that they were in
those days very curious in determining the exact kind; and doubtless
any moss, which happened to grow upon an human skull, was sufficient
for the purposes designed.


2. Lichenes fruticulosi.

_Such as consist of a tough flexible matter, formed into ramifications,
in some species almost simple, in others resembling small shrubs: in
some of the species the branches are quite solid, in others tubular._

This order comprehends the third of Dillenius’s genus of _coralloides_;
the whole _cladonia_ of Hill; the second, and several species of the
third order of Haller’s lichens; several species of the fifth, and
the whole sixth, order of Micheli; and the _lichenes fruticulosi_ of
Linnæus.

The plants of this genus grow principally upon the ground on heaths,
forests, and mountainous barren places; except the _orcelle_, or
Canary-weed, which is found upon the rocks on the sea-coast.

To this division belongs the horned moss[83]. It is found with us in
rocky barren ground, and upon old walls not uncommon. It was formerly
in great credit as a pectoral; but is now quite in disrepute.

The common branched coralline-moss[84] is one of the most useful
plants of all the tribe of lichens. It is pretty frequent with us on
our heaths, forests, and mountains. The northern regions afford it in
abundance; and there it is peculiarly and singularly useful. It is
indeed the very support and foundation of all the Lapland œconomy, and
without which the inhabitants could not sustain their rein-deer in the
winter time. Linnæus tells us[85], that Lapland affords no vegetables
in such plenty as this, and other of the lichens. Plains of several
miles extent are totally covered over with it, as if with snow; and
where no other plant will even take root, this will thrive and be
luxuriant. These dreary and inclement wastes, these _terræ damnatæ_,
as a foreigner would readily call them; these, are the Lapland fields
and fertile pastures. On this lichen the rein-deer, those sources of
all their wealth, feed in the winter time, when it is in its most
flourishing condition, and no other vegetable is to be had: with this
too they will even become fat. The riches of the Laplanders consist in
their number of these cattle: they are cloathed with their skins, fed
with their flesh, and from their milk they make both butter and cheese.
Nature, by the inclemency of their seasons, has almost denied them
the cultivation of their earth: they neither sow nor reap; but live a
perpetual migratory life, tending their flocks of rein-deer, upon which
their whole care is centered and employed.

The milk of the rein-deer is very remarkably fat and rich: it tastes
indeed like cow’s milk, with which some butter, and a small quantity of
fat or suet, has been intimately united. Dr. Haller[86] suspects, that
this richness of the milk is owing to the animals feeding upon this
moss. Most of the plants of this family are of an astringent quality,
which indeed they manifest to the taste. This astringency of their food
will doubtless contribute much to that effect.

The rein-deer are not the only animals that will feed upon the
coralline moss. The Novaccolæ[87] gather vast quantities of it to
fodder their oxen with in the winter. They take the opportunity of
raking it together in the rainy seasons, when it is tough; for in dry
weather it easily crumbles into powder. This they moisten with a little
water in the winter season when they use it, and find it excellent
fodder.

The coralline mosses are subject to great variation: and altho’ there
are several really distinct species, yet they run so into one another,
that it is no easy matter to fix upon the real specific distinctions,
in many instances. Some species are perfectly white; others have the
extremities of the branches reddish, some brown, and others almost
black. The common coralline moss in Lapland not unfrequently grows to
be several inches long, and even a foot high.

The tubular or hollow branched coralline mosses are not the only
kinds upon which the rein-deer will feed. Almost all the lichens
are abundantly more plentiful in those northern, than in these more
southerly climates. There are several species with solid branches; one,
which Dillenius calls _The crisp warty Alpine coralloides_[88], which
is almost as plentiful as the common sort, and is equally acceptable
to those animals[89]. It was before observed, that, in defect of these
mosses, the black _mane usnea_ is a substitute equally acceptable to
those animals.

Another of the most remarkable and useful plants of this division
is the _orchel_[90], or _argol_, as it is commonly called. This
enters more into œconomical uses among us than any other of the whole
genus. How considerable an article it forms in the dying trade, in
which its uses are various and extensive, is very well known. Its
tinging property has been known from ancient times; and some of our
most celebrated botanic writers are of opinion, that it was used as a
dye even in the days of Theophrastus. That father of botany mentions
a _fucus_, which, he says, grew upon the rocks about the island of
Crete; and that they dyed woollen garments of a purple, or rather a red
colour, with it. It grows on the rocks by the sea-coast in many parts
of the Archipelago, and in the Canary Islands; from whence we generally
import it, as well as from the Cape Verd, which afford it in plenty.
The demand for _orchel_ is so great, that Mr. Hellot[91], of the Royal
Academy of Sciences, informs us, they gather yearly, upon an average,
from the isle of Teneriffe 500 quintals, which amounts to 25 ton
weight; from the Canary Islands 400 quintals, from Forteventura 300,
from Lancerota 300, the same from Gomera, and from Ferro 800.

The way of manufacturing the _orchel_ for the uses of dying, was for
a considerable time a secret in few hands; but it is now done in
London, and other parts of Europe, to great perfection. Mr. Ray, from
Imperatus, gives a brief account of the process[92]. Micheli has since
delivered a more exact detail of it. His, at least, seems to be the
method[93], which the dyers at Florence used. From both these accounts,
urine and pot-ash appear to be the principal ingredients used in
extracting its colour.

Many other plants of this genus contain the same tophaceous matter as
the _orchel_; and upon trial have been found to strike a good colour.
Micheli, after he has related the preparation of the _orchel_, suggests
the same thing; and M. Hellot, in the treatise before mentioned, tells
us, there are many other mosses, which will give as good a colour as
the _orchel_. In fact, he adds, that M. Bernard de Jussieu brought him
some from the forest of Fontainbleau, which, upon experiments with
urine and lime, took a purple colour. In the sequel of this memoir we
shall point out some of these kinds. M. Hellot has given us a process,
which he made use of for discovering whether any of these lichens
would yield a red or purple colour. It is as follows: “Put about two
drachms of any of these lichens into a little glass jar: moisten it
well with equal parts of strong lime-water, and volatile spirit of _sal
ammoniac_; tie a wet bladder close over the top of the vessel, and let
it stand three or four days. At the end of this time, if the lichen
is likely to answer, that small quantity of liquor, which you will
find in the glass, will be of a deep crimson red; and the plant will
retain the same colour when the liquor is all dried up. If neither the
liquor nor the plant have taken any colour, it is needless to make any
further trials with it.” This process is simple and easy, and well
worth observation by all who are disposed to prosecute experiments of
this nature: and indeed it is worth the trial, whether several lichens,
which we have plentifully enough in England, would not answer in this
respect.


3. Lichenes pyxidati.

_Such as consist of a firm tough flexible matter, formed into simple
tubular stalks, whose tops are expanded into the form of little cups._

This division contains the cup-mosses of authors; the second order of
_coralloides_ of Dillenius; great part of the first order of lichens in
Haller; the 7th, 8th, 9th, and 10th order in Micheli; and the _lichenes
schyphiferi_ of Linnæus. Dr. Hill has constituted a genus intirely of
these cup-mosses, under the name of _pyxidium_.

They are common with us on heaths, and other dry and barren places.
Some of them are proliferous, even to the third degree, and form a very
beautiful appearance. Some have tubercles on the edges of the cups, of
a beautiful scarlet colour.

The cup-moss[94] was a long time in great and established use for
coughs, and especially for the whooping cough in children; for which
it was long accounted a specific. To this end it was given in various
forms. Gerard and Parkinson recommend the powder to be taken for
several days together. Dr. Willis was particularly one of its patrons.
He has given us[95] several forms for its exhibition, as that of the
powder, a decoction, and a syrup from it.

The present practice has quite exploded it, and very justly perhaps, as
in any degree specific in the above disorder. Nevertheless, it seems to
have sustained that character with as great a reputation, and perhaps
with as good a title to it, as almost any of the specifics of that age.
It has been observed before, on another occasion, that this tribe of
mosses have in general an astringent property; as such, the cup-mosses
are consequently of a strengthening nature: it is no wonder, therefore,
that they should be helpful in this disorder, merely as corroborants.
That they were useful in some measure can scarcely be doubted; and
our very eminent Dr. Huxham[96], in treating upon this obstinate
complaint, seems to allow this of the cup-moss in preference to other
idle specifics. Happily for us, the Peruvian bark supplies a remedy of
infinitely more use, where such analeptics are required.

Dr. Lister, in some ingenious observations of his, printed in the
Philosophical Transactions[97], touching colours and dyes, observes,
that the scarlet heads of these mosses, upon the affusion of lye, will
strike a purple which will stand.


4. Lichenes crustacei.

_Such as consist of a dry and friable matter, more or less thick,
formed into flat crusts, very closely adhering to whatever they grow
upon._

Some of the species of this division consist of an exceeding fine thin
crustaceous, or rather, as Micheli calls it, farinaceous matter, the
fructifications appearing in the form of tubercles. Others consist of
a thicker scabrous crust, having the fructifications in the form of
little cups, called _scutellæ_.

This division contains the first order of the _lichenoides_ of
Dillenius; the 5th, 6th, and 7th orders of Haller’s lichens; the
_lichenes leprosi_ and _crustacei_ of Linnæus; and several of the
_placodium_ of Hill.

The species are numerous, and most of them very common on rocks,
stones, old walls, the bark of trees, old pales, _&c._ which are
commonly covered over with them, in undisturbed places. They form a
very agreeable variety, and some of them have a very elegant appearance.

Dr. Dillenius describes a species of this order, which he found upon
the tops of the mountains in Caernarvonshire in Wales; and which the
inhabitants told him they used as a red dye, and found it preferable
to the cork, or arcel, which they call _kenkerig_. He has intitled it,
in English, _The white tartareous scarlet-dying lichenoides_[98]. He
is of opinion, that this is the moss which Martin mentions, in his
account of the Western Islands of Scotland, under the name of _corkir_;
with which the inhabitants of the island of Sky dye a scarlet colour.
They prepare it by drying, powdering it, and then steeping it for three
weeks in urine. Linnæus queries whether this moss be not the same as
his _lichen calcareus_[99]; a species so peculiar to limestone rocks,
that where-ever that stone occurs among others, it may be distinguished
at the first view by this moss growing upon it. This is a singularity
which Dr. Dillenius has not mentioned in his moss: on the other hand,
Linnæus does not mention any tinging property in his.

The _pérèlle d’Auvergne_, or _orseille de terre_, of the French,
belongs to this order of lichens, and is called by Dillenius[100] _The
crayfish-eye-like lichenoides_. It is gathered in large quantities in
the province of Auvergne, and is used as _orchel_; to which however
it is greatly inferior. They prepare it with lime and urine; and were
acquainted with its use as a dye long before the Canary weed was
known[101] to them; and it is at this day in more common use than
the _orchel_. We have it frequent with us upon old walls, rocks, and
stones; but it is to be had in larger quantities in several other parts
of Europe.

The mealy tartareous _lichenoides_[102] with brown dishes, forms an
article of trade with the people of West Gothland. They manufacture
a beautiful red dye from it, which they sell under the name of
_byttelet_[103]. Dr. Hill says we have this moss abundantly in
Leicestershire and Warwickshire.

The Welch make a red dye, with urine, from another moss of this order,
which Dillenius describes[104] by the name of _The large leprous
lichenoides with yellow plates_. These are not the only species, which
are endowed with a tinging quality: other kinds have been observed to
give a red or purple colour to paper in which they have occasionally
been inclosed. Doubtless several would, upon sufficient trials, be
found to answer equally well with the _orchel_.

With regard to these crustaceous mosses in general, it is highly
worthy our regard, that in the œconomy of nature they answer singular
and important uses. To an unobserving eye, no class of vegetables may
appear more insignificant, or less adapted to advantageous purposes
in the creation, than these. This vulgar estimation of things is
frequently erroneous; and it is certainly so in the instance before
us. These minute and seemingly insignificant mosses serve, under some
circumstances, to valuable purposes. No sooner is a rock left bare by
the sea, but these lichens lay the foundation for its future fertility.
Their seeds, which are presently brought thither by the winds, soon
cover it all over. These corrupting, presently afford a soil sufficient
to nourish other smaller mosses; which, in their turn, form one deep
enough for larger plants and trees; and thus the rock becomes a fertile
island[105].


5. Lichenes foliacei scutellati.

_Such as consist of a more lax and flexible matter, formed into a
foliaceous appearance, having the parts of fructification in the form
of_ scutellæ.

Some of the plants of this division are interspersed with the former
in some of the systems of botanic authors. In general this division
contains the whole first series of the second order of _lichenoides_
in Dillenius; the first division of the second series, and the latter
part of the second division, of the same: it comprehends the _lichenes
imbricati_ and _umbilicati_ of Linnæus; and many of the _placodium_ of
Hill.

The plants of this order are many of them not less common in England
than the foregoing, on rocks, stones, old pales, trees, _&c._ Some
adhere very closely to what they grow upon, and seem to be only
foliaceous about the edges: others adhere but loosely, and are much
expanded and divaricated, so as to form something like ramifications.

It was remarked, from Linnæus’s observation, that one of the
crustaceous lichens was scarcely ever found growing but upon limestone
rocks. On the contrary, the same author has observed of a foliose
lichen belonging to this order, that it will thrive on all kind of
rocks but limestone rocks. This species[106] Dillenius calls _The
common grey-blue pitted lichenoides_. It is very common with us upon
trees, old wooden pales, _&c._ as well as upon rocks and stones. It is
the _usnea cranii humani_ of the old _materia medica_. Linnæus adds,
that it will dye a purplish colour.

Hither likewise must be referred the cork or arcel[107], which is
used by the Scotch, and others, to dye a purple or scarlet colour.
The preparation of it is by powdering, and making it into a mass with
urine. Parkinson tells us[108] the poor people in Derbyshire scrape
it from the rocks, and make the same use of it. Mr. Ray[109] adds to
this account, that the Welch, who call it _kenkerig_, have long been
acquainted with this property, and have it in common use. The colour
from this moss is but very dull; but if the same methods were taken
to improve it, as have been with the _orchel_, it would undoubtedly
be rendered much better, and more durable. Linnæus relates[110], that
there is an immense quantity of this moss about the rocks of the isle
of Aland in the Baltick; where the good women themselves make a yellow
dye with it from a simple decoction of the plant, without the addition
of any saline article. He adds, that those, who would heighten the
colour, add a small quantity of _roucou_[111] to the decoction.

Professor Linnæus tells us, that the Gothlanders manufacture a yellow
dye from the common curled _lichenoides_ with yellow leaves and
plates[112]. He adds, that it is a celebrated medicine in the esteem
of the country people, as a specific in the jaundice[113]. Helwingius,
in the Supplement to the _Flora Prussica_, affirms, that this moss
will tinge paper and linen of a lively carnation colour, which too
will stand the test of being exposed to the open sun for a long time
without fading. It seems very probable, however, that he must mean some
other plant of this genus, as Dillenius tells us he made the experiment
unsuccessfully.

Sweden affords a moss of this order, which, as far as hitherto appears,
seems to be unknown to former botanists, and which Linnæus says will
dye a deep purple colour[114].


6. Lichenes erecti ramosi plani.

_Such as consist of a firm tough matter, disposed into flat and thin
ramifications growing erect, and bearing their scutellæ upon the edges,
surfaces, and at the extremities._

This division comprehends the flat branched tree-mosses of authors;
many of the fourth order of Haller’s lichens; the first part of the
second division of series the second in Dillenius; and the _platisma_
of Hill.

The plants of this division grow upon old trees, especially in thick
and unfrequented woods; some of them upon rocks: they are many of them
extremely common in England upon all kinds of trees. As they were some
of the most obvious, so they were some of the first lichens noticed by
the old writers, by whom they were called _lichenes arborum_.

The mosses of this order were substituted in the room of the _usnea_
in the composition of the _pulvis cyprius_. The very species, which
was most frequently used for this purpose, was the channel-leaved
_lichenoides_ of Dillenius[115], on account of its being easily reduced
into a fine powder, of a good white colour. Nevertheless, others are
undoubtedly as well adapted to the same purposes: and, if it was of
importance enough to employ them to any purposes of the like nature in
our own country, they might be procured in sufficient plenty.

One of the plants of this order is applicable to the same uses as
the Canary-weed, and is reckoned not much inferior to it; and as it
is found in the same places, it is very often packed up with it in
considerable quantities. Dillenius calls it _The flat dyers lichenoides
with longer and sharper horns_[116]. It is truly and properly a plant
of the lichen genus, tho’ the older writers of the last century
called it a fucus. They were led into this mistake by its having flat
ramifications, and from its growing on the rocks by the sea side. It is
found in the East Indies upon trees, and is frequent on the coasts of
the Mediterranean, as well as about the Canary Islands.


7. Lichenes peltati.

_Such as consist of a tough or coriaceous matter, disposed into a
foliaceous appearance; on the edges of which, in general, the parts of
fructification are placed, in the form of flattish oblong bodies, in
these mosses called_ shields _or_ pelts.

This division contains the third series of the second order of
Dillenius’s _lichenoides_; the _lichenes coriacei_ of Linnæus; and
several of the _placodium_ of Hill.

That celebrated and well-known plant, the ash-coloured ground
liverwort[117] of Ray belongs to this order. It is very common all over
England on dry and barren ground; and indeed almost all Europe, and
America too, seems to afford it in sufficient plenty, as we find it
observed by almost all the botanic writers since Ray, who was one of
the first that described it.

The earliest account we have of its use for the bite of a mad dog is in
the Philosophical Transactions[118], from Mr. Dampier, in whose family
it had been a secret for a number of years. It was communicated first
to Sir Hans Sloane, as a kind of fungus, or Jew’s-ear; and, at the
request of Dr. Mead, was some years afterwards received into the London
dispensatory. Scarce any of the boasted specifics of former ages ever
acquired so great reputation as this plant has done in modern times,
for its prevalence against the bite of a mad dog; and the patronage
of the late learned Dr. Mead made it sufficiently known throughout
all the world. Happy would it be indeed, if it fully deserved the
high encomiums, which have been bestowed upon it. A great and eminent
physician[119] has doubted its efficacy at all in such cases; and
it is well known, that Boerhaave even laughed at it. Dr. Mead had
certainly an high opinion of it: he tells us it never failed, thro’
the course of thirty years experience, where it was duly given before
the _hydrophobia_ came on[120]. Later instances have shewn, that it is
not infallible; and Dr. Van Swieten’s supposition is but too likely
to prove true. It must be confessed, that Dr. Mead’s exhibition of it
seems too much complicated with other means to leave room for judging
fully of its real efficacy; and it may really be questioned, whether
bleeding, pepper, and cold-bathing, have not had more to do in the case
than the lichen.

The _muscus pulmonarius officinarum_[121], tree-lungwort, or oak-lungs,
belongs to this order. It is found about old oaks, and upon rocks and
stones overgrown with moss, in many of our thick woods in England; but
not in any great plenty.

Few, perhaps, of the antiquated simples were in more repute, in their
day, than this plant. It was celebrated for ages, on account of its
supposed prevalence in pulmonary complaints of almost all kinds; and
yet, upon inquiry into the original of its use in such cases, it would
probably appear, that it arose more from a fansied resemblance they
found in the plant to the lungs themselves, than from any real and
well-grounded proofs of its efficacy. As a gentle astringent, like most
other species of the family, it would doubtless contribute to relieve
in many cases where the lungs were affected, as in _hæmoptoës_, and
some others: but it does not seem, by any means, to deserve that high
character in medicine which has been given to it.

The people in Herefordshire, where this moss is called _rags_, dye
their stockings of a brown colour with it. This is done by a very
strong but simple decoction in water, and the colour stands well[122].

The fine green _lichenoides_ with black warts[123], is a celebrated
medicine, and in very frequent use, with the country people about
Upsal, for the thrush in children: to this end they give an infusion
of it in milk. A medicine of this kind is of great importance in those
countries, where that disorder occurs much more frequently than with
us[124]. It is not received into the Swedish dispensatory; but is known
however in the shops, under the name of _muscus cumatilis_. We have it
not in England; and Dillenius found it but in one place about Geissen:
in the woods of Sweden it is more plentiful. A singular case, which
is related in the _Amænitates Academicæ_[125], has given rise to an
opinion of its usefulness in the worms also. The case briefly was this:
A country girl had, for near half a year, complained of excruciating
pains in her stomach and bowels, which were attended with vomiting,
anxiety, and great watchfulness. All that had been prescribed for her
by Professor Linnæus and others, who took her case for the worms,
proved altogether fruitless. Being afterwards left to the care of her
neighbours and relations, some good women gave her a decoction of this
moss, which the Uplanders call _elfnefwer_. After she had taken it a
few days, she vomited up six or seven roundish worms, and was cured.
These were found, upon examination, to be the maggots of a kind of
brown bee-fly, described by Mr. Ray[126], and by Linnæus[127].

However insufficient this history may be, to prove the usefulness of
this plant as a vermifuge, it will at least serve to exemplify this
fact; namely, that other animals of the insect kind, besides the
_teniæ_, _lumbrici_, and _ascarides_, may subsist a long time in the
_primæ viæ_ of the human body, and be the cause of great disturbances
therein[128].

Necessity is frequently the parent of the most useful and important
discoveries: and the uses to which a plant of this order is
appropriated by the natives of Iceland, is a standing proof of the
truth of this observation. That climate will scarcely permit the
cultivation of any kind of grain; but the want of it is in a great
measure happily supplied by the eryngo-leaved _lichenoides_[129], which
is abundant in the northern regions; and in that island particularly
the natives have long been acquainted with the methods of applying it
both to the purposes of food and of physic.

Ray has long since informed us[130], from Bartholine, that in the
spring time, while it is young, it will purge; in consequence of which
it is used as common spring physic. This quality it loses in a short
time; and what serves for physic in the spring, is converted the
remaining part of the year into food. They collect large quantities
of it, grind it into meal, and make both pottage and bread of it. It
is in common use not only with the islanders, but in several parts
of Sweden also, where it is found to be a very appropriate diet in
phthisical cases[131]. These accounts of the excellent use of this
lichen correspond perfectly well with the last accounts of it in Mr.
Horrebow’s Natural History of Iceland, just published; and which I
shall take the liberty of transcribing as follows: “There is another
herb, called _muscus catharticus islandiæ_, or mountain-grass, which
they cook up into a delicate dish. I have often eat of it; at first out
of curiosity, but afterwards for its palateableness and wholesomeness.
The excellent qualities of this herb are described in the Memoires
of the Society of Arts and Sciences in Sweden. It grows in great
abundance; and those that live near the places, where it is found,
gather great quantities for their own use, and to send to market.
People that live at a great distance will send and fetch horse-loads
away. Many use no meal or flour at all, when they are stocked with this
herb, which in every respect is good and wholesome food”[132].

This moss is not very common in the southern countries of Europe.
England affords it but very sparingly. Mr. Newton and Dr. Dillenius
found it in Wales; Sibbald, in Scotland. It is frequent on the Alps of
Switzerland; and Dr. Haller mentions it in his _Iter Hercynium_. Sweden
and Lapland have it in plenty: and on account of its great abundance
and usefulness in Iceland, Bartholine, and after him others, called it
_muscus islandicus_.


CONCLUSION.

I cannot help remarking, by way of conclusion, that we have in this
genus of plants a convincing instance of the utility which may
result from the study of natural science in general, and even of
its minuter and hitherto most neglected branches. From a view of
the foregoing memoir it is evident, I presume, that the œconomical
uses of the lichens, in the various parts of the world, are already
very considerable and important: and altho’ it does not appear, that
the sensible qualities of any of them, or the experience of former
ages, will warrant our ascertaining any singular powers to them in a
medicinal way, yet posterity will doubtless find the means of employing
them to many valuable purposes in human life to us unknown.

It will at once be acknowleged, that the vegetable kingdom supplies
us with the far greater share of the necessaries, the conveniences,
and even the elegancies, of life. The cultivation of that knowlege,
which leads to the investigation of its subjects, cannot, therefore,
but be highly useful and necessary: and altho’ the bare science of
natural knowlege is of itself worthy of applause, yet it ought to
be considered, in reality, as the necessary means only of applying
the subjects of nature’s kingdoms to their true ends and purposes,
the service of mankind. To know and distinguish, by determined and
specific characters, even but a small share of that amazing multitude
of objects, with which the great Parent of nature has furnished our
globe, is a task far more than equal to the duration of human life. To
investigate and ascertain their various qualities and uses is equally
arduous and impracticable. While the naturalists, therefore, are
employed in distinguishing the forms of things, let others exert the
united efforts of genius and application to investigate their various
properties and uses. I need not say the field for both is boundless:
it doubtless will be so for ages yet to come. The hopes of discovering
some latent property, which may turn out to the advantage of his
fellow creatures, will animate the man, whose mind is truly formed for
relishing the pleasures of natural science; and however the result may
be, the inspection and contemplation of nature’s productions will ever
afford that satisfaction, which will amply repay him for his trouble.
The minuter, and, as they are commonly estimated, the most abject and
insignificant things are not beneath our notice; and an attentive mind
will readily conceive how much farther, and more extensively useful,
every branch of nature’s kingdom may yet prove in the œconomy of
human life. The man, therefore, whom a genius and love for natural
history has allured into its pursuits, and whose leisure permits his
gratification in such researches, if he is not happy enough to be
crowned with success, at least deserves it, and merits the thanks of
his fellow-creatures for his application and diligence.




XCII. _An Account of the fossile Bones of an Allegator, found on
the Sea-shore, near_ Whitby _in_ Yorkshire. _In a Letter to_ John
Fothergill, _M. D. from Capt._ William Chapman.

                                          Whitby, 20th of 1st mo. 1758.

[Read May. 4, 1758.]

A Few days since we discovered on the sea-shore, about half a mile from
this place, part of the bones of an animal, appearing as in the annexed
figure (_See_ TAB. XXII.). The ground they laid in is what we call
allum-rock; a kind of black slate, that may be taken up in flakes, and
is continually wearing away by the surf of the sea, and the washing of
stones, sand, _&c._ over it every tide.

The bones were covered five or six feet with the water every full
sea, and were about nine or ten yards from the cliff, which is nearly
perpendicular, and about sixty yards high, and is continually wearing
away, by the washing of the sea against it; and, if I may judge by
what has happened in my own memory, it must have extended beyond
these bones less than a century ago. There are several regular strata
or layers of stone, of some yards thickness, that run along the cliff,
nearly parallel to the horizon and to one another. I mention this to
obviate an objection, that this animal may have been upon the surface,
and in a series of years may have sunk down to where it lay; which will
now appear impossible, at least when the stones, _&c._ have had their
present consistence.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXII(b) _p. 689_.

_J. Mynde sc._]


_References to the Draught._

_A_, _B_, _C_, the head and bill, not in the same line or range with
the rest of the bones.

_a_, _b_, A bone, with its processes, which I take to be similar to
that, which includes the brain in fishes. The part between the bone and
outlines appeared to be a smooth membrane; but was so thin, that in
taking up it broke.

  It is evident this is the upper part of the head inverted.

_B_, _C_, the superior _maxilla_ intire, and in some places covered
with the inferior one for four or five inches together. Where this
happens, the vacuity is filled with matter like the rock in which it
lays; and there are large teeth in each jaw, at such distances, and so
posited, that those in one jaw fill up the vacuities in the other, and
appear like one continued row, the mouth being shut.

  Where there is only the superior _maxilla_ remaining, there are
  no teeth; but the sockets are visible and deep, and at the same
  distances from each other as the teeth in the other part of the jaw.
  The tip or extremity of the bill was intire for four or five inches,
  having both _maxillæ_, with their teeth, and towards the point large
  fangs. Part of the bill and head were covered with the rock; which
  was removed before they appeared as in the figure.

_A_, _D_, _F_, _G_, cavities in the rock, about two inches deep, where,
I suppose, the wanting _vertebræ_ have laid, as they are exactly suited
to have received them.

_D_, _F_, Ten _vertebræ_, from three to four half inches in diameter,
and about three inches long, some of them separated in taking up. They
were about two inches in the rock.

_E,_ Here we observed something like bone to stretch from the
_vertebræ_, and intending to take it up whole, begun to cut at what
we thought a proper distance; but found we cut thro’ a bone; and with
the _vertebræ_ brought up three or four inches of the _os femoris_,
with the ball, covered with the _periosteum_: but the animal has been
so crushed hereabouts, that we could make little of the socket or _os
innominata_. Several of the ribs came up with the _vertebræ_: they were
broke, and laid parallel to the _vertebræ_; but not quite close, there
being some of the rock between them. The _periosteum_ is visible on
many of the bones.

_G_, _H_, Twelve _vertebræ_ remaining in the rock, with which they are
almost covered, especially towards the extremity.

The place, where these bones lay, was frequently covered with sea-sand,
to the depth of two feet, and seldom quite bare; which was the occasion
of their being rarely seen: but being informed that they had been
discovered by some people two or three years ago, we had one of them
with us upon the spot, who told us, that when he first saw it, it
was intire, and had two short legs on that part of the _vertebræ_
wanting towards the head. Altho’ we could not suspect the veracity of
this person, we thought he was mistaken; for we had hitherto taken
it for a fish. But when we took it up, and found the _os femoris_
above-mentioned, we had cause to believe his relation true, and to rank
this animal amongst those of the lizard kind: by the length (something
more than ten feet) it seems to have been an allegator; but I shall be
glad to have thy opinion about it.

                           I am thy friend,
                        William Chapman _Sen._

_The bones were sent up, and are herewith presented to the Royal
Society by_

                                                         J. Fothergill.




XCIII. _De rariori quadam_ Orthoceratitis _Specie, in_ Suecia _reperta,
tractatus; in literis a_ Nicholao de Himsel, _M. D._ Riga Livono, _ad_
Gul. Watson, _M. D. R.SS._

[Read May 11, 1758.]

ORthoceratiti recti in loco quodam Kelwika dicto, prope Fahlunam in
Dahlia, reperti. Inhærebant lapidi cineracei coloris calcareo, variæ
magnitudinis orthoceratiti, quorum portiones hic delineatas describo.


_Vide_ TAB. XXIII.

_Fig. A._ Orthoceratitis portio, cujus pars inferior saxo adhuc
adhæret; ex lapide calcareo constans lente in apicem decrescens.
Licet ex parvis ejus fragmentis judicari possit, cylindrum esse
orthoceratitem, ea tamen si conjunguntur, verum formant conum, et mihi
videtur ex crassitie siphonis, orthoceratitem hunc conicum duos fere
superavisse pedes. Vidi orthoceratitem in alio lapide calcareo, quem
etiam ibidem loci, Kelwikæ, reperi, longitudine duorum cum semisse
pedum: sed impossibile erat, integrum eum excutere, nimis enim fragile
erat. Est portio hæc orthoceratitis testa sua ambiente vestita in _a b
c_. Quinque conspiciuntur articuli, thalami quondam, arctissime sibi
invicem insidentes, per quos a latere procedit sipho _m n_ sat crassus,
qui in omnibus fere, quas possideo portionibus orthoceratitarum, a
centro semper remotus, hic ad peripheriam positus conspicitur. Sipho
admodum lente decrescit, ex quo etiam de longitudine coni hujus
judicare licet. Crustæ vel testæ _a b c_ interior pars, quæ articulos
tegit, crysstallina est, ex spati crystallis tenuioribus irregularibus
constans.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXIII. _p. 692_.

_J. Mynde sc._]

_Fig. B._ Portio alia, in qua articuli minus crassi; sipho quoque ad
peripheriam positus, testa sua in _a_ tecta. Conspicitur septum illud
testaceum in _b_, communi tenuior, quod ab ipso articulo superiori
procedens, siphonis partem _r s_ investit.

_Fig. B, C._ Portio orthoceratitis ex lapide calcareo cineracei
coloris: sipho vero, fluore spatoso egregie crystallisato, constat.

_Fig. C._ Portio alia per axin divisa, cujus pars exterior, testa quæ
striis circularibus levioribus externe ornata, investita conspicitur.

 Ex parte interiori _Fig. D._ confirmatio ejus interna adparet. Sipho
_x z_ gracilior, inter centrum et peripheriam positus, dimidia parte
ambiente articulo denudatus adparet; dimidia altera, inferiori articulo
_c d e_ tegitur. Articulus _a b_ spato crystallisato pellucido polygono
repletus est. Articulus _c d e_ vero, saxo spatoso incarnato paululum
repletus est. _x_. Siphonis pars superior, ubi radii a peripheria ad
centrum tendentes conspiciuntur. Inter crystallos spatosos in articulo
_a b_ striæ hinc et inde adparent nigræ, asphalto repletæ; ita etiam
cavitas articuli _a b_, æque ac superficies convexa articuli _c e_, quæ
in primam concavam recipitur, lamina asphalti vestitæ sunt.

_Fig. E._ Pars alia orthoceratitis majoris, et quidem facies exterior.

_Fig. F._ Facies ejus interior, in medio divisi, cum siphone transeunte
satis crasso. _a b c_ et reliquæ striæ leves, sunt diaphragmata,
articulos _a b_ invicem separantia, siphonem proprie constituentia,
siphonisque tenuiorem membranam, quæ in _o_ et _p_ adhuc conspicitur,
ambientia. Sunt diaphragmata hæc crassiora in siphonis vestigiis, et
sibi invicem ab inferiori parte insident. Sipho hic inter centrum et
peripheriam positus est.

_Fig. G._ Materies calcarea, quæ siphonem replevit striata, et quidem
pars ejus interior, qua centrum orthoceratitis respicit, peripheriæ
opposita.

_Fig. H._ Facies posterior, peripheriæ propior.

_Fig. I._ Pars concava articuli majoris orthoceratitis, in qua
diaphragmatis testacei jam crystallisati portiunculæ albicantes _m n r_
conspiciuntur cum siphone transeunte.

_Fig. K._ Portio alia orthoceratitis majoris, ejusque facies
exterior, cum siphone _g_ ad peripheriam posito. Conspiciuntur his
diaphragmata, quæ ab utroque latere, ab articulis procedunt, se invicem
conjungunt, et siphonem ab exteriori parte obtegunt. _a_ est testæ
satis crassæ portiuncula, qua portio hæc orthoceratitis vestita adhuc
est.




XCIV. _A further Account of the Effects of Electricity in the Cure of
some Diseases[133]: In a Letter from Mr._ Patrick Brydone _to Dr._
Robert Whytt, _Professor of Medicine in the University of_ Edinburgh,
_and F.R.S._

                                        Coldinghame, January 9th, 1758.

[Read May 11, 1758.]

A Young woman of Aiton, a village about two miles from this place, had
her right leg drawn back by a contraction of the muscles that bend the
knee, so that she had not been able to put that foot to the ground
for near a twelvemonth. She had taken the advice of some Surgeons in
the country, and had used several remedies to no purpose. At last,
hearing of the cure of the paralytic woman, whose case I sent you
some time ago, she insisted on being brought hither; and underwent a
course of electrical shocks for near two months, receiving every day
at least fifty or sixty in the following manner. She sat close by the
machine, and grasping the phial in her hand, she presented the wire to
the barrel or conductor, and drew the sparks from it for about half a
minute. The phial being thus charged, she then touched her knee with
the wire, and thereby received such severe strokes, as would sometimes
instantly raise a blister on the part. The joint was at last so much
relaxed, as that she could walk home with the help of a crutch, tho’
her leg was so weak, that she had very little use of it. After she had
continued in this state for some weeks, she was advised to use the cold
bath: but that soon brought back the contraction; and I have been since
informed that she was worse than ever.


A soldier’s wife, a genteel looking woman, of about 30 years of age,
was seized with a slight palsy, about Newcastle, on her way to this
country: but before she got to this place, she had lost all the feeling
in her left side, and so far the power of it, that she was brought to
us in a cart. After receiving 600 strokes from the electrical machine
in the usual way, and in the space of two days, she recovered the use
of her side, and set out on foot to make out the rest of her journey.
However, for fear of a relapse, I gave her a recommendatory letter
to Mr. Sommer, Surgeon at Haddington, as she was to pass thro’ that
town, and as I knew that he was likewise provided with an electrical
apparatus.


A young woman from _Home_, a village in this shire, but at a good
distance, complained of a coldness and insensibility in her left hand
and wrist, of two years standing. When I felt that hand, it was as cold
as a stone, whilst the other was sweating; and she told me, that it
never had been warmer all that time. I made her draw the sparks from
an egg (which for some other purpose was suspended by a wire from the
conductor) for about half an hour; and at the end of that time I found
the dead hand in a far greater sweat than the other. She then wrapt
it up in a piece of flannel, as she used to do, and retired. Next day
she told me, that since the operation she had been able to put off and
on her cloaths without help, which she had not been able to do for a
twelvemonth before. She was again electrised; and believing she was
then quite well, she went away: but some weeks after, upon the coldness
of her hand beginning to return, she made me another visit, was again
electrised, and was dismissed a second time apparently cured. This is
about two months ago, and I have heard nothing of her since.


As these two last women are at such a distance, I cannot pretend to
send you their own testimony of their cure. But for the two cases in
the separate paper, as the persons are inhabitants of this place, I
have taken care that they themselves should sign them, along with my
father; since you have acquainted me, that accounts of this kind should
have the attestation both of the patients and the minister of the
parish.

I shall only add here, that several persons have been relieved of
rheumatic pains, by electrising the parts affected. And a woman
was cured of a deafness of six months standing, contracted, as she
imagined, by cold. This woman held the phial in her hand, whilst
another person standing on a cake of resin gave her the shock, by
putting the end of the wire into her ear. This manner of electrising
brought always on a profuse sweat over the head, which we encouraged,
by wrapping it up in flannel. The first day she came here, she could
scarce hear what was spoken by those about her; but in five days she
seemed to be perfectly cured.

                              I am, _&c._
                           Patrick Brydone.


_Copy of the separate Paper before mentioned._

Robert Haigs, of Coldinghame, a labouring man of about 45, after having
been for ten days ill of a regular tertian ague, at my desire underwent
the electrical shocks in the common way. After having received about
thirty or forty very severe ones, he grew pale, and staggering for
several steps, would have fallen down, had he not been supported. He
then fell into a sweat, which continued near half an hour. I desired
him to come back the next morning, immediately before the fit, which
he said came on about ten o’clock. He accordingly came, and told me he
had not the usual symptoms preceding the fit. He was that day again
strongly electrised; and has been without any aguish symptom ever
since; _viz._ for the space of four months.

The truth of this is attested by

                                      ROBERT HAIGS, _the person cured_.
                              ROBᵗ. BRYDONE, _Minister of Coldinghame_.


Ann Torry, of Coldinghame, a young woman of about 20, had a regular
tertian (being the first time she ever had the ague) for near a
fortnight. The fit came on early in the morning. She was electrised on
her well day in the afternoon; and the next morning, having had only a
slight shivering, she was electrised again about ten o’ clock, and has
had no symptom of the ague since; _viz._ for three months.

The above is attested by

                                         ANN TORRY, _the person cured_.
                              ROBᵗ. BRYDONE, _Minister of Coldinghame_.




XCV. _An Account of the Black Assize at_ Oxford, _from the Register of_
Merton College _in that University. Communicated by_ John Ward, _LL. D.
With some additional Remarks._

_Anno nono_ D. Bickley _Custodis_, 1577.

[Read May 25, 1758.]

VIcessimo[134] primo Julii in vestiario Dñus custos et octo Seniores
dispensarunt cum _Decreto de concione et appictantia habendis, die
Dominico post festum Sᵗⁱ Petri ad vincula_; ne vocata et conveniente
turba, morbus ille, qui ante quinque dies quamplurimos infestarat,
dissipatior et periculosior fiat. Etenim 15, 16, et 17, hujus Julii
aegrotant plus minus trecenti homines; et infra duodecim dierum spatium
mortui sunt (ne quid errem) centum scholares, praeter cives non paucos.
Tempus sine dubio calamitosissimum et luctu plenum. Nam quidam
lectos differentes[135], agitati nescio quo morbi et doloris furore,
suos custodes baculis caedunt et abigunt; alii per areas et plateas
insanientium more circumcursant; alii in profundam aquarum praecipites
insiliunt; nemo tamen, summo Deo gratia, desperanter perit. Franguntur
omnium animi. Fugiunt medici, non propter necessitatem fratrum, sed
propter se et cistas creati. Relinquuntur miseri. Domini, doctores,
et collegiorum praefecti, ad unum pene omnes abeunt. Custos noster,
longe omnium vigilantissimus, domi apud nos manet; in aegrotis omnem
curam, laborem, diligentiam impensus[136] collocat; die toto, et nocte
etiam intempesta, eos sedulo invisit. Moriuntur e nostris quinque.
Omnis aula, omne collegium, aut domi, aut in via ad patriam, suos habet
mortuos. Mirari quis posset multitudinem ad medicastrorum domos cum
matulis citato cursu properantium. Pharmacopolarum etiam conservata
syrupos, olea, aquas dulces, pixides, cujusque generis confectiones,
brevissimo tempore exhausta. Laborant aegroti vehementissimo tum
capitis tum stomachi dolore; vexantur phrenesi; privantur intellectu,
memoria, visu, auditu, et caeteris etiam sensibus. Crescente morbo,
non capiunt cibos, non dormiunt, ministros aut custodes non patiuntur.
Semper, vel in ipsa morte, mirae orum strenuitas et corporis robur;
et eo declinante, omnia modis impense contrariis eveniunt. Nulli
complexioni aut constitutioni parcitur; cholericos tamen praecipue
hic morbus molestos habet; cujus ut causas, sic et curas ignorant
medici. Natum suspicantur multi, vel ex foetido et pestilenti furum e
carceribus prodeuntium aëre (quorum duo vel tres sunt ante paucos dies
in vinculis mortui) vel ex artificiosis diabolicis et plane papisticis
flatibus e Lovaniensi barathro excitatis, et ad nos scelestissime et
clam emissis. Nam illi solum et hic et alibi decumbunt aegroti, qui in
castro, et _guilda_, quam appellant, aula, quinto et sexto hujus mensis
adsunt[137]. Assisiorum judices, dominus Robertus Bell, capitatis baro
scaccarii etc. qualem hactenus non peperit Anglia; dominus Johannes
Barrham, dominae reginae serviens ad legem; papisticae pravitatis
uterque apertissimi hostes et acerrimi vindices: vicecomes Oxoniensis
comitatis[138], equites aurati duo, armigeri et pacis justiciarii
octo, generosi plures, horum non pauci famuli, omnes (uno aut attero
exceptis) _de grandi_, ut loquuntur, _jure_, statim post fere relictam
Oxoniam mortui sunt. Et ut quisque fortissimus, ita citissime moritur.
Foeminae non petuntur, nec certe pauperes; neque etiam inficitur
quisquam, qui aegrotorum necessitatibus subministrarit, aut eos
inviserit. Sed ut fuit morbus hic insigniter violentus, ita neque diu
duravit. Nam infra unius mensis curriculum ad pristinam pene sanitatem
restituuntur omnes; ut jam denuo mirari possis tot scholares, tot
etiam cives, urbem et plateas linteis capitibus obambulantes, et nomen
clementissimi Dei nostri in omne aevum suspicere[139].

Vicessimo quarto Julii Joannes May, socius et artium magister, in
collegio vitam finit. Sepelitur in ecclesia.

Vicessimo septimo ejusdem Browne clericus moritur in collegio.

Vicessimo octavo ejusdem Gaunte portionista moritur in collegio.

Vicessimo nono Dnus Lea, electus probationarius 20 Julii, moritur in
collegio.


