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                             THE TELESCOPE




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 [Illustration: Galileo’s Telescopes. (_Frontispiece_) (_Bull. de la
 Soc. Astron. de France._)]




                             THE TELESCOPE

                                  BY

                           LOUIS BELL, PH.D.

   CONSULTING ENGINEER; FELLOW, AMERICAN ACADEMY OF ARTS & SCIENCES;
     PAST-PRESIDENT, THE ILLUMINATING ENGINEERING SOCIETY; MEMBER,
                     AMERICAN ASTRONOMICAL SOCIETY

                             FIRST EDITION

                    MCGRAW-HILL BOOK COMPANY, INC.
                     NEW YORK: 370 SEVENTH AVENUE
                  LONDON: 6 & 8 BOUVERIE ST., E. C. 4
                                 1922




                        COPYRIGHT, 1922, BY THE
                    MCGRAW-HILL BOOK COMPANY, INC.

                        THE MAPLE PRESS YORK PA




PREFACE


This book is written for the many observers, who use telescopes for
study or pleasure and desire more information about their construction
and properties. Not being a “handbook” in two or more thick quartos, it
attempts neither exhaustive technicalities nor popular descriptions of
great observatories and their work. It deals primarily with principles
and their application to such instruments as are likely to come into
the possession, or within reach, of students and others for whom the
Heavens have a compelling call.

Much has been written of telescopes, first and last, but it is for
the most part scattered through papers in three or four languages,
and quite inaccessible to the ordinary reader. For his benefit the
references are, so far as is practicable, to English sources, and
dimensions are given, regretfully, in English units. Certain branches
of the subject are not here discussed for lack of space or because
there is recent literature at hand to which reference can be made.
Such topics are telescopes notable chiefly for their dimensions, and
photographic apparatus on which special treatises are available.

Celestial photography is a branch of astronomy which stands on its
own feet, and although many telescopes are successfully used for
photography through the help of color screens, the photographic
telescope proper and its use belongs to a field somewhat apart,
requiring a technique quite its own.

It is many years, however, since any book has dealt with the telescope
itself, apart from the often repeated accounts of the marvels it
discloses. The present volume contains neither pictures of nebulæ nor
speculations as to the habitibility of the planets; it merely attempts
to bring the facts regarding the astronomer’s chief instrument of
research somewhere within grasp and up to the present time.

The author cordially acknowledges his obligations to the important
astronomical journals, particularly the Astro-physical Journal,
and Popular Astronomy in this country; The Observatory, and the
publications of the Royal Astronomical Society in England; the
Bulletin de la Société Astronomique de France; and the Astronomische
Nachrichten; which, with a few other journals and the official reports
of observatories form the body of astronomical knowledge. He also
acknowledges the kindness of the various publishers who have extended
the courtesy of illustrations, especially Macmillan & Co. and the
Clarendon Press, and above all renders thanks to the many friends
who have cordially lent a helping hand—the Director and staff of the
Harvard Observatory, Dr. George E. Hale, C. A. R. Lundin, manager of
the Alvan Clark Corporation, J. B. McDowell, successor of the Brashear
Company, J. E. Bennett, the American representative of Carl Zeiss,
Jena, and not a few others.

  LOUIS BELL.

  BOSTON, MASS.,
  _February, 1922_.




CONTENTS


                                                          PAGE

  PREFACE                                                  vii

  CHAP.

     I. THE EVOLUTION OF THE TELESCOPE                       1

    II. THE MODERN TELESCOPE                                31

   III. OPTICAL GLASS AND ITS WORKING                       57

    IV. THE PROPERTIES OF OBJECTIVES AND MIRRORS            76

     V. MOUNTINGS                                           98

    VI. EYE-PIECES                                         134

   VII. HAND TELESCOPES AND BINOCULARS                     150

  VIII. ACCESSORIES                                        165

    IX. THE TESTING AND CARE OF TELESCOPES                 201

     X. SETTING UP AND HOUSING THE TELESCOPE               228

    XI. SEEING AND MAGNIFICATION                           253

  APPENDIX                                                 279

  INDEX                                                    281




THE TELESCOPE




CHAPTER I

THE EVOLUTION OF THE TELESCOPE


In the credulous twaddle of an essay on the Lost Arts one may generally
find the telescope ascribed to far antiquity. In place of evidence
there is vague allusion of classical times or wild flights of fancy
like one which argued from the Scriptural statement that Satan took
up Christ into a high mountain and showed him all the kingdoms of the
earth, that the Devil had a telescope—bad optics and worse theology.