_Additional Remarks, by_ Tho. Birch, _D. D. Secret. R. S._

CAmden, in his Annals of Queen Elizabeth[140], observes, that almost
all, except women and children, who were present at the assizes at
Oxford, at the tryal of Rowland Jenkes, a Bookseller there, for
seditious words, died, to the number of about three hundred. Mr.
John Stow, in his _Chronicle of England_[141], enlarges this number,
and affirms, that there died in Oxford three hundred persons, and in
other places two hundred and odd, from the 6th of July to the 12th of
August; _after which died not any of that sickness; for one of them
infected not another_: And this historian agrees with Camden, that not
any one woman or child died thereof. Dr. George Ethryg, a physician,
who practised at that time at Oxford[142], in the 2d book of his
_Hypomnemata quædam in aliquot Libros Pauli Æginetæ, seu Observationis
Medicamentorum, quæ hâc ætate in usu sunt_, printed at London in 1588,
in 8vo, mentions, that on the first night of the appearance of the
dissease about six hundred fell sick of it; and that the next night
an hundred more were seized in the villages near Oxford. Lord Bacon,
in his _Natural History_, evidently refers to this, and one or two
more instances of the same kind, in the following passage, _Century_
X. _Nº._ 914. “The most pernicious infection next the plague is the
smell of the goal, where prisoners have been long and close and nastily
kept; whereof we have had in our time experience twice or thrice, when
both the judges, that sat upon the goal, and numbers of those, that
attended the business, or were present, sickened upon it, and died.
Therefore it were good wisdom, that in such cases the goal were aired
before they be brought forth.” We have likewise an account in Mr.
Anthony Wood[143], that at the quarter-session at Cambridge, in Lent in
the year 1522, and the 13th of the reign of Henry VIII. the justices,
gentlemen, and bailiffs, with most of the persons present, were seized
with a disease, which proved mortal to a considerable number of them;
those, who escaped, having been very dangerously sick. With regard to
the unhappy instance of the same kind of contagion, which happened at
the session in the Old Baily in May 1750, see Dr. Pringle’s excellent
work, intitled, _Observations on the Diseases of the Army in Camp and
in Garison_[144].




XCVI. _A Description of the Plan of_ Peking, _the Capital of_ China;
_sent to the Royal Society by Father_ Gaubil, è Societate Jesu.
_Translated from the_ French.

KING CHE. THE COURT.

[Read June 1, 1758.]

IN this plan are the inclosures of walls, which form as it were three
cities.

[Kong tching, Tse kin.]

The first is the imperial palace, or imperial city. It is called _Kong
tching_ or _Tse kin_. The numbers 11, 17, 21, 24, mark the great gates
of this inclosure.

[Hoang tching.]

The second inclosure is _Hoang tching_. The numbers 3, 18, 30, 86, mark
four great gates of this inclosure.

[King tching.]

The third inclosure is _King tching_, or Royal City. The numbers 235,
1, 99, 146, 173, 183, 188, 109, 211, mark nine gates of this inclosure.

At the four angles east and west of the north and south walls is a
large pavillion in the form of a fortress. It is a kind of arsenal
or magazine of arrows, bows, guns, bucklers, cuirasses, pikes, small
cannon, _&c._

Observe the angle made by the inclosure _Hoang tching_ on the south of
the gate Nº. 84, to the north of Nº. 260. The inclosure extends to the
east, then to the south, and continues to the east, passing by Nº. 3.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXIV. _p. 704_.

_J. Mynde sc._ ]

[Illustration: _Philos. Trans. Vol. L._ TAB. XXV. _p. 704_.

_J. Mynde sc._]

1. is the great gate _Hien men_. As you go on to the north, 2, 143,
214, are three gates of a great court with magnificent walls. Thro’ the
gate 3 you enter into a court, where is the _Tay miao_ Nº. 7. There are
reposited the tablets of the ancestors of the reigning emperor, and of
the illustrious subjects deceased, who have served the dynasty. This
_miao_ or palace is a vast one, and well kept. At regular times the
emperor, princes, and great men, go thither to perform ceremonies.

Nº. 9 is the _Che tsi tan_, where are performed, at regular times, the
ceremonies to the ancients, who have taught the art of agriculture.
This palace is a very beautiful one. 4, 5, 6, are the gates of a court,
where the _reguli_ and princes go frequently to receive the emperor’s
orders. There are halls for their reception. The mandarins give them
tea to drink, and mark their names in a register. When upon the fixed
days they cannot attend, they are required to give notice of it. It is
in this court, that the tributary princes, or their envoys, do homage,
and receive the presents of the emperor; which presents are considered
as rewards.

Nº. 11 is _Ou men_, the great gate with a beautiful pavillion of a
considerable height, in which is a large bell[145]. This gate, with
those marked Nº. 12, 13, are those of the great court; whence going
to the north, you enter into the beautiful and vast court _Tay ho
tien_, the gates and galleries of which, with the balconies, make a
fine appearance. In this court, on the first day of the year, and on
other fixed days, the mandarins, according to their ranks, perform the
ceremony to the emperor, who is seated on his throne in the hall called
_Tay ho tien_. This hall is a vast and magnificent one. The princes,
ministers, and great men of the first order, place themselves there
by the emperor. It is in this hall, that the emperor gives audience
to foreign princes and their ambassadors. You go up to this hall by
magnificent steps.

To the north of _Tay ho tien_ is a large court, whither the princes,
great men, ministers, and principal mandarins, go in turns every day,
to receive the emperor’s orders, or to present their petitions. To the
north of this court are the apartments of the emperor, the empress, the
queens, and ladies. The great gate of the place, where these apartments
are, is Nº. 23. All these apartments are in the space contained within
the walls, which have this figure

  +-----   -----+
  |     23      |.
  +----- A -----+

At A is a beautiful gate to the south. The walls of the inclosure of
the apartments of the emperor and empress are higher than those of the
inclosures of the queens and ladies. In them are orchards, jets d’eau,
flowering shrubs, and a great number of small chambers for the eunuchs.

To the west of the court _Tay ho tien_ is the fine palace _Tsi ning
kong_. The empress-mother lives there at present. Every thing in this
palace is beautiful. There are little gardens very neat and well kept.
At the east of the _Tay ho tien_ is likewise a fine palace, where
the prince heir, with his court, resided in the time of the emperor
_Kanghi_. It is a very beautiful palace, and highly ornamented.

In the inclosure of _Kong tching_, or _Tse kin_, there are tribunals, a
great number of magazines, manufactures, the imperial apothecary’s shop
and printing-house; schools for the Chinese and Tartar languages; and
several temples of idols, one of which, lately made for the lamas, cost
immense sums.

Nº. 26, 28, 29, are the gates of the great inclosure called _Kin chan_.
It is properly a beautiful pleasure-house, which the present emperor
has caused to be extremely embellished. There are in it fine gardens
with walks of trees, very rich and elegant apartments, halls for the
musicians and comedians. From the mountain _m_, the last emperor of the
dynasty _Ming_, seeing the city taken by the rebels, hanged himself
on the morning of the 15th of April of the year of our Lord 1644. On
the day before, the 14th of April, the empress hanged herself in the
evening in the palace. The mountain in _Kin chan_ was made by art a
long time ago.

At the west of the inclosure _Kin chan_ and _Tse kin_ observe the
great laos. 54 is the _peta_, or white pyramid. This pyramid stands
on a small mountain, which makes an island. The present emperor has
built there, in the form of an amphitheatre, I do not know how many
apartments with covered and open galleries, well built, and in a good
taste: the point of view is charming, and the galleries, which run
over the lake, are extremely beautiful. There are two or three temples
of idols. 53 is a fine building with a temple of idols; and in it a
statue of _Fo_ of an extraordinary height. It is of copper, gilt, and
cost great sums. 76 is a very beautiful palace called _Yng tay_, with
fine gardens, fine halls, and fine walks.

55 is the palace, in which is placed the tablet of the emperor _Kang
hi_, grandfather to the present emperor, who at regular times goes
thither, in order to honour the memory of that great prince, one of the
most illustrious and fortunate sovereigns of the empire of China.

81 is the house and church of the French Jesuits. The house stands in
39° 55´ of northern latitude, or possibly some seconds more, and 114°
to the east of the observatory of Paris. This situation, with regard
to latitude and longitude, is founded upon a considerable number of
astronomical observations. By means of a scale, which may be made, we
have the distance between this house and the other parts of the city,
north and south, east and west; as likewise the latitude and longitude
of all the places in the city of Peking. 248 is the house and church
of the Portuguese Jesuits; 170 the house and church of the Portuguese
Jesuits[146]; 131 the house and church of the Russians. A little to the
east of Nº. 176 is a small house and chapel for the Russians settled at
Peking for above seventy years past.

31 is _Kou leou_[147], the Tower of the Drum; 32 is _Tchong leou_, the
Tower of the Bell; in which is a very large bell[148].

179 was formerly the palace of the fourth son of the emperor _Kang hi_
after the death of _Kang hi_. This prince reigned under the name of
_Yong tching_. His son the present emperor caused this palace to be
demolished, and to be rebuilt with an extraordinary magnificence. In
the hall is the tablet of _Yong tching_; and there are in this palace
grand apartments for the emperor, when he goes thither to honour the
memory of his father. The emperor has erected here a temple of idols
for the lama of Thibet; and there are apartments for above three
hundred lama’s. These have Chinese and Tartar disciples to the number
of two hundred. Here are taught, in the Thibetan language, called here
_Tan gout_, the sciences, arts, mathematics, physic, spirituality, and
the pagan religion. In this beautiful inclosure there are statuaries
and painters. This building is not at all inferior in beauty and
magnificence to those of the palace of Peking, or to those, which the
present emperor is going on to erect in his pleasure-houses.

180 _Koue he kien_ is the imperial college. The great hall, where
Confucius is honoured, is a very beautiful one. There are likewise
halls for honouring the disciples of this philosopher and several
eminent Chinese learned men, who have followed his doctrine with
success. The emperor goes thither sometimes to perform the ceremony to
Confucius as master and instructor to the empire. The avenues, courts,
and apartments, of _Koue he kien_ have a most majestic appearance.

70 the smaller observatory.

108 the imperial observatory, built by _Kia hing_, emperor of the last
dynasty _Ming_.

136 the tribunal of mathematics, _Kin tien kien_.

137 the tribunal of mandarins, _Ly pou_.

139 the tribunal of rites and ceremonies[149], _Ly pou_.

133 _Ping pou_, the tribunal of war.

134 _Kong pou_, the tribunal for public works.

140 _Heu pou_, the tribunal for the finances.

142 the tribunal of princes, _Tsong gin fou_.

168 _Hing pou_, the tribunal for criminal causes.

144 _Li fan yuen_, the tribunal for foreign nations, Thibetans,
Eleuthians, Russians, and indeed for all foreigners, who come by the
way of Tartary from the west.

369 _Tou tcha yuen_, the tribunal of the censors of the empire. It has
under it the _provosts_ and _mare-chaussée_.

233 the tribunal of _Kieou men ti tou_, or governor of the nine gates,
that is, the governor of the city.

185 the tribunal of the judge of the city. This judge is here called
_Fou yn_. He has under him two judges named _Tchi hyen_. One of these
is the judge of the district called _Ouang ping hien_ 193. The other is
called the district of _Tay tsing hien_ 182. These districts are within
the city and without it. What is called at Peking _tou yn_ is called
elsewhere _tchi fou_.

128 is the tribunal of _Han lin_, or the chosen doctors of the empire.
This tribunal, called _Han lin yuen_, is a very considerable one: it
has the care of the registers for the Chinese history. All the learned
men of the empire, and the colleges and schools, depend upon this
tribunal. Here are chosen the judges and examiners of the compositions
for the degrees of the learned men; as likewise those, who are most
capable of writing verses and pieces of eloquence for the use of the
palace and emperor.

107 _Kong yuen_ is the inclosure, where the compositions are drawn up
for the examination of the learned men. Here are a great number of
little chambers or cells for the composers, and fine apartments for the
mandarins appointed to preserve good order, and to prevent those, who
compose, from making use of the compositions of others.

273 _Tchoua kou ting_ is a pavillion, in which is a drum. Mandarins
and soldiers keep guard here day and night. In ancient times, when any
person had not justice done him, and thought himself oppressed, he went
and beat this drum; at the sound of which the mandarins ran, and were
obliged to carry the complaint of the party oppressed to the great
men or ministers. Upon which information was taken of the fact, and
justice done. At present the use of this drum is abolished; but it has
been thought proper to preserve this ancient monument of the Chinese
government.

217 _Ti ouang miao_ is a palace, wherein are the tablets of a great
number of the ancient emperors of China. At the time of the equinoxes
the emperor goes thither to perform the ceremonies to these deceased
emperors. See the notes on the _Ti ouang miao_, p. 723.

92, and the continuation of the buildings to the north, contain the
magazines of gunpowder, salt-petre, and nitre. In the city are many
other magazines. I do not name them here. They have their numbers.
These magazines are of cloth, mats, skins, oil, wine, vinegar, wood,
coal, porcelain, tea, varnish, silk, _&c._

The city is divided into eight quarters for the bannieres of the
Tartars _Mantcheou_, the Tartars _Mongou_, and the Chinese called _Han
kun_, who follow the Tartars _Mantcheou_, and submitted to them when
they entered China. Since that time the Chinese _Han kun_ are become
numerous and powerful. These eight bannieries are divided by this
means as it were into twenty-four; _viz._ eight of _Mantcheou_, eight
of _Mongou_, and eight of _Han kun_. Each banniery has its officers,
magazines, and arsenal. These are pretty spacious inclosures, each of
which has its number.

94 is an inclosure, in which are kept tygers; and 240 an inclosure,
wherein are elephants.

65 _Tsan yuen_ is an inclosure for silk-worms.

147, 150, 151, are public granaries, very well built. Without the gates
146, 173, are many of these public granaries; as also in the environs
of the city to the north, south, east, and west. The largest and most
magnificent are in the city of _Tong tcheou_, four French Leagues to
the east of Peking.

37, 38, 42, 52, 54, 59, 60, 66, 80, 83, 84, 85, 91, 93, 117, 118, 152,
154, 156, 160, 165, 178, 196, 203, 210, 215, 218, 225, 229, 230, 250,
255, 261, these numbers mark temples of idols. Some of these numbers
mark halls for honouring of illustrious deceased persons; but of
these there are only a few. There are several small _miao_, which are
not numbered. In the Chinese city, in the suburbs, are many temples
of idols; and some even in the emperor’s palace. And almost all the
palaces of the princes have idol temples.

33, 35, 36, 61, 62, 64, 67, 68, 71, 109, 126, 128, 133, 134, 135,
136, 137, 139, 140, 141, 142, 144, 180, 182, 185, 193, 219, 222, 233,
243, 251, 252, 253, 254, 255, 259, 260, 267, 268, 269, 270, 271, 297,
these numbers mark the tribunals, as well those, which I have already
mentioned, as many other subaltern ones, which depend on them. There is
one for the physicians.

101, 119, 121, 124, 125, 129, 148, 149, 155, 161, 162, 166, 172, 174,
175, 176, 192, 194, 195, 202, 208, 209, 216, 220, 221, 224, 232,
237, 238, 239, 241, 244, 247, 249, 262, 263, 264, mark the palaces
of the princes of the blood, who are divided into several classes
_Tsing ouang_, _reguli_ of the first order; _Kun ouang_, _reguli_ of
the second order; _Pey le_, _reguli_ of the third order; _Pey tse_,
_reguli_ of the fourth order; _Kong_, or counts, divided still farther
into other classes; and _Tsiang kun_, or generals of armies, divided
likewise into other classes.

Some years ago the emperor caused to be measured the circumference of
the walls of _King tching_, of _Hoang tching_, and of _He kin_, _&c._
as likewise the breadth of the streets, the space filled by the _miao_,
our three churches, that of the Russians, palaces, _&c._ The Chinese
city was not measured. A drawing of all this was made at large,
and then reduced to a smaller scale, as it appears here. I will not
undertake for the perfect exactness of it, either in the measures or
the reduction. All this is by a Chinese hand. The foot made use of in
this mensuration is to that of France as 1000 to 1016. 1800 of these
feet make a _ly_[150]. By the scale to be seen in the small plan, and
from the dimensions of the south and east walls of _King tching_, may
be deduced all the dimensions. The circumference of the walls of the
Chinese city has been formerly measured, and well, by several measures;
and the result of them may be seen here by the scale.

The south wall of _King tching_ is from east to west eleven _ly_ and
near a third. The east wall from north to south is nine _ly_ and some
paces. So that the city is not square, as several persons have written.

The persons employed by the emperor to measure did not think of
measuring the space, which contains the house and church of the
congregation _de propagandâ fide_. This house and church are situated
to the south between number 207 and a small bridge to the west of
number 201.

In the accounts sufficient mention has been made of the walls and gates
of the city of _King tching_; for which reason it is not necessary for
me to say any thing concerning it.

In the year of our Lord 1267, the Tartar emperor _Koublay han_ (in
Chinese _Yuen chi tsou_) built the city called _Ta tou_. It is the
principal part of the present city of _King tching_. It contained the
_Kin chun_, a palace _Yng tay_, _Hoang tching_, _Tse kin_, &c. the
walls of the city, an observatory, the towers of the Drum and the
Bell. _Yong lo_, emperor of the last dynasty _Tay ming_, made great
alterations in the city built by _Yuen chi tsou_.

In the year 1406 the emperor _Yong lo_ undertook to build stronger and
higher walls, and more magnificent gates, to the city; to rebuild the
_Hoang tching_, the emperor and empress’s proper habitation, and the
several parts of _Tse kin_, the courts, hall of the throne or of _Tay
ho tien_, the _Kou leou_, the _Tchong leou_. He undertook also to build
the _Sien nong tan_ and _Tien tan_, which are now in the Chinese city.
On account of the wars with the Tartars, the works undertaken by _Yong
lo_ were not finished till the year of our Lord 1421. Since that time,
in the _Kin tchin_ some alterations have been made in the palace, and a
good number of new _miao_ and palaces have been built. The emperor _Kia
tsing_ built the Chinese city in the year of Christ 1544.

The gates and walls of the Chinese city are not all equal in beauty to
those in the city _King tching_. The streets are neither so broad, nor
so well kept in repair. More than a third of the space of the Chinese
city is not inhabited. It consists only of fields and gardens. The
spaces occupied by the _Sien nong tan_ and the _Tien tan_ are vast;
and between these two there is a very broad road. In this Chinese
city are some mosques for the Mahometans. The inhabited part of this
city is much more so than the city _King tching_ and _Hoang tching_.
In the Chinese city are vast inns for those, who come out of the
southern provinces to Peking. Here are likewise a curious manufacture
of _lieou ly_ or Chinese glass, rich merchants of women’s ornaments,
of gold, of the plant _gin cheng_ so much esteemed and so dear here,
of varnished furniture, tea, stuffs of value, _&c._ The booksellers
shops are also in this city. It is to be remarked, that the walls of
the Chinese city and _King tching_ do not run directly north and south
and east and west, but decline towards the north-west 2° 30´, and
as much south-east. It is probable, that the architects employed in
directing the building of these walls made use of a compass; and that
the declinatiation of the needle was then what is mentioned above.

What I have said of the walls of the city is likewise to be said of the
walls of _Hoang tching_ and of _Tse king_.

At the time of building the city _King tching_, and the Chinese city,
the Chinese astronomers very well understood, that the north and south
of the compass was not the north and south of the heavens at Peking;
they knew, that the needle declined to the north-west and south-east;
but that this declination was not considerable.

Without the gates of the Chinese city, and of _King tching_, I mark the
suburbs; which are very full of people and merchants, and like so many
cities. In most of these suburbs there are fine temples of idols.

The _Sien nong tan_ in the Chinese city is almost six _ly_ in circuit.
These three words signify, The hill of the ancient husbandmen.

The emperor goes thither every year in the spring to till the ground,
and sacrifices on that hill to heaven. The emperor’s apartments there
have nothing magnificent in them; but the ceremony of ploughing is a
solemn and curious one, and deserves a particular description. The
emperor tills under a small covering of mat. When he has ploughed
about half an hour, he ascends a large alcove, from whence he sees
the princes, great men, and mandarins, plough in the fields, which
are not covered with mats. While the emperor is ploughing, a good
number of peasants sing ancient songs on the importance of ploughing.
The emperor, princes, and great men, are dressed in the habit of
plough-men, and their instruments of husbandry are very neat, and
kept in a magazine. There are granaries for the grain produced by
this tillage; and it is carefully remarked, that the grain from the
emperor’s tillage is much better than that from the labour of others.
From this grain are made several cakes for the various sacrifices to
Heaven or _Chang ti_. The emperor prepares himself for this ceremony by
fasting, prayers to heaven, and a kind of retreat: and the intention
of it is to keep up a memorial of those times, in which the princes
themselves tilled the ground. This ceremony is of the highest antiquity
in China.

Over against the _Sien nong tan_ is the _Tien tan_, or Hill of Heaven,
near ten _ly_ in circuit. Every thing here is magnificent. The emperor
goes thither every year at the winter solstice to sacrifice to heaven.
He prepares himself three days for this ceremony by fasting, in a
palace of _Tien tan_, called the _palace of fasting_. The hill, on
which the emperor sacrifices, is magnificently adorned. At the four
avenues are beautiful triumphal arches of fine marble; and the hill is
ascended by elegant steps. In this ceremony are introduced many usages
contrary to the ancient Chinese doctrine concerning the sacrifice to
heaven. On the day of the winter solstice are added the honours paid
to the five planets, that is, to their spirit. These ceremonies added
to the sacrifice to heaven are not very ancient. There are likewise
honours to the first founders of the reigning dynasty. At several other
times the emperor goes to _Tien tan_ to perform a sacrifice to heaven,
and to honour his deceased ancestors.

To the north of the Hill of Heaven is a large and high terrace, on
which is a most magnificent hall in honour of _Chang ti_, or the
sovereign Lord, and of his ancestors. On the frontispiece of this hall
the present Tartar emperors have caused an inscription to be placed
to _Ap cai han_, or the Lord of heaven. To this Tartar inscription
answers the Chinese character _Kien_; which has the same meaning as
the character _Tien_, heaven; and it signifies the _Chang ti_, who is
intended to be honoured in this hall. The tablet for the _Chang ti_ is
in a place, which shews, that the honour paid to _Chang ti_ is of a
different kind from the honour paid to ancestors.

Without the eastern gate of _King tching_, Nº. 145, is _Ge tan_, or
Hill of the Sun. At the vernal equinox the emperor sends hither a
prince or great man to honour the sun, that is, the spirit of the sun.
This inclosure, tho’ elegant enough, has nothing very remarkable; nor
is the ceremony very ancient.

Without the north gate of _King tching_, at Nº. 183, is _Ti tan_, or
the Hill of the Earth. At the summer solstice the emperor goes thither
to sacrifice to the earth on the hill. Many of the learned men at
present distinguish this sacrifice in the _Ti tan_ from the sacrifice
in the _Tien tan_. But, according to the doctrine of Confucius, the
sacrifice to the earth has the same object as the sacrifice to heaven.
In both the supreme Lord _Chang ti_ is to be honoured. I do not know,
whether the emperor adheres to the pure doctrine of Confucius, and
whether he does not pretend to honour the earth, or spirit of the
earth, by performing a sacrifice, which originally had for its object
the _Chang ti_, as we are assured by Confucius. The inclosure of _Ti
tan_ is a vast one; but is not at all equal in beauty to the _Tien tan_.

Without the western gate of _King tching_, Nº. 211, is _Yue tan_, the
Hill of the Moon. At the autumnal equinox the emperor sends thither a
prince or great man to honour the moon, or spirit of the moon. This
ceremony is not very ancient. This inclosure is a neat one, and pretty
large.

Between the two north gates of _King tching_, Nº. 183 and 188, is a
vast esplanade for the exercise of the troops both horse and foot.

To the north of this esplanade are two beautiful temples of idols for
the lamas. These two monasteries are very elegant. The emperor and the
Tartars _Mon gou_ lay out great sums on these two monasteries and the
two temples of the lamas.

In the year 1111 before Christ, _Ou ouang_, founder of the dynasty
_Tcheou_, nominated his brother _Tchao kong_ prince of _Yen_. _Yen_ is
the ancient name of a pretty extensive country, in which Peking stands.
This prince of _Yen_ built a city there, a league and half south-west
of the city _King tching_. This city was called _Yen king_, or the
court of _Yen_. It became afterwards considerable; and the prince of
_Yen_ very powerful in the country of _Petcheli_ and _Leao tong_. In
the year 222 before Christ the emperor _Tsin chi hoang_ destroyed the
power of the princes of _Yen_, the defendants of _Tchao kong_, and
seized their dominions. The founder of the dynasty _Han_ destroyed the
power of the family of _Tsin chi hoang_. In the time of the dynasty
_Tsin_, before the Christian æra, and of the dynasty _Han_, the city
of _Yen_ was an important government, on account of the neighbourhood
of the Tartars. Some time after the dynasty _Han_ several Tartar
princes _Sien pi_ made themselves masters of the country of _Yen_.
During the dynasty of _Tang_ the city of _Yen_ was still a considerable
one. After the destruction of that dynasty the Tartars _Ki tan_[151]
made themselves masters of Tartary, and the provinces of _Chansy_,
_Petcheli_, and _Leao tong_. Their power was formidable to the Chinese.
Their court was in the city of _Yen_, which they adorned and inlarged.
These Tartars had, like the Chinese emperors, tribunals; one for the
mathematics, and another for history[152]. They had likewise some
illustrious princes, and kept some correspondence with the Caliphs.

The Tartars _Nuntche_ destroyed the power of _Leao_. Their court was
also at _Yen_; and they made it as magnificent and large a city as
Peking is now. The Mogol Tartars destroyed the empire of the _Nuntche_
or _Kin_. Their court was at first at _Yen_; but the Tartar Mogol
emperor _Koublay_ demolished that city, and built what is now called
_King tching_: at least _King tching_ is a good part of the city built
by _Koublay_, which was some _ly_ larger. The emperor’s palace was
likewise larger.

This city _King tching_ is that, which Marco Paulo calls _Cambalu_.
_Car_ is _khan_, which signifies a _king_; and _balu_ is a corruption
of an old Mogol word _balga_, or _balah_, which signifies a _city_:
whence is formed the word _balgasan_ in Mogol or Mongou, which
signifies city. _Khan balu_, or _khan balou_, signifies the royal
city. _King tching_, in the time of Marco Paulo, was the capital of
the empire of China. The Persians and Arabians, from the Mongou word
_khan balou_, or _khan balgasun_, or _khan balga_, formed the word
_khan balik_ or _khan balek_, which signifies also the royal city.
This name was given by the eastern people to the city of _Caifong
fou_, the capital of _Honan_, and to that of _Nanking_, the capital of
_Kiangnan_, at the time when these cities were the court of princes.
This name was also given to the cities of Tartary, when some powerful
princes kept sometimes their court there. What I have remarked
concerning the words _khan balik_, _khan balek_, _khan balga_, &c. is
to be applied to the words _ordo balik_, _ordou balik_. _Ordo_, or
_ordou_, or _orto_, signifies royal, imperial, in the Mogol or Mongou
language. So _ordou balik_ signifies a court, a royal city; and these
words are in fact the names of some old cities, where the Mogol or
Mongou kings kept their courts.


REMARKS _on_ Nº. 5, _Fan king tchang_; which is the place where the
foreign classical books are kept.

_Tchang_ signifies magazine, or large place, where any thing is
contained. _Fan_ signifies stranger or foreigner; and _king_ signifies
a classical book.

The Jews of _Caifong fou_, the capital of _Honan_, first told the
Jesuit missionaries, that they conceived, that the Hebrew Bible was
preserved at Peking in the place called _Fan king tchang_. These first
missionaries neglected to make a search for it at Peking, or did not
think of it. But it did not escape the attention of Father Bouvet,
a French Jesuit, who went to _Fan king tchang_. The antient place,
where the foreign books were kept, had been destroyed; and those books
removed into a neighbouring _miao_ where there were bonzes. Father
Bouvet went to this _miao_ with two other French Jesuits; but they
found only the Koran, fragments of the classical books of the Indians,
and the classical books of the lamas; the whole in bad condition.
Father Bouvet thought, that he saw in an old coffer Chaldee, Syriac,
and Hebrew characters. The bonze would not shew the place, where Father
Bouvet thought that he had seen those characters, which, on returning
to the _miao_, were not found. The emperor had ordered the bonzes
to shew every thing to Father Bouvet. All the classical books were
afterwards removed to the palace; the _miao_ was demolished; and there
remained nothing but the name of _Fan king tchang_. When I passed thro’
_Caifong fou_, the Jews, in the presence of Father Gozani, who served
me as interpreter, assured me, that I should find the Bible in the _Fan
king tchang_. These Jews had not been at Peking. What they said was in
consequence of what they had been told by old Jews, who were deceased.
When I arrived at Peking, I made inquiries myself, and caused inquiries
to be made by others; but I could not find the Bible. It is not yet an
hundred years since there were at Peking some Jewish families; which
afterwards turned Mahometans. A Mahometan, who was a man of parts,
assured me several times, that the Bible was in the possession of the
Mahometans here, whose ancestors were Jews. But when, in consequence of
what he said, inquiries were made, nothing was found. This Mahometan
informed me likewise, that he had made inquiries; but if he had done
so, his researches proved unsuccessful.


REMARKS _on the_ Ti ouang miao, Nº. 217.

1. The emperors, whose memory is honoured there, are

The emperors _Tou hi_, _Chin Nong_, _Hoang ti_.

The emperors _Chao hao_, _Tchouen hiu_, _Ty co_, _Yao_, _Chun_.

The emperor _Yu_, the founder of the dynasty _Hia_, and thirteen other
emperors of that dynasty.

The emperor _Tching tang_, the founder of the dynasty _Chang_, and
twenty-five emperors of that dynasty.

The emperor _Ou ouang_, the founder of the dynasty _Tcheou_, and
thirty-one emperors of that dynasty.

The founder of the dynasty _Han_, and twenty emperors of that dynasty,
who are called western _Han_, eastern _Han_, and later _Han_.

The founder of the dynasty _Tang_, and fourteen emperors of that
dynasty.

The founder of the dynasty _Song_, and thirteen emperors of that
dynasty; which is called the northern _Song_ and the southern _Song_.

_Gen tchis khan_, or _Temoug in_, the founder of the dynasty _Yuen_,
is the dynasty of the Mongol or Mogol Tartars. Besides the founder
of this dynasty, there are ten other emperors of this dynasty, whose
memory is honoured in the _Ti ouang miao_. The four first emperors of
this dynasty, _viz. Gen tchis khan_, _Ogo tay_, _Kouey yevou_, and
_Meng ko_, reigned in the northern provinces, and had not conquered all
China. The emperor _Cobilay_, or _Koublay_, in Chinese _Yuen chitsou_,
completed the conquest of China.

The founder of the dynasty _Ming_, and the eleven emperors of this
dynasty.

The emperor _Ogo tay_, the second of the dynasty _Yuen_, completed
the destruction of the dynasty of the eastern Tartars, called _Kin_.
It reigned to the north as long as the dynasty _Song_ reigned to the
south. In the _Ti ouang miao_ is honoured the memory of the founder of
this dynasty _Kin_, and four other emperors of it.

The founder of the Tartar dynasty _Kin_ destroyed the dynasty of the
Tartars _Ki tan_, called _Leao_, which conquered a great part of North
China and Tartary.

In the _Ti ouang miao_ is honoured the memory of this Tartar dynasty
_Leao_, and five other emperors of the Tartars _Ki tan_, whose country
was in that of Parin in Tartary, among the Mongou or Mogols.


_Continuation of the Remarks on the_ Ti ouang miao.

2. In the palace of Peking, and elsewhere, there are great halls, in
which honours are paid to the memory of the deceased emperors of the
reigning dynasty of the _Mantcheou_. The first and second emperor
reigned in East Tartary. The emperor _Chun tchi_ began to reign in
China. If we reckon the present emperor in the number, there are six
emperors _Mantcheou_. Father Couplet, and others, are mistaken in
reckoning one more. This error was occasioned by the years of the
reign of _Tay hong_, the second emperor, having had two names. Father
Couplet, and others, took the two names of the years of the reign for
the name or title of the two emperors.

3. In the _Ti ouang miao_ is honoured the memory of some illustrious
persons in the different dynasties. The same is done in the hall, where
honour is paid to the memory of the deceased emperors _Montcheou_: and
there are there tablets for so many illustrious persons among those
emperors.

4. In the _Ti ouang miao_ are placed none of the emperors of the
dynasty _Hin_ before Christ, nor any of those between the dynasties
_Tang_ and _Han_, nor of those of the five small dynasties after that
of _Tang_. Besides, in each dynasty there are some emperors, whose
tablets are not placed in the _Ti ouang miao_. The reigning dynasty has
not thought it a duty to pay honours to those emperors, but considered
them as unworthy the pompous title of _Tin tse_, or _Sons of Heaven_.

5. The Tartars _Sien pi_, who came from the confines of _Leao tong_ and
Mongol or Mogol Tartary, had hords named _To pa_. One of these hords
made themselves masters of Tartary _Leao tong_, and of several northern
provinces of China. This Tartar power has the Chinese name of _Ouey_.
It has produced several great princes. The year of Christ 386 is
reckoned the first of that dynasty[153], which reigned above 180 years.
I do not know why the reigning dynasty has not placed the name of any
of these emperors in the _Ti ouang miao_.

6. If we suppose, first, that all the books of the history of China
should be lost, or the contents of them should not be known in Europe;
and secondly, that the catalogue of the emperors, who are mentioned
in the _Ti ouang miao_, should fall into the hands of some European
critics; it is probable, that such a catalogue would occasion many
false reasonings with relation to the succession of the emperors, who
have reigned in China.




XCVII. _An Attempt to improve the Manner of working the Ventilators by
the Help of the Fire-Engine. In a Letter to_ Tho. Birch, _D. D. Secret.
R. S. from_ Keane Fitz-Gerald, _Esq; F.R.S._

[Read June 8, 1758.]

SIR,

THE reverend and ingenious Dr. Hales, from whom mankind has received
such benefit by his useful application of ventilators, being inclined
to extend its use to those, who work in mines at great depths under
ground, where the lives of many are lost by damps and noxious vapours,
occasioned by the want of a free circulation of air; and finding by
experience, that ventilators worked by wind do not operate above one
third part of the year, and in calm hot weather, when most wanted, do
not operate at all; did me the honour of applying to me for assistance
in contriving a machine to work the ventilator, by the help of the
fire-engine, which is now generally used in all mines for drawing off
the water; and which I have accordingly attempted, and hope it will
answer the purpose.

As the lever of the fire-engine works up and down alternately, and
performs at a common medium about a dozen strokes in a minute, it
was necessary to contrive some way to make the beam, tho’ moving
alternately, to turn a wheel constantly round one way, and also to
increase the number of strokes to fifty or sixty in a minute.

The model of a machine for this purpose is composed of four wheels of
different sizes, two clicks, three pinions, and a fly; which is put
into motion by the part of a wheel fixed to the arch of the lever of
the fire-engine.

The wheel, which is turned by the lever, or rather moved up and down
by it, is loose on its arbor; and likewise one of the rochets, and the
wheel next to it. The outside rochet and outside wheel are fixed on the
arbor.

There are two pinion-wheels fixed on the arbor; one on each side, near
the edge of the wheel moved by the lever, which turns them.

There are also two clicks; one fixed to the great wheel, the other to
the frame. These exclusive of the wheel that moves the fly.

The effect is, When the lever moves the wheel downwards, its click
forces the rochet fixed on the arbor to move along with it, and the
other wheels the same way. When it moves upwards, the click fixed on
the frame stops the larger rochet, and the wheel next to it, which are
pinned together. This wheel being stopped, and the great wheel carried
upwards by the lever, the pinion towards the edge of the great wheel
is forced round it, and moves the pinion on the other side the great
wheel; which pinion moves the wheel fixed on the arbor, the contrary
way to the great wheel, which is carried upwards by the lever. By which
means, the arbor is constantly turned the same way, when the lever of
the fire-engine is moved either upwards, or downwards.

Upon the arbor there is also another great wheel fixed, which turns
a pinion: on the arbor of which pinion is a crank to move the
ventilator, and also a fly fixed to the end, to help the motion of the
crank, which in the model is turned three times for each stroke of the
lever, and may be increased or diminished, according to the number of
teeth in the pinion.

The number of teeth in the great wheel moved by the lever is sixty-six;
but need not have teeth above half way round.

The wheel fixed to the rochet has thirty-three teeth, and its pinion
eleven.

The wheel fixed on the arbor, on the outside, has twenty-four teeth,
and its pinion sixteen.

The wheel, which turns the fly, has ninety teeth, and the pinion turn’d
by this wheel ten.

The greater the number of teeth in the rochets, the better.

This machine may also be applied to other useful purposes at mines; and
it may be easily made to turn a mill to grind corn; or to turn a wheel
to raise coals, or whatever else is wanted to be raised from the mines.
As I have not met with any thing of the kind described, I take the
liberty of desiring you to lay it before the Society; and I hope it may
be made some way useful to the public.

I am, Sir,

                  Your most obedient humble Servant,
                           Kea. Fitz-Gerald.

Poland-Street, June 7th, 1758.


_Explanation of the Three Tables._

The wheel A (_Tab. 26._), which is turned by the lever B (_Tab. 27._),
or rather moved up and down by it, is loose on its arbor; and likewise
one of the rochets C (_Tab. 26._), and the wheel next to it D. The
outside rochet E, and outside wheel F, are fixed on the arbor.

There are two pinion-wheels G and H fixed on one arbor; one on each
side, near the edge of the wheel A, moved by the lever.

There are also two clicks _a_ and _b_; one _a_ fixed to the great wheel
A, the other _b_ fixed to the frame. These exclusive of the wheel I,
that moves the pinion _c_, on the arbor of which, the crank _d_, and
fly _e_, (_Tab. 27._) are fixed.

The effect is, when the lever B moves the wheel A downwards; its click
_a_, forces the rochet E, fixed on the arbor K, to move along with it,
and the other wheels the same way. When it moves upwards, the click _b_
fixed to the frame, stops the larger rochet C, and the wheel D next to
it, which are pinned together; and as the wheel A is carried upwards
by the lever, the pinion G towards the edge of it, is forced round the
wheel D, and moves the pinion H, on the other side the great wheel A,
which moves the wheel F fixed on the arbor K, the contrary way to the
wheel A. By which means, the arbor K is constantly turned the same way,
when the lever of the fire-engine moves either upwards, or downwards.

The pinion G, by being made proportionally smaller than the pinion H,
keeps the arbor K in the same swiftness of motion, when the lever is
moved upwards, as downwards.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXVI. _p. 730_.

_J. Mynde sc._]

[Illustration: _Philos. Trans. Vol. L._ TAB. XXVII. _p. 730_.

_J. Mynde sc._]

[Illustration: _Philos. Trans. Vol. L._ TAB. XXVIII. _p. 730_.

_J. Mynde sc._]

The great wheel I, fixed on the arbor K, turns the pinion _c_, on the
arbor of which the crank _d_ (to move the ventilator), and the fly
_e_ (to help the motion), are fixed. The pinion _c_, is turned three
times by each alternate motion of the lever; which may be increased, or
diminished, according to the number of teeth in the pinion _c_.

The number of teeth in the wheel A is sixty-six, but need not be
toothed above half way. Instead of this wheel there might be a barrel,
with a chord round it, fixed at each end of the arch of the lever, and
projecting somewhat from it; which, by the motion of the lever, would
work in the same manner in other respects, and be easier made, and at
less expence.

The wheel D fixed to the rochet C has thirty-three teeth, and its
pinion G eleven.

The wheel F fixed on the arbor K has twenty-four teeth, and its pinion
H sixteen.

The greater the number of teeth in the rochets, the better.

_Tab. 26._ contains the plan (in parts) of the whole machine, except
the lever B and fly _e_, which are in _Tab. 27._

_Tab. 27._ also contains the elevation of the arbor, with its different
fixtures; _viz._

_Fig. 1._ The rochet C and wheel D (_Tab. 26._) fixed together.

      2. The outside wheel F that works the pinion-wheel H (_Tab. 26_).

      3. The two pinion-wheels H and G (_Tab. 26._) fixed on their arbor.

      4. The same fixed to the wheel A (_Tab. 26._) by means of two cocks
        _u_ and _w_ (_Tab. 26._).

      5. The arbor, with the wheel L and rochet E fixed; _t_ the place,
        where the wheel A is fixed.

      6. The elevation of the whole arbor.

_Tab. 28._ The elevation of the whole machine, the lever B (_Tab. 27._)
working the wheel A (_Tab. 26_).

    _s_ (_Tab. 26._) a thin piece of metal screwed to the wheel A, to
      keep it in its place _t_ on the arbor K (_Tab. 27._)

    _u_ (_Tab. 26._) the cock, that fastens the pinion G, to the inside
      of the wheel A.

    _w_ (_Tab. 26._) the cock, that fastens the pinion H on the outside
      of the wheel A.

    _x_ (_Tab. 27._) the arbor, on which the pinions G and H are fixed.

    _y_ (_Tab. 26._) a spring, that keeps the click _a_ in its place.

    L (_Tab. 26._) a frame-plate with the centers marked.

    _z_ The opposite hole enlarged, to admit the pinion _c_ to pass
      through.




XCVIII. _An Account of some Experiments concerning the different
Refrangibility of Light. By Mr._ John Dollond. _With a Letter from_
James Short, _M. A. F.R.S. Acad. Reg. Suec. Soc._

[Read June 8, 1758.]

               _To the Rev. Dr._ Birch, _Secret. R. S._

Dear Sir,

I Have received the inclosed paper from Mr. Dollond, which he desires
may be laid before the Royal Society. It contains the theory of
correcting the errors arising from the different refrangibility of
the rays of light in the object-glasses of refracting telescopes; and
I have found, upon examination, that telescopes made according to
this theory are intirely free from colours, and are as distinct as
reflecting telescopes. I am,

                               Dear Sir,
                  Your most obedient humble Servant,
                              Ja. Short.

Surrey-street, 8th June, 1758.


IT is well known, that a ray of light, refracted by passing thro’
mediums of different densities, is at the same time proportionally
divided or spread into a number of parts, commonly called homogeneal
rays, each of a different colour; and that these, after refraction,
proceed diverging; a proof, that they are differently refracted, and
that light consists of parts that differ in degrees of refrangibility.

Every ray of light passing from a rarer into a denser medium, is
refracted towards the perpendicular; but from a denser into a rarer
one, from the perpendicular; and the sines of the angles of incidence
and refraction are in a given ratio. But light consisting of parts,
which are differently refrangible, each part of an original or compound
ray has a ratio peculiar to itself; and therefore the more a heterogene
ray is refracted, the more will the colours diverge, since the ratios
of the sines of the homogene rays are constant; and equal refractions
produce equal divergencies.

That this is the case when light is refracted by one given medium only,
as suppose any particular sort of glass, is out of all dispute, being
indeed self-evident; but that the divergency of the colours will be
the same under equal refractions, whatsoever mediums the light may be
refracted by, tho’ generally supposed, does not appear quite so clearly.

However, as no medium is known, which will refract light without
diverging the colours, and as difference of refrangibility seems thence
to be a property inherent in light itself, Opticians have, upon that
consideration, concluded, that equal refractions must produce equal
divergencies in every sort of medium: whence it should also follow,
that equal and contrary refractions must not only destroy each other,
but that the divergency of the colour from one refraction would
likewise be corrected by the other; and there could be no possibility
of producing any such thing as refraction, which would not be affected
by the different refrangibility of light; or, in other words, that
however a ray of light might be refracted backwards and forwards by
different mediums, as water, glass, _&c._ provided it was so done, that
the emergent ray should be parallel to the incident one, it would ever
after be white; and, conversely, if it should come out inclined to the
incident, it would diverge, and ever after be coloured. From which it
was natural to infer, that all spherical object-glasses of telescopes
must be equally affected by the different refrangibility of light, in
proportion to their apertures, whatever material they may be formed of.

But it seems worthy of consideration, that notwithstanding this notion
has been generally adopted as an incontestable truth, yet it does not
seem to have been hitherto so confirmed by evident experiment, as the
nature of so important a matter justly demands; and this it was that
determined me to attempt putting the thing to issue by the following
experiment.

I cemented together two plates of parallel glass at their edges, so as
to form a prismatic or wedge-like vessel, when stopped at the ends or
bases; and its edge being turned downwards, I placed therein a glass
prism with one of its edges upwards, and filled up the vacancy with
clear water: thus the refraction of the prism was contrived to be
contrary to that of the water, so that a ray of light transmitted thro’
both these refracting mediums would be refracted by the difference only
between the two refractions. Wherefore, as I found the water to refract
more or less than the glass prism, I diminished or increased the angle
between the glass plates, till I found the two contrary refractions to
be equal; which I discovered by viewing an object thro’ this double
prism; which, when it appeared neither raised nor depressed, I was
satisfied, that the refractions were equal, and that the emergent rays
were parallel to the incident.

Now, according to the prevailing opinion, the object should have
appeared thro’ this double prism quite of its natural colour; for
if the difference of refrangibility had been equal in the two equal
refractions, they would have rectified each other: but the experiment
fully proved the fallacy of this received opinion, by shewing the
divergency of the light by the prism to be almost double of that by
the water; for the object, tho’ not at all refracted, was yet as much
infected with prismatic colours, as if it had been seen thro’ a glass
wedge only, whose refracting angle was near 30 degrees.