In point of fact there is not any indication that either in classical
times, or in the black thousand years of hopeless ignorance that
followed the fall of Roman civilization, was there any knowledge of
optical instruments worth mentioning.

The peoples that tended their flocks by night in the East alone kept
alive the knowledge of astronomy, and very gradually, with the revival
of learning, came the spirit of experiment that led to the invention of
aids to man’s natural powers.

The lineage of the telescope runs unmistakably back to spectacles, and
these have an honorable history extending over more than six centuries
to the early and fruitful days of the Renaissance.

That their origin was in Italy near the end of the thirteenth century
admits of little doubt. A Florentine manuscript letter of 1289 refers
to “Those glasses they call spectacles, lately invented, to the great
advantage of poor old men when their sight grows weak,” and in 1305
Giordano da Rivalto refers to them as dating back about twenty years.

Finally, in the church of Santa Maria Maggiore in Florence lay
buried Salvino d’Amarto degli Armati, (obiit 1317) under an epitaph,
now disappeared, ascribing to him the invention of spectacles. W.
B. Carpenter, F. R. S., states that the inventor tried to keep the
valuable secret to himself, but it was discovered and published before
his death. At all events the discovery moved swiftly. By the early
fourteenth century it had spread to the Low Countries where it was
destined to lead to great results, and presently was common knowledge
over all civilized Europe.

It was three hundred years, however, between spectacles and the
combination of spectacle lenses into a telescope, a lapse of time
which to some investigators has seemed altogether mysterious. The
ophthalmological facts lead to a simple explanation. The first
spectacles were for the relief of presbyopia, the common and lamentable
affection of advancing years, and for this purpose convex lenses of
very moderate power sufficed, nor was material variation in power
necessary. Glasses having a uniform focus of a foot and a half or
thereabouts would serve every practical purpose, but would be no
material for telescopes.

Myopia was little known, its acquired form being rare in a period of
general illiteracy, and glasses for its correction, especially as
regards its higher degrees, probably came slowly and were in very small
demand, so that the chance of an optical craftsman having in hand the
ordinary convex lenses and those of strong negative curvature was
altogether remote. Indeed it was only in 1575 that Maurolycus published
a clear description of myopia and hypermetropia with the appropriate
treatment by the use of concave and convex lenses. Until both of these,
in quite various powers, were available, there was small chance of
hitting upon an instrument that required their use in a highly special
combination.

At all events there is no definite trace of the discovery of telescopic
vision until 1608 and the inventor of record is unquestionably one Jan
Lippershey, a spectacle maker of Middelburg in Zeeland, a native of
Wesel. On Oct. 2, 1608 the States-General took under consideration a
petition which had been presented by Lippershey for a 30-year patent
to the exclusive right of manufacture of an instrument for seeing at a
distance, or for a suitable pension, under the condition that he should
make the instrument only for his country’s service.

The States General pricked up its ears and promptly appointed on Oct. 4
a committee to test the new instrument from a tower of Prince Maurice’s
palace, allotting 900 florins for the purchase of the invention should
it prove good. On the 6th the committee reported favorably and the
Assembly agreed to give Lippershey 900 florins for his instrument, but
desired that it be arranged for use with both eyes.

Lippershey therefore pushed forward to the binocular form and two
months later, Dec. 9, he announced his success. On the 15th the new
instrument was examined and pronounced good, and the Assembly ordered
two more binoculars, of rock crystal, at the same price. They denied a
patent on the ground that the invention was known to others, but paid
Lippershey liberally as a sort of retainer to secure his exclusive
services to the State. In fact even the French Ambassador, wishing to
obtain an instrument from him for his King, had to secure the necessary
authorization from the States-General.

[Illustration: _Bull. de la Soc. Astron. de France._ FIG. 1.—Jan
Lippershey, Inventor of the Telescope.]

It is here pertinent to enquire what manner of optic tube Lippershey
showed to back up his petition, and how it had come to public
knowledge. As nearly as we may know these first telescopes were about a
foot and a half long, as noted by Huygens, and probably an inch and a
half or less in aperture, being constructed of an ordinary convex lens
such as was used in spectacles for the aged, and of a concave glass
suitable for a bad case of short sightedness, the only kind in that day
likely to receive attention.