  _N. B._ This experiment will be readily perceived to be the same as
  that which Sir Isaac Newton mentions[154]; but how it comes to differ
  so very remarkably in the result, I shall not take upon me to account
  for; but will only add, that I used all possible precaution and care
  in the process, and that I keep the apparatus by me to evince the
  truth of what I write, whenever I may be properly required so to do.

I plainly saw then, that if the refracting angle of the water-vessel
could have admitted of a sufficient increase, the divergency of
the coloured rays would have been greatly diminished, or intirely
rectified; and there would have been a very great refraction without
colour, as now I had a great discolouring without refraction: but the
inconveniency of so large an angle, as that of the vessel must have
been, to bring the light to an equal divergency with that of the glass
prism, whose angle was about 60 degrees, made it necessary to try some
experiments of the same kind, by smaller angles.

I ground a wedge of common plate glass to an angle of somewhat less
than 9 degrees, which refracted the mean rays about 5 degrees. I then
made a wedge-like vessel, as in the former experiment, and filling it
with water, managed it so, that it refracted equally with the glass
wedge; or, in other words, the difference of their refractions was
nothing, and objects viewed thro’ them appeared neither raised nor
depressed. This was done with an intent to observe the same thing over
again in these small angles, which I had seen in the prism: and it
appeared indeed the same in proportion, or as near as I could judge;
for notwithstanding the refractions were here also equal, yet the
divergency of the colours by the glass was vastly greater than that
by the water; for objects seen by these two refractions were very
much discoloured. Now this was a demonstration, that the divergency
of the light, by the different refrangibility, was far from being
equal in these two refractions. I also saw, from the position of the
colours, that the excess of divergency was in the glass; so that I
increased the angle of the water-wedge, by different trials, till the
divergency of the light by the water was equal to that by the glass;
that is, till the object, tho’ considerably refracted, by the excess
of the refraction of the water, appeared nevertheless quite free from
any colours proceeding from the different refrangibility of light;
and, as near as I could then measure, the refraction by the water was
about ⁵⁄₄ of that by the glass. Indeed I was not very exact in taking
the measures, because my business was not at that time about the
proportions, so much as to shew, that the divergency of the colours, by
different substances, was by no means in proportion to the refractions;
and that there was a possibility of refraction without any divergency
of the light at all.

Having, about the beginning of the year 1757, tried these experiments,
I soon after set about grinding telescopic object-glasses upon the
new principles of refractions, which I had gathered from them;
which object-glasses were compounded of two spherical glasses with
water between them. These glasses I had the satisfaction to find,
as I had expected, free from the errors arising from the different
refrangibility of light: for the refractions, by which the rays were
brought to a focus, were every-where the differences between two
contrary refractions, in the same manner, and in the same proportions,
as in the experiment with the wedges.

However, the images formed at the foci of these object-glasses were
still very far from being so distinct as might have been expected
from the removal of so great a disturbance; and yet it was not very
difficult to guess at the reason, when I considered, that the radii of
the spherical surfaces of those glasses were required to be so short,
in order to make the refractions in the required proportions, that
they must produce aberrations, or errors, in the image, as great, or
greater, than those from the different refrangibility of light. And
therefore, seeing no method of getting over that difficulty, I gave up
all hopes of succeeding in that way.

And yet, as these experiments clearly proved, that different substances
diverged the light very differently, in proportion to the refraction;
I began to suspect, that such variety might possibly be found in
different sorts of glass, especially as experience had already shewn,
that some made much better object-glasses, in the usual way, than
others: and as no satisfactory cause had as yet been assigned for such
difference, there was great reason to presume, that it might be owing
to the different divergency of the light by their refractions.

Wherefore, the next business to be undertaken, was to grind wedges
of different kinds of glass, and apply them together, so that the
refractions might be made in contrary directions, in order to discover,
as in the foregoing experiments, whether the refraction and divergency
of the colours would vanish together. But a considerable time elapsed
before I could set about that work; for tho’ I was determined to try
it at my leisure, for satisfying my own curiosity, yet I did not
expect to meet with a difference sufficient to give room for any great
improvement of telescopes; so that it was not till the latter end of
the year that I undertook it, when my first trials convinced me, that
this business really deserved my utmost attention and application.

I discovered a difference, far beyond my hopes, in the refractive
qualities of different kinds of glass, with respect to their divergency
of colours. the yellow or straw-coloured foreign sort, commonly called
Venice glass, and the English crown glass, are very near alike in that
respect, tho’ in general the crown glass seems to diverge the light
rather the least of the two. The common plate glass made in England
diverges more; and the white crystal or flint English glass, as it is
called, most of all.

It was not now my business to examine into the particular qualities of
every kind of glass that I could come at, much less to amuse myself
with conjectures about the cause, but to fix upon such two sorts
as their difference was the greatest; which I soon found to be the
crown, and the white flint or crystal. I therefore ground a wedge of
white flint of about 25 degrees, and another of crown of about 29
degrees, which refracted nearly alike; but their divergency of the
colours was very different. I then ground several others of crown to
different angles, till I got one, which was equal, with respect to the
divergency of the light, to that in the white flint: for when they were
put together, so as to refract in contrary directions, the refracted
light was intirely free from colour. Then measuring the refractions
of each wedge, I found that of the white glass to be to that of the
crown nearly as 2 to 3; and this proportion would hold very nearly in
all small angles. Wherefore any two wedges made in this proportion,
and applied together, so as to refract in a contrary direction, would
refract the light without any difference of refrangibility.

To make therefore two spherical glasses, that shall refract the light
in contrary directions, it is easy to understand, that one must be
concave, and the other convex; and as the rays are to converge to a
real focus, the excess of refraction must evidently be in the convex;
and as the convex is to refract most, it appears from the experiment,
that it must be made with crown glass, and the concave with white flint
glass.

And further, as the refractions of spherical glasses are in an inverse
ratio of their focal distances; it follows, that the focal distances
of the two glasses should be inversely as the ratio’s of the fractions
of the wedges: for being thus proportioned, every ray of light, that
passes thro’ this combined glass, at whatever distance it may pass from
its axe, will constantly be refracted, by the difference between two
contrary refractions, in the proportion required; and therefore the
different refrangibility of the light will be intirely removed.

Having thus got rid of the principal cause of the imperfection of
refracting telescopes, there seemed to be nothing more to do, but to go
to work upon this principle: but I had not made many attempts, before
I found, that the removal of one impediment had introduced another
equally detrimental (the same as I had before found in two glasses with
water between them): for the two glasses, that were to be combined
together, were the segments of very deep spheres; and therefore the
aberrations from the spherical surfaces became very considerable, and
greatly disturbed the distinctness of the image. Tho’ this appeared
at first a very great difficulty, yet I was not long without hopes
of a remedy: for considering, the surfaces of spherical glasses admit
of great variations, tho’ the focal distance be limited, and that by
these variations their aberrations may be made more or less, almost at
pleasure; I plainly saw the possibility of making the aberrations of
any two glasses equal; and as in this case the refractions of the two
glasses were contrary to each other, their aberrations, being equal,
would intirely vanish.

And thus, at last, I obtained a perfect theory for making
object-glasses, to the apertures of which I could scarce conceive any
limits: for if the practice could come up to the theory, they must
certainly admit of very extensive ones, and of course bear very great
magnifying powers.

But the difficulties attending the practice are very considerable.
In the first place, the focal distances, as well as the particular
surfaces, must be very nicely proportioned to the densities or
refracting powers of the glasses; which are very apt to vary in the
same sort of glass made at different times. Secondly, the centres
of the two glasses must be placed truly on the common axis of the
telescope, otherwise the desired effect will be in a great measure
destroyed. Add to these, that there are four surfaces to be wrought
perfectly spherical; and any person, but moderately practised in
optical operations, will allow, that there must be the greatest
accuracy throughout the whole work.

Notwithstanding so many difficulties, as I have enumerated, I have,
after numerous trials, and a resolute perseverance, brought the matter
at last to such an issue, that I can construct refracting telescopes,
with such apertures and magnifying powers, under limited lengths, as,
in the opinion of the best and undeniable judges, who have experienced
them, far exceed any thing that has been hitherto produced, as
representing objects with great distinctness, and in their true colours.

                                                          John Dollond.




XCIX. _An Account of some extraordinary Effects arising from
Convulsions; being Part of a Letter to_ John Huxham, _M.D. and F.R.S.
from_ William Watson, _M.D. F.R.S._

                                                          6 June, 1758.

[Read June 15, 1758.]

IN the month of January 1757, I was concerned for a young gentle-woman,
who, if the number, continuance, and frequency of their returns,
be considered, suffered the most violent and severe convulsions I
ever knew. At some times the muscular spasms were general; at other
times single muscles only, or a number of them, subservient to some
particular purpose in the animal oeconomy, were affected. And such
was the peculiarity of this case, that after and in proportion as
any single muscle, or any determined number of muscles, had been in
a state of spasm, a paralytic inability succeeded to those muscles,
which very much disordered and impaired, and several times even for no
small continuance prevented the patient from performing, several of
her necessary functions. When the muscles, for instance, subservient to
deglutition had been convulsed, for many hours after the fits had left
her, she has not been able to swallow a single drop of liquid: so that
when attempts have been made to cause her to drink, unless the liquor
was immediately thrown back, there was imminent danger of her being
strangled. When her eyes have been affected, several times a compleat
_gutta serena_, and total blindness, has ensued; the patient being able
to bear the strong day-light with open eyes, without being sensible of
its influence, or in the least contracting her widely dilated pupils.
After one of these fits the blindness continued full five days; and I
began to be in fear for the return of her sight.

You, Sir, who are so excellently well versed in the animal oeconomy,
are not to be informed, that vocification is performed in the _aspera
arteria_; but that the articulation of sounds into syllables and words
is modulated principally by the tongue, and muscles about the larynx.
In the case before you, very early in the disease, the spasms seized
the muscles about the larynx: the consequence of which was, that after
they were over, the patient was unable to utter a word. This faculty
however she again once recovered; but it continued a very short time,
as the fits returned, which again left her deprived of the power
of speech. After having lost her voice a second time, her power of
speech did not return, even after she was freed from her convulsions,
and her general health restored. Fourteen months passed, whilst this
patient continued absolutely speechless; when, after having violently
heated herself by four hours dancing, on a sudden her power of speech
returned, and it has continued perfectly free ever since.

What is still further remarkable in this case is, that during the whole
time of this patient’s continuing speechless, her life was rendered yet
more uncomfortable by her having, from the injury to her brain by the
spasms, forgot how to write, so as to express her meaning that way: but
upon the recovery of her speech, this faculty likewise returned, which
she has retained ever since. During the severity of this disease, which
continued several weeks, almost every day of which, from the number
and violence of the convulsions, I feared would be the patient’s last,
nothing was left unattempted, which I imagined could tend to prevent
the return of the spasms, or lessen their effects. My endeavours so far
happily succeeded, that her fits did not return; but the consequences
of them continued, more particularly her inability to speak. After some
months however, when she was recruited in her strength, I was desirous
of trying the effects of electricity, more particularly applied about
her throat. This was accordingly attempted; but such was the state of
her nerves, and their sensibility to its effects, that electrizing
brought back the fits, which again affected her sight: so that I was
compelled to desist, lest, in endeavouring to restore her speech, I
might not only fail in this attempt, but might bring possibly on a
permanent blindness. I determined therefore to trust the whole to time,
which has happily removed all her complaints.




C. _An Account of an extraordinary Storm of Hail in_ Virginia. _By_
Francis Fauquier, _Esq; Lieutenant Governor of_ Virginia, _and F.R.S.
Communicated by_ William Fauquier, _Esq; F.R.S._

_To the Rev._ Tho. Birch, _D. D. Secret. R. S._

[Read Nov. 9, 1758.]

SIR,

IN a letter I received from my brother, the lieutenant governor of
Virginia, he gives an account of a very remarkable storm of hail;
which, if you think it worth communicating to the Society, is very much
at their service.

It happened on Sunday the 9th of July, about four o’clock in the
afternoon, and was preceded by some thunder and lightning. It was a
small cloud, that did not seem to threaten much before its breaking,
and did not extend a full mile in breadth. It passed over the middle of
the town of Williamsburgh, and the skirts of the town had but little of
it. Its course was from N. by W. to S. by E. The hail-stones, or rather
pieces of ice, were most of them of an oblong square form; many of them
an inch and half long, and about three fourths of an inch wide and
deep; and from one side of most of them there proceeded sharp spikes,
protuberant at least half an inch. He says he cooled his wine, and
froze cream, with some of them the next day; and they were not totally
dissolved when he went to bed on Monday night. This storm broke every
pane of glass on the north side his house, and destroyed all his garden
things intirely.

He mentions likewise the heats to have been rather more than usual in
that country this summer; and particularly on the 9th of August his
thermometer (which is hung on the outside of his house on the north
aspect) was at 97, by Fahrenheit’s graduation, and some other days as
high as 94 or 95. I am,

                                 SIR,
                  Your most obedient humble Servant,
                             Wm. Fauquier.

Jermyn street, 18 October, 1758.




CI. _An Account of an extraordinary Case of a diseased Eye; In a Letter
to_ Matthew Maty, _M. D. F.R.S. By_ Daniel Peter Layard, _M. D. F.R.S._

[Read Nov. 9. 1758.]

                                            Huntingdon, 20th May, 1758.

Dear Sir,

IN October 1755. I communicated to you, and you inserted in the last
volume of your _Journal Britannique_, the case of Susannah Earle, of
Hemmingford-Grey in this County, who, in consequence of the whooping
cough, was afflicted with a protruded eye. The case I now send you,
somewhat similar to that young girl’s in its first appearance and
progress, but by accident attended with a second disease, will perhaps
deserve your attention, and not seem unworthy of being presented to
the Royal Society.

John Law, of Fenny-Stanton, also in the County of Huntingdon, a strong
and robust lad, thirteen years and six months old, in Easter week
1756, beating dung about a close with unusual force, on a sudden felt
a violent pain in his left eye. The pain increased, an inflammation
ensued, and the eye grew daily larger. The poor boy’s mother followed
the directions, which she received, without the least benefit to her
child, after having, besides other expences, been defrauded by a quack
of two guineas; a great sum for a poor cottager!

The widow Law, in her distress, heard of Susannah Earl’s cure. She
went to see her; and determined to bring her son to Huntingdon, for
Mr. Hopkins’s assistance. Accordingly, October the 7th 1756, she came
to Mr. Daniel Hopkins, surgeon, in this town; and having desired my
opinion, we both examined the eye together.

The left eye was protruded out of its orbit, and hung down over the
cheek to the upper lip. The coats were greatly discoloured, all the
vessels turgid, the sight totally lost, and the humours appeared like
fluctuating pus. We saw the necessity of an immediate extirpation, to
save the right eye, already greatly inflamed; and having apprized the
mother and boy of the state the eye was in, a consultation was desired
with two surgeons of St. Ives. Mr. Dawkes, who was present with Mr.
Skeeles at Susannah Earle’s operation, being dead since that time, Mr.
Thomas Skeeles and Mr. Thomas Want very charitably met Mr. Hopkins and
me the next day, October the 8th, at the widow Law’s cottage.

The eye appeared to these gentlemen as I have related: and upon Mr.
Want’s pressing with his finger on the pupil, the globe burst at the
edge of the _Iris_, and discharged pus. The extirpation of the eye was
unanimously agreed upon, and immediately performed.

Mr. Hopkins made a puncture with a lancet close to the external and
small canthus of the eye, and then with a pair of crooked scissars took
off all the distended globe close to the eye-lids. He then cleaned the
cavity of the purulent humours, and filled it with soft lint, over
which he applied bolsters dipped in warm red wine and water, and the
_monoculus_ bandage to keep on the whole dressings. The lad was bled
in the arm; nitrous medicines, and anodynes, were prescribed, and a
suitable regimen. The fever, and inflammation of the eye, gradually
decreased; the suppuration of the wound in few days was good, the
distended eye-lids contracted, and a cure was soon expected.

But on November the 7th the lad went to open the street-door, and
it being a cold and rainy evening, he quickly felt the bad effects
of the cold wind, which drove the rain in upon him. That night the
wound became again very painful, the eye-lids puffed up, and next
day appeared much inflamed, as were all the contents of the orbit.
Fungous excrescences soon followed, and an intermittent fever. An
emetic being improper, he was purged with rhubarb, and afterwards took
the bark infused in red wine. The fever was removed after some time;
but the contents of the orbit continued increasing, and the fungous
excrescences became so large and spongy, as to be of equal bulk with
the diseased eye before extirpation. All topical applications, to
contract this fungus, were ineffectual, and the application of caustics
or escharotics was prudently avoided, lest they should produce a
carcinomatous ulcer. The discharge was chiefly a purulent serum: on
which account, ever since the beginning of November he was kept upon a
dry diet.

In February 1757. the remaining coats of the eye began to appear at
the most prominent parts of the excrescence, and seemed white like a
part of the _conjunctiva_. On touching it with the finger, a distinct
fluctuation was felt, and an _hydrophthalmia_ perfectly discovered; but
neither the thickness of the coats, nor the sensibility of the parts,
would permit a puncture to be made, till the cyst, which appeared
formed by the distension of one of the coats of the eye, was freer from
the fungus.

The cyst continued daily to extend itself, and to separate the fungous
edges; the fluctuation became more manifest, and the membranes thinner.
At length, on the 15th of June 1757, Mr. Hopkins opened the cyst
with the point of a lancet, and let out a large cup-full of limpid
serum, without smell or taste. The boy felt very little pain in this
operation. The cavity was filled with dry lint, and compresses dipt in
warm red wine and water were applied over it. All the night following,
and several days after, a great discharge of serum came away. On the
19th the fungus was considerably lessened. Mr. Hopkins then dressed
the wound with warm _unguentum é gummi elemi_, and washed the fungus
with a lotion of _aquarum calcis_, _rosarum_, _et tincturæ myrrhæ_.
On the 23d, upon his removing the dressings, he saw the cyst loose
and collapsed; which he extracted with his forceps, without the least
difficulty, or pain to his patient. The fungus daily wasted afterwards,
the wound digested well, and the lad was intirely cured on the 7th of
August.

His right eye is perfectly strong, and he has been free from complaint
ever since. The remainder of the coats of the eye, and of the muscles,
bear up the eye-lids, that when uncovered he only seems to have closed
the left eye: however, he has wore all the winter a back patch over it,
to guard against fresh cold.

The cyst, when first taken away, measured three inches and half in
length, one inch and half in diameter, and contained a large cup-full
of water. It appeared to be the _tunica sclerotica_, was of a clear
pellucid white, and of so delicate a texture, as scarce to admit of
being touched without tearing; and when dried with all possible care,
became so brittle, that Mr. Hopkins could hardly preserve it in the
manner I now send it.


REMARKS.

In both Susannah Earle and John Law’s cases, the eye was distended by
the accumulation of the aqueous humour, separated in great quantity
by the repeated straining of the blood-vessels in the whooping cough,
which might gradually relax and enlarge the aqueous ducts of Susannah
Earle’s eye; and possibly by the rupture of those ducts, and of some
blood-vessels, at the time John Law exerted himself violently in
beating dung about the close: for in either case the _impetus_ of the
blood must have been so violent, as to produce those effects. However,
from the _hydrophthalmia_ succeeding the operation on John Law, the
fungous excrescence, and continual serous discharge during several
months from the wound, it plainly appears, that an abundance of aqueous
humour was discharged at first by the distention or laceration of the
aqueous ducts, and latterly for want of a contraction of those vessels,
and of the lymphatics, which were no longer of use.

Both these cases shew the necessity of inquiring particularly into
the causes of diseases of the eyes, as well as of other parts of the
body; for by barely attending to the symptoms, the disease will not
be removed, tho’ the symptoms be alleviated. Bleeding, and moderate
evacuations, would certainly have, at first, decreased the tension and
pain, and assuaged the inflammation; but both topical applications, and
internal medicines, were properly to be adapted, and a suitable diet
regulated.

Not to mention the absurd and impertinent abuse of empirics, what
benefit could accrue, in both these cases, from unctuous, laxative,
or emollient applications, from drastic and mercurial purges? Tho’
such applications might be well intended, to take off the tension
and inflammation; yet, as the distension of the blood-vessels only
increased gradually, as the globe of the eye was enlarged; so whatever
application relaxed the coats of the eye, must infallibly stretch out
the vessels yet farther, and cause a greater pain and inflammation;
which drastic and mercurial purges would also increase.

The only method then to be pursued in such bad cases would be at first
to endeavour to remove the fullness of the blood, and make use of such
topical remedies as would contract without irritation. If the cause
remains, as the whooping cough in Susannah Earle’s case, no amendment
of the eye can be expected, while the patient’s blood-vessels are
continually strained by frequent coughing. This illness therefore
should be attended to, and removed as soon as possible.

But should the eye be so enlarged, as to protrude itself out of the
orbit, there seems no other way to lessen the bulk of the eye, than
by making a puncture with a proper instrument, to let out the aqueous
humour; and then apply such agglutinant and contracting _collyria_, as
may reduce the distended coats and vessels to their former size. This
operation should be performed before the humours are vitiated, the
sight lost, the vessels in a state of suppuration, and the coats of the
eye too far extended; for at that time nothing less than extirpation
can be of use.

Professor Nuck, in his _Tractatus de Ductibus Oculorum Aquosis_, p.
120, _& seq._ relates the success he had in curing a young man by five
repeated punctures, and a strict observance in a proper use of all the
non-naturals.

I am, with the greatest regard and esteem,

                               Dear Sir,
                    Your most affectionate Brother,
                       and very humble Servant,
                             D. P. Layard.




CII. _An Account of the Heat of the Weather in_ Georgia: _In a Letter
from his Excellency_ Henry Ellis, _Esq; Governor of_ Georgia, _and
F.R.S. to_ John Ellis, _Esq; F.R.S._

[Read Nov. 16, 1758.]

                                                Georgia, 17 July, 1758.

Dear Sir,

THO’ some weeks have passed since I wrote to you, yet so little
alteration has happened in the state of our affairs, that nothing
occurs to me relative to them worth committing to paper. This indeed
I need not regret, as one cannot sit down to any thing, that requires
much application, but with extreme reluctance; for such is the
debilitating quality of our violent heats at this season, that an
inexpressible languor enervates every faculty, and renders even the
thought of exercising them painful.

’Tis now about three o’ clock; the sun bears nearly S. W. and I am
writing in a piazza, open at each end, on the north-east side of my
house, perfectly in the shade: a small breeze at S. E. blows freely
thro’ it; no buildings are nearer, to reflect the heat, than 60 yards:
yet in a thermometer hanging by me, made by Mr. Bird, and compared by
the late Mr. George Graham with an approved one of his own, the mercury
stands at 102. Twice it has risen this Summer to the same height;
_viz._ on the 28th of June, and the 11th of July. Several times it has
been at 100, and for many days successively at 98; and did not in the
nights sink below 89. I think it highly probable, that the inhabitants
of this town breathe a hotter air than any other people on the face of
the earth. The greatest heat we had last year was but 92, and that but
once: from 84 to 90 were the usual variations; but this is reckoned
an extraordinary hot summer. The weather-wise of this country say it
forebodes a hurricane; for it has always been remarked, that these
tempests have been preceded by continual and uncommon heats. I must
acquaint you, however, that the heats we are subject to here are more
intense than in any other parts of the province, the town of Savannah
being situated upon a sandy eminence, and sheltered all round with high
woods. But it is very sufficient, that the people actually breathe so
hot an air as I describe; and no less remarkable, that this very spot,
from its height and dryness, is reckoned equally healthy with any other
in the province.

I have frequently walked an hundred yards under an umbrella, with a
thermometer suspended from it by a thread to the height of my nostrils,
when the mercury has rose to 105; which is prodigious. At the same
time I have confined this instrument close to the hottest part of my
body, and have been astonished to observe, that it has subsided several
degrees. Indeed, I never could raise the mercury above 97 with the heat
of my body.

You know, dear Sir, that I have traversed a great part of this globe,
not without giving some attention to the peculiarities of each climate;
and I can fairly pronounce, that I never felt such heats any-where as
in Georgia. I know experiments on this subject are extremely liable to
error; but I presume I cannot now be mistaken, either in the goodness
of the instrument, or in the fairness of the trials, which I have
repeatedly made with it. This same thermometer I have had thrice in the
equatorial parts of Africa; as often at Jamaica, and the West India
islands; and, upon examination of my journals, I do not find, that the
quicksilver ever rose in those parts above the 87th degree, and to that
but seldom: its general station was between the 79th and 86th degree;
and yet I think I have felt those degrees, with a moist air, more
disagreeable than what I now feel.

In my relation of the late expedition to the north-west, if I
recollect right, I have observed, that all the changes and variety of
weather, that happen in the temperate zone throughout the year, may be
experienced at the Hudson’s Bay settlements in 24 hours. But I may now
extend this observation; for in my cellar the thermometer stands at 81,
in the next story at 102, and in the upper one at 105; and yet these
heats, violent as they are, would be tolerable, but for the sudden
changes that succeed them. On the 10th of December last the mercury was
at 86; on the 11th it was so low as 38 of the same instrument. What
havock must this make with an European constitution? Nevertheless, but
few people die here out of the ordinary course; tho’ indeed one can
scarce call it living, merely to breathe, and trail about a vigorless
body; yet such is generally our condition from the middle of June to
the middle of September. Dear Sir,

                      Yours most affectionately,
                             Henry Ellis.




CIII. _The Invention of a General Method for determining the Sum of
every 2d, 3d, 4th, or 5th_, &c. _Term of a Series, taken in order; the
Sum of the whole Series being known. By_ Thomas Simpson, _F.R.S._

[Read Nov. 16, 1758.]

AS the doctrine of Series’ is of very great use in the higher branches
of the mathematics, and their application to nature, every attempt
tending to extend that doctrine may justly merit some degree of regard.
The subject of the paper, which I have now the honour to lay before the
Society, will be found an improvement of some consequence in that part
of science. And how far the business of finding fluents may, in some
cases, be facilitated thereby, will appear from the examples subjoined,
in illustration of the general method here delivered.

The series propounded, whose sum (_S_) is supposed to be given (either
in algebraic terms, or by the measures of angles and ratio’s, _&c._)
I shall here represent by _a_ + _bx_ + _cx_² + _dx_³ + _ex_⁴, &c. and
shall first give the solution of that case, where every third term is
required to be taken, or where the series to be summed is _a_ + _dx_³ +
_gx_⁶ + _kx_⁶, &c. By means whereof, the general method of proceeding,
and the resolution of every other case, will appear evident.

Here, then, every _third_ term being required to be taken, let the
series (_a_ + _dx_³ + _gx_⁶, &c.), whose value is sought, be conceived
to be composed of _three_ others.

    ⅓ × (_a_ + _b_ × (_px_) + _c_ × (_px_)² + _d_ × (_px_)³ + _e_ ×
    (_px_)⁴, &c.)

    ⅓ × (_a_ + _b_ × (_qx_) + _c_ × (_qx_)² + _d_ × (_qx_)³ + _e_ ×
    (_qx_)⁴, &c.)

    ⅓ × (_a_ + _b_ × (_rx_) + _c_ × (_rx_)² + _d_ × (_rx_)³ + _e_ ×
    (_rx_)⁴, &c.)

having all the _same form_, and the _same coefficients_ with the series
first proposed, and wherein the converging quantities _px_, _qx_, _rx_,
are also in a determinate (tho’ yet unknown) ratio to the original
converging quantity _x_. Now, in order to determine the quantities
of these ratios, or the values of _p_, _q_, and _r_, let the terms
containing the same powers of _x_, in the two equal values, be equated
in the common way:

So shall,

  ⅓ _b_ × _px_ + ⅓ _b_ × _qx_ + ⅓ _b_ × _rx_ = 0
  ⅓ _c_ × _p_²_x_² + ⅓ _c_ × _q_²_x_² + ⅓ _c_ × _r_²_x_² = 0
  ⅓ _d_ × _p_³_x_³ + ⅓ _d_ × _q_³_x_³ + ⅓ _d_ × _r_³_x_³ = _dx_³
  ⅓ _e_ × _p_⁴_x_⁴ + ⅓ _e_ × _q_⁴_x_⁴ + ⅓ _e_ × _r_⁴_x_⁴ = 0
  &c.

And consequently,

  _p_ + _q_ + _r_ = 0
  _p_² + _q_² + _r_² = 0
  _p_³ + _q_³ + _r_³ = 3
  _p_⁴ + _q_⁴ + _r_⁴ = 0, &c.

Make, now, _p_³ = 1, _q_³ = 1, and _r_³ = 1; that is, let _p_, _q_,
and _r_, be the three roots of the cubic equation _z_³ = 1, or _z_³ -
1 = 0: then, seeing both the second and third terms of this equation
are wanting, not only the sum of all the roots (_p_ + _q_ + _r_) but
the sum of all their squares (_p_² + _q_² + _r_²) will vanish, or be
equal to nothing (by common algebra), as they ought, to fulfil the
conditions of the two first equations. Moreover, since _p_³ = 1, _q_³
= 1, and _r_³ = 1, it is also evident, that _p_⁴ + _q_⁴ + _r_⁴ (= _p_
+ _q_ + _r_) = 0, _p_⁵ + _q_⁵ + _r_⁵ (= _p_² +_q_² + _r_²) = 0, _p_⁶
+ _q_⁶ + _r_⁶ (= _p_³ + _q_³ + _r_³) = 3. Which equations being, in
effect, nothing more than the first three repeated, the values of
_p_, _q_, _r_, above assigned, equally fulfil the conditions of these
also: so that the series arising from the addition of three assumed
ones will agree, in every term, with _that_ whose sum is required: but
those series’ (whereof the quantity in question is composed) having
all of them the _same form_ and the _same coefficients_ with the
original series _a_ + _bx_ + _cx_² + _dx_³, &c. (= _S_), their sums
will therefore be truly obtained, by substituting _px_, _qx_, and _rx_,
successively, for _x_, in the given value of _S_. And, by the very same
reasoning, and the process above laid down, it is evident, that, if
every _nᵗʰ_ term (instead of every third term) of the given series be
taken, the values of _p_, _q_, _r_, _s_, &c. will then be the roots of
the equation _zⁿ_ - 1 = 0[155]; and that, the sum of all the terms so
taken, will be truly obtained by substituting _px_, _qx_, _rx_, _sx_,
&c. successively for _x_, in the given value of _S_, and then dividing
the sum of all the quantities thence arising by the given number _n_.

The same method of solution holds equally, when, in taking every _n_ᵗʰ
term of the series, the operation begins at some term after the first.
For all the terms preceding _that_ may be transposed, and the whole
equation divided by the power of _x_ in the first of the remaining
terms; and then the sum of every _nᵗʰ_ term (beginning at the first)
will be found by the preceding directions; which sum, multiplied by
the power of _x_ that before divided, will evidently give the true
value required to be determined. Thus, for example, let it be required
to find the sum of every third term of the given series _a_ + _bx_ +
_cx_² + _dx_³ + _ex_⁴, &c. (= _S_), beginning with _cx_². Then, by
transposing the two first terms, and dividing the whole by _x_², we
shall have _c_ + _dx_ + _ex_² + _fx_³, &c. = (_S_ - _a_ - _bx_) ⁄
(_xx_) (= _S´_). From whence having found the sum of every third term
of the series _c_ + _dx_ + _ex_² + _fx_³, &c. beginning at the first
(_c_), that sum, multiplied by _x_², will manifestly give the true
value sought in the present case.

And here it may be worth while to observe, that all the terms preceding
_that_ at which the operation (in any case) begins, may (provided they
exceed not in number the given interval _n_) be intirely disregarded,
as having no effect at all in the result. For if in that part ((-_a_ -
_bx_) ⁄ _xx_) of the value of _S´_, above exhibited, in which the first
terms, _a_ and _bx_, enter, there be substituted _px_, _qx_, _rx_,
successively, for _x_ (according to the _prescript_) the sum of the
quantities thence arising will be

  - _a_ ⁄ (_p_²_x_²) - _a_ ⁄ (_q_²_x_²) - _a_ ⁄ (_r_²_x_²)
  - _b_ ⁄ _px_ - _b_ ⁄ _qx_ - _b_ ⁄ _rx_

which, because _p_³ = 1, _q_³ = 1, &c. (or _p_² = 1 ⁄ _p_, _q_² = 1 ⁄
_q_, &c.) may be expressed thus;

  - _a_ ⁄ _xx_ × (_p_ + _q_ + _r_)
  - _b_ ⁄ _x_ × (_p_² + _q_² + _r_²)

But, that _p_ + _q_ + _r_ = 0, and _p_² + _q_² + _r_² = 0, hath been
already shewn; whence the truth of the general observation is manifest.
Hence it also appears, that the method of solution above delivered,
is not only general, but includes this singular beauty and advantage,
that in all series’ whatever, whereof the terms are to be taken
according to the same assigned order, the quantities (_p_, _q_, _r_,
&c.), whereby the resolution is performed, will remain invariably the
same. The greater part of these quantities are indeed _imaginary_ ones;
and so likewise will the quantities be that result from them, when
substitution is made in the given expression for the value of _S_. But
by adding, as is usual in like cases, every two corresponding values,
so resulting together, all marks of _impossibility_ will disappear.

If, in the series to be summed, the alternate terms (_viz._ the 2d,
4th, 6th, _&c._) should be required to be taken under signs contrary to
what they have in the original series given; the reasoning and result
will be no-ways different; only, instead of making _p_³ + _q_³ + _r_³
(or _pⁿ_ + _qⁿ_ + _rⁿ_, &c.) = +3 (or +_n_), the same quantity must,
here, be made = -3 (or -_n_). From whence, _pⁿ_ being = -1, _qⁿ_ = -1,
&c. the values of _p_, _q_, _r_, &c. will, in this case, be the roots
of the equation _zⁿ_ + 1 = 0.

It may be proper, now, to put down an example, or two, of the use and
application of the general conclusions above derived. First, then,
supposing the series, whose sum is given, to be _x_ + _x²_ ⁄ 2 + _x³_
⁄ 3 + _x⁴_ ⁄ 4 ... + _xᵐ_ ⁄ _m_ + _xᵐ ⁺ ¹_) ⁄ (_m_ + 1) + _xᵐ ⁺ ²_ ⁄
(_m_ + 2) ... + _xᵐ ⁺ ⁿ_ ⁄ (_m_ + _n_) + _xᵐ ⁺ ⁿ ⁺ ¹_ ⁄ (_m_ + _n_ + 1)
+, &c. = - H. Log.(1-_x_) (= _S_); let it be required, from hence, to
find the sum of the series (_xᵐ_ ⁄ _m_ + _xᵐ ⁺ ⁿ_ ⁄ (_m_ + _n_) + _xᵐ
⁺ ²ⁿ_ ⁄ (_m_ + 2_n_) &c.) arising by taking every _nᵗʰ_ term thereof,
beginning with that whose exponent (_m_) is any integer less than _n_.
Here, the terms preceding _xᵐ_ ⁄ _m_ being transposed, and the whole
equation divided by _xᵐ_, we shall have 1 ⁄ _m_ + _x_ ⁄ (_m_ + 1) +
_x_² ⁄ (_m_ + 2) + _x_³ ⁄ (_m_ + 3), &c. = -(1 ⁄ _xᵐ_) × H. Log.(1 -
_x_) - (_x_ + ½_x_², &c.) ⁄ _xᵐ_. In which value, let _px_, _qx_, _rx_,
&c. be, successively, substituted for _x_ (according to prescript)
neglecting intirely the terms (_x_ + ½_x_²) ⁄ _xᵐ_, as having no effect
at all in the result: from whence we get -1 ⁄ (_(px)ᵐ_) × Log.(1 -
_px_) - (1 ⁄ _(qx)ᵐ_) × Log.(1 - _qx_) - (1 ⁄ _(rx)ᵐ_) × Log.(1 -
_rx_), &c. Which multiplied by _xᵐ_ (the quantity that before divided)
gives -1 ⁄ (_pᵐ_) × Log.(1 - _px_) - 1 ⁄ (_qᵐ_) × Log.(1 - _qx_) - 1 ⁄
(_rᵐ_) × Log.(1 - _rx_), &c. = _n_ times the quantity required to be
determined.

But now, to get rid of the imaginary quantities _q_, _r_, &c. by means
of their known values α + √(αα - 1), α - √(αα - 1), &c. it will be
necessary to observe, that, as the product of any two corresponding
ones (α + √(αα - 1) × (α - √(αα - 1)) is equal to unity, we may
therefore write (α - √(αα - 1))_ᵐ_ (= _rᵐ_) instead of its equal 1
⁄ (_qᵐ_), and (α + √(αα - 1))_ᵐ_ (= _qᵐ_) instead of its equal 1 ⁄
(_rᵐ_): by which means the two terms, wherein these two quantities
enter, will stand thus; -(α - √(αα - 1))_ⁿ_ × Log. (1 - _qx_) - (α +
√(αα - 1))_ᵐ_ × Log. (1 - _rx_).

But, if _A_ be assumed to express the co-sine of an arch (_Q_), _m_
times as great as that (360° ⁄ _n_) whose co-sine is here denoted by α;
then will _A_ - √(_AA_ - 1) = [156](α - √(αα - 1))_ᵐ_, and _A_ + √(_AA_
- 1) = (α + √(αα - 1))_ᵐ_: which values being substituted above, we
thence get

  -_A_ × (log. (1 - _qx_) + log. (1 - _rx_)) + √(_AA_
  - 1) × (log. (1 - _qx_) - log. (1 - _rx_));


whereof the former part (which, exclusive of the factor _A_, I shall
hereafter denote by _M_) is manifestly equal to -_A_ × log. ((1 - _qx_)
× (1 - _rx_)) (by the nature of logarithms) = -_A_ × log. 1 - (_q_ +
_r_)._x_ + _qrx_² = -_A_ × log. (1 - 2α_x_ + _xx_) (by substituting
the values of _q_ and _r_): which is now intirely free from imaginary
quantities. But, in order to exterminate them out of the latter part
also, put _y_ = log. (1 - _qx_) - log. (1 - _rx_); then will _ẏ_ =
-_qẋ_ ⁄ (1 - _qx_) + _rẋ_ ⁄ (1 - _rx_) = -((_q_ - _r_) × _ẋ_) ⁄ (1 -
(_q_ + _r_) × _x_ + _xx_) = -(2√(αα - 1) × _ẋ_) ⁄ (1 - 2α_x_ + _xx_)
= -(2√(-1) × √(1 - αα) × _ẋ_) ⁄ (1 - 2αx + xx); where (√(1 - αα) × ẋ)
⁄ (1 - 2α_x_ + _xx_) expresseth the fluxion of a circular arch (_N_)
whose radius is 1, and sine = (√(1 - αα) × _ẋ_) ⁄ (1 - 2α_x_ + _xx_);
consequently _y_ will be = -2√(-1) × _N_: which, multiplied by √(_AA_ -
1), or its equal √(-1) × √(1 - _AA_), gives 2√(1 - _AA_) × _N_; and,
this value being added to that of the former part (found above), and
the whole being divided by _n_, we thence obtain (-_AM_ + 2√(1 - _AA_)
× _N_) ⁄ _n_, or 1 ⁄_n_ × (-co-s. _Q_ × _M_ + sin. _Q_ × 2_N_) for that
part of the value sought depending on the two terms affected with _q_
and _r_. From whence the sum of any other two corresponding terms will
be had, by barely substituting one letter, or value, for another: So
that,

             { -log. (1 - _x_)
             { -co-s. _Q_   × _M_   + sin. _Q_ × 2_N_
  (1 ⁄ _n_) × { -co-s. _Q´_  × _M´_  + sin. _Q´_ × 2_N´_
             { -co-s. _Q´´_ × _M´´_ + sin. _Q´´_ × 2_N´´_
             { -&c.                 + &c.

will truly express the sum of the series proposed to be determined;
_M_, _M´_, _M´´_ &c. being the hyperbolical logarithms of 1 - 2α_x_ +
_xx_, 1 - 2β_x_ + _xx_, 1 - 2γ_x_ + _xx_, &c. _N_, _N´_, _N´´_ &c. the
arcs whose sines are _x_√(1 - αα) ⁄ √(1 - 2α_x_ + _xx_), _x_√(1 - ββ) ⁄
√(1 - 2β_x_ + _xx_), _x_√(1 - γγ) ⁄ √(1 - 2γ_x_ + _xx_), &c. and _Q_,
_Q´_, _Q´´_, &c. the measures of the angles expressed by (360° ⁄ _n_)
× _m_, 2 × (360° ⁄ _n_) × _m_, 3 × (360° ⁄ _n_) × _m_, &c. And here it
may not be amiss to take notice, that the series _xᵐ_ ⁄ _m_ + _xᵐ ⁺ ⁿ_
⁄ (_m_ + _n_) + _xᵐ ⁺ ²ⁿ_ ⁄ (_m_ + 2_n_) + &c. thus determined, is that
expressing the fluent of (_xᵐ ⁻ ¹ẋ_) ⁄ (1 - _xⁿ_); corresponding to one
of the two famous _Cotesian forms_. From whence, and the reasoning
above laid down, the fluent of the other _form_, _xᵐ ⁻ ¹ẋ_ ⁄ (1 +
_xⁿ_), may be very readily deduced. For, since the series (_xᵐ_ ⁄ _m_ -
_xᵐ ⁺ ⁿ_ ⁄ (_m_ + _n_) + _xᵐ ⁺ ²ⁿ_ ⁄ (_m_ + 2_n_) - _xᵐ ⁺ ³ⁿ_ ⁄ (_m_ +
3_n_) &c.) for this last fluent, is that which arises by changing the
signs of the alternate terms of the former; the quantities _p_, _q_,
_r_, &c. will here (agreeably to a preceding observation) be the roots
of the equation _zⁿ_ + 1 = 0; and, consequently, α, β, γ, δ, &c. the
co-sines of the arcs 180° ⁄ _n_, 3 × 180° ⁄ _n_, 5 × 180° ⁄ _n_, &c.
(as appears by the foregoing note). So that, making _Q_, _Q´_, _Q´´_,
&c. equal, here, to the measures of the angles (180° ⁄ _n_) × _m_, 3 ×
(180° ⁄ _n_) × _m_, 5 × (180° ⁄ _n_) × _m_, &c. the fluent sought will
be expressed in the very same manner as in the preceding case; except
that the first term, -log. (1 - _x_) (arising from the _rational_ root
_p_ = 1) will here have no place.

After the same manner, with a small increase of trouble, the fluent of
_xᵐ ⁻ ¹ẋ_ ⁄ (1 ± 2_lxⁿ_ + _x_²_ⁿ_) may be derived, _m_ and _n_ being
any integers whatever. But I shall now put down one example, wherein
the impossible quantities become exponents of the powers, in the terms
where they are concerned.

The series here given is 1 - _x_ + _x_² ⁄ 2 + _x_³ ⁄ (2.3) + _x_⁴
⁄ (2.3.4) - _x_⁵ ⁄ (2.3.4.5), &c. = the number whose hyp. log. is
-_x_, and it is required to find the sum of every _nᵗʰ_ term thereof,
beginning at the first. Here the quantity sought will (according to the
general rule) be truly defined by the _nᵗʰ_ part of the sum of all the
numbers whose respective logarithms are -_px_, -_qx_, -_rx_, &c.; which
numbers, if _N_ be taken to denote the number whose hyp. log. = 1,
will be truly expressed by _N⁻ᵖˣ_, _N⁻⒬ˣ_, _N⁻ʳˣ_, &c. From whence, by
writing for _p_, _q_, _r_, &c. their equals 1, α + √(αα - 1), α - √(αα
- 1), β + √(ββ - 1), β - √(ββ - 1), &c. and putting α´ = √(1 - αα), β´
= √(1 - ββ), &c. we shall have 1 ⁄ _n_ × (_N⁻ᵖˣ_ + _N⁻⒬ˣ_ + _N⁻ʳˣ_),
&c. = 1 ⁄ _n_ into _N⁻ˣ_ + _N⁻ᵃˣ_ × (_N⁻ᵃ‘ˣ_√⁻¹) + (_Nᵃ‘ˣ_√⁻¹) + _N⁻ᵝˣ_
× (_N⁻ᵝ‘ˣ√⁻¹_) + _Nᵝ‘ˣ√⁻¹_) + &c. But _N⁻ᵃ‘ˣ√⁻¹_ + _Nᵃ‘ˣ√⁻¹_ is known
to express the double of the co-sine of the arch whose measure (to the
radius 1) is α´_x_. Therefore we have 1 ⁄ _n_ into _N⁻ˣ_ + _N⁻ᵃˣ_ × 2
co-s. α´_x_ + _N⁻ᵝˣ_ × 2 co-s. β´_x_, &c. for the true sum, or value
proposed to be determined.

The solution of this case, in a manner a little different, I have
given some time since, in another place; where the principles of the
general method, here extended and illustrated, are pointed out. I shall
put an end to this paper with observing, that if, in the series given,
the even powers of _x_, or any other terms whatever, be wanting, their
places must be supplied with cyphers; which, in the order of numbering
off, must be reckoned as real terms.



CIV. _Observatio Eclipsis Lunæ Die_ 30 Julii 1757. _habita Olissipone
à_ Joanne Chevalier, _Congregationis Oratorii Presbytero, é Regia_
Londinensi _Societate. Communicated by_ Jacob de Castro Sarmiento,
_M.D. F.R.S._

Tubo optico 8 pedum.

[Read Nov. 16, 1758.]

                                                         h   ´  ´´
  Initium penumbræ                                       9  15  18
  Initium dubium eclipsis                                9  22  24
  Certo jam incœperat                                    9  23  34
  Umbra ad mare humorum observata vitro plano cæruleo    9  31   2
  Solo tubo optico observata                             9  31  29
  Vitro flavo observata                                  9  31  48
  Umbra tangit Grimaldum observata vitro plano cæruleo   9  31  20
  Solo tubo optico                                       9  31  50
  Vitro plano flavo                                      9  32   8
  Totus Grimaldus tegitur observatus vitro plano cæruleo 9  34   4
  Solo tubo optico                                       9  34  28
  Vitro flavo                                            9  34  47
  Umbra ad Tychonem observata vitro plano cæruleo        9  38  25
  Solo tubo optico                                       9  38  42
  Vitro flavo                                            9  38  59
  Umbra ad Harpalum vitro cæruleo observata              9  55   6
  Solo tubo optico                                       9  55  35
  Umbra ad Fracastorium                                  9  59  57
  Umbra ad Mare Nectaris                                10  00  50
  Observata vitro flavo                                 10   1   8
  Umbra ad Dionysium                                    10   5   2
  Umbra tangit Mare Tranquillitatis                     10   5  50
  Umbra ad Mare Serenitatis                             10  10  16
  Umbra tegit Menelaum observata vitro cæruleo          10  11   4
  Solo tubo optico                                      10  11  29
  Vitro flavo                                           10  11  50
  Totum Mare Fœcunditatis tegitur                       10  18  39
  Umbra tangit Mare Crisium vitro cæruleo observata     10  22  52
  Solo tubo optico                                      10  23  12
  Vitro flavo                                           10  23  29
  Umbra ad Proclum                                      10  23  33
  Possidonius totus tegitur                             10  23  50
  Totum Mare Serenitatis tegitur                        10  24  36
  Totum Mare Crisium ab umbra tegitur                   10  30  27
  Plato tegitur vitro cæruleo observatus                10  31  26
  Solo tubo optico                                      10  31  48
  Vitro flavo                                           10  32   4
  Obscuratio maxima                                     10  55  40

EMERSIONES.

                                                         h   ´  ´´
  Plato emergit observatus vitro flavo                  11  19   5
  Solo tubo optico                                      11  19  31
  Vitro cæruleo                                         11  19  50
  Aristarchus emergit                                   11  21   3
  Gassendus incepit emergere observatus vitro flavo     11  25  36
  Observatus solo tubo optico                           11  25  52
  Observatus vitro cæruleo                              11  26  11
  Gassendus totus extra umbram                          11  28   2
  Schicardus incipit emergere                           11  45  44
  Totus extra umbram                                    11  47  10
  Totum Mare Humorum extra umbram                       11  46  50
  Menelaus extra umbram                                 11  55  36
  Mare Serenitatis extra umbram                         11  59  46
  Tycho extra umbra observatus vitro flavo              12  00  33
  Solo tubo optico                                      12  00  52
  Vitro cæruleo                                         12   1  14
  Incipit emergere Mare Crisium                         12   8  31
  Totum Mare Crisium extra umbram                       12  16  28
  Finis eclipsis                                        12  28  26

Observatio hæc peracta é cœlo claro; umbra autem terræ ita diluta erat,
ut maculæ in ea conditæ satis dignoscerentur.




CV. _Singular Observations upon the_ Manchenille Apple. _By_ John
Andrew Peyssonnel, _M. D. F.R.S. Translated from the_ French.

[Read Nov. 16, 1758.]

THe cruel effects of the tree called Manchenille are known to all the
world: its milk, which the savages make use of to poison their arrows,
makes the wounds inflicted with them mortal. The rain, which washes
the leaves and branches, causes blisters to rise like boiling oil;
even the shade of the tree makes those who repose under it to swell;
and its fruit is esteemed a deadly poison. I was informed, as a very
extraordinary thing, that a breeding woman was so mad as to eat three
of them, which did her very little harm; and this was looked upon as a
miracle, and a proof of the surprising effects of the imagination and
longings of women with child.

But here is a fact, which will scarce be credited by many persons, who
have frequented these Islands: which I declare to be true.

One Vincent Banchi, of Turin in Piedmont, a strong robust man, and an
old soldier, of about forty-five years of age, belonging to the horse,
was a slave with the Turks eleven years, having been taken prisoner at
the siege of Belgrade. He was overseer of my habitation towards the
month of July of the year 1756. He was one day walking upon the sea
side, and seeing a great number of apples upon the ground, was charmed
with their beautiful colours, and sweet smell, resembling that of the
apple called d’apis: he took and eat of them, without knowing what they
were; he found they had a subacid taste; and having eaten a couple of
dozen of them, he fill’d his pockets, and came home, eating the rest as
he came. The Negroes, that saw him eat this cruel fruit, told him it
was mortal; upon which he ceased to eat them, and threw away the rest.

About four in the afternoon, _viz._ an hour after this repast, his
belly swelled considerably, and he felt as it were a consuming fire
in his bowels. He could not keep himself upright; and at night the
swelling of his belly increased, with the burning sensation of his
bowels. His lips were ulcerated with the milk of the fruit, and he was
seized with cold sweats; but my principal Negro made him a decoction of
the leaves of a _Ricinus_[157] in water, and made him drink plentifully
of it, which brought on a vomiting, followed by a violent purging;
both which continued for four hours, during which it was thought he
would die. At length these symptoms grew less; and my Negroes made him
walk, and stir about by degrees; and soon after they were stopped.
Rice-gruel, which they gave him, put an end to all these disorders; and
in four-and-twenty hours he had no more ailments nor pain; the swelling
of his belly diminished in proportion to his evacuations upwards and
downwards, and he has continued his functions without being any more
sensible of the poison. We see by this, that the effects of the poison
of the Manchenille are different from those of the fish at Guadaloupe,
which I mentioned.

Dec. 2. 1756.




CVI. _Abstract of a Letter from Mr._ William Arderon, _F.R.S. to Mr._
Henry Baker, _F.R.S. on the giving Magnetism and Polarity to Brass.
Communicated by Mr._ Baker.

[Read Nov. 16, 1758.]

Dear Sir,

FOR some time past I have been making experiments on the magnetism of
brass, and amongst many pieces that I have tried, find several that
readily attract the needle; but whether they have had this property
originally, or have received it by hammering, filing, clipping, or any
other such-like cause, I cannot yet determine.

I have a very handsome compass-box made of pure brass, as far as I can
judge: the needle being taken out, and placed upon a pin fixed properly
in a board, and clear of all other magnetics, the box will attract this
needle at half an inch distance; and, if suffered to touch, will draw
it full 90 degrees from the north or south points; and I think those
parts of the box marked north and south attract the strongest. The
cover of the box also attracts the needle nearly as much as the box
itself.

As to your supposition, that iron may be mixed with the brass, I do not
know; but I have been informed it cannot be, as brass fluxes with a
much less degree of heat than iron, and iron naturally swims on fluid
brass. Besides, many of the specimens of brass I have tried were new
as they came from the mill, where they were wrought into plates, and
I presume were not mixed[158]; yet these I have given the magnetic
virtue to, when they had it not; and some pieces of brass, which
naturally attract the needle, seem to the eye as fine a bright yellow
as any other, and are as malleable as any I ever met with.

Pieces of brass without any magnetic power, by properly hammering and
giving them the double touch, after Mr. Mitchel’s method, I have made
attract and repel the needle, as a magnet does, having two regular
poles: and I now send you one such piece of brass, which I have thus
made magnetical. You will also receive a couple of needles, which I
made myself after the late Zachary Williams’s method, and a little
stand whereon to place them, the better to shew how this magnetic bar
attracts and repels the needle when properly applied; for it must be
noted, that in making these experiments it is necessary to employ a
very good needle, about 3-½ inches long, well and tenderly set, and not
covered with glass.

You will observe, when you try this bar, that the same poles repel each
other, and the contrary poles attract; which proves this piece of brass
to be indued with true magnetic virtue and polarity. However it must be
noted, that though the same poles repel each other, yet, like natural
magnets, in contact, or nearly so, they attract each other; therefore
when you would shew the repelling power of this brass bar, you must not
bring it nearer the needle than ²⁄₁₀ of an inch.

Magnetic brass does not attract iron, not even the least particle, so
far as I can find: whether this is owing to the weakness of magnetism
in the brass, or to some other cause, I don’t pretend to know.

I have tried to infuse magnetic virtue into several pieces of copper,
lead and pewter; but all my endeavours have not been able to make them
attract the needle at all. Indeed, when I have held a piece of pewter,
that I have tryed to make magnetical, to the needle, the needle would
tremble, but not approach the pewter.

I send you another piece of brass, whose either end attracts either of
the poles; this I have infused the magnetic virtue into, and can at any
time, so as to attract and repel the needle; but, like steel that is
set a low blue, it loseth that polarity in a few hours; which may arise
for its being too short for its weight, or from its different temper of
hardness or softness.

A third piece I also send you, which with all my endeavours I cannot
make attract the needle in the least; and yet I can perceive no
difference between the appearance of this piece and that of those which
do.

Would some ingenious man pursue these experiments, perhaps we might
have needles made of brass to act as strongly as steel ones do, which
would have the advantage of being less liable to rust at sea than steel
ones are.

But my whole design was to shew, that brass is by no means a proper
metal to make compass-boxes of, or to be employed in any instrument
where magnetism is concerned. For as it is demonstrable, beyond
all contradiction, that some brass is found endued with a power of
attracting the magnetic needle; that other pieces are capable of
receiving it either by accident or design, (let it be from its being
mixed with iron, or any other cause whatever) brass must be a very
improper metal for compass-boxes, as it may occasion many sad and fatal
accidents.

Norwich, Octob. 20th, 1758.


It is well known, that brass has been sometimes found to affect and
disturb the magnetic needle; but, to give magnetism and polarity
to brass, has not, that I have yet heard, been before attempted. I
therefore have taken the liberty to lay the above account before this
Royal Society, and have also brought the pieces of brass mentioned
therein, which have been thus made magnetical.

                                                              H. Baker.

London, Nov. 15. 1759.




CVII. _An Account of the_ Sea Polypus, _by Mr._ Henry Baker, _F.R.S._

_To the Right Honourable the_ EARL _of_ MACCLESFIELD, President _of
the_ Royal Society.

[Read Nov. 23, 1758.]

My Lord,

I now return the marine animal your Lordship did me the honour to
recommend to my examination; which I find to be a species of one kind
of the Sea Polypi, mentioned by naturalists; but I think not very
accurately described.


The kinds of Sea Polypi are understood to be,

_First_, The Polypus, particularly so called, the Octopus, Preke, or
Pour-contrel: to which kind our subject belongs.

_Secondly_, The Sepia, or Cuttle-fish.

_Thirdly_, The Loligo, or Calamary. And each of these has its different
species and varieties[159]. The ancients add the Nautilus; and some
sorts of Star-fish might perhaps be not improperly ranged among them.

All of the first kind have eight arms, placed at equal distances round
the head; below the arms are two eyes, and the body is short and thick.

The Cuttle-fish, and the Calamary, have each of them ten arms; of which
eight are shorter ones, tapering gradually to a point from the head,
where they all rise, to their extremities: the other two (frequently
called Tentacula) are three or four times as long, perfectly round,
slender, and of an equal thickness for above two thirds of their whole
length; then spreading into a form nearly like that of the shorter
arms. Great numbers of _acetabula_, or suckers, are placed somewhat
irregularly on each of the shorter arms, and on the spreading parts of
the Tentacula, where some of the suckers are a great deal larger than
the rest.

The body of the Cuttle-fish is broad and flat, having within it a broad
friable white bone; that of the Calamary is a sort of cartilaginous
case holding the intestines, of a roundish oblong shape, furnished with
two fins, and having within it a thin transparent elastic substance
like Isinglass.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXIX. _p. 779_

  _G. Edwards delin AD. 1758_        _J. Mynde sc._]

The mouth of the Pour-contrel, Cuttle-fish, and Calamary, is placed in
the fore-part of the head, between the arms, having an horny beak, hard
and hooked like a parrot’s, which some writers call the teeth. The eyes
of them all are nearly in the same position.

As the subject under examination resembles in some particulars all the
above kinds of Polypi, this short account of them may, it is hoped,
render the following description of it the more intelligible: and
with the same view, Mr. George Edwards, Fellow of the Royal Society,
has been so obliging as to make drawings of the animal itself, in
four different positions, and of the natural size; which drawings are
herewith presented to your Lordship.

Our Polypus is of the Pour-contrel kind, and I believe of that species
called Bolytæna; which is said to have a musky smell; but if ours had
such a smell, the spirits wherein it lies have taken it quite away.

In the drawing [_See_ TAB. XXIX. _Fig._ 1.] is shewn the anterior part
of this animal, which has much the appearance of a Star-fish. Here
are eight arms about three inches in length, united at their roots,
and placed circularly at equal distances in the same plane, which has
a considerable sinking towards the center. These arms diminish from
their rise to their extremities, and end exceedingly small. Near the
head they are quadrilateral, but the under-side contracting gradually
to an edge, they become towards the ends trilateral. On the upper side
of each arm are two rows of _acetabula_, or suckers, standing in a
beautiful order, as close as they can well be placed, and beginning
from the center of all the arms. These suckers are perfectly circular,
with edges flat on the top, and a round cavity in the middle of each.
They are largest in the widest part of the arm, and lessen as the arm
diminishes, till they become so small as hardly to be discernable. It
is very difficult to tell their number: I counted as far as fifty in a
row, but am certain there are many more; and I don’t imagine the eight
arms have so few as a thousand on them. They rise some height above the
surface of the skin; and wherever they are not, the skin of the arms
(unless on the under-side) is granulated like shagreen[160].

As in the other kinds of Polypi the mouth is placed between the arms
conspicuously enough, I expected to find it so in this; but the spirits
had contracted it so much, that I could discern no opening at all
where I thought the mouth must be; and therefore could not say, with
assurance, that the mouth was placed there. Under this difficulty
I applied to Sir Hans Sloane’s most valuable collection of natural
history in the British Musæum, where I found several species of this
kind of Polypi, and amongst the rest a small dried specimen of the same
species as ours, and a much larger one in spirits, of a species that
comes very near it.

This large specimen afforded the information I stood in need of: for
though here also the mouth was closed, and the beak drawn down into
the center between the arms, so as not to be seen at all; yet, by the
help of Dr. Morton and Mr. Empson, I had the satisfaction to see the
mouth opened, and the beak in the same situation, and of the same form
and substance, as in the other kinds of Polypi. Having gained this
knowledge, by applying the point of a bodkin, I easily felt the beak
in our Polypus; but in so small a subject it cannot be brought to view
without dissection, which is the reason it does not appear in these
drawings.

_Fig. 2._ represents the Polypus so placed as to shew the situation of
the eyes and the form of its body, and also in what manner the arms
are turned back in the specimen before us; but we may suppose them
thus disposed merely in the act of dying, and that when alive they are
moveable in all directions.

On that side of the body opposite to the eyes, and which therefore may
be termed the belly-part, there appears a transverse slit or opening
in the skin, not in a strait line, but a little semicircular; from the
anterior part whereof a tube or pipe proceeds, about one third of an
inch in length, smaller at the extremity, where it opens with a round
orifice, than at the base, and reaching to within a small distance of
the arms. As both the Cuttle-fish and Calamary have a pipe nearly in
the same situation, though somewhat different in figure, through which
they occasionally discharge an inky liquor, and some writers say the
fæces also, it is probable the pipe in this animal may serve to a like
purpose; and as the body of the Calamary is included in a case, the
slit across the body of this animal shews its belly part to have also
a sort of case, though on its back there is no separation as in the
Calamary.

Out of the aforesaid slit or opening a bag issues with a very slender
neck, extending towards the tail, and enlarging gradually to its end.
This bag is above half the length of the body, and appears like another
body appendant thereto. I should be intirely at a loss concerning
this bag, did not some passages in Mr. Turberville Needham’s curious
observations on the milt vessels of the Calamary enable me to form some
conjectures about its use.

Having dissected several Calamaries on the coast of Portugal, without
the least indication of milt or roe, and consequently without knowing
which were male or female, he was much surprised (about the middle
of the month of December) to find a new vessel forming itself in an
obvious part, and replete with a milky juice. This was an oval bag, in
which the milt vessels formed themselves gradually, the bag unfolding
as these framed and disposed themselves in bundles. Before that time
he had observed two collateral tubes, which are alike in both sexes;
but a regular progress in the expansion of the milt-bag and formation
of the milt-vessels had not presented itself before. Those tubes till
then appeared open at one extremity, much resembling the female parts
of generation in a snail, but did not terminate in a long oval bag
extending in a parallel with the stomach more than half the length of
the fish, as he found them afterwards when the milt vessels that filled
the whole cavity were ripe for ejection. The same ducts without the bag
are found in the female also, perhaps for the deposition of the spawn.
Vid. _Needham’s Microscopical Discoveries, cap._ v.

It appears from this account that the male Calamary (at a certain time
of the year only) has a bag wherein the milt-vessels are contained,
and that the female has no such bag. Since therefore the bag of our
Polypus is found in the same situation as that of the Calamary, (which
is also a kind of Polypus) we may suppose it to be the milt bag, and
that our Polypus is a male, taken at a time when the milt was ready for
ejection. In the dried specimen at the British Museum, and also in the
other specimens, there is the same opening, with the pipe that rises
above it towards the arms, but not the least appearance of the bag in
question: they are therefore probably females, or if males, were caught
before such bag was formed.

_Fig. 3._ presents another view of this Polypus, its arms extended
circularly with their under-sides next the eye, and the body so
disposed as to shew the transverse opening _a_, the oval bag issuing
therefrom _b_, and the pipe rising upwards towards the arms _c_.

_Fig. 4._ shews the Polypus with its transverse opening and the pipe
rising therefrom, but without the oval bag; it is figured thus by
Rondeletius and Gesner, and the specimen at the British Museum has also
this appearance. It is here shewn with the arms extended forwards. K
is a magnified figure of one of the _acetabula_, or suckers; of which
there are two rows on each arm of this Polypus, as before described.

Mr. Needham, in his description of the suckers of the Calamary,
(which he had many opportunities of examining whilst alive, and whose
mechanism is probably the same as in those of our Polypus) informs
us, “that the action of the suckers depends partly on their shape,
which, when they are extended resembles nearly that of an acorn-cup,
and partly upon a deep circular cartilaginous ring, armed with small
hooks, which is secured in a thin membrane something transparent,
by the projection of a ledge investing the whole circumference about
the middle of its depth, and not to be extracted without some force.
That each sucker is fastened by a tendinous stem to the arm of the
animal: which stem, together with part of the membrane that is below
the circumference of the cartilaginous ring, rises into and fills
the whole cavity when the animal contracts the sucker for action. In
this state whatever touches it is first held by the minute hooks, and
then drawn up to a closer adhesion by the retraction of the stem and
inferior part of the membrane, much in the same manner as a sucker of
wet leather sustains the weight of a small stone.” Vid. _Microscopical
Discoveries_, p. 22.

M shews one of the cartilaginous rings armed with small hooks, of its
real size. The ring this is drawn from was taken out of a large sucker
of a larger Polypus, and is presented herewith.

By these suckers the Polypus can fix itself to rocks, and prevent its
being tossed about in storms and tempests; but their principal use
must undoubtedly be to seize and hold its prey: and to this purpose
they are most admirably adapted; for when they are all applied and act
together, unless the Polypus pleases to withdraw them, nothing can get
from it whose strength is insufficient to tear off its arms. Something
like these suckers is found by the microscope in the minute fresh water
Polype, whereby it is able to bind down and manage a worm much larger
and seemingly stronger than itself[161]. In like manner the _stella
arborescens_ (which may also be called a Polypus), though it has not
suckers, yet by the hooks along its arms, and the multiplicity of
their branchings, which have been counted as far as 80,000, it can, by
spreading its arms abroad like a net, so fetter and entangle the prey
they inclose when they are drawn together, as to render it incapable of
exerting its strength: for however feeble these branches or arms may
singly be, their power united becomes surprising. And we are assured
nature is so kind to all these animals, that if in their struggles any
of their arms are broken off, after some time they will grow again; of
which a specimen at the British Museum is an undoubted proof; for a
little new arm is there seen sprouting forth in the room of a large one
that had been lost.

It is evident from what has been said, that the Sea Polypus must be
terrible to the inhabitants of the waters, in proportion to its size
(and Pliny mentions one whose arms were thirty feet in length); for the
close embraces of its arms and the adhesion of its suckers must render
the efforts of its prey ineffectual either for resistance or escape,
unless it be endued with an extraordinary degree of strength.

Sea Polypi are frequent in the Mediterranean: but Mr. Haviland of Bath,
to whom we are obliged for this, which is of a different species,
thinks it came from the West Indies, where it is called a Cat-fish.
That like it in the British Museum also came from thence.

As the Polypus I have endeavoured to describe is much contracted by
lying long in spirits, and dissection would destroy a specimen well
worth preserving, I hope to be excused if this account should be found
deficient in several particulars, or chargeable with some mistakes.

Permit me the honour to be,

                               My LORD,
                            Your Lordship’s
                   Most humble and obedient Servant,
                               H. Baker.

Strand, Nov. 23d, 1758.




CVIII. _A Description of the fossil Skeleton of an Animal found in the
Alum Rock near_ Whitby. _By Mr._ Wooller. _Communicated by_ Charles
Morton, _M. D. F.R.S._

[Read Nov. 23, 1758.]

IT is in this rock, that the Ammonitæ, or Snake-stones, as they are
commonly called, are found, which have undoubtedly been formed in the
_exuviæ_ of fishes of that shape; and though none of that species
are now to be met with in the seas thereabouts, yet they in many
particulars resemble the Nautilus, which is well known. The internal
substance of those stones, upon a section thereof, appears to be
a stony concretion, or muddy sparr. Stones of the same matter or
substance, in the shape of muscles, cockles, &c. of various sizes,
are also found therein, and now and then pieces of wood hardened and
crusted over with a stony substance are likewise found in it.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXX. _p. 787_.

_Part of the Fossil Skeleton of an Animal as it appeared on and united
to the Allom Rock near_ Whitby, _Jan. 3. 1758_.

a. a. _&c. The Ammonitæ or Snake Stones_.

_J. Mynde sc._]

Many naturalists have already observed, that among the vast variety
of extraneous substances found at several depths in the earth, where
it is impossible they should have been bred, there are not so many
productions of the earth as of the sea; and it appears by the accounts
of authors both ancient and modern, that bones, teeth, and sometimes
entire skeletons of men and animals, have been dug up or discovered
in all ages, and the most remarkable for size commonly the most taken
notice of. In the first particular this skeleton will most probably
appear to have belonged to an animal of the lizard kind, quadruped and
amphibious; and as to its size, much larger than any thing of that kind
ever met with or found in this part of the world; though, from the
accounts of travellers, something similar is still to be met with in
many of the rivers, lakes, &c. of the other three.

When the annexed drawing thereof was taken January 5, 1758. [_See_
TAB. XXX.] there remained no more of the _vertebræ_ than is therein
expressed; that is, 10 between D and F, and 12 between G and H: but
when it was first discovered, about 10 years ago, they were compleat;
and there was besides the appearance of what was then thought to have
been fins, near the back part of the head at A, the same as appeared
further backward at E, when this design was made. The _vertebræ_, &c.
now wanting having been either dug up by curious persons, or washed
away by the violence of the waves at high water, and the accidental
beating about of stones, sand, &c. during that time; the water covering
this skeleton several feet at high water in spring tides; the cavities
in the rock still remaining as in the design.

The substance of the bones, with their _periostium_, on the covered
or under side, in most parts remains intire, and their native colour
in some places in a good measure preserved, and the teeth with their
smooth polish plainly to be discovered. Part of the mandible near the
extremity was covered with a shelf of the rock about three inches
thick; which being cut away and removed, both the mandibles appeared
under it compleat, with the teeth of the upper and under one, plainly
locking or passing by each other. These appeared to be of the _dentes
exerti_ or fang kind, as well as all the others in the narrow part of
the mandible, and further backwards they were not observed. From this
ledge or shelf the mandible towards B is single, and appears to be the
upper one of the living animal; and from the head not being exactly
in the line of the body, that part has been inverted, or quite turned
over, and the body itself, as appears from the transverse processes of
the _vertebræ_, lies on the right side. There appears one row of teeth
only on each side of the mandible, and they are about ¾ of an inch
asunder.

The mandible B A, the _cranium g h_, and the _vertebræ_ from D to F,
were attempted to be taken up whole; but the bones being rendered
extremely brittle, and the rock in which they were fixed being a
brittle blackish slate, with joints or fissures running in every
direction, would not hold together: the whole therefore fell in many
pieces, the _vertebræ_ in the joints only, which makes them easy to
join together again, and besides shows very plainly the transverse and
spinal processes thereof, with the foramen in the latter for the spinal
marrow. It was now that a piece of the _os femoris_, about four inches
long, shewed itself in the sparry concreted substance at E, together
with a piece of the _os innominatum_, to which it had been articulated
or joined. This, with what has been before remarked, will sufficiently
prove this to have been an animal of the quadruped, and probably, from
the shape of the cranium peculiar to fishes, of the amphibious kind. At
the same time many pieces of the _costæ_ or ribs, as broke and crushed
up against the _vertebræ_, were plainly visible. The cavities of all
the bones were filled with a substance, which appeared the same as the
rock itself; and the substance on each side the _vertebræ_, as they
laid, was a mixture of sparry concreted matter with that of the rock
itself, which is a blackish slate. The animal, when living, must have
been at least 12 or 14 feet long. And the dimensions of the whole,
or particular parts of the skeleton, may be measured from the scale
annexed thereto.

This skeleton lay about six yards from the foot of the cliff, which is
about sixty yards in perpendicular height, and must have been covered
by it probably not much more than a century ago. The cliff there
is composed of various _strata_, beginning from the top, of earth,
clay, marle, stones both hard and soft, of various thicknesses, and
intermixed with each other, till it comes down to the black slate or
alum rock, and about 10 or 12 feet deep in this rock, this skeleton
laid horizontally, and exactly as designed. The probability, that this
cliff has formerly covered this animal, and extended much more into
the sea, is not in the least doubted of by those that know it. The
various _strata_, of which it is composed, are daily mouldering and
falling down; and the bottom, being the slaty alum rock, is also daily
beat, washed, and wore away, and the upper parts undermined, whence
many thousand tuns often tumble down together. Many antient persons now
living, whose testimony can be no way doubted of, remember this very
cliff extending in some places twenty yards further out than it does at
present. In short there is sufficient evidence, that at the beginning
it must have extended near a mile further down to the sea than it does
at present; and so much the sea has there gained of the land.

These are the principal facts and circumstances attending the situation
and discovery of this skeleton; which from the condition it is in, and
from the particular disposition of the _strata_ above the place where
it is found, seem clearly to establish the opinion, and almost to a
demonstration, that the animal itself must have been antediluvian,
and that it could not have been buried or brought there any otherwise
than by the force of the waters of the universal deluge. The different
_strata_ above this skeleton never could have been broken through at
any time, in order to bury it, to so great a depth as upwards of 180
feet; and consequently it must have been lodged there, if not before,
at least at the time when those _strata_ were formed, which will not
admit of a later date than that above-mentioned.

  _P. S._ In the xlixth vol. page 639, of the _Philosophical
  Transactions_, an animal is described by Mr. Edwards, which was
  brought from the Ganges, and resembles this in every respect. He
  calls it _Lacerta (crocodilus) ventre marsupio donato, faucibus
  Merganseris rostrum æmulantibus_.




[Illustration: _Philos. Trans. Vol. L._ TAB. XXXI. _p. 791_.

PHŒNICIAN Coins.

_J. Mynde sc._]




CIX. _A Dissertation upon the_ Phœnician _Numeral Characters antiently
used at_ Sidon. _In a Letter to the Rev._ Thomas Birch, _D. D. Secret.
R. S. from the Rev._ John Swinton, _M. A. of_ Christ-Church, Oxon.
_F.R.S._

[Read Dec. 7, 1758.]

Reverend Sir,

HAVING, by the assistance of the Palmyrene numeral characters, lately
made a discovery, which may perhaps hereafter be of considerable
service to chronology; I could not longer defer, though now deeply
engaged in other matters, communicating it to the Royal Society. Nor
will the memoir containing this, I flatter myself, be deemed altogether
unworthy the attention of that learned and illustrious body. For,
unless I am greatly deceived, it will bid fair to ascertain, with a
sufficient degree of precision, the Phœnician dates of several antient
Sidonian coins, one of which was struck above a century before the
birth of CHRIST, hitherto utterly unknown; and evince the notation of
the Phœnicians, at least those of Sidon, when they first appeared, to
have been extremely similar to, if not nearly the same with, that of
the Palmyrenes.


I.

A small brass coin of Sidon[162], now in my possession, exhibits on the
reverse three Phœnician letters, that form the word SIDON, over the
prow of a ship, the usual symbol of the city wherein it was struck.
This coin, which is in good conservation, I formerly[163] published and
explained. The characters however in the exergue, which I could then
make nothing of, were not with sufficient accuracy described. This has
induced me to transmit you another draught of the same medal, wherein
proper care has been taken to remedy that defect. The two first of
those characters, though somewhat imperfect, appear manifestly enough
to be _Schin_ and _Tzade_; as the former occurs on the Palmyrene[164]
marbles, and the latter on several very valuable[165] Phœnician coins.
The others so nearly resemble the numeral characters of the Palmyrenes,
that they may undoubtedly be considered as pointing out to us a date.
Which if we admit, the _Schin_ and _Tzade_ will seem to be the initial
letters of the words צה שנת, THE YEAR OF SIDON, or IN THE YEAR OF
SIDON; as the elements _Pe_ and _Schin_ apparently denote שנת פסח, THE
PASCHA OF THE YEAR, or IN THE BEGINNING OF THE YEAR, on the reverse of
the famous Samaritan coin of Bologna, published by Sig. Bianconi[166]
not many years since. Nor can the phrase, THE YEAR OF SIDON, or IN THE
YEAR OF SIDON, intimating the year of the proper æra of that city, be
looked upon as repugnant either to the Jewish or Phœnician genius; a
similar expression having been used, both in their writings[167] and
on their coins[168], about the time that the Phœnician medal before
me was struck, by the Jews. That the first of the numeral characters
here stands for TWENTY, we may infer from the correspondent one of the
Palmyrenes, to the form of which it is by no means unlike. This will
likewise be confirmed by the dates preserved on other Phœnician coins,
which will be immediately produced. The next, denoting a lesser number,
and not representing FIVE, which we find always expressed by minute
right lines on the Sidonian medals, must indubitably occupy the place
of TEN. The six following strokes, after what has been just observed,
will be acknowleged to add SIX to the foregoing numbers; so that the
inscription in the exergue will no longer remain a mystery, the whole
only importing, IN THE YEAR OF SIDON XXXVI.


II.

I have three other coins of Sidon[169], of almost intirely the same
type; only one of them exhibits a date in Greek numerals, and two bear
Phœnician dates. The Greek numerals are EOT, CCCLXXV; and the Phœnician
correspond with the numbers CXX, CXXVII, to both of which are prefixed
the above-mentioned initial letters. We meet with draughts of two
similar medals in[170] Arigoni, adorned with characters, expressing the
numbers CXXVIII, CXXX. All these coins present to our view a turrited
head and a branch of palm, pointing out to us the country to which they
belong, and on the reverse the usual symbol of Sidon. The year handed
down to us by the Greek date EOT, is the 375th of the æra of Seleucus;
and those denoted by the Phœnician numerals answer to the 120th, 127th,
128th, and 130th, of the proper æra of Sidon, as will be hereafter more
fully evinced. Hence we may certainly collect, that these pieces were
struck at Sidon in the years of CHRIST 11, 18, 19, 21, and 64.


III.

Three coins of Sidon, different from the former, occur in[171] Sig.
Haym, and seven[172] more in my little cabinet, whose type is
altogether the same, with Phœnician dates, preceded by the two
aforesaid initial letters, upon them. To which we may add five,
preserved in the noble[173] cabinet bequeathed to Christ-Church,
Oxon. by Archbishop Wake, and another in the valuable collection of
the Rev. Dr. Barton[174], Canon of the said collegiate church, and a
worthy member of this Society. On one side these medals all exhibit
the head of Jupiter, and on the reverse the prow of a ship, the common
symbol of Sidon. Most of them had various Phœnician letters at first
imprest on the upper part of the reverse, and one of them (which is
pretty remarkable) nearly the same characters there that appear in
the exergue. The first of the coins mentioned here was struck in the
year of Sidon 5. This has been perfectly well preserved, and is more
curious than any of the rest; which were emitted from the mint at Sidon
in various years of the proper æra of that city, _viz._ the 107th,
108th, 110th, 111th, 112th, 114th, 115th, 116th, 117th, and 119th. We
meet on none of these medals with the figure denoting TWENTY, used
by the Sidonians, during the period I am now upon. It not a little
resembles that which prevailed at Tadmor[175] in the reign of the
emperor Claudius, about forty-nine years after the birth of CHRIST. The
most antient of the Phœnician coins I am now considering preceded the
commencement of the Christian æra 104 years, and is consequently 153
years older than the earliest Palmyrene inscription that has hitherto
come to our hands[176].


IV.

Some years since I published a small brass medal of Sidon[177], with
the heads of Jupiter and Juno on one side, and the prow of a ship
on the reverse; but did not accurately enough describe the numeral
characters, and two initial letters, in the exergue. I therefore take
the liberty to send[178] you a new draught, perfectly well done,
of that inscription. Two more coins of the same type I have since
acquired, and another may be seen in[179] Sig. Haym. These four pieces
only exhibit the years of Sidon 125 and 132.


V.

My small collection likewise affords two[180] other Phœnician medals
of Sidon,[181] and Archbishop Wake’s noble cabinet one, of the same
type, with different Phœnician dates in the exergue. To these may be
added five, with the publication of which the learned world has been
obliged by Sig. Arigoni[182]. The anterior faces of these coins are
adorned with a veiled head, representing the genius of the city wherein
they were struck; and the reverses with a human figure leaning upon
a pillar, and holding a branch of palm in its right hand. Several
Phœnician letters also there appear, which may perhaps at first sight
seem to render it somewhat doubtful, whether the medals belong to
Sidon or not. But every suspicion arising from hence must immediately
vanish, when we cast our eyes upon the two initial elements, and the
numeral characters, in the exergue; which clearly enough indicate the
pieces to have been struck at Sidon, in the 83d, 87th, 95th, 105th,
106th, 108th, 114th, and 116th years of the æra peculiar to that city.
A Phœnician coin of Sidon likewise occurs in one[183] of Sig. Arigoni’s
plates, and another[184] in my collection, with the turrited head and
branch of palm visible on three of the[185] medals above described,
which indisputably appertain to that city, together with the very
Phœnician letters and symbol imprest on the Sidonian coins now before
me. This, exclusive of other considerations, that might be offered,
must set the point I am here insisting upon beyond dispute.


VI.

I have another brass Phœnician medal of Sidon[186], not a little
resembling those above-mentioned, both in workmanship and size,
presenting to our view on one side the head of Jupiter, and on the
other a human figure with a lance in its right hand. This coin, which
has never yet been published, is adorned with a Phœnician legend
on the reverse, different from those of all the others that have
hitherto appeared. I therefore judged that a draught of it would not
be unacceptable, though the date imprest originally in the exergue
(answering to the 26th year of Sidon) has a little suffered from the
injuries of time.


VII.

The next Phœnician medal of Sidon, which I shall take the liberty here
to describe, is a small brass one[187], now in my hands, with a veiled
head on the anterior face, and the prow of a ship on the reverse.
M. Bouterouë[188], who has published it, rightly asserts it to be a
Phœnician coin. The year of Sidon, preserved in the exergue of mine,
is 74; and that in the exergue of M. Bouterouë’s, 73, though the first
numeral character of the latter is somewhat deformed.


VIII.

The last Phœnician medals I shall at present produce, in order to
settle the point in view, are[189] two in my possession, intirely
agreeing both in type and form, as remarkable as any of the others here
touched upon. A similar coin has been published by Sig. Arigoni[190],
and another[191] by M. Bouterouë; both of which, on several accounts,
merit the attention of the learned. They exhibit on one side the
head of Jupiter laureated, with a beard; and on the reverse a double
cornucopia, together with three or four Phœnician elements, one or
two of which are in a great measure defaced. A brass medal of Sidon
occurs in Archbishop Wake’s[192] collection, as well as one in[193]
mine, with the head of Jupiter done exactly after the same manner
as that on the pieces before me, and Europa carried by a bull on
the reverse; which, exclusive of the inscriptions in the exergue,
demonstrate the latter to belong to Sidon. The first of mine was struck
in the 143d year of the proper æra of that city, and the second five
years after. They correct the barbarous date assigned by Sig. Arigoni
to his coin. M. Bouterouë has not favoured the learned world with an
explication of the medal, of which he has given us a draught. Nor has
M. l’Abbé Barthelemy, who likewise mentions this very coin, informed
us to what place it appertains; but contented himself with barely[194]
observing, that the letters preserved on the reverse are Phœnician. I
flatter myself therefore that I shall not be charged with plagiarism
by this celebrated antiquary, in case what is here submitted to the
consideration of the Royal Society should be so happy as to meet with
the approbation of that learned and illustrious body; not even by
_only_ acquainting the public, with a sort of _politesse_ so peculiar
to his countrymen, that it is now become one of the most distinguishing
characteristics of their nation[195], “that a certain Oxford doctor has
done him the honour to _adopt_ the explication he had given.”


IX.

For the farther illustration of what has been here advanced, it will
be requisite to observe, that two æra’s were antiently followed at
Sidon; the æra of Seleucus, and another peculiar to the inhabitants
of that city[196]. On the Greek brass coins of Sidon, according to
F. Frœlich[197], both these epochs seem to have been used. However,
the supputation pointed out to us by the date on the Greek medal
above-mentioned was undoubtedly made according to the æra of Seleucus;
since otherwise the year exhibited by that date must have been nearly
coincident with the 266th of CHRIST, which by those versed in this kind
of literature will never be allowed. For had the piece presented to
our view so recent a date, as Sidon first became a Roman colony in the
reign of Elagabalus[198], above forty years before; the reverse ought
to have been adorned with some other letters intimating this, as were
those of the Sidonian[199] coins posterior to that event. As certain
is it that all the Phœnician medals of Sidon, whose numeral characters
have been interpreted here, acknowledge no other epoch than the proper
one of that city, which commenced in the year[200] of Rome 643. This, I
flatter myself, from the following considerations, exclusive of others
that might, with equal facility, be offered, will even to demonstration
appear.

1. The fifth year mentioned by the oldest of these coins cannot be
the fifth year of the æra of Seleucus, because the Sidonians were
then subject to Antigonus[201], in whose territories the supputation
according to that epoch did not take place; and consequently the piece
itself must have been struck in the fifth year of the proper æra of
Sidon, nearly coincident with the 648th of Rome[202].

2. No dates ever occurred upon the medals of the Syrian kings presiding
over the people of Sidon, either to F. Frœlich or Dr. Vaillant[203],
who have so eminently distinguished themselves in this branch of
literature, before the year of Seleucus 112; and therefore neither
the Phœnician dates preserved on the aforesaid Sidonian coins whose
numeral characters do not amount to 112, nor the Greek dates on others
falling short of that number, can rationally be supposed to bear any
relation to the æra of that prince. This certainly must be considered
as a strong presumption, or rather an incontestable proof, that the
last-mentioned Phœnician dates were deduced from the commencement of
the proper Sidonian epoch, as from their genuine cardinal point. Which
reasoning will by analogy extend, as the numeral characters exhibited
by all the coins here explained are of the same kind, to every one of
the rest.

3. None of the medals of the Syrian kings, with Phœnician letters
upon them[204], hitherto published, bear any Phœnician dates. This,
after what has been said, renders it extremely probable, that the
pieces of Sidon I am considering were posterior to those coins; and
even that their Phœnician dates referred to an æra different from that
of Seleucus, followed by the Greek dates on the medals of the Syrian
kings. Which if we admit, this æra could have been no other than the
new one of the Sidonians, that commenced in the seventh century of Rome.

4. That the dates visible on these coins were supputed according to
the latter epoch of Sidon, will be manifest from an examination of
the Greek and Phœnician brass medals of that city explained, in[205]
the beginning of this paper; whose type and workmanship are extremely
similar, if not almost intirely the same. For this circumstance is
to me an evident proof, that they could not have been struck at very
distant times. Now if we take the Greek coin to have followed the æra
of Seleucus, as was undoubtedly the case, and the others that peculiar
to Sidon; the first of the Phœnician dates[206] will not be prior to
the Greek one above fifty-three years, nor the last of them precede it
above forty-three years. Whereas if we suppose the numeral inscriptions
in the exergues of the Phœnician Sidonian coins to have been supputed
according to the Seleucian epoch, the difference between the aforesaid
dates will be five times as much; which with the similarity of
workmanship and type, already observed, will be altogether incompatible.

5. As the Jews[207], about the time that the first of our medals was
struck, denominated the æra of Seleucus, THE ÆRA OF THE KINGDOM OF
THE GREEKS; we cannot well doubt but it went amongst the Sidonians,
who were neighbours to the Jews, under the same denomination. From
whence it will follow, that the epoch styled by them emphatically, THE
ÆRA OF SIDON, must have been different from the æra of Seleucus; and
consequently that which, after the 643d year of Rome, was peculiar to
them.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXXII. _p. 804_

PHŒNICIAN Numerals antiently used at SIDON, from _One_ to a _Thousand_.

_J. Mynde sc._]

The powers of the Phœnician numeral characters antiently used at Sidon,
which I flatter myself are now discovered, having been for many ages
unknown; the Society will perhaps not be displeased to see accurate
draughts of the principal Phœnician medals, from whence they are
deduced. I have therefore taken the liberty to transmit them[208] such
draughts, which may be intirely depended upon. I have also constructed
a table[209] of the numeral characters themselves, from UNITY TO A
THOUSAND; which will demonstrate, in the clearest manner possible, the
great affinity between them and those of the Palmyrenes.

1. From this table it plainly appears, that the people of Sidon had
no particular character to denote Five, whilst the Phœnician numerals
here explained were in vogue amongst them; that they expressed TWENTY
by a character, during that period, not very different from the
correspondent one used at Tadmor; and that in all other respects the
Phœnician notation then prevailing at Sidon was, in a manner, the same
with that of the[210] Palmyrenes.

2. It may not be improper to observe, that two of the Sidonian coins I
have been considering[211] exhibit the Phœnician word מא, equivalent
to the Hebrew מאה, and Syriac מאא, AN HUNDRED, instead of the centenary
numeral character. This, in conjunction with the appearance of that
character, occupying the very place of the term אמ, on others of those
coins, first induced me to believe, that the inscription preserved by
every one of them in the exergue could be nothing else but a date.

3. I shall beg leave farther to remark, that none of the indubitable
medals of Tyre, adorned with Phœnician letters, as far as I have been
able to discover, present to our view any Phœnician dates at all.
This still more clearly evinces the second element prefixed to the
Phœnician numerals in the exergue to point out to us the city of Sidon,
and not that of Tyre; which[212], indeed, seems already to have been
sufficiently proved.