It probably magnified no more than three or four diameters and was most
likely in a substantial tube of firmly rolled, glued, and varnished
paper, originally without provision for focussing, since with an eye
lens of rather low power the need of adjustment would not be acute.

As to the invention being generally known, the only definite attempt
to dispute priority was made by James Metius of Alkmaar, who, learning
of Lippershey’s petition, on Oct. 17, 1608, filed a similar one,
alleging that through study and labor extending over a couple of years
he, having accidentally hit upon the idea, had so far carried it out
that his instrument made distant objects as distinct as the one lately
offered to the States by a citizen and spectacle maker of Middelburg.

He apparently did not submit an instrument, was politely told to
perfect his invention before his petition was further considered,
and thereafter disappears from the scene, whatever his merits. If he
had actually noted telescopic vision he had neither appreciated its
enormous importance nor laid the facts before others who might have
done so.

The only other contemporary for whom claims have been made is Zacharius
Jansen, also a spectacle maker of Middelburg, to whom Pierre Borel,
on entirely second hand information, ascribed the discovery of the
telescope. But Borel wrote nearly fifty years later, after all the
principals were dead, and the evidence he collected from the precarious
memories of venerable witnesses is very conflicting and points to about
1610 as the date when Jansen was making telescopes—like many other
spectacle makers.[1]

 [1] There is a very strong probability that Jansen was the inventor of
 the compound microscope about the beginning of the seventeenth century.

Borel also gave credence to a tale that Metius, seeking Jansen,
strayed into Lippershey’s shop and by his inquiries gave the shrewd
proprietor his first hint of the telescope, but set the date at 1610.
A variation of this tale of the mysterious stranger, due to Hieronymus
Sirturus, contains the interesting intimation that he may have been of
supernatural origin—not further specified. There are also the reports,
common among the ignorant or envious, that Lippershey’s discovery was
accidental, even perhaps made by his children or apprentice.

Just how it actually was made we do not know, but there is no reason to
suppose that it was not in the commonplace way of experimenting with
and testing lenses that he had produced, perhaps those made to meet a
vicious case of myopia in one of his patrons.

When the discovery was made is somewhat clearer. Plainly it antedated
Oct. 2, and in Lippershey’s petition is a definite statement that an
instrument had already been tested by some, at least, of the members of
the States-General. A somewhat vague and gossipy note in the _Mercure
Française_ intimates that one was presented to Prince Maurice “about
September of the past year” (1608) and that it was shown to the Council
of State and to others.

Allowing a reasonable time between Lippershey’s discovery and the
actual production of an example suitable for exhibition to the
authorities, it seems likely that the invention dates back certainly
into the summer of 1608, perhaps even earlier.

At all events there is every indication that the news of it spread
like wild-fire. Unless Lippershey were unusually careful in keeping
his secret, and there are traditions that he was not, the sensational
discovery would have been quickly known in the little town and every
spectacle maker whose ears it reached would have been busy with it.

If the dates given by Simon Marius in his _Mundus Jovialis_ be correct,
a Belgian with an air of mystery and a glass of which one of the
lenses was cracked, turned up at the Frankfort fair in the autumn of
1608 and at last allowed Fuchs, a nobleman of Bimbach, to look through
the instrument. Fuchs noted that it magnified “several” times, but
fell out with the Belgian over the price, and returning, took up the
matter with Marius, fathomed the construction, tried it with glasses
from spectacles, attempted to get a convex lens of longer focus from a
Nuremburg maker, who had no suitable tools, and the following summer
got a fairly good glass from Belgium where such were already becoming
common.

With this Marius eventually picked up three satellites of Jupiter—the
fourth awaited the arrival of a superior telescope from Venice. Early
in 1609 telescopes “about a foot long” were certainly for sale in
Paris, a Frenchman had offered one in Milan by May of that year, a
couple of months later one was in use by Harriot in England, an example
had reached Cardinal Borghese, and specimens are said to have reached
Padua. Fig. 2 from the “_Mundus Jovialis_,” shows Marius with his
“Perspicilium,” the first published picture of the new instrument.
Early in 1610 telescopes were being made in England, but if the few
reports of performance, even at this date, are trustworthy, the “Dutch
trunk” of that period was of very indifferent quality and power, far
from being an astronomical instrument.