4. From the foregoing observations we may likewise collect, that
the coin assigned to Demetrius III. by Mr. Masson, F. Frœlich[213],
and Sig. Haym, exhibiting a Phœnician legend, without a Phœnician
date, in the exergue, ought in reality to be attributed to Demetrius
I. Those three learned men therefore have been guilty of a mistake in
this particular. Nor can the head on this medal be denied to bear some
resemblance to that of Demetrius I.[214] with a moderate beard, as it
appears on a coin published by Dr. Vaillant, and in one of F. Frœlich’s
plates. That the letters A K, behind the head, indicate the piece
to have been struck in the twenty-first year of the proper Sidonian
æra[215], as Mr. Masson and F. Frœlich are pleased to assert, can never
be proved. On the contrary, the improbability of such a notion may be
inferred from two similar letters, behind the turrited head of the _Dea
Syria_[216], on a Phœnician coin, which Mr. Masson makes to point out
the forty-first year of the proper epoch of Sidon; whereas, in truth,
that piece seems to have been struck either in the reign of Demetrius
I. or Antiochus IV.[217] many years before. Nay, that it was actually
struck when Demetrius I. sat upon the Syrian throne, is rendered almost
incontestable by a medal of that prince now in my possession, with a
_Beta_ behind the head on the anterior part, and the very reverse of
the last-mentioned coin. From the former of which circumstances it
farther appears, that the alphabetic characters MA, supposed by Mr.
Masson to denote 41, are by no means to be taken for a date. To which
we may add, that the head on a Phœnician medal, with the two Greek
elements AK behind it, published by Mr. Reland[218], is apparently that
of Demetrius I.; and that the posterior part of this coin is nearly
the same, in all respects, with the reverse of that supposed to[219]
appertain to Demetrius III. by Mr. Masson and Sig. Haym. But to wave
all other considerations, relative to the point in view, that may
occur, the features and turns of the face on the medals of Demetrius
III. are so different[220], that no inference of any validity can be
drawn from the pretended identity or similitude of them, in support of
Mr. Masson’s opinion.

5. The Palmyrene and Phœnician numerals, deduced from coins and
inscriptions, may perhaps be thought not unworthy a place amongst the
arithmetical characters of various nations, formerly[221] collected
by Bishop Beveridge; and consequently may be allowed to render
somewhat more complete the chronological institutions, or rather the
chronological arithmetic, of that learned and judicious author.

You will pardon the prolixity of this letter, which the novelty of
the subject may perhaps render a little more excusable than it would
otherwise have been; and believe me to be, with the most perfect
consideration and esteem,

                                 SIR,
                  Your most obedient humble Servant,
                              J. Swinton.

Christ Church, Oxon. Nov. 17. 1758.




[Illustration: _Philos. Trans. Vol. L._ TAB. XXXIII. _p. 809_.

_J. Mynde sc._]




CX. _Of the Irregularities in the Motion of a Satellite arising from
the spheroidical Figure of its Primary Planet: In a Letter to the Rev._
James Bradley _D. D. Astronomer Royal, F.R.S. and Member of the Royal
Academy of Sciences at_ Paris; _by Mr._ Charles Walmesley, _F.R.S.
and Member of the Royal Academy of Sciences at_ Berlin, _and of the
Institute of_ Bologna.

[Read Dec. 14, 1758.]

Reverend Sir,

SINCE the time that astronomers have been enabled by the perfection of
their instruments to determine with great accuracy the motions of the
celestial bodies, they have been solicitous to separate and distinguish
the several inequalities discovered in these motions, and to know their
cause, quantity, and the laws according to which they are generated.
This seems to furnish a sufficient motive to mathematicians, wherever
there appears a cause capable of producing an alteration in those
motions, to examine by theory what the result may amount to, though
it comes out never so small: for as one can seldom depend securely
upon mere guess for the quantity of any effect, it must be a blameable
neglect entirely to overlook it without being previously certain of its
not being worth our notice.

Finding therefore it had not been considered what effect the figure
of a planet differing from that of a sphere might produce in the
motion of a satellite revolving about it, and as it is the case of the
bodies of the Earth and Jupiter which have satellites about them, not
to be spherical but spheroidical, I thought it worth while to enter
upon the examination of such a problem. When the primary planet is an
exact globe, it is well known that the force by which the revolving
satellite is retained in its orbit, tends to the center of the planet,
and varies in the inverse ratio of the square of the distance from
it; but when the primary planet is of a spheroidical figure, the
same rule then no longer holds: the gravity of the satellite is no
more directed to the center of the planet, nor does it vary in the
proportion above-mentioned; and if the plane of the satellite’s orbit
be not the same with the plane of the planet’s equator, the protuberant
matter about the equator will by a constant effort of its attraction
endeavour to make the two planes coincide. Hence the regularity of
the satellite’s motion is necessarily disturbed, and though upon
examination this effect is found to be but small in the moon, the
figure of the earth differing so little from that of a sphere, yet in
some cases it may be thought worth notice; if not, it will be at least
a satisfaction to see that what is neglected can be of no consequence.
But however inconsiderable the change may be with regard to the moon,
it becomes very sensible in the motions of the satellites of Jupiter
both on account of their nearer distances to that planet when compared
with its semidiameter, as also because the figure of Jupiter so far
recedes from that of a sphere. This I have shewn and exemplified in
the fourth satellite; in which case indeed the computation is more
exact than it would be for the other satellites: for as my first design
was to examine only how far the moon’s motion could be affected by
this cause, I supposed the satellite to revolve at a distance somewhat
remote from the primary planet, and the difference of the equatoreal
diameter and the axis of the planet not to be very considerable. There
likewise arises this other advantage from the present theory, that
it furnishes means to settle more accurately the proportion of the
different forces which disturb the celestial motions, by assigning the
particular share of influence which is to be ascribed to the figure of
the central bodies round which those motions are performed.

I have added at the end a proposition concerning the diurnal motion
of the earth. This motion has been generally esteemed to be exactly
uniform; but as there is a cause that must necessarily somewhat alter
it, I was glad to examine what that alteration could amount to. If we
first suppose the globe of the earth to be exactly spherical, revolving
about its axis in a given time, and afterwards conceive that by the
force of the sun or moon raising the waters its figure be changed into
that of a spheroid, then according as the axis of revolution becomes a
different diameter of the spheroid, the velocity of the revolution must
increase or diminish: for, since some parts of the terraqueous globe
are removed from the axis of revolution and others depressed towards
it, and that in a different proportion as the sun or moon approaches
to or recedes from the equator, when the whole quantity of motion
which always remains the same is distributed through the spheroid, the
velocity of the diurnal rotation cannot be constantly the same. This
variation however will scarce be observable, but as it is real, it may
not be thought amiss to determine what its precise quantity is.

I am sensible the following theory, as far as it relates to the motion
of Jupiter’s satellites, is imperfect and might be prosecuted further;
but being hindered at present from such pursuit by want of health and
other occupations, I thought I might send it you in the condition it
has lain by me for some time. You can best judge how far it may be of
use, and what advantage might arise from further improvements in it. I
am glad to have this opportunity of giving a fresh testimony of that
regard which is due to your distinguished merit, and of professing
myself with the highest esteem,

                             Reverend Sir,
                       Your very humble Servant,
                             C. Walmesley.

Bath, Oct. 21. 1758.


LEMMA I.

_Invenire gravitatem corporis longinqui ad circumferentiam circuli
ex particulis materiæ in duplicatâ ratione distantiarum inversè
attrahentibus constantem._

ESTO NIK (_Vid._ TAB. xxxiii. _Fig._ 1.) circumferentia circuli,
in cujus puncta omnia gravitet corpus longinquum S locatum extra
planum circuli. In hoc planum agatur linea perpendicularis SH, et per
circuli centrum X ducatur recta HXK secans circulum in I et K, et SR
parallela ad HX: producatur autem SH ad distantiam datam SD, et agantur
rectæ DC, XC, ipsis HX, SD, parallelæ. Tum ductâ chordâ quavis MN ad
diametrum IK normali eamque secante in L, ex punctis M, N, demittantur
in SR perpendiculares MR, NR, concurrentes in R; junctisque SM, SN,
erit SM = SN, MR = NR, SR = HL. Dicantur jam SD, _k_; HX sive DC,
_h_; XL, _x_; CX, _z_; XI, _r_; eritque HL = _h_ - _x_, et SH = _k_
- _z_. Est autem SM ad SH ut attractio (1 ⁄ (SM)²) corporis S versus
particulam M in directione SM ad ejusdem corporis attractionem in
directione SH, quæ proinde erit SH ⁄ (SM)³: sed est SR = HL, et (SM)²
= (SR)² + (MR)² = (SR)² + (SH)² + (ML)²; unde sit SH ⁄ (SM)³ = SH ⁄
((HL)² + (SH)² + (ML)²⁽³⁄²⁾), et ductâ _mn_ parallelâ ad MN, vis qua
corpus S attrahitur ad arcus quàm minimos M_m_, N_n_, exponitur per
(SH × 2M_m_) ⁄ (SM)³ = SH × 2M_m_ × ((HL)² + (SH)² + (ML)²⁽⁻³⁄²⁾). Est
autem (HL)² + (SH)² + (ML)² = _kk_ - 2_kz_ + _zz_ + _hh_ - 2_hx_ +
_rr_, hincque ponendo _kk_ + _hh_ = _ll_, ((HL)² + (SH)² = (ML)²)⁽⁻³⁄²⁾
= (1 ⁄ _l_³) + (3_kz_ ⁄ _l_⁵) + (3_hx_ ⁄ _l_⁵) - (3_rr_ ⁄ 2_l_⁵) -
(3_zz_ ⁄ 2_l_⁵) + (15_kkzz_ ⁄ 2_l_⁷) + (15_khzx_ ⁄ 2_l_⁷) + (15_hhxx_
⁄ 2_l_⁷), neglectis terminis ulterioribus ob longinquitatem quam
supponimus corporis S. Quarè, si scribatur _d_ pro circumferentiâ IMKN,
gravitas corporis S ad totam illam circumferentiam secundum SH, sive
fluens fluxionis SH × 2M_m_ × ((HL)² + (SH)² + (ML)²)⁽⁻³⁄²⁾ evadit (_k_
- _z_) × _d_ in (1 ⁄ _l_³) + (3_kz_ ⁄ _l_⁵) - (3_rr_ ⁄ 2_l_⁵) - (3_zz_
⁄ 2_l_⁵) + (15 _kkzz_) ⁄ (2 _l_⁷) + (15 _hhrr_) ⁄ (4 _l_⁷). Simili
modo obtinebitur gravitas ejusdem corporis S secundum SR. _Q. E. I._


LEMMA II.

_Corporis longinqui gravitatem ad Sphæroidem oblatam determinare._

Retentis iis quæ sunt in lemmate superiori demonstrata; esto C centrum
sphæroidis, cujus æquatori parallelus sit circulus IMK. Sphæroidis
hujus semiaxis major sit _a_, semiaxis minor _b_, eorum differentia
_c_, quam exiguam esse suppono; et dicatur D circumferentia æquatoris.
Centro C et radio æquali semiaxi minori describi concipiatur
circulus qui secet IK in _i_, eritque gravitas in directione SD, qua
urgetur corpus S versus materiam sitam inter circumferentiam IMKN et
circumferentiam centro X et radio X_i_ descriptam, æqualis gravitati
in lemmate præcedenti definitæ ductæ in rectam I_i_. Sed est I_i_.
_c_∷ IX. _a_, atque _d_. D∷ IX. _a_; unde I_i_ × _d_. D × _c_∷ (IX)².
_aa_, hoc est, ex naturâ ellipseos, ob CX = _z_, et IX = _r_, I_i_
× _d_. D × _c_∷ _bb_ - _zz_. _bb_, adeoque I_i_ × _d_ = (D × _c_) ⁄
(_bb_) × (_bb_ - _zz_), atque _rr_ = _aa_ - (_aazz_) ⁄ (_bb_); scribi
autem potest in sequenti calculo _bb_ - _zz_ pro _rr_ ob parvitatem
differentiæ semiaxium in quam omnes termini ducuntur. Gravitas igitur
corporis S in materiam inter circumferentias supradictas consistentem
exprimetur per (D × _c_) ⁄ (_bb_) × (_bb_ - _zz_) × (_k_ - _z_) in 1
⁄ _l_³ + (3_kz_) ⁄ _l_⁵ - (3_bb_) ⁄ (2_l_⁵) - (15_zz_) ⁄ (4_l_⁵) +
(15_bbhh_) ⁄ (4_l_⁷) + (45_kkzz_) ⁄ (4_l_⁷). Et si addatur gravitas
in similem materiam ex alterâ parte centri C ad æqualem à centro
distantiam, quia tunc CX sive _z_ evadit negativa, gravitas corporis S
in hanc duplicem materiam erit (D × _c_) ⁄ _bb_ × (_bb_ - _zz_) in 2_k_
⁄ _l_³ - 6_kzz_ ⁄ _l_⁵ - 3_kbb_ ⁄ _l_⁵ + 15_k_³_zz_ ⁄ _l_⁷ + 15_hhkbb_
⁄ 2_l_⁷ - 15_hhkzz_ ⁄ 2_l_⁷. Ducatur jam gravitas hæc in _ż_, et sumptâ
gravitatum omnium summâ, factâ _z_ = _b_, gravitatio tota corporis S
in totam materiam globo interiori superiorem secundum directionem SD
æquatori perpendicularem prodit (D × _c_) × (4_kb_ ⁄ 3_l_³ - 4_kb_³ ⁄
5_l_⁵ + 2_khhb_³ ⁄ _l_⁷). Simili ratiocinio gravitatio corporis S in
eamdem materiam secundum directionem SR æquatori parallelam invenitur
æqualis D × _c_ × (4_hb_ ⁄ 3_l_³ + 2_hb_³ ⁄ 5_l_⁵ - 2_hkkb_³ ⁄ _l_⁷).
Tum si addatur gravitatio corporis S in globum interiorem, ex unâ parte
scilicet 2_b_³_k_D ⁄ 3_al_³, et ex alterâ 2_b_³_h_D ⁄ 3_al_³, habebitur
gravitas corporis S in totum sphæroidem. _Q. E. I._


COROLL.

Igitur gravitas corporis S secundum SD est ad ejusdem gravitatem
secundum SR sive DC in materiam sphæroidis globo interiori incumbentem
ut 2_k_ ⁄ 3 - 2_kb_² ⁄ 5_l_² + _khhb_² ⁄ _l_⁴ ad 2_h_ ⁄ 3 + _hb_² ⁄
5_l_² - _hkkb_² ⁄ _l_⁴, adeoque si gravitas prior exponatur per _k_,
posterior exprimetur per _h_ - 3_hb_² ⁄ 5_l_² quamproximè. Unde cum
sit DC = _h_, patet gravitatem corporis S in sphæroidem oblatam non
tendere ad centrum C, sed ad punctum _c_ rectæ DC in plano æquatoris
jacentis vicinius puncto D.


PROPOSITIO I.

PROBLEMA.

_Vires determinare quibus perturbatur motus Satellitis circa Primarium
suum revolventis._

Exhibeat jam sphærois prædicta planetam quemvis figurâ hac donatum,
et corpus S satellitem circa planetam tanquàm primarium gyrantem.
Quantitas materiæ globo sphæroidis interiori incumbentis æqualis est
4_bbc_D ⁄ 3_a_ sive 4_bc_D ⁄ 3 proximè, et si materia illa locaretur
in centro sphæroidis C, attraheret satellitem S secundum SC vi 4_bc_D
⁄ 3_l_², quæ reducta ad directionem SD fit 4_bck_D ⁄ 3_l_³, et ad
directionem DC fit 4_bch_D ⁄ 3_l_³. Cum igitur vis 4_bc_D ⁄ 3_l_² non
turbat motum satellitis, utpote quæ tendat ad centrum motûs et quadrato
distantiæ ab eodem centro sit reciprocè proportionalis, vires illæ
4_bck_D ⁄ 3_l_³, 4_bch_D ⁄ 3_l_³, in quas resolvitur, etiam motum non
turbabunt. Itaque ex vi D × _c_ × (4_kb_ ⁄ 3_l_³ - 4_kb_³ ⁄ 5_l_⁵ +
2_khhb_³ ⁄ _l_⁷) auferatur vis 4_bck_D ⁄ 3_l_³, et ex vi D × _c_ ×
(4_hb_ ⁄ 3_l_³ + 2_hb_³ ⁄ 5_l_⁵ - 2_hkkb_³ ⁄ _l_⁷) auferatur 4_bch_D
⁄ 3_l_³, et remanebunt vires D × _c_ × - (4_kb_³ ⁄ 5_l_⁵ + 2_khhb_³ ⁄
_l_⁷), D × _c_ × (2_hb_³ ⁄ 5_l_⁵ - 2_hkkb_³ ⁄ _l_⁷), motuum satellitis
S perturbatrices. Designetur vis D × _c_ × (2_hb_³ ⁄ 5_l_⁵ - 2_hhkb_³ ⁄
_l_⁷) per rectam S_r_ (_Fig. 2._) ac resolvatur in vim S_q_ tendentem
ad centrum planetæ primarii C et ob triangula similia S_rq_, SDC,
æqualem D × _c_ × (2_b_³ ⁄ 5_l_⁴ - 2_kkb_³ ⁄ _l_⁶), existentibus ut
priùs, SD = _k_, DC = _h_, SC = _l_; et in vim _rq_ rectæ SD parallelam
et æqualem D × _c_ × (2_kb_³ ⁄ 5_l_⁵ - 2_k_³_b_³ ⁄ _l_⁷); atque hæc vis
posterior subducta ex vi D × _c_ × - (4_kb_³ ⁄ 5_l_⁵ + 2_khhb_³⁄_l_⁷)
relinquet D × _c_ × 4_kb_³ ⁄ 5_l_⁵ pro vi perturbatrice in directione
SD. Unde cum massa tota planetæ sit 2_ab_D ⁄ 3, gravitas satellitis
tota in planetam erit 2_ab_D ⁄ 3_l_² proximé, vel etiam 2_bb_D ⁄ 3_l_²,
et hæc gravitas est ad vim D × _c_ × 4_kb_³ ⁄ 5_l_⁵ ut 1 ad 6_kbc_ ⁄
5_l_³.

Deinde vis illius D × _c_ × 4_kb_³ ⁄ 5_l_⁵ secundum SD pars ea quæ agit
in directione SC est D × _c_ × 4_kkb_³ ⁄ 5_l_⁶, quæ addita vi Sq dat D
× _c_ × (2_b_³ ⁄ 5_l_⁴ - 6_kkb_³ ⁄ 5_l_⁶) vim perturbatricem tendentem
ad centrum planetæ primarii, atque hæc vis est ad satellitis gravitatem
2_bb_D ⁄ 3_l_² in primarium ut 3_bc_ ⁄ 5_l_² - 9_kkbc_ ⁄ 5_l_⁴ ad 1.
_Q. E. I._


COROLL.

Designet CK (_Fig._ 3.) lineam intersectionis planorum æquatoris
planetæ et orbitæ satellitis, et resolvatur vis SD = 6_kbc_ ⁄
5_l_³, quæ agit perpendiculariter ad planum æquatoris, in vim DR
perpendicularem ad planum orbitæ satellitis, et in vim SR jacentem
in eodem plano. Producatur SR donec occurrat CK in K, eritque SK
normalis ad CK, et planum SDK normale ad planum orbis satellitis;
ac proptereà ob similia triangula SDK, SRD, si _m_ denotet sinum ad
radium 1 et _n_ cosinum anguli SKD, inclinationis scilicet orbitæ
satellitis ad æquatorem planetæ, erit DR = SD × _n_ = 6_kbcn_ ⁄
5_l_³, et SR = SD × _m_ = 6_kbcm_ ⁄ 5_l_³, existente 1 gravitate totâ
satellitis in primarium suum. Jam quoniam vis SR jacet in plano orbitæ
satellitis, hujus plani situm non mutat; accelerat quidem vel retardat
motum satellitis revolventis, sed hæc acceleratio vel retardatio ob
brevitatem temporis ad quantitatem sensibilem non exurgit: vis DR eidem
plano perpendicularis continuò mutat ejus situm, et motum nodi generat,
quem sequenti propositione definiemus.


PROPOSITIO II.

PROBLEMA.

_Invenire motum nodi ex prædictâ causâ oriundum._

Per motum nodi in hac propositione intelligo motum intersectionis
planorum æquatoris planetæ et orbitæ satellitis; orbitam autem
satellitis quamproximé circularem suppono. Esto S locus satellitis in
orbe suo SN cujus centrum C, (_Fig._ 4.) SF arcus centro C descriptus
perpendicularis in circulum æquatoris planetæ FN; SB arcus eodem
centro descriptus perpendicularis ad orbem SN, atque in SB sumatur
lineola S_r_ æqualis duplo spatio, quod satelles percurrere posset
impellente vi DR in Coroll. præced. determinatâ, quo tempore in
orbe suo describeret arcum quàm minimum _p_S: per puncta _r_, _p_,
describatur centro C circulus _rpn_ secans equatorem in _n_, qui
exhibebit situm orbitæ satellitis post illam particulam temporis, nodo
N translato in _n_. Agantur SC, CN, et SH perpendicularis in lineam
nodorum CN, et N_m_ perpendicularis in _rpn_. Jam cum sint lineolæ
S_r_, N_m_, ut sinus arcuum S_p_, SN, erit S_p_. S_r_∷ SH. N_m_; deinde
in triangulo rectangulo N_mn_ habetur _m_. 1∷ N_m_. N_n_; unde per
compositionem rationum S_p_ × _m_. S_r_∷ SH. N_n_ = ((S_r_ × SH) ⁄
(S_p_ × _m_)): dato igitur arcu S_p_, est N_n_ sive motus nodi ut S_r_
× SH. In triangulo sphærico rectangulo SFN est sinus anguli N, hoc est,
anguli inclinationis orbitæ satellitis ad æquatorem planetæ, ad sinum
arcûs SF, ut radius ad sinum arcûs SN, id est, _m_. (_k ⁄ l_)∷ 1. SH,
adeoque _k ⁄ l_ = _m_ × SH; est igitur _k ⁄ l_ ut SH. Vis autem S_r_
per Coroll. Prop. præced. est ut _k ⁄ l_, adeoque ut SH; quamobrem
est S_r_ × SH, proindeque et N_n_, ut (SH)², hoc est, motus horarius
nodi vi præfatâ genitus est in duplicatâ ratione distantiæ satellitis
à nodo. Et quoniam summa omnium (SH)², quo tempore satelles periodum
suam absolvit, est dimidium summæ totidem (SC)², ideò motus periodicus
est subduplus ejus qui, si satelles in declinatione suâ maximâ ab
æquatore planetæ continuò perstaret, eodem tempore generari posset.
Sit igitur satelles in maximâ suâ declinatione sive in quadraturâ cum
nodo, eritque SN quadrans circuli, et N_m_ mensura anguli N_pm_ sive
S_pr_, eritque in hoc casu N_n_ sive motus horarius nodi ad N_m_, hoc
est, ad angulum S_pr_, ut 1 ad _m_; est autem angulus S_pr_ ad duplum
angulum, quem subtendit sinus versus arcûs S_p_ satellitis gravitate
in primarium eodem tempore descripti, id est, ad angulum SC_p_ qui est
motus horarius satellitis circa primarium, ut vis S_r_ ad gravitatem
satellitis in primarium, hoc est (per Coroll. Prop. I.), ut (6_kbcn_) ⁄
5_l_³ ad 1, sive, quia est in hoc casu _k_ ⁄ _l_ = _m_, ut (6_bcmn_) ⁄
5_l_² ad 1. Unde conjunctis rationibus est motus horarius nodi ad motum
horarium satellitis ut (6_bcn_) ⁄ 5_l_² ad 1; et si S denotet tempus
periodicum solis apparens, et L tempus periodicum satellitis circa
primarium suum, cum sit motus horarius satellitis ad motum horarium
solis ut S ad L, erit motus horarius nodi ad motum horarium solis ut
(6_bcn_) ⁄ 5_l_² × S ⁄ L ad 1, et in eadem ratione erit motus nodi
annuus ad motum solis annuum, hoc est, ad 360°. Quarè, si satelles
maneret toto anno in maximâ suâ declinatione ab æquatore primarii, vis
prædicta ex figurâ sphæroidicâ planetæ primarii proveniens generaret
eodem tempore motum nodi æqualem (6_bcn_) ⁄ 5_l_² × S ⁄ L × 360°, et
ex supradictis motus verus nodi annuus erit hujus subduplus, nempe
(3_bcn_) ⁄ 5_l_² × S ⁄ L × 360°. _Q. E. I._


COROLL.

Si computatio instituatur pro lunâ, assumendo mediocrem ejus orbitæ
inclinationem ad æquatorem terrestrem, erit _n_ cosinus anguli 23°
28´½; et posito semiaxi terræ _b_ = 1, erit distantia lunæ à centro
terræ mediocris _l_ = 60 circiter, indeque in hypothesi quod sit
differentia semiaxium _c_ = ¹⁄₂₂₉, erit (3_bcn_) ⁄ (5_l_²) × S ⁄ L ×
360° = 11´´ ½; et si fuerit _c_ = ¹⁄₁₇₇, manente terrâ uniformiter
densâ, erit ille motus = 15´´. Hic erit motus nodorum annuus lunæ
regressivus in plano æquatoris terrestris, qui reductus ad eclipticam,
uti posteà docebitur, pro vario nodorum situ evadet multò velocior.

Notabilis multò magis erit motus intersectionis orbitarum satellitum
Jovis in plano æquatoris Jovialis; et computabitur satis accuratè per
formulam suprà traditam, modò satelles non sit Jovi nimis vicinus.
Sic pro satellite extimo erit L = 16ᵈ 16ʰ 32´, _b_ = 1, _l_ = 25,299
circiter, semiaxium Jovis differentia _c_ = ¹⁄₁₃; et positâ orbis hujus
satellitis inclinatione ad æquatorem Jovis æquali 3°, erit _n_ cosinus
hujus inclinationis, atque inde prodibit (3_bcn_) ⁄ (5_l_²) × S ⁄ L ×
360° = 34´ circiter, motus scilicet nodorum annuus satellitis quarti in
plano æquatoris Jovis in antecedentia. Si minùs vel magìs inclinatur
orbis ad Jovis æquatorem, augeri vel minui debet hic motus in ratione
cosinûs hujus inclinationis.

Cæterùm patet motum hunc nodorum in plano æquatoris planetæ primarii,
æstimando distantiam satellitis in semidiametris primarii, generatìm
esse, dato tempore, in ratione compositâ, ex ratione directâ
differentiæ semiaxium planetæ et cosinûs inclinationis orbis satellitis
ad planetæ æquatorem, conjunctìm; et ex ratione inversâ temporis
periodici satellitis et quadrati distantiæ satellitis à centro planetæ,
item conjunctìm.


PROPOSITIO III.

PROBLEMA.

_Motum nodorum Lunæ supra determinatum ad Eclipticam reducere._

Sunto NAD (_Fig._ 5.) æquator, AGE ecliptica secans æquatorem in A,
E æquinoctium vernum, A autumnale, LGN orbis lunæ secans eclipticam
in G et æquatorem in N, LD circulus maximus perpendicularis in
æquatorem; et sunto DN, LN, quadrantes circuli. Tempore dato
vi prædictâ transferratur intersectio N in _n_, et describatur
circulus L_gn_ exhibens situm orbis lunaris post illud tempus,
secetque eclipticam in _g_. Ut autem intersectiones N et G sine
verborum ambagibus distinguantur, priorem in posterum vocabo _Nodum
Æquatorium_, posteriorem _Nodum Eclipticum_. Ductis itaque N_m_, G_d_,
perpendicularibus in orbem lunæ, est N_n_: N_m_∷ 1: sin. GNA, et N_m_:
G_d_∷ 1: sin. LG, itemque G_d_: G_g_∷ sin. G_gd_: 1; unde conjunctis
rationibus provenit N_n_: G_g_∷ sin. G_gd_: sin. GNA × sin. LG, adeoque
G_g_ = N_n_ × (sin. GNA × sin. LG) ⁄ sin. G_gd_. Scribantur _s_ pro
sinu et _t_ pro cosinu anguli G_gd_, inclinationis scilicet orbitæ
lunaris ad eclipticam, ad radium 1, _v_ pro sinu et _u_ pro cosinu
arcûs EG, _p_ pro sinu et _q_ pro cosinu obliquitatis eclipticæ; atque
per resolutionem trianguli sphærici GAN, habebitur cos. GNA = _n_ =
_qt_ + _psu_, indeque sin. GNA = √(1 - _qqtt_ - 2_pqstu_ - _p_² _s_²
_u_²); sed scribi potest 1 pro _t_, et rejici terminus _p_² _s_² _u_²
ob exiguitatem sinûs _s_ anguli 5° 8´ ½, proindeque erit sin. GNA =
√(_pp_ - 2_pqsu_); prætereà est sin. GNA: sin. GA sive _v_∷ sin. GAN
sive _p_: sin. GN, ideoque sin. GN sive cos. LG = (_pv_ ⁄ sin. GNA),
et sin. LG = _u_ - (_qsvv_ ⁄ _p_), ac sin GNA × sin. LG = pu - qs
quamproximé. Quarè fit Gg = Nn × ((_pu_ - _qs_) ⁄ _s_), atque hic est
motus nodorum lunarium tempore dato in plano eclipticæ: quod si tempus
illud datum sit annus solaris, habetur N_n_ = (3_bcn_ ⁄ 5_l_²) × (S
⁄ L) × 360°, unde motus ille eclipticus nodorum annuus, nullâ habitâ
ratione mutationis sitûs nodorum ex aliâ causâ per id temporis factæ,
fiet (3_bc_ ⁄ 5_l_²) × (_qt_ + _psu_) × ((_pu_ - _qs_) ⁄ _s_) × (S ⁄ L)
× 360°, vel etiam (3_bcq_ ⁄ 5_l_²) × ((_pu_ - _qs_) ⁄ _s_) × (S ⁄ L) ×
360° proximé. _Q. E. I._

Quo motum nodi lunaris in hac propositione ad eclipticam reduximus,
eodem prorsùs ratiocinio motus nodi satellitis cujusvis ad orbitam
planetæ primarii reducetur.


COROLL. I.

Exinde liquet nullum esse hunc motum nodi, ubi sin. LG = 0, vel etiam
ubi _pu_ = _qs_, quod contingit ubi orbitæ lunaris arcus GN eclipticam
et æquatorem æqualis est 90°, sive ubi nodi lunares versantur in
punctis declinationis lunaris maximæ, sive ubi arcus AG, cujus cosinus
est _u_, evadit æqualis 78° 5´, id est, ubi nodus ascendens lunæ
versatur in 11° 55´ Cancri, vel 18° 5´ Sagittarii. Eritque progressivus
hic motus, id est, fiet secundum seriem signorum, dum nodus ascendens
lunæ transit retrocedendo ab 18° 5´ Sagittarii ad 11° 55´ Cancri,
regressivus autem in reliquâ parte revolutionis; et maximus evadit
motus regressivus, ubi _u_ = -1, id est, ubi nodus ascendens versatur
in principio Arietis; et maximus progressivus, ubi _u_ = 1, id est,
ubi idem nodus occupat initium Libræ. Itaque cùm motus ille nodorum
annuus, de quo hîc agitur, universaliter sit æqualis (3_bcq_ ⁄ 5_l_²) ×
((_pu_ - _qs_) ⁄ _s_) × (S ⁄ L) × 360°, hoc est, per Coroll. Prop. 2.
æqualis 11´´ ½ × ((_pu_ - _qs_) ⁄ _s_) vel 15´´ × ((_pu_ - _qs_) ⁄ _s_)
prout differentia semiaxium terræ fuerit ¹⁄₂₂₉ vel ¹⁄₁₇₇, existentibus
scilicet _p_ sinu et _q_ cosinu anguli 23° 28´ ½, atque _s_ sinu anguli
5° 8´ ½; eo anno, in cujus medio circiter nodus lunæ ascendens tenuerit
principium Arietis, motus nodorum regressivus, qui et maximus, erit
1´ 2´´ vel 1´ 20´´; ubi verò idem nodus subierit signum Libræ, motus
maximus progressivus erit 41´´ vel 53´´. In aliis nodorum positionibus
eodem modo computabitur.


COROLL. II.

Si desideretur excessus regressûs nodi supra progressum in integrâ
nodi revolutione, sequenti ratione investigabitur. Jungantur equinoctia
diametro EA, in quam demittatur perpendiculum GK, et sumpto arcu
G_h_ quem describit nodus eclipticus G quo tempore nodus equatorius
N describit arcum N_n_, ducatur _hc_ perpendicularis in GK. Per hanc
propositionem est G_g_. N_n_∷ ((_pu_ - _qs_) ⁄ _s_). 1, sive, quia
est 1. _u_ ∷ G_h_. G_c_, fit G_g_. N_n_∷ ((_p_ × G_c_) ⁄ _s_) - _q_ ×
G_h_. G_h_; adeoque summa omnium G_g_ erit ad summam omnium N_n_, hoc
est, motus nodi ecliptici in integrâ sui revolutione erit ad motum nodi
æquatorii eodem tempore factum, ut summa omnium in circulo quantitatum
((_p_ × G_c_) ⁄ _s_) - _q_ × G_h_ ad summam totidem arcuum G_h_, hoc
est, ut - _q_ ad 1. Signum autem--denotat motum fieri in antecedentia
sive regressum nodi excedere ejusdem progressum. Unde cum motus nodi
æquatorii N fit 11´´ ½ vel 15´´ quo tempore nodus eclipticus describit
19° 20´ ½, motus ille nodi æquatorii tempore nodi ecliptici periodico
evadit 11´´ ½ × (360° ⁄ 19° 20´ ½) = 3´ 34´´ vel 15´´ × (360° ⁄ 19° 20´
½) = 4´ 39´´; quo pacto prodit motus nodi ecliptici præfatus æqualis
_q_ × 3´ 34´´ vel _q_ × 4´ 39´´, proindeque _est radius ad cosinum
obliquitatis eclipticæ ut_ 3´ 34´´ _vel_ 4´ 39´´ _ad motum quæsitum_,
nempe 3´ 16´´, existente ¹⁄₂₂₉ differentiâ axium terræ, vel 4´ 16´´ eâ
existente ¹⁄₁₇₇: atque hic est excessus regressûs nodi supra progressum
in integrâ nodi revolutione vi prædictâ genitus. Excessu igitur hoc
minuatur motus nodi lunaris periodicus 360°, et remanebit motus ille
quem generat vis solis.


PROPOSITIO IV.

PROBLEMA.

_Variationem inclinationis orbis lunaris ad planum eclipticæ ex figurâ
terræ spheroidicâ ortam determinare._

Esto ANH (_Fig._ 6.) æquator, AG ecliptica, et A punctum æquinoctii
autumnalis: fit NGRM orbis lunæ secans eclipticam in G et æquatorem in
N, in quo sumantur arcus NL, GR, æquales quadrantibus circuli. Jam
si nodus æquatorius N per temporis particulam vi prædictâ transferri
intelligatur in _n_, et per punctum L describatur circulus _n_L_r_,
exhibebit hic situm orbis lunæ post tempus elapsum, et si in eumdem
demittantur perpendicula N_m_ et R_r_, posterius R_r_ designabit
variationem inclinationis orbitæ lunaris ad eclipticam eodem tempore
genitam. Est autem N_n_: N_m_∷ 1: _m_, itemque N_m_: R_r_∷ 1: sin. LR;
sed ob NL = GR, est NG = LR; unde conjunctis rationibus est N_n_: R_r_∷
1: _m_ × sin. NG; ex quo patet variationem inclinationis momentaneam
esse proportionalem sinui distantiæ nodi lunaris ecliptici à nodo
æquatorio. Ad diametrum NM demittatur perpendiculum GK, et existente
G_h_ decremento arcûs NG facto quo tempore nodus æquatorius N describit
arcum N_n_, agatur _hk_ parallela ipsi GK, eritque 1: GK sive sin.
NG∷ G_h_. K_k_; proindeque jam erit N_n_: R_r_∷ G_h_: _m_ × K_k_,
adeoque summa omnium variationum R_r_, quo tempore nodus eclipticus
G descripsit arcum MG, genitarum erit ad summam totidem motuum N_n_,
hoc est, ad motum nodi æquatorii N eodem tempore factum, ut summa
omnium K_k_ ducta in _m_, ad summam totidem arcuum G_h_, id est, ut
_m_ × MK ad MG. Sit NH motus nodi N tempore revolutionis nodi G ab uno
equinoctio ad alterum, eritque variatio inclinationis eodem tempore
genita, hoc est, variatio tota æqualis ((2_m_ × NH) ⁄ MGN). Unde cùm NH
⁄ MGN exprimat rationem motûs nodi æquatorii ad motum nodi ecliptici,
prodit theorema sequens: _Est motus nodi lunaris ecliptici ad motum
nodi æquatorii, ut sinus duplicatus inclinationis mediocris orbitæ
lunaris ad æquatorem, ad sinum variationis totius inclinationis ejusdem
orbitæ ad eclipticam._

In hoc computo inclinationem mediocrem orbis lunaris ad æquatorem,
nempe 23° 28´ ½, usurpo, cum in revolutione nodi tantum ex unâ
parte augetur, quantum ex alterâ minuitur, et omnes minutias hîc
expendere supervacaneum foret. Motus autem nodi lunaris ecliptici
est ad motum nodi lunaris æquatorii ut 19° 20´ ½ ad 11´´ ½ vel 15´´,
sive ut 6055 vel 4642 ad 1, unde per theorema supra traditum prodit
variatio inclinationis tota æqualis 27´´ vel 35´´, prout differentia
axium terræ statuitur ¹⁄₂₂₉ vel ¹⁄₁₇₇. Hac igitur quantitate augetur
inclinatio orbis lunaris ad eclipticam in transitu nodi ascendentis
lunæ ab æquinoctio vernali ad autumnale, et tantumdem minuitur in
alterâ medietate revolutionis nodi. In loco quolibet G inter æquinoctia
variatio inclinationis est ad variationem totam ut sinus versus arcûs
MG ad diametrum, ut patet; sive differentia inter semissem variationis
totius et variationem quæsitam est ad ipsam semissem variationis totius
ut cosinus arcûs MG ad radium, hoc est, ut _u_ - (_qsvv_ ⁄ _p_) ad 1.
_Q. E. I._


PROPOSITIO V.

PROBLEMA.

_Motum apsidum in orbe satellitis quamproximé circulari, quatenùs ex
figurâ planetæ primarii sphæroidicâ oritur, investigare._

Per propositionem primam vis perturbatrix, quâ trahitur satelles
ad centrum planetæ primarii, est ad satellitis gravitatem in ipsum
primarium, ut (3_bc_ ⁄ 5_l_²) - (9_kkbc_ ⁄ 5_l_⁴) ad 1, sive, quia
per Prop. 2. est (_k ⁄ l_) = _m_ × SH (_Fig._ 4.) ponendo scilicet
_m_ pro sinu inclinationis orbitæ satellitis ad æquatorem primarii,
et scribendo _y_ pro SH, ut (3_bc_ ⁄ 5_l_²) × (1 - 3_m_²_y_²) ad 1;
et summa harum virium in totâ circumferentiâ cujus radius est 1, est
ad gravitatem satellitis toties sumptam ut (3_bc_ ⁄ 5_l_²) × (1 -
(3_m_² ⁄ 2)) ad 1. Vis igitur mediocris, quæ uniformiter agere in
satellitem supponi potest, dum revolutionem suam in orbitâ propemodùm
circulari absolvit, est ad ejus gravitatem in primarium ut (3_bc_ ⁄
5_l_²) × (1 - (3_m_² ⁄ 2)) ad 1; atque hac vi movebuntur apsides, si
nulla habeatur ratio vis alterius quæ orbis radio est perpendicularis
et per medietatem revolutionis satellitis in unum sensum tendit, per
alteram medietatem in contrarium. Jam quia ex demonstratis in hac et
primâ propositione sequitur gravitatem satellitis circa planetam, cujus
figura est sphærois oblata, revolventis in distantiâ _l_ generaliter
esse ad ejusdem gravitatem in majori distantiâ L, ut (1 ⁄ _l_²) + (B ⁄
_l_⁴) × (1 - (3_m_² ⁄ 2)) ad (1 ⁄ L²) + (B ⁄ L⁴) × (1 - (3_m_² ⁄ 2)),
existente B quantitate datâ exigui valoris, sive ut (1 ⁄ _l_²) ad (1
⁄ L²) - (B ⁄ _l_²L²) × (1 - (3_m_² ⁄ 2)) + (B ⁄ L⁴) × (1 - (3_m_² ⁄
2)) quamproximé, ideò gravitas satellitis diminuitur in majori quam
duplicatâ ratione distantiæ auctæ quoties _m_ minor est quantitate
√⅔ id est, ubi inclinatio orbitæ satellitis ad planetæ æquatorem non
attingit 54° 44´; diminuitur autem in minori ratione, quoties est _m_
major quàm √⅔, id est, ubi illa inclinatio superat 54° 44´; adeoque
in priore casu progrediuntur apsides orbis satellitis, in posteriori
regrediuntur. Quantitas autem hujus progressûs vel regressûs sic
innotescet.

Per exemplum tertium prop. 45 lib. 1. _Princ. Math. Newt._ si vi
centripetæ, quæ est ut 1 ⁄ _l_², addatur vis altera ut _e ⁄ l_⁴, hoc
est, quæ sit ad vim centripetam 1 ⁄ _l_² ut _e ⁄ l_² ad 1, angulus
revolutionis ab apside unâ ad eamdem erit 360° √((1 + _e_) ⁄ (1 -
_e_)) vel 360° ⁄ (1 - _e_) quamproximé, existente _e_ quantitate valdé
minutâ. Porrò cum sit motus satellitis in orbitâ suâ revolventis ad
motum apsidis ut 360° ⁄ (1 - _e_) ad 360° ⁄ (1 - _e_) - 360°, hoc est,
ut 1 ad _e_, erit motus apsidis tempore revolutionis satellitis ad
fidera æqualis 360° × _e_, et hic motus apsidis erit ad ejusdem motum
tempore alio quovis dato ut tempus periodicum satellitis ad tempus
datum. Est autem in hac nostrâ propositione _e_ = (3_bc_ ⁄ 5_l_²) × (1
- (3_m_² ⁄ 2)); unde datur motus apsidum quæsitus. _Q. E. I._


COROLL.

Si ad lunam referatur hæc determinatio, habebuntur _b_ = 1, _l_ = 60,
_m_ = sinui anguli 23° 28´ ½, et si fuerit _c_ = ¹⁄₂₂₉, erit _e_ =
¹⁄₁₈₀₃₂₀₃, atque motus apogæi lunæ spatio centum annorum æqualis 16´
proximé in consequentia; si fuerit _c_ = ¹⁄₁₇₇, erit _e_ = ¹⁄₁₃₉₃₇₄₂,
et motus apogæi æqualis 20´, 7. Hac igitur quantitate minuendus est
motus medius apogæi lunæ prout observationibus determinatur, ut
habeatur motus ille quem generat vis solis.

Pro quarto autem Jovis satellite, erunt _b_ = 1, _l_ = 25,299, _c_ =
¹⁄₁₃, _m_ = sinui anguli 3°, _e_ = ¹⁄₁₃₉₂₄,₇; hincque motus apsidis
spatio unius anni solaris prodit 33´, 95 vel ferè 34´ in consequentia,
qui tempore annorum decem fit 5° 40´. Insuper autem notandum est vi
solis perturbari motum satellitis simili modo quo perturbatur motus
lunæ; ideoque, quoniam vis solis, quâ perturbatur motus lunæ est ad
lunæ gravitatem in terram in duplicatâ ratione temporis periodici lunæ
circa terram ad tempus periodicum terræ circa solem, hoc est, ut 1 ad
178,725; pariter vis solis, qua perturbatur motus satellitis Jovialis,
est ad ipsius satellitis gravitatem in Jovem in duplicatâ ratione
temporum periodicorum satellitis circa Jovem et Jovis circa solem, hoc
est, ut 1 ad 67394,6: vires igitur, quibus perturbantur motus lunæ
et satellitis, sunt ad se invicem, relativé ad eorum gravitates in
planetas suos primarios ut ¹⁄₁₇₈,₇₂₅ ad ¹⁄₆₇₃₉₄,₆ sive ut 37,708 ad
1. Unde cum viribus similibus proportionales sunt motus his viribus
dato tempore geniti, si vis prior vel ejusdem vis pars quælibet
motum apsidis generat æqualem 40° 40´ ½ in orbe lunari annuatìm, vis
posterior vel ejusdem pars similis et proportionalis motum apsidis
eodem tempore generabit æqualem 6´ ½ in orbe satellitis, atque decem
annorum spatio 1° 5´ in consequentia. Addatur 1° 5´ ad 5° 40´, et motus
apsidum totus in orbe satellitis extimi Jovialis ex duabus prædictis
causis oriundus spatio decem annorum erit 6° 45´ in consequentia.
Observationibus Astronomicis collegit Ill. _Bradleius_ hunc motum
tempore prædicto esse quasi 6°; differentia illa qualiscumque 45´ inter
motum observatum et computatum actionibus satellitum interiorum debebit
ascribi.


SCHOLIUM.

Ex præcedentibus colligere licet motuum lunarium inæqualitates originem
suam omnem non ducere ex vi solis, sed earum partem aliquam deberi
actioni Telluris quatenùs induitur figurâ sphæroidicâ. Sufficiat hîc
illarum computasse valorem, et legem, quâ generantur, demonstrasse:
utrum autem hujusmodi correctiones tales sint ut tabulis Astronomicis
inscribi mereantur, dijudicent Astronomi.

Item manifestum est præter inæqualitates eas, quæ in motibus satellitum
Jovialium ex vi solis et actionibus satellitum in se invicem nascuntur,
oriri alias ex figurâ Jovis sphæroidicâ ita notabiles ut Observationes
Astronomicas continuò afficere debeant.


_De Variatione motûs Terræ diurni._

Si terra globus esset omninò sphæricus quicumque foret revolutionis
axis, manente eâdem in globo motûs quantitate, eadem maneret rotationis
velocitas: secùs autem est, ubi ob vires solis et lunæ terra induit
formam sphæroidis oblongæ per aquarum ascensum. Hîc enim non considero
figuram telluris oblatam ob materiæ in æquatore redundantiam, sed
sphæricam suppono nisi quatenùs per aquarum elevationem et depressionem
in sphæroidicam mutatur. Jam verò in sphæroide hujusmodi, quamvis eadem
maneat motûs quantitas, mutatâ inclinatione axis transversi ad axem
revolutionis, mutabitur revolutionis velocitas, uti satis manifestum
est: cùm autem axis transversus transit semper per solem vel lunam,
singulis momentis mutabit situm suum respectu axis revolutionis ob
motum quo hi duo planetæ recedunt ab æquatore terrestri et ad eum
vicissìm accedunt.


PROBLEMA.

_Variationem motûs terræ diurni ex prædictâ causâ oriundam investigare._

Exhibeat sphærois oblonga ADC_d_ (_Fig._ 7.) terram fluidam, cujus
centrum T, AC axis transversus jungens centra terræ et solis vel lunæ,
D_d_ axis minor, EO diameter æquatoris, et XZ axis motûs diurni. Centro
T et radio TD describatur circulus BD_d_ secans axem transversum
AC in B, et agatur BK perpendicularis in TE: tum ex quovis circuli
puncto P ductâ PM ad axem XZ normali quæ secet TA in H, sit P_pr_
circumferentia circuli quam punctum P rotatione suâ diurnâ describit,
ad cujus quodvis punctum _p_ ducatur T_p_ et producatur donec occurrat
superficiei sphæroidis in _q_; deinde demissâ _p_G perpendiculari
in PM, et GF perpendiculari in TA, si per puncta A_q_C transire
intelligatur ellipsis ellipsi ADC similis et æqualis, erit ex naturâ
curvæ, quia sphærois nostra parùm admodùm differt à sphærâ, _pq_ = AB
× ((TF)² ⁄ (TP)²) quamproximé. Jam designet U velocitatem particulæ in
terræ æquatore revolventis motu diurno circum axem XZ ad distantiam
semidiametri TP, eritque ((U × PM) ⁄ TP) velocitas particulæ P circulum
P_pr_ describentis, et cum sit TF =(((GM - HM) × TK) ⁄ TP) + TH, erit
motus totius lineolæ _pq_ æqualis _pq_ × ((U × PM) ⁄ TP) = ((U × AB ×
PM) ⁄ (TP)³) × (((GM - HM) × (TK)²) ⁄ TP) + TH, adeoque summa horum
motuum in circuitu circuli P_pr_, hoc est, motus superficiei inter
circulum P_pr_ et sphæroidem in directione T_p_ contentæ, æquabitur
circumferentiæ hujus circuli ductæ in ((U × AB × PM) ⁄ (TP)³) × (((TK)²
× (PM)²) ⁄ 2(TP)²) + ((TK)² × (HM)²) ⁄ (TP)²) - ((2TK × HM × TH) ⁄ TP)
+ (TH)²) sive quia est HM. TM ∷ TK. BK, et TH. HM∷ TP. TK, scribendo
D pro circumferentiâ circuli BD_d_, æquabitur ille motus quantitati
((U × AB × D) ⁄ 2(TP)⁶) × ((TK)² × (PM)⁴ + 2(BK)² × (TM)² × (PM)²).
Deinde horum motuum summa in toto circuitu globi collecta, hoc est,
motus totius materiæ globo BD_d_ incumbentis prodibit æqualis ((U ×
AB × DD) ⁄ 32) x ((3(TP)² - (BK)²) ⁄ (TP)²). Ubi planeta in plano
æquatoris consistit, fit BK = 0, et motus prædictus æqualis ((U × 3AB
× DD) ⁄ 32). Motus autem globi QPR circa eumdem axem est (uti facilé
demonstratur) ((U × TP × DD) ⁄ 16), adeoque motus terræ totius fit ((U
× TP × DD) ⁄ 16) + ((U × AB × DD) ⁄ 32) × ((3(TP)² - (BK)²) ⁄ (TP)²),
qui cum idem semper manere debeat, denotet V velocitatem in superficie
æquatoris terrestris ubi planeta versatur in plano æquatoris, eritque
((U × TP × DD) ⁄ 16) + ((U × 3AB × DD) ⁄ 32) = ((U × TP × DD) ⁄ 16)
+ ((U × AB × DD) ⁄ 32) × ((3(TP)² - (BK)²) ⁄ (TP)²); unde scribendo
1 pro TP quatenùs est radius ad sinum BK anguli BTK, habetur V. U∷
TP + (3AB ⁄ 2) - ((AB × (BK)²) ⁄ 2). TP + (3AB ⁄ 2), indeque, quia
minima est altitudo AB respectu semidiametri TP, U - V. V∷ AB × (BK)².
2TP, et U - V = V × ((AB × (BK)²) ⁄ 2TP): pro V autem patet scribi
posse velocitatem angularem terræ mediocrem quia ab eâ differt quam
minimé et ducitur in quantitatem perexiguam ((AB × (BK)²) ⁄ 2TP), et
quia tempora revolutionum terræ circa centrum suum sint reciprocé ut
motus angulares U, V, fiet differentia revolutionum terræ ubi planeta
æquatorem tenet et ubi ab æquatore distat angulo BTK, æqualis 23ʰ 56´
× (AB × (BK)²) ⁄ 2TP. Quoniam igitur est acceleratio horaria ad motum
terræ horarium mediocrem circa centrum suum ut AB × (BK)² ad 2 TP sive
(quia est sinus _p_ inclinationis eclipticæ ad æquatorem ad radium 1
ut sinus BK ad sinum distantiæ planetæ ab æquinoctio, quem sinum dico
K) ut AB × _p_² × K² ad 2 TP; adeoque acceleratio horaria rotationis
terræ crescit in ratione duplicatâ sinûs distantiæ planetæ à puncto
æquinoctii, et summa omnium illarum accelerationum, quo tempore transit
planeta ab æquinoctio ad solstitium, est ad summam totidem motuum
horariorum mediocrium, hoc est, acceleratio tota eo tempore genita est
ad tempus illud ut summa quantitatum omnium AB × _p_² × K² in circuli
quadrante ad summam totidem 2TP, id est, quia summa omnium K² in
circuli quadrante dimidium est summæ totidem quadratorum radii, ut AB ×
_p_² ad 4 TP. Quamobrèm, si denotet P quartam partem temporis planetæ
periodici circa terram, erit acceleratio tota motûs terræ circum axem
suum in transitu planetæ ab æquinoctio ad solstitium genita æqualis
(AB × P × _p_²) ⁄ 4TP, atque eadem erit retardatio in transitu planetæ
à solstitio ad æquinoctium. Unde sponte nascitur hoc Theorema: _Est
quadratum diametri ad quadratum sinûs obliquitatis eclipticæ ut quarta
pars temporis periodici solis vel lunæ ad tempus aliud_; deinde, _est
semidiameter terræ ad differentiam semiaxium ut tempus mox inventum ad
accelerationem quæsitam_.

Ascensus aquæ AB vi solis debitus est duorum pedum circiter,
existente semidiametro terræ mediocri TP = 19615800, unde prodit per
theorema acceleratio terræ circa centrum suum gyrantis facta quo
tempore incedit sol ab æquinoctio ad solstitium, æqualis 1´´´ 55ⁱᵛ
in partibus temporis; et si vi lunæ ascendunt aquæ ad altitudinem
octo pedum, acceleratio revolutionis terræ inde orta, quo tempore
luna transit ab æquatore ad declinationem suam maximam, erit 34ⁱᵛ: et
summa harum accelerationum, quæ obtinet ubi hi duo planetæ in punctis
solstitialibus versantur, cum non superet duo minuta tertia temporis
cum semisse sive 37 minuta tertia gradûs, vix observabilis erit. _Q. E.
I._

Cùm igitur tantilla fit hujusmodi variatio in hypothesi sphæricitatis
terræ; qualis evaderet, terrâ existente sphæroide oblatâ, frustrà quis
inquireret.




CXI. _Some Observations on the History of the_ Norfolk _Boy. By_ J.
Wall, _M. D. In a Letter to the Rev._ Charles Lyttelton, _LL.D. Dean
of_ Exeter.

[Read Dec. 14, 1758.]

SIR,

THE history of the Norfolk Boy, which, you inform me, has been
communicated to the Royal Society, seems to deserve a place in the
memoirs of that illustrious body, as well on account of its utility, as
its singularity.

The symptoms in this case most evidently arose from worms in the
intestines; which often occasion unaccountable complaints, and
frequently elude the most powerful medicines, as they did in the
instance before us, till at last they were dislodged by the enormous
quantity of oil-paint, which the poor boy devoured; and the cause being
thus removed, all the effects ceased.

At first sight it appears wonderful, that this immense quantity of
white lead did not prove fatal; and that it was not so, could be owing
to nothing but the oil, by which it was enveloped, and its contact and
immediate action on the coats of the intestines thereby prevented. But
the oil did not only obviate the dangerous effects of this mixture, but
appears, to me at least, to have been the chief cause of the success,
with which it was happily attended. I speak this with some restriction,
because the lead, as its stypticity was thus covered, might, by its
weight, assist in removing the verminous filth, especially as the
bowels were made slippery by the oil.

Oil has long been observed to be noxious to insects of all kinds, so
that not only those, which survive after being cut into several pieces,
but those also, which live long with very little air, and those, which
revive by warmth after submersion in water, die irrecoverably, if they
are immerged in, or covered with oil. Rhedi and Malpighi have made many
experiments to this purpose; and account for the event very rationally
from the oil stopping up all the air-vessels, which in these animalcula
are very numerous, and distributed almost over their whole bodies.

On this account oil has been recommended as a vermifuge both by Andry
and Hoffmann, though I believe it has been seldom used in practice in
that intention; or at least has not been given in quantities sufficient
to answer it. Indeed Hoffmann[222] himself seems not to lay much
stress on it as an anthelmintic, recommending it only as serving
to line the inside of the intestines, and to relax spasms in them;
and therefore as a proper preparative to be given before any acrid
purgatives are ventured on.

The medicines commonly prescribed, and most depended on, are either
of a virulent and drastic nature, or such as are supposed to be able
to destroy those animals by some mechanical qualities _e. g._ to cut,
tear, or otherwise affect their tender bodies, and yet not have force
enough to lacerate or injure the stomach or intestines. Of the former
kind are the leaves and juice of helleboraster, the bark of the Indian
cabbage-tree, coloquintida, resin of jalap, glass of antimony, and
the like; the effects of which are commonly violent and dangerous,
and sometimes fatal. Of the latter class are crude mercury, and the
milder preparations of that mineral, aloes and other bitters, tin
filings, neutral salts, and vitriolic acids. Every one conversant in
practice too well knows, how often these medicines are administred
ineffectually. When I had therefore attentively considered the history
of the Norfolk Boy, I determined to try the efficacy of oil in such
cases, as it seemed capable of producing great effects, and yet could
not be attended with any hazard or danger.

The first person, to whom it was given, with this view, was ----
----, a patient of our Infirmary, who was judged to have worms, but
had taken several approved medicines for a considerable time without
success. In a consultation with the other physicians, the following
form was prescribed.

  ℞. _Ol. Oliv. lb.ss. Sp. vol. aromat. ʒij M. cap. Cochl. iii. mane et
  H. S._

The volatile spirit was added here to make the oil saponaceous, and
by that means more easily miscible with the juices in the stomach and
_primæ viæ_. This medicine answered our expectations, and in a few days
brought away several worms.

---- Lacy, a poor boy of the parish of Feckenham in this county, aged
13 years, was, as I was informed, about three or four years ago seized
with convulsive fits, which gradually deprived him of his senses, and
reduced him to a state of idiocy. He had taken several anthelmintics
and purgatives, particularly the _Pulv. Cornachin._ but never had
voided any worms, though all the symptoms seemed plainly to shew, that
they were the cause of his disorder. As he greedily swallowed any
thing, which was offered him, without distinction, I at first ordered
him a mixture of linseed oil ℥vij _Tinct. sacr._ ℥j: of which he took
four large spoonfuls night and morning. He persisted in the use of this
one whole week without at all nauseating it, towards the latter end of
which time he voided one round worm of a great length. He now began
to shew much aversion to the medicine; on which account the _Tinctur.
sacr._ was omitted, and he was ordered to take the oil alone in the
same quantities. This he continued to do a fortnight longer, during
which time he voided 60 more worms, and in a great measure recovered
the use of his reason[223]. This account I had from the Apothecary,
who, by my directions, supplied him with the medicines.

Soon after this I ordered the same medicine to be given to Elizabeth
Abell, a poor girl in the same neighbourhood, reduced by epileptic fits
to such a state of idiocy, as to eat her own excrements. It caused her
to void several worms, but she did not recover her senses.

Since this time I have given the oil to several persons with good
success, and therefore I cannot but recommend a further tryal of it;
since it is a remedy, which may be used with safety in almost any
quantity; a character, which very few of the anthelmintic medicines
deserve.

It is probable, that some oils are more destructive to worms than
others. Andry (_Traité de la Generation des Vers, cap. 8_) prefers
nut oil, and tells us, that a human worm, voided alive, being put
into that oil, died instantly; whereas another worm, voided at the
same time, lived several hours in oil of sweet almonds, though in a
languishing state. This difference he afterwards (_Cap. 9_) endeavours
to account for, by supposing, that the oil of almonds is more porous,
and consequently less able to preclude the entrance of air into the
worms. And indeed there is some reason to conclude, that oils, which
dry in the open air, such as nut and linseed oils, are of a closer
texture, less mixed with water, and consequently more anthelmintic,
than those oils, which freeze by cold, and will not dry in the open
air;[224] such as those from olives or almonds. Andry tells us, that at
Milan the mothers have a custom to give their children once or twice
a week toasts dipt in nut oil, with a little wine, to kill the worms:
and I know a lady in the country, who gives the poor children in her
neighbourhood the same oil with great success.

I would recommend this remedy to be used in as large doses as the
stomach will well bear: to which purpose it may be adviseable to join
it either with aromatics, bitters, or essential oils, such as the
case may require. Andry orders the oil to be taken fasting, assigning
this for a reason, that the stomach being then most empty, it more
readily embraces and stifles the worms. During this course it will be
necessary, at proper intervals, to give rhubarb, mercurial or aloetic
medicines.

I cannot close this paper without observing, that, from the history
of the Norfolk Boy, we may learn, in similar cases, where the head is
not idiopathic, never to despair absolutely of a cure, notwithstanding
the disease has been of very long standing. For in this boy, though
the oppression in the brain and nerves had continued many years, and
had been so violent, as to deprive him not only of his intellectual
faculties, but almost all his sensations; yet were not the organs much
impaired thereby, but he recovered all his senses again, as soon as
the irritation and spasms in the intestines, which first caused all
these terrible symptoms, were removed. The same thing in a less degree
was observable in the Feckenham Boy, mentioned before; and we have had
two remarkable instances of the same kind at the Worcester Infirmary;
where a boy and his sister, of the name of Moyses, received a perfect
cure, and recovered the entire use of their senses, after having been
rendered idiots (though not in so high a degree as the Norfolk Boy) for
more than two years, by epileptic fits proceeding from worms.

                                                               J. Wall.

Worcester Dec. 7, 1748.

  _P. S._ As the following history has some analogy with the subject we
  are now upon, I beg leave to subjoin it by way of postscript.

   A young girl of the name of Lowbridge, at Ledbury, in
  Herefordshire, nine years old, had been long troubled with a gnawing
  pain at the stomach, which growing gradually more violent, I was at
  last called to her. About a quarter of an hour before I reached the
  house, she was seized with a violent vomiting, whereby she brought
  up an amazing number of living animals supposed, to be upwards of
  a thousand, together with a vast quantity of clear viscid phlegm.
  In shape they exactly resembled millepedes, except that some of
  them, being examined by a magnifying glass, appeared to have a
  small filament, which arose from the middle of the belly, and might
  probably have served to fix them to their nidus. They were of
  different sizes, from that of the largest millepede, to some, that
  were scarce perceptible; so that they appeared to have been generated
  at different times, and grown in the stomach. As the child was
  suddenly seized with this effort to vomit, she discharged her stomach
  on the floor of the parlour where she was sitting. The millepedes,
  they told me, were at first very lively, and crept briskly different
  ways; but they did not live long in the open air. They were lying in
  the slime when I came to her, so that I could not be imposed on as to
  the verity of the fact. After this evacuation, the child’s stomach
  grew perfectly easy, and continued so.




CXII. _Observations upon the_ Corona Solis Marina Americana; _The_
American Sea-Sun-Crown. _By_ John Andrew Peyssonel, _M.D. F.R.S.
Translated from the_ French.

[Read Dec. 14, 1758.]

I Shall call this insect by this name, because of the resemblance it
bears to the flower called _Corona Solis_; since it is, like this, open
and spread.

This insect adheres to the rocks by its basis, which is flat and round;
and tho’ this roundness is sometimes mis-shapen, it is only occasioned
by the inequalities of the rocks, to which it sticks. Its diameter is
about two or three inches, bearing, from the center, certain rays,
like white nerves, upon a moist flesh, of a livid violet colour.
These rays or nerves pass from the centre to the circumference; they,
too, consist of a soft fleshy substance, which resembles bowels or
intestines; the whole length of which is covered with glandulous bodies
of a dirty grey colour; and all these glands filled up the middle of
the fish, making the flowrets, or petals, that form the disk of the
flowers. There is an infinite number of these glands attached to those
filets or nerves, all very distinct from one another: these filets are
well ranged when viewed downwards; but the upper part is covered by
these glands, which are placed in a confused manner. These filets pass
to the circumference, forming an edge full of rugosities, which leaves
the body of the animal full of flaws. These hard bodies, upon which
it lives, are not always permanent in the same place, but capable of
changing their places from this edge or circumference; like a skin or
texture of fibres or flesh, such as the body of the sea snail I have
already described; of the same thickness, of a greenish colour, and
sometimes of a greenish spotted grey, without shell, bone, or stay. The
body or muscular fleshy skin raises itself up perpendicularly to three
inches; rounds itself at the top, when it is touched; but it leaves
a hole like a sphincter, formed by the reunion of the fleshy body,
which enlarges itself again. The base opens to the whole extent of the
bottom, makes a reversed prepuce, and immediately brings to view three
rows of _papillæ_, which are of a conical figure, of one or two lines
long, resembling the glands under the tongues of oxen, and which may
here be compared to the demi-flowers or radiated flowers of the _Corona
Solis_.

After this threefold ray of conical pointed _papillæ_, there appears a
body of a livid violet colour; I took it for a particular substance
or body; but having examined it, I observed it was only a pellicle,
or membrane, that covered a part of the _papillæ_ I mentioned. This
membrane has sixteen separations, which form kinds of purses, and yet
leave, in the center of the animal, an empty space, wherein several
glands are brought in view. I do not know, whether, in the natural
state, these membranes do not retire to the circumference, in order to
discover the glands within, which they usually hide, and which fill
up all the middle of the crown; but when the fleshy body is gone up
again, it covers all the interior parts, closes them in, and preserves
them from the touch of any extraneous body. I cannot tell how these
fishes live, or what is their mechanism; for I could not distinguish
either a mouth, or any _viscera_, nor any other organ serving to their
nourishment.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXXIV. _p. 845_.

Lepades Pedatæ.

  1. _Lepas nuda carnosa aurita_
  1 a. _Ejusdem pars superior interna_
  1 b _Foramen auris internum_
  1 c _Currhi_ (1.d) _Proboscis et_ (1.c) _Os_
  1 f _Dens terratus quorum octo sunt_
  1 g. _Idem per. Microscopium visus_
  1 h. _Scapus longitudinatiter dessectus_
  2 _Scalpellum Norwegicum Keratophytium_
  2 a. _Idem per. Microscopium visum_
  3 _Scalpellum ex mare Britannico_
  4. _Cornu copia Poussepieda Gallorum_
  5. _Concha Anatifera vulgaris_
  6. _Concha Anatifera prolifera_
  A. _Animal Lepadis sen Triton Linnæi_

Barnicles _with Stems_.

  1. _Naked fleshy Barnicle with Ears_
  1 a. _The inside of the upper part of the same_
  1 b. _The internal opening of the Ear_
  1 c. _The Plumes_ (e. d) _trunck_ (e. e) _and mouth_
  1 f. _A saw edg’d tooth of which there are 8_
  1 g. _The same magnified_
  1 h. _The Stem cut in two lengthways_
  2. _The Norway Seafan Penknife._
  2 a. _The same magnified._
  3. _The British Channel Penknife._
  4. _The Horn of plenty or French Poussepieds_
  5. _The common Duckbearing Barnicle_
  6. _The branch’d Duckbearing Barnicle_
  A. _Animal of the Barnicle or Linnaeus’s Triton_

Lepades Sessiles Balani dictæ.

  7. _Pediculus Ceti_ (7.a). _Idem reversus_
  8. _Calyciformis Orientalis_
  9. _Tintinabuliformis._
  10. _Tulipiformis ex Corallio rubro_
  11. _Fistulosa conica_ (11.a) _eadem reversa_
  12. _Verrum Testudinaria_ (12.a) _eadem reversa_
  13. _Verrum Canesti Americani_ (13.a) _eisdem statere_
  14. _Lapensis ore obliquo_ (14.a) _cum opserastis cornutis_
  15. _Subovatis crassa ore minore_
  16. _Cornulacensis conicas ore minores_
  17. _Anglica vulgaris ore patulo_
  18. _Aretica Patelliformis_
  19. _Calceolus_ (19.a) _Idem. hierophylis involutus_
  20. _Diadema Persarum_

Barnicles _adhering by the base of these Shells_.

  7. _The Whales. Louse_ (7.a) _The underside_
  8. _The East India cup shap’d Barnicle_
  9. _The Bell shap’d Barnicle_
  10. _The Red Coral Tulip Barnicle_
  11. _The pipy conical Barnicle_ (11.a) _The underside_
  12. _The Tortoise Wart_ (12. a) _The underside_
  13. _The American Crabs Wart_ (13.a) _The same sideways_
  14. _The Cape sidemouth Barnicle_ (14.a) _with_ oblique edge
  15. _The Eggshap’d thick Barnicle with a small mouth_
  16. _The Cornish cone Barnicle with a small_ edge
  17. _The common English Barnicle with a_ wide mouth
  18. _The Greenland Limpet shap’d Barnicle_
  19. _The Slipper_ (19.a) _The same cover’d with hierophylis_
  20. _The Persian Crown_]




CXIII. _An Account of several rare Species of Barnacles. In a Letter to
Mr._ Isaac Romilly, _F.R.S. from_ John Ellis, _Esq; F.R.S._

[Read Dec. 21, 1758.]

                                                 London, Dec. 21. 1758.

Dear Sir,

THOSE rare and very extraordinary new species of Barnacles, which you
have lately received from abroad, are so different from any of the
common species, that I have seen, that I was resolved to inquire into
the nature of an animal, which, like a Proteus, appears in so many
different shapes or coverings in different parts of the world. For this
end I have consulted that excellent collection in the British Museum,
and some others in the cabinets of my curious friends.

In this inquiry I met with some very rare ones, which have not yet
been described, as you will observe in the annexed plate [_See_ TAB.
XXXIV.], where I have given exact drawings of yours, as well as the
other species of this genus.

This marine animal is called, by writers on natural history, Balanus,
and Concha Anatifera: but the celebrated Professor at Upsal, Dr.
Linnæus, calls the internal active part, or fish, the Animal Triton,
and the covering or testaceous habitation Lepas, which he says is a
multivalved shell, composed of unequal valves. The Animal Triton he
describes, as having an oblong body, a mouth with a tongue in it,
twisted about in a spiral manner; sixteen tentacula or claws: six of
the hinder ones on each side, he says, are cheliferous.

This account differing from that given by the ingenious Mr. Turberville
Needham, F.R.S. in his Microscopical Essays, I shall give the character
of this animal, as it appeared to me from the many observations I made
on it, while alive in salt water; and these I compared not only with
many dried specimens of other varieties, but likewise with some of
yours, that were preserved in spirits; and I found that the parts of
the animal agree in all the species.

The experiments, that I made, were on the common English Barnacle,
which is very frequently met with, at this time of the year, on oysters
and other shell-fish. The microscope, that I made use of to observe
it, was Mr. Cuff’s aquatic one; where the animal, when taken out of the
shell, may be put into the watch-glass with salt water, or spread on
the round glass plate on the stage of the microscope, and kept moist
with a hair pencil and salt water during the time of observation: this
will keep the claws and proboscis alive and in motion for many hours
together.

This animal has 24 claws, or cirrhi (_See Fig._ A), which are disposed
in the following manner: the 12 longest stand erect, arising from the
back part of the animal: they are all joined in pairs near the bottom,
and inserted in one common base. These appear like so many yellow
curled feathers: they are clear, horny, and articulated. Every joint is
furnished with two rows of hairs on the concave side. The animal, in
order to catch its prey, is continually extending and contracting these
arched hairy claws, which serve it for a net.

The 12 smallest claws are placed next to these, six on each side: these
are divided into pairs; that is, two claws to one stem, like the chelæ
or claws of the crab. These are more pliable, and fuller of hairs, than
the others, and seem to do the office of hands for the animal.

The whole number of claws lessen in size gradually each way, from the
tallest in the back, to the last but one of each side in the front;
which last two are of the middle size.

The proboscis, or trunk, rises from the middle of the base of the
larger claws, and is longer than any of them: this the animal moves
about in any direction with great agility: it is of a tubular figure,
transparent, composed of rings lessening gradually to the extremity,
where it is surrounded with a circle of small bristles, which likewise
are moveable at the will of the animal. These, with other small hairs
on the trunk, disappear when it dies.

Along the inside of this transparent proboscis the spiral dark-coloured
tongue appears very plain: this the animal contracts and extends at
pleasure.

The mouth appears like that of a contracted purse, and is placed
in front, between the fore claws. In the folds of this membraneous
substance are six or eight horny laminæ or teeth standing erect, each
having a tendon proper to direct its motion. Some of these teeth are
serrated, others have tufts of sharp hairs instead of indentations on
the convex side, that point down into the mouth; so that no animalcule
that becomes their prey can escape back.

Under the mouth lie the stomach, intestines, and the tendons by which
they adhere to the shell.

This then is the general character of the animal of the whole genus,
whether with stems or without.

I shall now give you a short description of the several kinds I have
met with, besides those of your own, and shall divide them into two
kinds; those that have stems, and those that adhere by their shelly
bases.

The first and most remarkable of those that have stems is the Barnacle,
_Fig._ 1. This differs from the Lepas of Linnæus in not having a
testaceous, only a cartilaginous or fleshy covering. On the top of it
are two erect tubular figures like ears: these have a communication
with the internal parts of the animal (_See Fig. 1. b_). These inner
parts agree with the general character already given. The stem, which
is here dissected, was full of a soft spongy yellow substance, which
appeared, when magnified, to consist of regular oval figures, connected
together by many small fibres, and no doubt are the spawn of the animal.

This extraordinary animal (of which there were seven together) was
found sticking to the Whale Barnacle (_See fig._ 1. & 7.), by Mr. Smith
of Stavenger in Norway, who cut both kinds together off a whale’s
lip, that was thrown upon that coast last year, 1757, and immediately
immersed them in spirits of wine; by which means we have been able more
exactly to describe them.

I have called this animal the Naked Fleshy Barnacle with Ears; but it
appears to claim the name of Triton rather than Lepas, according to
Linnæus, as having no shelly habitation.

_Fig._ 2. is the next animal of this class: this is not yet described.
I found several of them sticking to the Warted Norway Sea Fan, which
Dr. Pantoppidan, the Bishop of North Bergen, sent you: from its
appearance, I have called it the Norway Sea Fan Penknife. The stem
of this is covered with little testaceous scales. The upper part of
the animal is inclosed in thirteen distinct shells, six on each side,
besides the hinge-shell at the back, which is common to both sides:
these are connected together by a membrane that lines the whole inside.
One of these is magnified a little at fig. 2. _a_, in order to express
the figure and situation of each shell the better.

_Fig._ 3. is taken from D’Argentville’s _Lithologie, Pl. 30. fig._
H, who says it is found in the British channel sticking to sea
plants; and that these shells consist of five pieces. This, from its
appearance, I have called the British Channel Penknife, to distinguish
it from the other.

_Fig._ 4. is a species of Barnacle called Poussepieds by the French,
and described by Rondeletius as commonly found adhering to rocks on
the coast of Brittany. He says the people there boil and eat the stem,
which is first of a mouse-colour, and afterwards becomes red like our
prawns. There are many heads, that arise out of one stem, each of which
consists of two shells, in which are the same parts of the animal as in
the other species. This I have called the Cornucopia Barnacle. Some of
the shells of this Barnacle were drawn from a specimen in the British
Museum. This Lepas is the Mitella of Linnæus.

_Fig._ 5. and 6. are the Barnacles called Conchæ Anatiferæ: these are
the sorts so well known to sailors, and formerly supposed to produce a
large species of duck called a Barnacle. These consist of five shells.
The tube, that supports one of these kinds, branches out like some
species of corallines, bearing a shelled animal at the end of each
branch. They are generally found adhering to pieces of wood in the sea,
and most ships have some of them sticking to their bottoms. Those of
the southern and warmer climates are generally of a larger kind than
those of the colder and more northern climates.

The next division of these animals is, those that adhere by the base of
their shells, having no stems.

Here I must observe, that the bottoms of the several species of this
division conform in shape to the substances they adhere to, or grasp
them in such a peculiar manner, as to render their situation secure
from the violence of the element they live in. Another provision of
nature for the security of these animals are the four opercula, which,
upon their retreating into the great shell, they can draw to so close
after them, as to secure themselves from outward danger.

_Fig._ 7. represents the Whale Barnacle, called Pediculus Ceti, just
as it was cut off the whale’s lip, with the seven naked Barnacles with
ears, already described. _Fig._ 7.a is the bottom of the shell. This
has the appearance of the gills of a mushroom. All the spaces between
these laminæ were filled with the blubber of the whale: by this means
they adhere to the gristly skin of the fish. The narrow cavities
between the branched laminæ are the places where the ligaments or
tendons, that move the opercula, are inserted.

_Fig._ 8. is the Cup Barnacle, taken off an East India ship from
Sumatra. The testaceous flat bottom of this was marked with the seams
and lines of the sheathing, and with the rust of the nails. In one of
these shells the animal is represented protruding his claws thro’ the
opercula.

_Fig._ 9. is called the Bell-shaped Barnacle. This was taken off the
bottom of a ship from Jamaica, and had its flat testaceous base marked
as the former.

_Fig._ 10. This represents part of a most elegant specimen in the
curious collection of Dr. John Fothergill. It is called the Tulip
Barnacle, and very properly, as well from the shape of its shell, as
the beautiful stripes of red mixt with white. It adheres to a piece
of the true red coral, and was fished up near Leghorn, on the coast
of Italy. It is not improbable, but that these groups of Barnacles,
growing at the same time with the animals that formed the red coral,
may have received an addition to their fine red colour from the coral.

_Fig._ 11. is a group of Barnacles of a conical form, composed of
purplish tubes like small quills. _Fig._ 11.a represents one of the
same, with a view of its base, from the collection of Mr. Peter
Collinson, F.R.S. This was brought from the East Indies. The insides of
these shells have the appearance of the spongy parts of bones.

_Fig._ 12. is called the Tortoise-wart Barnacle, being often found upon
that animal. This shell is of a plano-convex shape, and looks like
polished ivory. The divisions between the valves represent a star with
six points. If these shells are put into soap lees, they will in a few
hours separate into six pieces or valves, each shelly valve having
two ears, like the scallop-shell: so that this species has its valves
connected by membranes, instead of testaceous sutures, as most of the
others have. _Fig. 12. a_ represents the under part of the same shell.

_Fig._ 13. This shell is marked with six rays like a star, as the
former; but is much deeper in proportion to its diameter. Several
of this kind were found sticking to a crab, that was lately brought
from the island of Nevis; from whence I have called it the American
Crabs-wart.

_Fig._ 14. is called the Side-mouth Barnacle. This was found on
the southern coast of Africa, near the Cape of Good Hope, where it
adheres to a particular species of striated purple muscle. _Fig._ 14.a
represents two of the opercula of this Barnacle remarkably horned. The
shell of this is very thin; but its obliquity may probably be owing to
its situation.

_Fig._ 15. This egg-shaped Barnacle with a small mouth is found in
clusters sticking to the Buccinum tribe of shells in the West Indies.

_Fig._ 16. is the Cornish Barnacle, shaped like a cone, and with a
small mouth. This is described and figured by the Revᵈ. Mr. William
Borlase, F.R.S. in his Natural History of Cornwall, lately published.

_Fig._ 17. This is the common English Barnacle, that is found in such
plenty upon all rocks and shells round this island. From the animal of
this, examined in the microscope, I have taken the character of the
fish of the Barnacle genus.

_Fig._ 18. This I have called the Limpet-shaped Barnacle, from its
likeness to some species of that shell. I am indebted to our late
worthy member, Mr. Arthur Pond, for this shell, who assured me it
was brought to him from Greenland. It was, with several more, found
sticking to a very large species of muscle.

_Fig._ 19.a. This Sea-Fan, with the Barnacles inclosed in it, was
brought from Gibraltar. I have called it the Slipper Barnacle, from its
shape. _See Fig._ 19. These shell-fish adhere, while they are young, to
the slender branches, which are produced by the animals that compose
this species of Sea-fan; and as the next succession of young animals of
this sea-fan creep up its sides, to increase the bulk and extension of
these first-formed ramifications, they inclose the shells all round,
leaving only their mouths or apertures open, for the Barnacles to
procure their food. But it frequently happens, that the animals of the
Sea-fans destroy these Barnacles, by overrunning and involving them in
the very center of their stems. These small Barnacles, interspersed
here and there on the branches, have been taken for fruit or berries
by some gentlemen, who look upon the internal or horny part of the
Sea-fans to be vegetables.

_Fig._ 20. is a very curious Barnacle, taken from an elegant specimen
in the British Museum; which, from its figure, I have called the
Persian Crown.


I shall now add some further observations on the nature of these
animals.

Upon opening the shells of many of the common English Barnacles (_Fig._
1.) while they were alive, I found the lower part of the shell, which
contained a cavity equal to two thirds of the whole, full of spawn;
so that the Barnacles, which adhere by the base of their shells, as
well as those that are supported by fleshy tubes, are propagated by
eggs, which they send forth in inconceivable numbers; as appears by the
clusters of young shells, which we find adhering not only to the parent
animals, but to all hard substances near them.

The bottom shell of these animals, as well as their upper shells, vary
in form according to their situation, which occasions some difficulty
in determining their several species with exactness. The form of the
base shell of our common English Barnacle, is the flat radiated figure
represented adhering to a scallop shell in the front of a group of them
at _Fig._ 17. The Barnacles at _Fig._ 8. 9. 14. 15. and 20. have the
same kind of base.

I have very lately observed a singular kind of flat Balanus, on a white
Mandrepora coral from the coast of Italy, in the possession of Mr.
Mendez D’Acosta, F.R.S. whose base appears sunk into the coral, and of
the form of an inverted cone, bending a little to one side. The inward
surface of this conical base shell appears curiously striated with
tubular radii, which terminate on the surface of the coral, to receive
the extremities of the six valves, that compose the upper shell. This
peculiar form of the base seems owing to the animals of the coral and
of the Barnacle growing up together, the latter keeping possession of
its proper space, while the former grew close about it.

The bottom shell of the Barnacle like a Limpet, at _Fig._ 18.
increases from a small point by many thin shelly margins, which
exactly correspond to the indentations which we observe on the base
of the outward shell; so that it appears not unlike the drawing of a
fortification in miniature.

I am,

                               Dear Sir,
                    Your most affectionate Friend,
                              John Ellis.

  _P. S._ The Rev. Mr. William Borlase is now of opinion, that the
  Cornish Barnacle at _Fig._ 16. which he has described in his History
  of Cornwall, is rather a Limpet or Patella.




CXIV. _A further Account of the poisonous Effects of the_ Oenanthe
Aquatica Succo viroso crocante _of_ Lobel, _or_ Hemlock Dropwort, _by_
W. Watson, _M.D. F.R.S._

_To the_ ROYAL SOCIETY.

[Read Dec. 21, 1758.]

Gentlemen,

IN the month of June 1746. I communicated to you some observations
concerning the _Oenanthe aquatica Succo viroso crocante_ of Lobel,
in relation to its poisonous effects upon some French prisoners
at Pembroke. These observations were afterwards published in the
_Philosophical Transactions_[225], with an accurate representation of
the plant itself, from an original drawing by that compleat artist Mr.
Ehret. This at that time I thought the more necessary, as it was of no
small importance to the public, to be well acquainted with a plant,
the effects of which, when taken into our bodies, were so much to be
dreaded. This account of mine, as well as the representation of the
plant, were republished from the Transactions into the periodical works
of that time; from whence a more extensive knowlege of and acquaintance
with this plant might have been hoped for. A late instance however has
evinced, that these endeavours have not had their full effect, as the
plant in question is not yet sufficiently known, and attended to.

John Midlane, a cabinet-maker of Havant in Hampshire, aged about 58,
and of a gross habit of body, was advised to make use of the water
parsnep, as a remedy for a severe scorbutic disorder, which he had long
been troubled with; and for which he had taken a variety of medicines.
Instead of the water parsnep, which he purposed to take, there were
gathered for him some roots of the _oenanthe_ above mentioned; a large
one of which was pounded in a mortar, and the juice thereof squeezed
through a linen cloth, and amounted to about five spoonfuls. This was
suffered to stand all night, and the next morning (Mar. 31. 1758.), at
about half an hour past five, he drank the whole quantity, except the
sediment.

In about an hour and half after he had taken this juice, he walked
about the town upon some business; and a little before seven, upon
his return home, about an hundred yards from his own house, he first
complained that he was ill; and having walked about thirty yards
further, was so bad as to go into a neighbour’s house to rest himself.
He was soon led from thence to his own house by two men, and told them,
that he was affected as though he had lost the use of his limbs. When
he was placed in his chair, he complained greatly of pain all over
him; but particularly in his head. His stomach was immediately after
affected, and he had great reachings to vomit. At the second attempt he
threw up about half a pint of a clear watry liquor; at the first and
third attempt he discharged scarce any thing. He was then seized with a
great propensity to go to stool, which went off in about three minutes.
After this, he with the greatest difficulty was conducted upstairs
to bed, where he pulled off part of his cloaths himself. When he was
put to bed, he was attacked with very severe convulsions, which in
about a quarter of an hour deprived him of his senses; and continued,
with a few intermissions, till he died, a little before nine o’clock;
which was about three hours and half after the juice had been taken.
A profuse sweat accompanied the whole of these symptoms: he foamed
considerably at the mouth, and his belly swelled greatly. He purged
very much soon after he was dead, but not before.

As this poor man had taken this dose before his family were up, no
one could imagine from whence his disorder arose; and consequently
the apothecary, who was called to him, was able to form a judgment
of his case only from the symptoms; as on his coming he found his
patient senseless, and who had not, while his mind was undisturbed,
told any one the probable cause of his complaints. He took from him
however about ten ounces of blood, and endeavoured to get some _vinum
ipecacuanhæ_ into his mouth: but his jaws were closed so fast, not
above a spoonful passed, and that by the accident of his mouth opening
of itself.

The symptoms, with which the person above-mentioned was attacked, were
much the same as those which were observed in the French prisoners, who
were poisoned by the same root at Pembroke. In both instances occurred
those severe muscular spasms, which kept the under jaw so close to the
upper, that, while the spasm continued, scarce any force could separate
them. In both instances likewise a considerable time passed before
the persons, who had eaten of this root, though they had taken enough
of it to destroy them, perceived themselves disordered by it.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXXV. _p. 859_.

_J. Mynde sc._]

I am obliged for this communication to Richard Warner, Esq; of
Woodford, a gentleman of great merit, whose zeal for the promotion of
useful knowlege I have many times experienced.

The expediency of laying before you observations of this sort, which
may tend, by making people careful of what they take, to the saving the
lives of many, makes no apology necessary for so doing. I am, with all
possible regard,

                              Gentlemen,
                  Your most obedient humble Servant,
                              W. Watson.

Lincoln’s-Inn-Fields, 20 Dec. 1758.




CXV. _Extract of a Letter to_ John Eaton Dodsworth, _Esq; from Dr._
George Forbes _of_ Bermuda, _relating to the_ Patella, _or_ Limpet
Fish, _found there_.

                                                         2 April, 1758.

[Read Dec. 21, 1758.]

AS a curiosity for your esteemed friend Mr. Theobald, the Captain
will deliver you two fishes, intirely singular here, and never before
observed amongst us. The one is of the shell kind, and changed its
figure so often, that it was difficult to make a drawing. However I
got a young man to take it in two different positions, and have sent
the drawings with the fish. _See_ TAB. XXXV.

The small one may be called the sea-batt; and in some sort resembles
that species of animals when it is swimming.


_Additional Remark by_ Charles Morton, _M.D. F.R.S._

The Patella, or Limpet Fish, whose generic characters, as enumerated
by Bishop Wilkins, are, that it is an exanguious testaceous animal,
not turbinated; an univalve, or having but one shell; being unmoved;
sticking fast to rocks or other things; the convexity of whose shell
doth somewhat resemble a short obtuse-angled cone, having no hole on
the top.




CXVI. _A Discourse on the_ Cinnamon, Cassia, _or_ Canella. _By_ Taylor
White, _Esquire, F.R.S._

[Read Dec. 21, 1758.]

THE Cinnamon, Cassia, or Canella, are shrubs of no great height: they
grow in Ceylon, Malabar, Java, Sumatra, and other places in the East
Indies; as I think, in the island of St. Thomas, and on the coast of
Coromandel.

They are described by Mr. Ray, in his _History of Plants_, vol. ii. f.
1559. under the title _de Arboribus Pruniferis_.

[Illustration: _Philos. Trans. Vol. L._ TAB. XXXVI. _p. 860_.

_J. Mynde. sc._]

Linnæus, in his _Species Plantarum_, places them under the title
_Enneandria Monogynia_, by the name Laurus.

The leaf, flower, and fruit, of this plant, are particularly described
by Mr. Ray.

The leaf is smooth and shining; has one large vein running thro’ the
midst, and a remarkable one on each side; the middle one generally
running near the length of the leaf.

The leaves differ in shape, some being more acute, others more oval or
obtuse.

The flowers grow in an umbel, somewhat like the Laurus Tinus; but they
are small, consisting of one petal, of a tubular form at the bottom,
and divided at the top into six segments in the form of a star.

The flowers are succeeded by berries growing out of a capsula, like
acorns in shape; which berries contain a shining seed.

The description of Mr. Ray of the flower, in his description of the
Cinnamon of Malabar, is extremely accurate; as is also the figure in
the _Hortus Malabaricus_, Nº. 54. and the description, fol. 107. under
the name Carua. I shall therefore refer to those.

I shall not trouble you with the question debated by Mr. Ray, whether
the Cinnamon and Cassia of the ancients were, or were not, the same
with those so called by the moderns? whether the Cinnamon of the
ancients was the twigs of the tree bearing cloves, or any plant now
unknown to us? Mr. Ray has largely treated on this subject; and to him
I refer such as are curious to be informed on this subject.

But as the Cinnamon and Cassia of the ancients are said to have been
used as perfumes, and to make perfumed ointments, I think they must
have differed from ours, whose smell is not very fragrant, nor is
emitted to any great distance.

The matter of the present inquiry is, whether the Cinnamon of Ceylon
is the same sort of plant with that growing in Malabar, Sumatra, _&c._
differing only by the soil or climate, in which it grows, which is the
opinion of Garcias; or from the culture or manner of curing the plant,
as I am inclined to believe; or whether it is really a different genus
or species of plant, as many people believe, and some botanical writers
seem to indicate.

I shall endeavour to explain this matter by producing, 1st, The
descriptions of the most celebrated authors:

2dly, By producing the most accurate figures of the plants of Sumatra
and Ceylon: [_See Tab._ xxxvi.]

3dly, By shewing the specimen of the leaves and branches brought from
Sumatra.

I have no specimen from Ceylon; but have carefully examined the
specimens kept in the British Museum, with the assistance of Dr. Maty
and Mr. Empson, and compared them with the specimens I have from
Sumatra; from whence I traced exactly the figures brought herewith:
which specimens are undoubtedly brought from Ceylon, and were the
collections of Boerhaave, Courteen, Plukenet, and Petiver.

But, previous to this inquiry, I would premise, that the writers, who
give the description of the Cinnamon of Ceylon, were probably not
acquainted with that of Malabar at the time of their publishing their
works.

Mr. Ray also, who so accurately describes the flower of the Cinnamon
of Malabar, seems not so well acquainted with its fruit; and probably
had then never seen the specimens of the Cinnamon from Ceylon; for his
description is plainly borrowed from others, and not his own. Tho’ I
have reason to think he afterwards saw the specimens of Mr. Courteen,
and was convinced, that the plants were the same.

In his description of the Cinnamon of Ceylon, he supposes differences
in the manner of veining the leaf, which are not found in the leaves
themselves. He supposes, that the Cinnamon of Ceylon differs from
that of Malabar by its berries growing in cups like acorns; which
is apparently the same in both, as may be seen in its figure in the
_Hortus Malabaricus_.

The other differences taken notice of by the botanic writers are as
follow:

In the _Flora Zeylanica_, p. 545. and in the _Materia Medica_, 190. the
Cinnamon of Ceylon is called _Laurus foliis trinerviis ovato-oblongis
nervis unientibus_: which description is adhered to in the _Hortus
Cliffordiensis_, p. 154. under the name _Laurus foliis oblongo-ovatis
nitidis planis_. And Burman, in his _Flora Zeylanica_, 62. T. 27. calls
it _Cinamomum foliis latis ovatis_. Whereas the Cassia of Sumatra is
distinguished by these writers: that in _Flora Zeyl._ 146. and in
_Materia Medica_, 191. is called _Laurus foliis trinerviis lanceolatis
nervis supra basin unitis_: and Burman, _Zeylan._ 63. T. 28. calls it
_Cinamomum perpetuo florens folio tenuiore acuto_.

The distinction therefore, which these writers would make us believe
there is between these plants, consists in the leaves of the one being
oval, the other sharp-pointed; and that the nerves are limited at the
bottom in the Cinnamon, but not so in the Cassia: for as to the _semper
florens_, mentioned by Burman, that must undoubtedly be common to both.

Now as to the different shape of the leaves, we know how often this
happens by seminal varieties, and from the age of plants, as in the
leaves of holly and ivy; and that even the shapes of leaves vary
greatly on the very same plant, and sometimes on the same branch; as in
the ash, and many other plants, the leaves of the young shoots are more
oval than those on the old boughs, which are generally more pointed.
But this variety is much more frequent in the plants of warm countries.
In the sassafras, part of the leaves generally near the bottom of the
plant are plain, whilst the other leaves are divided into three lobes
or segments. I have observed great difference also in the leaves of
almost every one of the American oaks.

In the Virginian cedar, the berries of the same plant produce some
plants with juniper leaves, and others with leaves like the savin; and
some plants with both leaves growing on the same plant.

I must observe that Burman has, in his figures of the two plants before
mentioned, made them extremely different. In that of Ceylon he has made
all the leaves oval; and, to make the difference greater, has drawn the
rudiments of the berries; to which he has added the flower, or part of
it, at the top of the style or rudiment of the fruit: and in that of
Malabar he has drawn the flower growing in the umbel.

On these drawings I must observe, that his drawing of the Cinnamon of
Ceylon agrees with no one specimen in the British Museum; and scarcely
is one leaf to be found of the shape, which he gives.

The first figure, which I shall produce, is a drawing which I procured
from the ingenious Mr. Ehret in the year 1754: which, as I am informed
by Mr. Empson, was from a specimen, given to Mr. Ehret by him in that
year, of the Cinnamon of Ceylon. _See Fig._ 1.

This agrees in every thing with the drawing of the Cinnamon of Malabar
in the _Hort. Malab._ fig. 54. fol. 107. and there called Carua; except
that it wants the fruit: but that defect is supplied by Mr. Ray’s
description of the Cinnamon of Ceylon above mentioned. _See fig. of the
fruit, Fig._ 2.

In the figure in the _Hort. Malabar._ it may be observed, that the
nerves do not go quite to the bottom of the leaf. But this is merely
accidental, as will appear by the leaves of the same plant brought from
Sumatra, which I shall produce; in which, part of the leaves have veins
going quite to the bottom, and united there, and the others not so.
_See Fig._ 3.

The next drawing I shall produce contains that of the leaves of the
Cinnamon plant, from specimens in the British Museum.

    _Fig._ 4. A specimen, with the flower, from the collection of
      Mr. Courteen, who lived long in Ceylon. These leaves were more
      pointed, but were broke at the end.

    _Fig._ 5. A whole leaf, with its point, in the same collection,
      growing on a branch, on which are the rudiments of the fruit.

    _Fig._ 6. A leaf in Plukenet’s specimens.

    _Fig._ 7. Another leaf of the same collection, and of the same
      plant.

    _Fig._ 8. A leaf of a large specimen from Boerhaave’s collection.

    _Fig._ 9. Another leaf on the same branch.

    _Fig._ 10. A specimen from Petiver’s collection. The points of the
      leaves are broken off.

    _Fig._ 11. The flower of the first specimen.

    _Fig._ 12. In the rudiment of the seed before formed, in the state
      given in Burman’s first drawing.

    _Note_, It is to be observed also, that the specimens of the
      Cinnamon of Ceylon are probably of cultivated plants.

From all these specimens it plainly appears, that the distinction of
_foliis ovatis & lanceolatis_ does not appear well founded.

But were it otherwise, and that the leaves of the plants differed, it
would by no means be a proof of any material difference in the nature
or quality of the plants; as is well known to persons conversant in
natural history.

Before I leave this subject of the description of the plant, it may
be proper to mention, that Bauhin calls the one of these plants
_Cinnamomum_ or _Canella Malabarica & Javanensis_, and the other
_Cinnamomum Canella Zeylanica_, Bauhin. _pinax_ 408 and 409; but
neither from these names, nor from his description, can any conclusive
argument be formed: and that Herman, in his _Hort. Lugd. Batav._ 129.
t. 1655. calls this Cinnamon of Ceylon _Cassia Cinnamonia_.

If any conjecture can arise from hence, it may be, that the Cinnamon of
Ceylon was formerly, as well as that of Sumatra and Malabar, called
Cassia; but that the Dutch writers, being acquainted with the excellent
qualities, which the ancients ascribed to their Cinnamon, chose to
add the name Cinnamon to that of Cassia: and in process of time they
have found the name of Cinnamon more profitable than that of Cassia,
by which we chuse to call our Canella, to our national loss of many
thousands a year.

Having now given an account of the figure of these plants, and in what
respect they are said herein to differ; I shall proceed to consider the
pretended differences in the Canella itself; which are supposed not
to be in form only, but substantial and material; and are generally
understood to be so by persons supposed to be acquainted with the
subject.

Mr. Ray states this matter fully in his _Hist. Plant._ vol. ii. p.
1560. in these words: _Officinæ nostræ Cassiam ligneam a Cinnamomo seu
Canella distinctam faciunt, Cassiam Cinnamomo crassiorem plerumque
esse, colore rubicundiorem, substantiâ duriorem, solidiorem &
compactiorem, gustu magis glutinoso, odore quidem & sapore Cinnamomum
aptius referre, tamen Cinnamomo imbecilliorum & minus vegetam esse, ex
accurata observatione Tho. Johnson._

From these reasons Mr. Ray draws a conclusion (I must own not very
instructive), that the Cinnamon of Ceylon is Cinnamon; and the Cinnamon
of Malabar, &c. is the Cassia of the shops.

From the specimens I shall now produce, it will most plainly appear,
that these differences are merely accidents arising from the age of the
Canella, the part of the tree from whence it is gathered, and from the
manner of cultivating and curing it.

In the _Philosoph. Transact._ Nº. 278. p. 1099. in Mr. Strachan’s
account of Ceylon, which is abridged by Eames and Martyn, vol. ii. p.
183. he says, that there are two sorts of Cinnamon-trees, of which the
tree, which is esteemed the best, has a leaf much larger and thicker
than the other; but otherwise no difference is to be perceived.

   _Note_, Here is no mention of the _folio ovato_.

I remember, in an account given some years ago to the Royal Society,
three or four sorts were mentioned; and it was said the best sort was
cut every three or four years.

This superiority I then guessed (as well as the difference of leaves
mentioned by Mr. Strachan) to arise from the cutting the tree down
every three or four years; which occasioned it to produce strong and
vigorous shoots, thicker and larger leaves, as well as greater quantity
of bark, and of a superior quality.

A large shoot or sucker of this plant was produced in the year 1750. or
51. by my worthy friend Dr. William Watson, together with an account
of the Cinnamon-tree; which is published in the _Philosoph. Transact._
vol. xlvii. p. 301. This shoot was a plain proof to me, that the
Cinnamon was frequently cut down, and that this shoot arose from the
root of a plant so cut; for it was of the size of a walking-cane; and
no shrub could have produced such a shoot, unless a strong plant cut
down.

This method of treating this plant accounts for the mistake of Garcias,
mentioned by Mr. Ray; _viz. Quæ Garcias habet de duplice hujus arboris
cortice ad modum suberis, nobis suspecta sunt, quæque de deliberatione
semel triennio facta; non enim puto renascitur cortex semel detractus._

This shews, that the bark was gathered every three years: but Mr. Ray
was not acquainted, that the plant was cut down, in order to take off
the bark, once in three years.

In the account above mentioned to be given to the Society by Dr.
Watson, no descriptions are given either of the plants of Ceylon, or
Malabar; but he quotes Burman, who says, that he had nine different
sorts of Cinnamon from Ceylon, of which that, which is the best, is
brought to us, and called by the name _Rasse Coronde_.

What the differences between these sorts were, does not appear; whether
in leaf or bark, or manner of culture. And I must observe, that in
all the specimens in the British Museum I could observe no difference
of species. But this is to be understood, that every sort coming from
Ceylon is, by the Dutch and by the shops, called Cinnamon; and that of
our own growth is by them always called Cassia. The reason is obvious.

The specimens, which I now produce, of the Canella or bark of the
Cinnamon of Sumatra, I procured in the year 1755. from Mr. Tho. Combes,
a gentleman then in the service of the East India Company in Sumatra,
by means of a friend.

I was then attempting to form a society for the carrying on a General
Natural History, to try proper experiments, and to employ proper
painters and engravers suitable to the importance of the subject; and
therefore attempted to establish a correspondence in those parts, whose
productions are as yet little known to the public.

I mention this design, because it would not be possible else to explain
what Mr. Combes means by the word _Society_, which he so often mentions
in his letter; of which I shall produce an extract, so far as it
relates to the present inquiry.

It seemed to me very improbable (as the same plants are generally found
in the same latitude and soil), that the spices now in the possession
of the Dutch should grow only in that small tract of land, which is in
their possession. And I had many credible informations, that, whatever
they may pretend to the contrary, this is only a pretence.

I therefore desired to obtain the best information of the nature and
culture of the plants producing spices, as well as of many other
things, which are foreign from this inquiry.

I desired to know, how the spices were dried and cured; and that
different specimens might be sent me of the plants, their seed, flower,
leaf, and bark, and properly cured and prepared.

This produced the answer I lay before you herewith, together with the
specimens now produced.

You see hereby, that the Dutch dry their Cinnamon in sand; probably to
take away that viscosity, which is complained of in the Cassia.

And you will observe also, that the specimen produced dried and cured
is also as free from any viscosity, as the Cinnamon of Ceylon: That it
agrees also with the Cinnamon in every other quality, and in colour;
and that none of the distinctions mentioned by Mr. Ray can be found
herein; but that they may arise from the part of the tree, from whence
the bark was taken; the inner bark of the large wood being red, as you
see by the other specimen produced. And the common Cassia taken from
the larger branches, and not cured, has the viscosity complained of
in some degree, tho’ much less than it had four years since, when I
received it.

Mr. Ray says, that one is weaker in taste, as he supposes, than the
other. That may be so from its manner of drying, or keeping of it.
Dried in large quantities, and by a stronger heat, it will probably be
stronger, than if it is dried in a lesser quantity, and slower.

As for the viscosity, the glutinous part is found in every plant in
some degree, as well as in every animal. It preserves the parts from
moisture; but will be consumed by heat or time; and it will be a
preservative to the plant, till it is destroyed; which was the reason,
as I suppose, that Mr. Ray mentions Cassia to have kept good thirty
years, the viscosity not having been destroyed by drying.

I suppose the reason, which the Dutch have to dry it, is to make it
sooner fit for the market, and possibly fitter for distillation.

You will see from Mr. Combes’s letters and specimens, that he thinks
there may be two sorts of Cassia or Cinnamon in Sumatra: possibly there
may be the same difference in Ceylon; but, if so, I suspect them both
to be only seminal varieties, and that their virtues are the same.

Mr. Barlow, some time since a Surgeon in the service of the India
company, made a considerable quantity of oil of the Cassia of Sumatra,
which was very little, if any thing, inferior to that drawn from
Cinnamon; and it was sold to great profit.

If these plants are really the same, or if they are of equal goodness,
supposing there was a small difference in the form of the leaf, it
might be well worth the attention of the East India company to try to
cultivate these plants in the manner they do in Ceylon; that is, to
make plantations in a proper soil; and to have regard to the proper
distance from the sea of the place, where they try the experiment: for
some plants require to be near the sea, and others far from it, in
Sumatra; which is the case of the Mango, and Mangosteen; the one of
which must be near the sea, the other at a distance from it.

I think the plants should be suffered to grow strong, to be six or
seven years old, and then cut every three years, the bark peel’d off
and dried in hot sand, and packed close and kept dry. This I take to be
all necessary to be done, to try, if our Cinnamon will not produce as
good a price as that of the Dutch.

Perhaps the plants need not stand so long before cut; for the
vegetation of plants in hot countries is very great.

There are many other most valuable vegetables in Sumatra, which might
be made staple commodities, as sagoe, camphire, several sorts of
ginger, rice, and many other, which are foreign to the present inquiry.

But it may not be amiss to recommend it to the traders to Sumatra to
bring some quantity of the twig-bark of the true Cassia, well cured;
and also to the company, to have a chemist at Sumatra, to extract
carefully the oil of Cassia; which is best, and in greatest quantities,
produced from the bark of the body, and of the larger branches of
the tree: and also that the company would procure an exemption of
all customs or duties on Cassia, or on the oil of Cassia, for some
time: and also that the college of physicians in their dispensatory
would direct Cassia or Cinnamon of Malabar or Sumatra to be used,
instead of the Cinnamon of Ceylon; and that the same should be used by
apothecaries and distillers, and in all simple and compound waters, in
which Cinnamon is used.


_Extract of a Letter from Mr._ THOMAS COMBES, _dated_ Fort Marlborough,
5 Jan. 1755.

IN regard to the first article of your paper, now before me, which is
the inquiry desired to be made concerning the spices, I am of opinion,
that the true Cinnamon grows no-where but on the island of Ceylon,
unless Cassia be allowed to be the same tree, which I am inclined to
think.

Nº. 9. contains seeds of the Cassia or wild Cinnamon-tree. As for the
seeds of the true Cinnamon-tree, I believe they are very difficult to
be got; for as the Dutch are the sole masters of this spice, and get
a good deal of money by it, I fancy, according to their usual custom,
they have very well guarded against the transplantation of it. I hope
however, that these seeds will not be unacceptable to the society, as
Cassia itself is of some value; and as I am very doubtful, whether this
tree is not the same with the true Cinnamon, being of opinion, that the
difference observed in them arises from the different method of curing
their barks, or from the taking the bark from different parts of the
tree, or at different seasons, or of different ages, or perhaps all
these.

I have made inquiry concerning this from some very intelligent persons,
and found them to be of opinion, that the Cassia and Cinnamon-tree
were of the same genus. I have inquired further concerning the method
of curing it at Ceylon; but as this is done by the natives, the Dutch
are not very well acquainted with it; nor could I obtain any good
account of it, different people giving me different relations. Some
said, it was the inner bark, some the middle, and some the outer; tho’
of the young branches, they seemed in general to agree, that it was
gathered at a certain season of the year, and that one part of the cure
was burying it in sand for some time. This may be tried with Cassia,
and may perhaps take away that viscosity or glutinous quality observed
by chewing it, and which is the principal mark for distinguishing it
from Cinnamon. As to their chemical oils, I have heard many people say,
that they are not distinguishable otherwise, than that from Cinnamon
is generally better, or, as it may be called, stronger, than that from
Cassia; and accordingly bears a better price. But the Dutch company’s
chemist at Batavia, if I may give him this title, informed me, that
they are essentially different, and plainly distinguishable. But I
must confess myself very doubtful of the knowlege or veracity of this
chemist, and strongly suspect, that they are no otherwise different
than in goodness, as many other oils drawn from the same subject are.

I observe the price of Cassia is greatly risen in England within these
two or three years; but whether this be owing to an increase in the
consumption, or a decrease in the importation of this commodity, I
cannot say.

The Dutch government of Batavia has this year, in some new regulations
of their trade, prohibited to all persons the dealing in any of the
fine quilled sort of Cassia, and declared the same to be contraband,
and reserved for their company only; and put it upon the same footing
as their Cinnamon.

What reasons induced them to this, I am yet a stranger to; but it makes
me suspect, that the rise of this commodity in Europe is owing to some
other cause than a deficiency in the importation thereof. Perhaps some
discovery has been made rendering Cassia equal to Cinnamon.

In Persia, I think, they make not so great a difference between them
as elsewhere; and I myself, for want of Cinnamon here for some months
past, made use of the fine quilled Cassia; and the difference I observe
between them I imagine to arise rather from the greenness and want of
dryness in the Cassia, than any thing else, or perhaps from the method
of curing it: for if there happens to be a little too much Cassia put
into my chocolate (and other things I use in it), a little bitterish
taste arises, something like what we meet with in most barks; tho’ I do
not remember to have observed this of Cinnamon: but as to its boiling
to a jelly, as Quincy mentions, I find no such thing, and think it
bears boiling as well as Cinnamon. Nor do I think its distilled water
more subject to an empyreuma than that of Cinnamon.

I have inquired of the country people here, who bring it us, and they
tell me the finest sort is the inner bark of the small branches; and
indeed that it is the inner bark, I think, is evident in Cinnamon as
well as Cassia; no outer bark of the youngest branches of any tree
having, in my opinion, that smooth surface observable in both these
barks.

I once thought, that it was better to take the bark from the body of
the tree than from the branches, imagining that the bark from the trunk
or body of all trees must in general be stronger, let its natural
taste be what it will, than from its branches. This I find to be so
in Cassia; and I have been informed, that the large ligneous pieces
of Cassia have afforded rather more oil in distillation than the fine
quilled sort, their weight being equal; but upon trial I could not make
the bark from the trunk curl or roll up, as it ought to do, owing, as I
suppose, to my unskilfulness, or to rigidity, or the natural position
of its fibres; for the bark of the younger branches curled of itself,
wanting hardly any other assistance than the sun.

I have already observed, that Cassia is found in chewing to have a
viscidness, which Cinnamon has not. I have endeavoured to remove this
in a little I send you, marked B: pray let me know, if it answers; and
be assured, it was taken from the younger branches of the tree, of
which I send you the seeds.

I send you also, marked C, some of the bark taken from the same tree;
as also some of the leaves, marked D.

I have sent you also a little of the bark of the trunk of a tree,
which, tho’ called Cassia, seems not to be so, marked E; and also the
leaves of the same tree, marked F.


END _of the_ FIFTIETH VOLUME.




                                  AN
                                 INDEX
                                TO THE
                            FIFTIETH VOLUME
                                OF THE
                      PHILOSOPHICAL TRANSACTIONS,
                     For the YEARS 1757 and 1758.


A

_AIR_, Remarks on the heat of it in July 1757, by Dr. J. Huxham; with
some additional ones by Dr. W. Watson, page 428.

---- ---- on its different temperature at Edystone from that observed
at Plymouth, between July 7 and 14, 1757, p. 488.

_Akenside_, Mark, M. D. his observations on the origin and use of the
lymphatic vessels in animals, p. 322.

_Alga Marina latifolia_, observations on it, p. 631.

_Allegator_, the fossil bones of one, found on the sea-shore near
Whitby, p. 688.

_America_, North, account of an earthquake felt in it Nov. 18. 1755. p.
1.

_American_ Sea Sun-Crown, observations on it, p. 843.

_Antiquities_, accounts of the late discoveries of some at Herculaneum,
p. 49. 88. 619.

_Aneurism_, remarkable case of one in the principal artery of the
thigh, p. 363.

_Apple_, the Manchenille, singular observations upon it, p. 772.

_Arderon_, Mr. William, abstract of a letter on giving magnetism and
polarity to brass, p. 774.

_Assize_, the Black, at Oxford, account of it, p. 699.


B

_Baker_, Mr. Henry, his account of the Opuntia, or Prickly Pear, and of
the Indigo plant, in colouring the juices of living animals, p. 296.

---- ---- ---- ---- of the Sea Polypus, p. 777.

_Bark_, remarkable case of its efficacy in a mortification, p. 379.

---- ---- ---- ---- ---- in the delirium of a fever, p. 609.

_Barnacles_, an account of several rare species, p. 845.

_Baster_, Job. observationes de corallinis, iisque insidentibus
Polypis, aliisque animalculis marinis, p. 258.

_Bladder_, human urinary, four rough stones extracted from it by the
lateral method of cutting for the stone, p. 579.

_Blisters_, remarkable effects of them in lessening the quickness of
the pulse in coughs attended with infarction of the lungs, p. 569.

_Bones_, some fossil ones of an allegator, found on the sea-shore near
Whitby, p. 688.

_Borlase_, Rev. Mr. Wm. his account of some trees discovered
under-ground on the sea-shore at Mount’s-Bay in Cornwall, p. 51.

---- ---- ---- ---- ---- of an earthquake in the west parts of
Cornwall, July 15. 1757, p. 499.

_Bradley_, James, D. D. his observations on the comet of Sept. and Oct.
1757, p. 408.

_Brakenridge_, Rev. Wm. D. D. his answer to the Rev. Mr. Forster’s
letter concerning the numbers and increase of the people of England, p.
465.

_Brass_, abstract of a letter on giving magnetism and polarity to it,
p. 774.

_Bridges_, concerning the fall of water under them, p. 492.

_Brydone_, Mr. Patrick, his account of a paralytic patient cured by
electricity, p. 392.

_Burrow_, James, Esq; his account of an earthquake felt at Linfield in
Surrey, and at Edenbridge in Kent, Jan. 24. 1758, p. 614.


C

_Carlsbad_ mineral waters, account of them, p. 25.

---- ---- ---- their lithontriptic virtue, with lime-water and soap, p.
386.

_Case_ of Lord Horace Walpole; being a sequel to that in Phil. Trans.
vol. xlvii. p. 43 and 47,--p. 205.

_Cassia_, or _Canella_, a discourse on it, by Taylor White, Esq.; p.
860.

_Cavendish_, Lord Charles, his description of some thermometers for
particular uses, p. 300.

_Chapman_, Capt. Wm. his account of a method of distilling fresh water
from sea-water by wood-ashes, p. 635.

---- ---- ---- ---- ---- of the fossil bones of an allegator found on
the sea-shore near Whitby in Yorkshire, p. 688.

_Characters_, Phœnician Numeral, antiently used at Sidon, dissertation
upon them, p. 791.

_Charts_ and Maps, a short dissertation on them, p. 563.

_Chevalier_, Joan. observatio eclipsis lunæ die 27 Martii 1755,
Olissipone habita, p. 374.

---- ---- ---- ---- ---- die 30 Julii 1757, Olissipone habita, p. 769.

---- ---- observationes eclipsium satellitum Jovis, Olissipone habitæ,
p. 377.

---- ----, &c. observationes eclipsium satellitum Jovis, anno 1757,
Olissipone habitæ, p. 378.

---- ---- et Theodor. de Almeida, observationes eclipsis lunæ die 4
Feb. ann. 1757, Olissipone habitæ, p. 376.

_Cinnamon_, a discourse on it, by Taylor White, Esq; p. 860.

_Coin_, a Parthian, with a Greek and Parthian legend, some remarks on
it, p. 175.

_Collet_, John, M. D. his letter concerning the peat-pit near Newbury
in Berkshire, p. 109.

_Comet_, observations on that of Sept. and Oct. 1757, made at the Royal
Observatory, p. 408.

---- ---- ---- ---- ---- ---- ---- ---- made at the Hague, p. 438.

_Convulsive Fits_, case of a boy troubled with them, cured by the
discharge of worms, p. 518.

_Convulsions_, some extraordinary effects arising from them, p. 743.

_Coral_, Red, a very singular kind from the Indies, p. 159.

_Corallinis_ de, iisque insidentibus polypis, aliisque animalculis
marinis observationes, p. 258.

_Cornwall_, account of an earthquake in the west parts of it, July 15,
1757, p. 499.

_Corona_ Solis Marina Americana, observations on it, p. 843.


D

_Da Costa_, Emanuel Mendez, his account of the impressions of plants on
the slates of coals, p. 228.

_Darwin_, Erasmus, M.D. his remarks on the opinion of Henry Eles, Esq;
concerning the ascent of vapour, p. 240.

_Delirium_, of a fever, an extraordinary case of the efficacy of the
bark in one, p. 609.

_Diseases_, effects of electricity in the cure of some particular ones,
p. 695.

_Dodson_ and Mountaine, tables of the variation of the magnetic needle
by them, adapted to every 5 degrees of lat. and long. in the more
frequented oceans, p. 329.

_Dollond_, Mr. John, his account of some experiments concerning the
different refrangibility of light, p. 733.

_Dust_, Black, an extraordinary shower, which fell in the island of
Zetland, Oct. 20. 1755, p. 297.


E

_Earthquake_, account of one in the island of Sumatra, in the East
Indies, Nov. and Dec. 1756, p. 491.

---- ---- ---- ---- in the west parts of Cornwall, July 15, 1757, p.
499.

---- ---- ---- ---- at Lingfield in Surrey, and Edenbridge in Kent,
Jan. 24, 1758, p. 614.

---- ---- ---- ---- at Herculaneum, p. 619.

---- ---- ---- ---- in New England, and the neighbouring parts of
America, Nov. 18, 1755, p. 1.

---- ---- observations upon a very particular tho’ slight one, p. 645.

_Eclipsis_ lunaris facta Matriti, a P. Joanne Wendlingen, die 30 Julii,
1757, p. 640.

---- lunæ observatio, die 30 Julii, 1757, Olissipone habita, p. 769.

---- ---- ---- ---- die 27 Martii, 1755, Olissipone habita, p. 374.

---- ---- ---- ---- die 4 Februarii, 1757, Olissipone habita, p. 376.

_Eclipsium_ satellitum Jovis observationes, Olissipone habitæ, anno
1757, p. 378.

---- ---- ---- ---- observationes, Olissipone habitæ, p. 377.

_Edystone_, remarks on the different temperature of the air there from
that observed at Plymouth, between July 7 and 14, 1757, p. 488.

_Edenbridge_, account of an earthquake felt there, Jan. 24. 1758, p.
614.

_Edwards_, Mr. Geo. his observations on an evening, or rather
nocturnal, solar Iris, p. 293.

---- ---- ---- ---- account of a new-discovered species of snipe, or
tringa, p. 255.

_Eles_, Henry, Esq; remarks on his opinion concerning the ascent of
vapour, p. 240.

_Electricity_, the effects of it in paralytic cases, p. 481.

---- further account of its effects in curing some diseases, p. 695.

---- its virtue in the cure of a palsey, p. 392.

_Ellis_, Mr. John, his account of a red coral from the East Indies, of
a very singular kind, p. 189.

---- ---- ---- remarks on Dr. Job. Baster’s observationes de
corallinis, &c. p. 280.

---- ---- ---- answer to the remarks upon his letter to Philip Carteret
Webb, Esq; p. 441.

---- ---- ---- account of several rare species of Barnacles, p. 845.

----, Henry, Esq; his account of the heat of the weather in Georgia, p.
754.

_Equator_, Terrestrial, resolution of a general proposition for
determining the horary alteration of the position of it, p. 416.

_Eye_, diseased, an extraordinary case of one, p. 747.


F

_Fauquier_, Francis, Esq; his account of an extraordinary storm of hail
in Virginia, p. 746.

_Fire-Engine_, further experiments for increasing the quantity of steam
in it, p. 370.

---- ---- attempt to improve the manner of working ventilators by the
help of it, p. 727.

_Fitz-Gerald_, Keane, Esq; his further experiments for increasing the
quantity of steam in a fire-engine, p. 370.

---- ---- ---- experiments on applying Dr. Hales’s method of distilling
salt water to the steam-engine, p. 53.

---- ---- ---- concerning an attempt to improve the manner of working
ventilators by the assistance of the fire-engine, p. 727.

_Flexor_ tendon, an account of one torn out in its whole extent,
together with the first joint of the thumb, p. 617.

_Forbes_, Dr. George, his letter concerning the Patella, or
Limpet-Fish, found at Bermuda, p. 859.

_Forster_, Rev. Mr. Richard, his extract of the register of the parish
of Great Shefford, with observations, p. 356.

---- ---- ---- ---- his letter concerning the number of the people of
England, p. 457.

_Fruits_, fossil, and other bodies, account of some found in the island
of Shepey, p. 396.


G

_Gaze_, Mr. John, his account of a boy cured of convulsive fits by the
discharge of worms, p. 521.

_Gall-stones_, two extraordinary cases relating to them, p. 543.

_Gaubil_, F. his description of the plan of Peking, p. 704.

_Georgia_, account of the heat of the weather there, p. 754.

_Glass_, in windows, dissertation on the antiquity of it, p. 601.

_Gravity_, Specific, of living men, essay towards ascertaining it, p.
30.

_Grindall_, Mr. Richard, his account of the efficacy of the bark in a
mortification, p. 379.

_Guadaloupe_, Isle of, account of a visitation of the leprous persons
there, p. 38.


H

_Hague_, state of thermometer there, Jan. 9, 1757, p. 148.

---- observations there on the comet in Sept. and Oct. 1757, p. 483.

_Hail_, an extraordinary storm in Virginia, p. 746.

_Herculaneum_, accounts of the late discoveries of antiquities made
there, p. 49, 88, 619.

_Heat_ of the air, July 1757, remarks on it by Dr. Huxham and Dr.
Watson, p. 428.

---- of the weather, account of that in July 1757, by Dr. Huxham, p.
523.

---- of the weather in Georgia, account of it, p. 754.

_Hemlock Dropwort_, further account of its poisonous effects, p. 556.

_Himsel de_, Nicholai, M. D. de rariori quadam specie, in Suecia
reperta, tractatus, p. 692.

_Home_, Robert, Surgeon, his account of the flexor tendon torn out in
its whole extent, and the first joint of the thumb torn off, p. 617.

_Horned Cattle_, the usefulness of inoculation to prevent the
contagious distemper among them, p. 528.

_Huxham_, John, M. D. his remarks on the heat of the air, July 1757, p.
428.

---- ---- ---- ---- ---- on the extraordinary heat of the weather in
July 1757, p. 523.


I

_Jenty_, Nicholas, his account of a man, whose intestines, &c. all
cohered, and who after death fell under his inspection, p. 550.

_Ileum_, the gut, cut thro’ by a knife, instance of the successful
treatment of it, p. 35.

_Indigo_ plant, effects of it, and of the opuntia, or prickly pear, in
colouring the juices of living animals, p. 296.

_Inoculation_, its usefulness on horned cattle, to prevent the
contagious distemper among them, p. 528.

_Intestines_, remarkable case of the cohesions of all of them in a man,
p. 550.

_Johnstone_, James, M. D. his account of two extraordinary cases of
gall-stones, p. 543.

_Iris_, solar, observations on an evening, or rather nocturnal one, p.
293.


K

_Klinkenberg_, Mr. D. his observations upon the comet in Sept. and Oct.
1757, p. 483.


L

_Lacteals_, experiment to prove that salt of steel does not enter them,
p. 594.

_Lanreath_, effects of a storm of thunder and lightning there, June 27,
1756, p. 104.

_Layard_, Daniel Peter, M. D. his account of an extraordinary case of a
diseased eye, p. 747.

---- Daniel Peter, M. D. his discourse on the usefulness of inoculating
the horned cattle, p. 528.

_Leprous_ persons in the isle of Guadaloupe, account of a visitation of
them, p. 38.

_Lestwithiel_, in Cornwall, effects of lightning upon the church and
steeple there, p. 198.

_Lewis_, William, M. B. his experimental examination of Platina, Paper
V. and VI. p. 148, 156.

_Lichen_, memoir concerning it, p. 652.

_Light_, some experiments concerning its different refrangibility, p.
733.

_Lightning_, its effects upon the church and steeple of Lestwithiel in
Cornwall, p. 198.

_Limax_ non cochleata, observations on it, p. 585.

_Lime-water_, its lithontriptic virtue, p. 386.

_Limpet-Fish_, found at Bermuda, account of it, p. 859.

_Linnæus_, his account of the faculty called Vigiliæ Florum, with an
enumeration of several plants subject to that law, p. 506.

_Lingfield_, in Surry, account of an earthquake felt there, Jan. 24,
1758, p. 614.

_Looe_, effects of a storm of thunder and lightning there, June 27,
1756, p. 104.


M

_Maps_, Geographical, the best form of them, p. 553.

---- and Charts, a short dissertation on them, p. 563.

_Magnetism_, and Polarity, given to brass, p. 774.

_Malverne_ waters, their good effects, p. 23.

_Memoir_, an historical one on the genus of plants called Lichen,
Usnea, Coralloides, and Lichenoides, p. 652.

_Men_, living, essay towards ascertaining their specific gravity, p. 30.

_Milles_, Jeremiah, D. D. letters to him, with accounts of the effects
of thunder and lightning at Looe and Lanreath, June 27, 1756, p. 104.

---- ---- ---- his account of the Carlsbad mineral waters in Bohemia,
p. 25.

_Miller_, Mr. Philip, concerning the effects of a storm at Wigton in
Cumberland, p. 194.

---- ---- ---- his remarks on a letter of Mr. John Ellis to P. C. Webb,
Esq; printed in Phil. Trans. vol. xlix. part ii. p. 806.--p. 430.

_Mitchell_, Sir Andrew, his account of an extraordinary shower of black
dust, that fell in the Island of Zetland, Oct. 20, 1755, p. 297.

_Mixtures_, effervescent, strange effects of some, p. 19.

_Moffat_, in Annandale, a new medicinal well lately discovered there,
p. 117.

_Mortification_, remarkable efficacy of the bark in one, p. 379.

_Mount’s-Bay_, account of some trees discovered underground on the
shore there, p. 51.

_Mounsey_, James, M. D. his account of the strange effects of some
effervescent mixtures, p. 19.

_Mountaine_ and Dodson, tables of the variation of the magnetic needle
by them, adapted to every five degrees of lat. and long. in the more
frequented oceans, p. 329.

---- Wm. his dissertation on maps and charts, p. 563.

_Murdoch_, Patrick, his description of the best form of geographical
maps, p. 553.

---- ---- his trigonometry abridged, p. 538.

_Munckley_, Nich. M. D. his account of the extraordinary efficacy of
the bark in the delirium of a fever, p. 609.


N

_Needle_, magnetic, its variation, p. 329.

_New England_, account of an earthquake felt there, Nov. 18, 1755. p. 1.

_Newbury_, in Berkshire, account of the peat-pit near it, p. 109.

_Nightshade_, deadly, botanical and medical history of it, p. 62.

_Nixon_, Rev. John, A. M. his account of some of the antiquities
discovered at Herculaneum, &c. p. 88.

---- ---- ---- ---- his account of the temple of Serapis at Pozzuoli in
Naples, p. 166.

---- ---- ---- ---- his dissertation on the antiquity of glass in
windows, p. 601.

_Norfolk_ Boy, observations on the case of one, who was cured of
convulsive fits by the discharge of worms, p. 836.

_Number_ of the people of England, observations on it, p. 356, 457, 465.


O

_Observationes_ anatomico-medicæ de monstro bicorporeo virgineo, p. 311.

_Oenanthe_ aquatica succo viroso crocante of Lobel, farther account of
its poisonous effects, p. 856.

_Oil_, its efficacy, taken as a vermifuge, p. 837.

_Operation_, an extraordinary one performed in the dock-yard at
Portsmouth, p. 288.

_Opuntia_, or prickly pear, effects of it, and of the Indigo plant, in
colouring the juices of living animals, p. 296.

_Orthoceratitis_, de rariori quadam specie, in Suecia reperta,
tractatus, p. 692.

_Oram_, Rev. Richard, his account of a boy cured of convulsive fits by
the discharge of worms, p. 518.

_Oxford_, account of the black assize there, p. 699.


P

_Paderni_, Camillo, his account of the late discoveries at Herculaneum,
p. 49.

---- ---- ---- ---- of an earthquake at Herculaneum, and of some late
discoveries there, p. 619.

_Palsey_, instance of the cure of it by electricity, p. 392.

_Pantheon_, at Rome, account of the alterations making in it, p. 115.

_Parsons_, James, M. D. his account of some extraordinary tumours upon
the head of a man in St. Bartholomew’s Hospital, p. 350.

---- ---- ---- his account of fossil fruits, and other bodies, found in
the island of Shepey, p. 396.

_Paralytic_ cases, the effects of electricity in them, p. 481.

_Patella_, or Limpet-Fish, found at Bermuda, account of it, p. 859.

_Peyssonel_, John Andrew, M. D. his account of a visitation of the
leprous persons in the isle of Guadaloupe, p. 38.

---- ---- ---- ---- his observations on the worms that form sponges, p.
590.

---- ---- ---- ---- observations on the Limax non cochleata purpur
ferens, p. 585.

---- ---- ---- ---- observations on the Alga marina latifolia, p. 631.

---- ---- ---- ---- observations on a slight but very particular
earthquake, p. 645.

---- ---- ---- ---- observations on the Manchenille apple, p. 772.

---- ---- ---- ---- observations on the Corona Solis Marina Americana,
or American Sea-Sun-Crown, p. 843.

_Peat-pit_, account of one near Newbury in Berkshire, p. 109.

_People_ of England, concerning the number of them, p. 457.

---- ---- ---- an answer to Mr. Forster’s letter, concerning their
number and increase, 465.

_Peking_, a description of the plan of it, p. 704.

_Perry_, Mr. his letter to Dr. Stukeley, concerning the Earthquake at
Sumatra in Nov. and Dec. 1756, p. 491.

_Phœnician_ numeral characters anciently used at Sidon, dissertation on
them, p. 791.

_Plants_, impressions of them on the slates of coals, p. 228.

---- catalogue of the fifty from Chelsea Garden, for 1756, p. 236.

---- observations on the sleep of them, p. 506.

---- catalogue of the fifty from Chelsea Garden, for 1757, p. 648.

_Platina_, experimental examination of it, Paper V. and VI. p. 148, 156.

_Platt_, Mr. Joshua, his account of the fossil thigh-bone of an animal
dug up at Stonesfield, near Woodstock, p. 524.

_Polarity_ and Magnetism, communicated to brass, p. 774.

_Polypus_, Sea, account of it, p. 777.

_Pozzuoli_, account of the temple of Serapis there, p. 166.

_Postscript_ to Dr. Whytt’s observations on Lord Walpole’s case, p. 385.

_Pringle_, John, M. D. on the virtues of soap in dissolving the stone,
p. 221.

---- ---- ---- ---- his account of the effects of electricity in
paralytic cases, p. 481.

_Problems_, isoperimetrical, a further attempt to facilitate the
solution of them, p. 623.

_Pulteney_, M. Richard, his botanical and medical history of the
Solanum Lethale, p. 62.

---- ---- ---- his observations on the sleep of plants, p. 506.

_Pulse_, quickness of it in coughs, attended with infarction of the
lungs, lessened by blisters, p. 569.


R

_Register_, Parish, extract of that in Great Shefford in Berkshire,
with observations, p. 356.

_Remarks_ on Dr. Job Baster’s Observationes de corallinis, &c. p. 280.

_Robertson_, Mr. John, his essay towards ascertaining the specific
gravity of living men, p. 30.

---- ---- ---- ---- account of an extraordinary operation performed in
Portsmouth dock-yard, p. 288.

---- ---- ---- ---- ---- of the fall of water under bridges, p. 492.


S

_Salt-water_, experiments on applying Dr. Hales’s method of distilling
it to the steam-engine, p. 53.

_Satellite_, concerning the irregularities in the motion of one,
arising from the spheroidical figure of its primary planet, p. 807.

_Sea-water_, method of making it fresh with wood-ashes, p. 635.

_Sea Alga_ with broad leaves, observations on it, p. 631.

_Series_, invention of a general method for determining the sum of
every 2d, 3d, 4th, 5th, &c. term of one, taken in order, p. 757.

_Serapis_, Temple of, at Pozzuoli, account of it, p. 166.

_Shepey_ Island, account of fossil fruits, and other bodies, found
there, p. 396.

_Short_, James, M. A. his account of some experiments concerning the
different refrangibility of light by Mr. John Dollond, p. 733.

_Shefford_, Great, extract of the parish register there, with
observations, p. 356.

_Simpson_, Mr. Tho. his resolution of a general proposition for
determining the horary alteration of the terrestrial equator, &c. p.
416.

---- ---- ---- ---- further attempt to facilitate the resolution of
isoperimetrical problems, p. 623.

---- ---- ---- ---- invention of a general method for determining the
sum of every 2d, 3d, 4th, or 5th, &c. term of a series, taken in order,
p. 757.

_Skeleton_ of an animal, description of a fossil one found in the alum
rock near Whitby, p. 786.

_Slates_ of Coals, account of the impressions of plants on some, p. 228.

_Sleep_ of plants, observations on it, p. 506.

_Smeaton_, Mr. John, concerning the effects of lightning upon the
church and steeple of Lestwithiel in Cornwall, p. 198.

---- ---- ---- his remarks on the different temperature of the air at
Edystone, from that observed at Plymouth, between July 7th and 14th,
1757, p. 488.

_Snail_, the naked, producing purple, observations on it, p. 585.

_Snipe_, or Tringa, a new-discovered species of it, p. 255.

_Solanum_ Lethale, Bella-Donna, or Deadly Nightshade, brief botanical
and medical history of it, p. 62.

_Soap_, its virtues in dissolving the stone, p. 221, 386.

_Sponges_, formed by worms, new observations on them, p. 590.

_Steam-Engine_, experiments on applying Dr. Hales’s method of
distilling salt-water to it, p. 53.

_Steam_, farther experiments for increasing the quantity of it in a
fire-engine, p. 570.

_Stone_, the virtues of soap in dissolving it, p. 221.

_Stones_, remarkable instance of four rough ones discovered in an human
urinary bladder, extracted by the lateral method of cutting for the
stone, p. 579.

_Storm_, effects of one at Wigton in Cumberland, p. 194.

---- ---- ---- ---- at Looe and Lanreath, p. 104.

_Stonesfield_, account of the fossil thigh-bone of an animal dug up
there, p. 524.

_Sumatra_, Island of, account of an earthquake felt there in Nov. and
Dec. 1756, p. 491.

_Swinton_, the Rev. John, his remarks on a Parthian coin with a Greek
and Parthian legend, never before published, p. 175.

---- ---- ---- ---- ---- dissertation upon the Phœnician numeral
characters antiently used at Sidon, p. 791.


T

_Tables_ of the variation of the magnetic needle, a sett, which exhibit
the result of upwards of fifty thousand observations, adapted to every
five degrees of lat. and long. in the more frequented oceans, p. 329.

_Tendon_, Flexor, one torn out in its whole extent, and the first joint
of the thumb torn off, p. 617.

_Thermometer_, state of it at the Hague, Jan. 9, 1757. p. 148.

_Thermometers_, description of some for particular uses, p. 300.

_Thigh-bone_ of a large animal, a fossil one dug up at Stonesfield,
near Woodstock, in Oxfordshire, p. 524.

_Thunder_ and Lightning, the effects of them in the parishes of Looe
and Lanreath, June 27th, 1756, p. 104.

_Torkos_, Just. Joan. observationes anatomico-medicæ de monstro
bicorporeo virgineo, p. 311.

_Travers_, Mr. Peter, his successful treatment of the gut ileum cut
thro’ by a knife, p. 35.

_Trees_, some discovered under-ground on the shore at Mount’s-Bay in
Cornwall, p. 51.

_Trembley_, Mr. Abraham, extract of a letter from him on several
curious subjects of natural history, p. 58.

---- ---- ---- his state of the thermometer at the Hague, Jan. 9, 1757,
p. 148.

_Trigonometry_, abridgement of it, p. 538.

_Tumours_, some extraordinary ones upon the head of a man in St.
Bartholomew’s-Hospital, p. 350.

_Tringa_, or Snipe, account of a new-discovered species, p. 255.


V

_Vapour_, remarks on the opinion of Henry Eles, Esq; concerning the
ascent of it, p. 240.

_Ventilators_, attempt to improve the manner of working them by the
help of a fire-engine, p. 727.

_Vessels_, lymphatic, of animals, observations on their origin and use,
p. 322.

_Vigiliæ florum_, account of that faculty, p. 506.

_Virginia_, remarkable storm of hail there, p. 746.


W

_Wall_, John, M.D. concerning the good effects of Malverne waters, p.
23.

---- ---- ---- his observations on the case of the Norfolk Boy cured of
convulsions by the discharge of worms, p. 836.

_Walmesley_, Mr. Charles, his letter on the irregular motions of a
satellite, p. 807.

_Walker_, Mr. John, his account of a new medicinal well lately
discovered at Moffat in Annandale, p. 117.

_Walpole_, Lord Horace, sequel to his account of his own case (Phil.
Trans. vol. xlvii. p. 43 & 472.) p. 205.

_Ward_, John, LL.D. letter communicated by him, with an account of the
alterations making in the Pantheon at Rome, p. 115.

---- ---- ---- his account of the black assize at Oxford, p. 699.

_Warner_, Jos. Surgeon, his account of a remarkable case of an
aneurism, &c. p. 363.

---- ---- ---- ---- instance of four rough stones extracted from the
urinary bladder of a man, by the lateral method of cutting for the
stone, p. 579.

_Water_, account of its fall under bridges, p. 492.

---- fresh, method of procuring it from salt water with wood-ashes, p.
635.

_Waters_, the Carlsbad mineral, account of them, p. 25.

---- ---- ---- ---- their lithontriptic virtue with lime-water and
soap, p. 386.

---- Malverne, the good effects of them, p. 23.

---- medicinal, at Moffat in Annandale, account of them, p. 117.
Various experiments on them, p. 121.

_Watson_, William, M. D. memoir concerning a genus of plants called
Lichen, &c. p. 652.

---- ---- ---- his account of some extraordinary effects arising from
convulsions, p. 743.

---- ---- ---- his further account of the poisonous effects of the
Oenanthe aquatica succo viroso crocanthe of Lobel, or Hemlock Dropwort,
p. 856.

_Well_, medicinal, a new one discovered near Moffat in Annandale, p.
117.

_Weather_, extraordinary heat of it in July 1757, p. 523.

---- ---- ---- ---- ---- in Georgia, p. 754.

_Wendlingen_, P. Joan. observatio eclipsis lunaris facta Matriti, die
30 Julii 1757, p. 640.

_White_, Taylor, Esq; his discourse on the Cinamon, Cassia, or Canella,
p. 860.

_Whytt_, Robert, M. D. his account of the lithontriptic virtue of the
Carlsbad waters, lime-water and soap, p. 386.

---- ---- ---- concerning the remarkable effects of blisters in
lessening the quickness of the pulse in coughs attended with infarction
of the lungs, p. 569.

_Wigton_, in Cumberland, effects of a storm there, p. 194.

_Winthrop_, Mr. Professor, concerning an earthquake felt in New
England, and the neighbouring parts of America, Nov. 18, 1755, p. 1.

_Windows_, dissertation on the antiquity of glass in them, p. 601.

_Wright_, Edward, M.D. his account of an experiment, whereby it appears
that salt of steel does not enter the lacteals, p. 594.

_Wood-ashes_, their use in distilling fresh water from sea-water, p.
635.

_Wooller_, Mr. his description of the fossil skeleton of an animal
found in the alum rock near Whitby, p. 786.

_Worms_, account of a boy cured of convulsive fits by the discharge of
some, p. 518. Other cases of the like nature, p. 839.

---- that form sponges, new observations on them, p. 590.


Z

_Zetland_, island of, account of an extraordinary shower of black dust
which fell there, Oct. 20, 1755, p. 297.




ERRATA.

_P._ 769. _l._ 3. _read_ the order of

_P._ 791. _l._ 6. _for_ Oxon, _with a comma, read_ Oxon. _with a
full-point_.

_P._ 792. _l._ 5. _of the quotations, for_ Froel. _read_ Frœl.

_In the Contents to Part_ I. _of this Vol. Page_ 5. _l._ 21. _for_ 115.
_read_ 117.


FOOTNOTES:

[1] Manna lies about 50 miles to the southward of Marlborough.

[2] The island of Sumatra is between 7 and 800 miles long from north to
south.

[3] Cumberland-house is a new well-built house for the governor of the
place.

[4] _N. B. Both these are contiguous to the fort._

[5] Laye house or factory is about 30 miles to the northward of
Marlborough, and Manna house or factory fifty miles to the southward.

[6] The sugar-plantation is five or six miles from Marlborough.

[7] The _qualloe_ is the country word for a river’s mouth.

[8] Poblo Point lies about three leagues to the southward of
Marlborough.

[9] _Doosoons_ are villages.

[10] Letter from William Veale, Esq;

[11] Letter from John Trehawk, Esq;

[12] A timber support of the deads.

[13] Loose rubbish and broken stones of the mine.

[14] Mr. J. Nantcarrow.

[15] Trifolium quoque inhorrescere et folia contra tempestatem
subrigere certum est. Hist. Nat. lib. xviii. cap. 35.

[16] Flor. Lappon. p. 222.

[17] Prosp. Alpin. de plantis Ægypti, cap. 10.

[18] It is not improbable, that a considerable portion of whiting might
be used instead of pure white lead, which is frequently done: and this
supposition is favoured by the mixture’s not proving fatal to the boy,
as such a quantity of white lead in all probability would.

[19] What Lhwyd calls _ostreum minus falcatum_, Nº. 451.

[20] Memoires de l’Acad. des Sciences, anno 1748. p. 326.

[21] Ibid. p. 338.

[22] Ibid. p. 337.

[23] See my Essay on the contagious Distemper, p. 70.

[24] Pag. 143 and 338.

[25] Essay on the Plague.

[26] See Logarith. Canon. deser. _Edinb._ 1614. p. 48.

[27] _Senex_ drew several of that form.

[28] See the Preface to the small Berlin Atlas.

[29] This constant logarithm contains the reduction of the diff. of
longitude to parts of radius unity, and to _Briggs_’s Modulus.

[30] See _Cotesii_ Logometr. prop. 6.

[31] Physiological Essays, p. 69.

[32] Physiological Essays, p. 69.

[33] Dr. Pringle’s Observations on the Diseases of the Army, part iii.
chap. 2.

[34] Vincentius Menghinus _de Ferrearum particularum progressu in
Sanguinem. Comment. Acad. Bonon._ T. II. P. 2. pag. 475.

[35] Phil. Transact. by Lowthorpe, vol. iii. p. 102. edit. 1749. the
same by Jones, vol. v. p. 259.

[36] Vol. I. art. xii. p. 364.

[37] In a paper read Feb. 24. 1757. See Art. xiii. p. 88.

[38] _Porticuum, in quibus spatiari consueverat (Domitianus) parietes
phengite lapide distinxit, e cujus splendore per imagines quicquid a
tergo fieret, provideret._ Sueton. Domit. c. 14.

[39] Plin. Nat. Hist. lib. xxxvi. c. 26. §. 66.

[40] Pliny mentions a kind of glass or jet called _obsidianum_:
--_nigerrimi coloris, aliquando et translucidi, crassiore visu, atque
in speculis parietum pro imagine umbras reddente_. Nat. Hist. lib.
xxxvi. c. 26. §. 67.

And that the practice of staining glass was known in his time, appears
from what he says concerning the _obsidianum_ mentioned above:--_Fit et
genere tincturæ--totum rubens vitrum, atque non translucidum_. Ibid.

[41] Panciroll. Rer. Mem. p. 288.

[42] These glass balls had sometimes water within them: _Cùm additâ
aquâ vitreæ pilæ sole adverso in tantum excandescant, ut vestes
exurant_. Plin. lib. xxxvi. c. 22. §. 45.

_Invenio medicos, quæ sunt urenda corporum, non alitèr utilius id fieri
putare, quam crystallinâ pilâ adversis positâ solis radiis._ Plin. Nat.
Hist. lib. xxxvii. c. 6. §. 10.

[43] Vid. Mons. Renaudot Memoires de l’Acad. des Inscript. tom. I.

[44] Vid. infra, not. 11.

[45] _Theatrum Scauri_----_scena ei triplex in altitudinem_ CCCLX
_columnarum_.----_Ima pars scenæ e marmore fuit_: media e vitro: _summa
e tabulis inauratis_. Nat. Hist. lib. xxxvi. c. 15.

[46] A. V. 678. Hard. not. Plin. lib. xxxvi. c. 8.

[47] _Agrippa in thermis, quas Romæ fecit, figlinum opus encausto
pinxit, in reliquis albaria adornavit: non dubiè_ vitreas facturus
cameras, si prius inventum id fuisset, _aut a parietibus scenæ--Scauri
pervenisset in cameras_. Lib. xxxvi. c. 25. §. 64.

[48] Seneca, exposing the luxury of the Romans with regard to their
baths, says, _Pauper sibi videtur ac sordidus, nisi parietes magnis ac
pretiosis orbibus refulserint--nisi_ vitro absconditur camera.--Ep. 86.

[49] Plin. Nat. Hist. lib. xxxvi. c. 22. §. 45.

[50] Nat. Hist. lib. xxxvi. c. 22. §. 45.

[51] Vid. Salmasius in a passage to be produced hereafter.

[52] Hist. de l’Acad. des Inscrip. tom. I.

[53] Montfauc. Antiq. vol. III. part i. lib. iii. c. 4. Lipsius in loc.
_&c._

[54] _Quædam nostrâ demum prodiisse memoriâ scimus; ut speculariorum
usum, perlucente testâ, clarum transmittentium lumen._ Sen. ep. 90.

[55] _Quod fenestris obducebatur ad translucendum, ac lucem
admittendam_ specular _vetens Latini vocârunt. Idque ex speculari
lapide, quí est_ φεγγιτης, _aut_ ex vitro _fiebat, aut aliâ translucidâ
materiâ. Nam_ specular dictum, non quod ex speculari lapide _factum
esset, sed quod visum transmitteret, ac per id_ speculari _liceret_.
Salm. Exerc. Plin. in Solin. tom. II. p. 771.

[56] Villa’s of the Anc. illustrated, p. iv.

[57] One of Pliny’s cautions for preserving apples is--_Austros
specularibus arcere_. Nat. Hist. lib. xv. c. 16.

Martial further informs us, that the Romans used to screen their
orchards of choice fruit-trees with _specularia_. Lib. viii. epig. 14.

[58] I suppose he means that of Fortuna Seia. Lib. xxxvi. c. 22.

[59] Salmasius, speaking of the custom of adorning chambers with glass,
says--_Quod proximè ætatem suam incepisse fieri narrat Plinius. Quum M.
Scaurus_----Ex. Plin. tom. II. p. 854.

I do not find this expresly asserted by Pliny: but it might have been
so in fact. This fashion indeed was not begun till after Agrippa had
built his _thermæ_: but if we suppose that to have been even as late as
his third consulship, _viz. ante Christ._ 27. (_Helvicus_), when he
erected the Pantheon (or at least its portico), near adjoining to those
_thermæ_, there would have been sufficient room, from that period to
the birth of Pliny (_viz. anno Christi_ 24), for the introduction of
this usage.

[60] Plin. Ep. V. I. 111.

[61] Plin. Nat. Hist. lib. xxxvi. c. 26. §. 66.

[62] Vid. supra.

[63] Anno Christi 80.

[64] In order to justify my placing the testimony of this Father so
high, I would observe, that St. Jerome (_De Scriptor. Eccles._) says,
that Lactantius--_Extremâ senectute magister Cæsaris Crispi filii
Constantini in Gallia fuit_. He must probably have exercised this
charge between _anno Christi_ 309, when Constantine began to reign,
and 320. If he was then of a great age, he might have composed the
treatise, out of which this authority is produced, and which was one
of the earliest of his works, that are extant (_Vid. Sparkii præf. ad
Lactant._), 40 years before, _viz._ about _anno Christi_ 280; which
brings us up to 200 years after the overthrow of Herculaneum, as above.

[65] Lib. i. c. 20. See this subject largely discussed in Bodæus à
Stapel Comment. in Theoph. p. 156. et seq.

[66] Opera omnia à C. B. edit. 1598. p. 64.

[67] _Usnea vulgaris loris longis implexis_ Hist. Musc. p. 56. _Lichen
plicatus_ Lin. Sp. Pl. 1154. _Muscus arboreus: Usnea_ Officin. C. B.
Raii Syn. III. p. 64.

[68] _Usnea barbata loris tenuibus fibrosis_ Hist. Musc. p. 63. _Lichen
barbatus_ Lin. Sp. Pl. 1155. _Quercus excrementum villosum_ C. B. p.
422. Bauhine took this to be the true _Usnea Arabum_.

[69] _Usnea ceratoides candicans glabra et odorata_ Hist. Musc. p. 71.
_Muscus arboreus candicans et odorifer_ Camelli Raii Hist. III. Append.
p. 3.

[70] Civil and Natural History of Jamaica, p. 80.

[71] Hist. Plant. I. par. ii. p. 88.

[72] Flor. Lap. p. 342. Ɛ. Flor. Suec. Ed. II. p. 416.

[73] Flor. Lap. p. 348.

[74] Hist. Plant. I. p. 115.

[75] _Usnea jubata nigricans._ Dillen. Hist. Musc. p. 64. _Lichen
jubatus_ Lin. Sp. Pl. 1155. _Muscus corallinis saxatilis fæniculaceus_,
Rock-hair. Raii Syn. III. p. 65. n. 7.

[76] _Usnea capillacea et nodosa_ Dillen. Hist. Musc. 60. _Muscus
arboreus nodosus_ C. B. p. 361. Raii Syn. III. p. 65. n. 4.

[77] Raii Hist. Pl. III. p. 28.

[78] Natural History of Norway, p. 148.

[79] _Usnea capillacea citrina frutriculi specie._ Hist. Musc. p. 73.
_Muscus aureus tenuissimus_ Merret. Pin. p. 79. Raii syn. p. 65. nº. 8.

[80] Flor. Suec. Ed. II. p. 427.

[81] Hist. Plant. III. P. ii. lib. 9. p. 273.

[82] _Usnea dichotoma compressa segmentis capillaceis teretibus._ Hist.
Musc. 72. _Muscus arboreus aurantiacus flaminibus tenuissimis_ Pluk.
Alm. p. 254. Raii Hist. III. 28.

[83] _Coralloides corniculis longioribus et rarioribus._ Dillen. Hist.
Musc. p. 103. _Muscus corniculatus_ Ger. p. 1372. Park. 1308. Raii
Hist. I. p. 112. III. p. 28. _Lichenoides tubulosum cinereum minus
crustaceum minusque ramosum_ Raii Syn. 3. p. 67.

[84] _Coralloides montanum fruticuli specie ubique candicans_ Hist.
Musc. p. 107. _Lichen rangiferinus_ Lin. Sp. Pl. 1153. _Muscus
corallinus._ Tab. Ger. em.

[85] Flor. Lappon. p. 332.

[86] Enum. Stirp. Helv. p. 69. Nº. 38.

[87] The Novaccolæ are a people originally sprung from the Finlanders:
they fixed themselves in Lapland not long since, and traffick with the
old inhabitants.

[88] _Coralloides crispum et botryforme Alpinum_ Hist. Musc. p. 114.
_Lichen paschalis_ Lin. Sp. Pl. _Lichenoides non tubulum cinereum
ramosum totum crustaceum_ Raii Syn. III. 66. N. 11. This moss is not
common in England. Dr. Dillenius found it upon some of the mountains in
Wales. It is found in many places on Charley-forest, Leicestershire.

[89] Flor. Lappon. Nº. 489.

[90] _Coralloides corniculatum fasciculare tinctorium fuci teretis
facie_ Dillen. Hist. Musc. p. 120. _Cladonia tophacea_ Hill. Hist.
Pl. p. 93. _Fucus capillaris tinctorius_ Raii Hist. I. p. 74. _Lichen
(Rocelia) fruticulosus solidus aphyllus subramosus tuberculis alternis_
Lin. Sp. Pl. 1154.

[91] L’Art de la Teinture des lains et des Etoffes de lain; Paris 1750,
p. 543.

[92] Raii Hist. Plant. I. p. 74.

[93] Nova Plant. Gener. p. 78.

[94] _Coralloides schyphiforme tuberculis fuscis_ Hist. Musc. 79.
_Lichenoides tubulosum pyxidatum cinereum._ Raii Syn. III. p. 68.
_Pyxidium margine leviter serrato._ Hill. Hist. Plant. p. 94.

[95] Willis Pharm. Rational. sect. I. cap. 6. _de tussi puerorum
convulsiva_.

[96] De Aëre et Morbis epidemicis, p. 76, 77. vol. I.

[97] Lowthorp’s Abridgment, vol. II. p. 660.

[98] _Lichenoides tartareum tinctorium candidum tuberculis atris._
Hist. Musc. p. 128.

[99] _Lichen (calcareus) leprosus candidus tuberculis atris_ Spec.
Plant. 1140.

[100] _Lichenoides leprosum tinctorium scutellis lapidum Caneri figura_
Hist. Musc. 130. _Lichenoides crustaceum et leprosum scutellare
cinereum._ Raii Syn. p. 70.

[101] Tournefort’s Voyage to the Levant, Eng. edit. Lond. 1741. in 8º,
vol. I. p. 248.

[102] _Lichenoides tartareum farinaceum scutellarum umbone fusco._
Hist. Musc. 132. _Placodium bracteis majusculis limbo albo cinctis_
Hill. Hist. Pl. p. 97.

[103] Flor. Suec. Ed. II. p. 407.

[104] _Lichenoides crustaceum et leprosum acetabulis majoribus luteis
limbis argenteis_ Raii Syn. p. 71. N. 46. Hist. Musc. p. 132.

[105] _Vide_ Œconom. Natur. in Amœn. Acad. vol. II. p. 17.

[106] _Lichenoides vulgatissimum cinereo-glaucum lacunosum et cirrosum_
Hist. Musc. p. 88. _Lichenoides crusta foliosa superne cinereo-glauca,
inferne nigra et cirrosa scutellis nigricantibus._ R. Syn. p. 72.

[107] _Lichenoides saxatile tinctorium foliis pilosis purpureis_ Raii
Syn. p 74. Nº. 70. Hist. Musc. p. 185. _Lichen petræus purpureus
Derbiensis_ Park. Theat. p. 1315. _Lichen omphalodes_ Lin. Spec. Pl.
1143.

[108] Park. Theat. Botan. p. 1315.

[109] Raii Hist. Plant. p. 116.

[110] Flor. Lappon. p. 343. V.

[111] Otherwise called _arnotto_.

[112] _Lichenoides vulgare sinuosum foliis et scutellis luteis._ Hist.
Musc. p. 180. _Lichenoides crusta foliosa scutellata flavescens._ Raii
Syn. p. 72. Nº. 59.

[113] Flor. Suec. Ed. II. p. 416. Nº. 1093.

[114] Linnæus has intitled this moss _Lichen (stygius) imbricatus,
folio is palmatis incurvis atris_. Fl. Suec. I. 949. Spec. Plant. 1143.
Fl. Suec. II. Nº. 1079.

[115] _Lichenoides coralliforme rostratum et canaliculatum._
Hist. Musc. 170. _Lichenoides arboreum ramosum angustioribus
cinereo-virescentibus ramulis._ Raii Syn. 75. _Lichen calicaris_ Lin.
Spec. Plant. 1146.

[116] _Lichenoides fuciforme tinctorium corniculis longioribus et
acutioribus._ Hist. Musc. 168. _Platysma corniculatum._ Hill Hist.
Plant. 90. _Lichen fuciformis_ Lin. Sp. Pl. 1147.

[117] _Lichenoides digitatum cinereum lactucæ foliis sinuosis_ Dillen.
Hist. Musc. 200. _Platysma sinuosum scutellis ovato-rotundis_ Hill
Hist. Pl. 89. _Lichen caninus_ Lin. Sp. Pl. 1149.

[118] See Lowthorp’s Abridgment, vol. III. p. 284.

[119] Dr. Van Swieten. See Comment. in Boerh. Aphor. §. 1147.

[120] Mechanical Account of Poisons, ed. 4th, p. 156.

[121] _Lichenoides pulmonium reticulatum vulgare marginibus peltiferis_
Dill. Hist. Musc. 212. _Lichenoides peltatum arboreum maximum._ Raii
Syn. p. 76. _Musc. pulmonarius_ C. B.

[122] Dillen. Hist. Musc. p. 213.

[123] _Lichenoides digitatum læte virens verrucis nigris notatum._
Ibid. p. 207.

[124] Boerhaav. Aphorism. §. 982.

[125] Vol. II, p. 69. _De Tœnia._

[126] _Musca apiformis, tota fusca, cauda obtusa, ex ejula caudata in
latrinis degente orta._ Raii Hist. Insect, p. 272.

[127] Faun. Suecica, Nº. 1084.

[128] See two cases nearly of this kind observed by Dr. Lister.
Lowthorp’s Abridgment, vol. III. p. 135.

[129] _Lichenoides rigidum eryngii folia referens_ Dillen. Hist. Musc.
p. 209. Raii Syn. p. 77. _Lichen foliis oblongis laciniatis marginibus
conniventibus ciliaribus._ Flor. Lappon. Hall. Helv. 75. _Lichen
(islandicus) foliaceus adscendens laciniatus marginibus elevatis
ciliaribus_ Lin. Flor. Suec. I. 959. II. 1085. Mat. Med. Nº. 493. Spec.
Plant. 1145.

[130] Raii Hist. Plant. p. 114.

[131] Flor. Lappon. Nº. 445.

[132] Horrebow’s Natural History of Iceland, p. 36.

[133] For the first account, see part first, p. 392.

[134] Sic in regist. et postea haud semel.

[135] Sic in regist.

[136] Sic in regist.

[137] Sic in regist.

[138] Sic in regist.

[139] Sic in regist.

[140] Page 285. edit. Lugd. Batav. 1625.

[141] Page 681. edit. London, 1631.

[142] Wood Hist. et Antiqu. Universit. Oxon. lib. i. p. 295. and Athen.
Oxon. vol. I. col. 237.

[143] Hist. & Antiquit. Universit. Oxon. ubi supra.

[144] Page 290, 2d edit.

[145] When the emperor goes out or comes into the palace, this bell is
rung.

[146] In these two houses are Jesuits of other nations. They are stiled
Portuguese, because these houses and churches depend on the mission of
the Jesuits founded by the king of Portugal.

[147] There are beaten there the five watches of the night. The sound
is heard thro’ the whole city.

[148] _Yong lo_, emperor of the last dynasty _Ming_, built these two
towers.

[149] The tribunals of the ministers and grand masters of the emperor’s
house are in the inclosure _Tse kin_.

[150] The feet are different in China; but 1800 feet always make a
_ly_. According to the measure of the foot the _ly_ will be greater or
less.

[151] This power is called in China the dynasty _Leao_.

[152] There is extant, in the Chinese and Tartar _Mantcheou_ languages,
an history of the dynasty of _Ki tan_.

[153] Of which dynasty there is extant a very curious history.

[154] Book I. Part ii. Prop. 3. Experiment 8. of his Optics.

[155] If α, β, γ, δ, _&c._ be supposed to represent the co-sines of the
angles 360° ⁄ _n_, 2 × 360° ⁄ _n_, 3 × 360° ⁄ _n_, _&c._ (the radius
being unity); then the roots of the equation _zⁿ_ - 1 = 0 (expressing
the several values of _p_, _q_, _r_, _s_, _&c._) will be truly defined
by 1, α + √(αα - 1), α - √(αα - 1), β + √(ββ - 1), β - √(ββ - 1), _&c._
The demonstration of this will be given farther on.

[156] Because -_ẋ_ ⁄ √(1 - _xx_) and -_Ẋ_ ⁄ √(1 - _XX_) are known to
express the fluxions of the circular arcs whose co-sines are _x_ and
_X_, it is evident, if those arcs be supposed in any constant ratio of
1 to _n_, that _nẋ_ ⁄ √(1 - _xx_) = _Ẋ_ ⁄ √(1 - _XX_), and consequently
that _nẋ_ ⁄ √(_xx_ - 1) (= _nẋ_ ⁄ (√-1 × √(1 - _xx_)) = _Ẋ_ ⁄ (√-1 ×
√(1 - _XX_)) = _Ẋ_ ⁄ √(_XX_ - 1). From whence, by taking the fluents,
_n_ × Log. (_x_ + √(_xx_ - 1)) (or Log. (_x_ + √(_xx_ - 1))_ⁿ_) = Log.
_X_ + √(_XX_ - 1); and consequently (_x_ + √(_xx_ - 1))_ⁿ_ = _X_ +
√(_XX_ - 1): whence also, seeing _x_ - √(_xx_ - 1) is the reciprocal
of _x_ + √(_xx_ - 1), and _X_ - √(_XX_ - 1) of _X_ + √(_XX_ - 1), it
is likewise evident, that (_x_ - √(_xx_ - 1))_ⁿ_ = _X_ - √(_XX_ - 1).
Hence, not only the truth of the above assumption, but what has been
advanced in relation to the roots of the equation _zⁿ_ - 1 = 0, will
appear manifest. For if _x_ ± √(_xx_ - 1) be put = _z_, then will _zⁿ_
(= (_x_ ± √(_xx_ - 1))_ⁿ_) = _X_ ± √(_XX_ - 1): where, assuming _X_
= 1 = co-s. 0 = co-s. 360° = co-s. 2 × 360° = co-s. 3 × 360°, _&c._
the equation will become _zⁿ_ = 1, or _zⁿ_ - 1 = 0; and the different
values of _x_, in the expression (_x_ ± √(_xx_ - 1)) for the root _z_,
will consequently be the co-sines of the arcs, 0 ⁄ _n_, 360° ⁄ _n_, (2
× 360°) ⁄ _n_, _&c._ these arcs being the corresponding _submultiples_
of those above, answering to the co-sine _X_ (= 1).----In the same
manner, if _X_ be taken = -1 = co-s. 180° = co-s. 3 × 180° = co-s. 5 ×
180°, _&c._ then will _zⁿ_ = -1, or _zⁿ_ + 1 = 0; and the values of _x_
will, in this case, be the co-sines of 180° ⁄ _n_, 3 × (180° ⁄ _n_), 5
× (180° ⁄ _n_), _&c._

[157] _Avellana purgatrix_; in French, _medicinier_.

[158] This refers to Mr. Baker’s having supposed, that old iron and old
brass may be mixt sometimes, and melted down together.

[159] Vide Wilkins’s real Character, p. 131. Bellon. aquat. p. 330.

[160] Some of the Pour-contrel kind have but one row of suckers on the
arms: such an one I have seen, whose arms were thirty inches long.

[161] Of this I gave an account some years ago, in my attempt towards a
Natural History of the Polype, chap. v.

[162] See Plate xxxi. Fig. 1.

[163] _De Num. quibusd. Sam. et Phœn. &c. Dissert._ p. 56-59. & Tab.
II. Oxon. 1750.

[164] _Marm. Palmyren. a Cl._ Dawk. _edit._ pass.

[165] Vid. Hadr. Reland. _Palæst. Illustrat._ p. 1014. Traject.
Batavor. 1714. Erasm. Frœl. ad _Annal. Compendiar. Reg. & Rer. Syr._
Tab. VIII. &c. Viennæ, 1754.

[166] _De Antiq. Hebræor. et Græcor. Lit. Libel._ Joan. Baptist.
Biancon. p. 31, 32. Bononiæ, 1748.

[167] 1. Maccab. i. 10.

[168] Hadr. Reland. _De Num. Vet. Hebr._ pass. Trajecti ad _Rhenum_,
1709.

[169] See Plate xxxi. Fig. 2.

[170] Honor. Arigon. _Num. Phœnic._ Tab. I. Num. 3, 6. Tarvisii, 1745.

[171] Nicol. Haym Roman. _Del Tesor. Britan._ Vol. i. p. 106. In
Londra, 1719.

[172] See Plate xxxi. Fig. 3.

[173] See Plate xxxi. Fig. 3.

[174] See Plate xxxi. Fig. 3.

[175] See the Phœnician Numerals in Plate xxxii.

[176] _Philosoph. Transact._ Vol. xlviii. Par. ii. p. 726.

[177] _De Num. quibusd. Sam. et Phœn. &c. Dissert._ p. 59-61. & Tab.
II. Oxon. 1750.

[178] See Plate xxxi. Fig. 4.

[179] Haym, ubi sup. p. 107.

[180] See Plate xxxi. Fig. 5.

[181] See Plate xxxi. Fig. 5.

[182] Honor. Arigon. _Num. Phœnic._ Tab. I, II. Tarvisii, 1745.

[183] Id. ibid. Tab. I. N. 5.

[184] See Plate xxxi. Fig. 6.

[185] See p. 793, 794.

[186] See plate xxxi. Fig. 7.

[187] See Plate xxxi. Fig. 8.

[188] _Recherches Curieuses des Monoyes de France &c. Par_ Claude
Bouterouë, p. 33. A Paris, 1666.

[189] See Plate xxxi. Fig. 9.

[190] Honor. Arigon. ubi sup. Tab. I. Num. 2.

[191] Claud. Bouterouë, ubi sup. p. 24.

[192] See Plate xxxi. Fig. 9.

[193] See Plate xxxi. Fig. 9.

[194] _Mémoires de Litterature, tirés des Registres &c._ Tom. xxiv. p.
64. A Paris, 1756.

[195] The whole note, here referred to, in the original runs thus.
“J’avois lû ce Mémoire à l’Académie en 1749, je le communiquai dans le
même temps à un étranger qui se trouvoit alors à Paris, & qui ayant
passé tout de suite en Angleterre, fit part à un docteur d’Oxford
de l’explication que j’avois donnée de la médaille de Jonathan. Ce
dernier _m’a fait l’honneur de l’adopter_ dans une savante Dissertation
imprimée a Oxford en 1750, à la suite d’une autre Dissertation sur
deux inscriptions Phéniciennes.” _Mémoires de Litterature, tirés des
Registres de l’Académie Royale des Inscriptions & Belles-Lettres, &c._
Tom. xxiv. p. 60. A Paris, 1756.

For the better understanding of this note, it will be proper to
observe, that the stranger therein mentioned was M. Brucker, Professor
of History in the University of Basil; with whom I contracted an
acquaintance when at Oxford, towards the close of March 1750. This
gentleman then informed me, that M. l’Abbé Barthelemy communicated
to him draughts of three Samaritan coins of Jonathan, prince and
high-priest of the Jews. He added, that one of these exhibited
the words ΒΑΣΙΛΕΩΣ ΑΛΕΞΑΝΔΡΟΥ; which, according to him, M. l’Abbé
Barthelemy interpreted of Alexander the Great, taking the piece
to have been twice struck. This M. Brucker afterwards in a great
measure confirmed, by a letter he wrote to me at Oxford; which I
published intire in 1750, and endeavoured to prove, that the foregoing
inscription was to be understood of Alexander I. king of Syria, and not
of Alexander the Great. The Samaritan inscription, which M. Brucker
only just touched upon, as is manifest from his letter, I likewise
attempted to explain; producing proper vouchers, in support of what I
advanced. Thus stands the fact, which seems to have given some offence
to M. l’Abbé, stated in the most concise manner possible; and from it,
thus stated, as I apprehend, are naturally deducible the following
observations.

1. As I differed in opinion from M. l’Abbé, with regard to the words
ΒΑΣΙΛΕΩΣ ΑΛΕΞΑΝΔΡΟΥ, as well as in several other respects, and
supported by indisputable authorities what I in all points advanced,
without receiving from any person whatsoever the least information
relative thereto; it very evidently appears, that I did not _adopt_ M.
l’Abbé’s explication of the coin in question.

2. By publishing M. Brucker’s letter, which I have still by me,
intire, I both did him justice, and clearly acknowledged M. l’Abbé to
have first discovered the medals it treats of to belong to Jonathan,
prince and high-priest of the Jews; and therefore have by no means
endeavoured, as he would insinuate, to rob him of the glory of such a
discovery.

3. As M. l’Abbé in effect owns himself to have seen my dissertation,
and has (if M. Brucker rightly informed me) since the reading of
his memoir, substituted my notion, relating to the words, ΒΑΣΙΛΕΩΣ
ΑΛΕΞΑΝΔΡΟΥ, in the room of his own; some people may perhaps imagine,
that I have at least as much reason to recriminate on this occasion,
as he had to charge me with the _adoption_ of his explication. Nay,
as he expresly acquaints the public, that M. Brucker imparted to
me the very interpretation of the coin he (M. l’Abbé) had before
communicated to him, and as this interpretation most evidently makes
it to have been first struck in the reign of Alexander the Great;
every unprejudiced person, unacquainted with the elevated genius and
extensive erudition of M. l’Abbé, will be strongly induced to believe,
that there would be no great injustice in a recrimination. But far
be it from me to retort the accusation upon M. l’Abbé. His uncommon
learning, his singular modesty, his strict honour, his utter contempt
of vanity and ostentation in every shape, so conspicuous to all the
world, must set him infinitely above the reach of such an imputation.
However, notwithstanding the superior merit and exalted abilities of
M. l’Abbé, notwithstanding the known aversion of the French writers
to the practice here hinted at, and their most generous and candid
treatment hitherto of those belonging to the British nation, it will
perhaps hereafter be thought expedient, by the ACADEMY OF INSCRIPTIONS
AND BELLES LETTRES, not frequently to suffer an interval of seven years
to elapse, between the reading and publication of their memoirs. For
by such unaccountable delays, if often repeated, a handle may possibly
be given to many of the _haughty islanders_ of reflecting upon, or at
least entertaining unfavourable sentiments of, some of the members of
that illustrious body.

See _De Num. quibusd. Sam. & Phœn. &c. Dissert._ p. 61-72. Oxon. 1750.

[196] F. Henric. Nor. Veronens. _An. et Epoch. Syromaced. &c._ p.
414-424. Lipsiæ, 1696.

[197] Erasm. Frœl. _Annal. Compend. Reg. et Rer. Syr._ p. 113. Viennæ,
1754.

[198] Joan. Harduin. _Op. Select._ p. 155, 156. Amst. 1709. Joan.
Foy-Vaillant Bellovac. _Numismat. Ær. Imperator. &c. Par. Alt._ p. 97.
Parisiis, 1695.

[199] Iidem ibid. & alib.

[200] F. Henr. Nor. Veronens. ubi sup.

[201] Diod. Sic. lib. xix. Plutarch. in _Demetr._ Appian. in _Syriac_.

[202] F. Henr. Nor. Veronens. ubi sup.

[203] Erasm. Frœl. ubi sup. p. 39. Joan. Foy-Vaill. _Seleucidar,
Imper._ p. 1-150. Lutet. Parisior. 1681.

[204] Joan. Foy-Vaill. Erasm. Frœl. Nicol. Haym Roman. &c.

[205] See above, p. 793, 794.

[206] Erasm. Frœl. ubi sup. p. 101.

[207] 1. Maccab. i. 10.

[208] See Plate xxxi.

[209] See Plate xxxii.

[210] It may not however be amiss to remark, that most of the forms of
the Phœnician centenary and decimal numeral characters rather resemble
the correspondent Palmyrene numerals of Gruter than those of Mr.
Dawkins; as will be obvious to every one, who shall think proper to
compare all those different characters one with another. _Philosoph.
Transact._ Vol. xlviii. Par. ii. p. 721, 741.

[211] See Plate xxxi. Fig. 5. & Arigon. Tab. II. Num. 11.

[212] See above, p. 791, 792.

[213] Nicol. Haym Roman. ubi sup. p. 100. Erasm. Frœl. ubi sup. p. 111.
Tab. XV.

[214] Joan. Foy-Vaill. ubi sup. p. 238. Erasm. Frœl. ubi sup. p. 57.
Tab. VII. Num. 1.

[215] Nicol. Haym Roman. ubi sup. p. 101. Erasm. Frœl. ubi sup. p. 111.

[216] Nicol. Haym Roman. ubi sup. p. 105, 106.

[217] Joan. Foy-Vaill. ubi sup. p. 200. Erasm. Frœl. ubi sup. p. 63.
Tab. VIII. Num. 30.

[218] Hadr. Reland. _Palæst. Illustrat._ p. 1014.

[219] Nicol. Haym Roman. ubi sup. p. 100, 101.

[220] Joan. Foy-Vaill. ubi sup. p. 375, 378. Haym, ubi sup. p. 100.
Erasm. Frœl. ubi sup. p. 111. Tab. XV.

[221] Gul. Bevereg. _Institut. Chronologic._ p. 278-331. Eond. 1721.

[222] Oleosis magna tribuitur efficacia, quæ maxime experimento
Fr. Rhedi videtur confirmata, dum muscas et alia insecta variis
liquoribus immersa in vivis permansisse refert, exceptis aliis oleo
perunctis et infusis, quæ invicem mortua vitam non receperunt, licet
radiis solaribus fuerint exposita. Equidem libenter concedo hæc omnia
veritati esse consona, atque etiam oleosa, ut ol. oliv. rapar. et
amygd. dulc. non sine fructu adhiberi: sed scire licet minime illa
eo unquam scopo posse offerri, ut vermes enecent, quia admodum magna
oleorum copia requireretur, si immediatè vermes per totum intestinorum
volumen dispersos deberent extinguere. Multo magis oleosa in gravibus
a lumbricis symptomatibus ideo censerem utilia, quia sensibiles
intestinorum tunicas spasmo constrictas relaxant, et mucilagine quasi
obliniunt atque defendunt, ut postea acriora quaædam et purgantia
remedia magis secure et sine læsione exhiberi possint. Ita ego sæpius
mirabili cum effectu ad vermes enecandos et symptomata lenienda ol.
amygd. d. ad aliquot cochlearia, imo ℥j vel ℥ij circa lecti introitum
vel summo mane pueris præscripsi sumendum, subjungendo aliquot horas
post pilulas ex extracto panchymagogo Crollii, resina jalappæ, et
mercurio dulci paratas.

 _Hoffmann. Supplement. ad Med. Systemat. de Infant. Morb. cap. 10. de
 Vermibus._

[223] I have since been informed, that the boy’s parents being
extremely poor, the medicines were left off as soon as he began to
recover; and that, upon their disuse for some time, he was again
attacked with the same fits as before.

[224] All oils dry more readily after they have been boiled; by which
the superfluous aqueous parts are carried off. Drying oils are also
made by the addition of such substances, as absorb humidities.

[225] See Phil. Trans. Nº. 480. p. 227.




Corrections

Contents

 CVI. A Discourse on the Cinnamon
 CXVI. A Discourse on the Cinnamon

p. 593

  the sea, nor to any other accident whatesover,
  the sea, nor to any other accident whatsoever,

p. 616

  and also heard a noise, like the distant dicharge of a cannon:
  and also heard a noise, like the distant discharge of a cannon:

p. 618

  that the whole weight of his body was supended by it,
  that the whole weight of his body was suspended by it,

p. 681

  by almost all the the botanic writers
  by almost all the botanic writers

Index

  _Vapour_, remarks on the opinion of Henry Eeles, Esq; concerning the
  ascent of it, p. 240.

  _Vapour_, remarks on the opinion of Henry Eles, Esq; concerning the
  ascent of it, p. 240.

p. 712

  are pretty spacious inclosures, each of which has it number.
  are pretty spacious inclosures, each of which has its number.

p. 730

  When it moves upwards, the click _b_ fixed to the frame, stops the
  larger rocket C,

  When it moves upwards, the click _b_ fixed to the frame, stops the
  larger rochet C,

p. 735

  which would not be affected by the different refrangibilty of light;
  which would not be affected by the different refrangibility of light;

p. 741

  Having thus got rid of the principal cause of the imperfection of
  refracting telelescopes

  Having thus got rid of the principal cause of the imperfection of
  refracting telescopes

p. 759

  and the _same cofficients_ with the original series
  and the _same coefficients_ with the original series

p. 766

  the measures of the angles expressed by (360° ⁄ _n_) × _m_, 2 × (360
  ⁄ _n_) × _m_, 3 × (360 ⁄ _n_) × _m_, &c.

  the measures of the angles expressed by (360° ⁄ _n_) × _m_, 2 × (360°
  ⁄ _n_) × _m_, 3 × (360° ⁄ _n_) × _m_, &c.

p. 768

  The soluion of this case, in a manner a little different,
  The solution of this case, in a manner a little different,

p. 773

  We see by this, that the effects of the poison of the Manchinelle are
  different

  We see by this, that the effects of the poison of the Manchenille are
  different

p. 842

  I beg leave to subjoin it by way of postcript.
  I beg leave to subjoin it by way of postscript.

p. 846

  coverings in different parts of the the world.
  coverings in different parts of the world.

Index

  _Vapour_, remarks on the opinion of Henry Eeles, Esq; concerning the
  ascent of it, p. 240.

  _Vapour_, remarks on the opinion of Henry Eles, Esq; concerning the
  ascent of it, p. 240.


Errata

p. 497

Also (2_a_)²: _vv_∷ _a_: _vv_ ⁄ 4_a_

should be

Also (2_a_)²: _vv_∷ _a_: (25b ⁄ 21c)² × _vv_ ⁄ 4_a_

p. 542

sin. (AC + AM) ⁄ 2 × sin. (AC - AM) ⁄ 2 = ((_b_ + _d_) × (_b_ - _d_) =)
(sin. ½ AC + sin. ½ AM) × (sin. ½ AC - sin. ½ AM).

should be

sin. (AC + AM) ⁄ 2 × sin. (AC - AM) ⁄ 2 = ((_b_ + _d_) × (_b_ - _d_)) =
(sin. ½ AC + sin. ½ AM) × (sin. ½ AC - sin. ½ AM).

p. 830

hincque motus apsidis spatio unius anni solaris prodit 33´, 95 vel ferè
34´ in consequentia, qui tempore

should be

hincque motus apsidis spatio unius anni solaris prodit 33´, 95’’ vel
ferè 34´ in consequentia, qui tempore