[Illustration: _The Observatory._ FIG. 2.—Simon Marius and his
Telescope.]

One cannot lay aside this preliminary phase of the evolution of the
telescope without reference to the alleged descriptions of telescopic
apparatus by Roger Bacon, (c. 1270), Giambattista della Porta (1558),
and Leonard Digges (1571), details of which may be found in Grant’s
_History of Physical Astronomy_ and many other works.

Of these the first on careful reading conveys strongly the conviction
that the author had a pretty clear idea of refraction from the
standpoint of visual angle, yet without giving any evidence of
practical acquaintance with actual apparatus for doing the things which
he suggests.

Given a suitable supply of lenses, it is reasonably certain that Bacon
was clever enough to have devised both telescope and microscope, but
there is no evidence that he did so, although his manifold activities
kept him constantly in public view. It does not seem unlikely, however,
that his suggestions in manuscripts, quite available at the time, may
have led to the contemporaneous invention of spectacles.

Porta’s comments sound like an echo of Bacon’s, plus a rather muddled
attempt to imagine the corresponding apparatus. Kepler, certainly
competent and familiar with the principles of the telescope, found his
description entirely unintelligible. Porta, however, was one of the
earliest workers on the _camera obscura_ and upon this some of his
cryptic statements may have borne.

Somewhat similar is the situation respecting Digges. His son makes
reference to a Ms. of Roger Bacon as the source of the marvels he
describes. The whole account, however, strongly suggests experiments
with the _camera obscura_ rather than with the telescope.

The most that can be said with reference to any of the three is that,
if he by any chance fell upon the combination of lenses that gave
telescopic vision, he failed to set down the facts in any form that
could be or was of use to others. There is no reason to believe that
the Dutch discovery, important as it was, had gone beyond the empirical
observation that a common convex spectacle lens and a concave one of
relatively large curvature could be placed in a tube, convex ahead,
at such a distance apart as to give a clear enlarged image of distant
objects.

It remained for Galileo (1564-1647) to grasp the general principles
involved and to apply them to a real instrument of research. It was in
May 1609 that, on a visit to Venice, he heard reports that a Belgian
had devised an instrument which made distant objects seem near, and
this being quickly confirmed by a letter from Paris he awakened to the
importance of the issue and, returning to Padua, is said to have solved
the problem the very night of his arrival.

Next day he procured a plano-convex and a plano-concave lens, fitted
them to a lead tube and found that the combination magnified three
diameters, an observation which indicates about what it was possible
to obtain from the stock of the contemporary spectacle maker.[2] The
relation between the power and the foci of the lenses he evidently
quickly fathomed for his next recorded trial reached about eight
diameters.

 [2] The statement by Galileo that he “fashioned” these first lenses
 can hardly be taken literally if his very speedy construction is to be
 credited.

With this instrument he proceeded to Venice and during a month’s stay,
August, 1609, exhibited it to the senators of the republic and throngs
of notables, finally disclosing the secret of its construction and
presenting the tube itself to the Doge sitting in full council. This
particular telescope was about twenty inches long and one and five
eighths inches in aperture, showing plainly that Galileo had by this
time found, or more likely made, an eye lens of short focus, about
three inches, quite probably using a well polished convex lens of the
ordinary sort as objective.

[Illustration: _Lodge “Pioneers of Science.”_ FIG. 3.—Galileo.]

Laden with honors he returned to Padua and settled down to the hard
work of development, grinding many lenses with his own hands and
finally producing the instrument magnifying some 32 times, with which
he began the notable succession of discoveries that laid the foundation
of observational astronomy. This with another of similar dimensions is
still preserved at the Galileo Museum in Florence, and is shown in the
Frontispiece. The larger instrument is forty-nine inches long and an
inch and three quarters aperture, the smaller about thirty-seven inches
long and of an inch and five-eighths aperture. The tubes are of paper,
the glasses still remain, and these are in fact the first astronomical
telescopes.

Galileo made in Padua, and after his return to Florence in the autumn
of 1610, many telescopes which found their way over Europe, but quite
certainly none of power equalling or exceeding these.

In this connection John Greaves, later Savilian Professor of Astronomy
at Oxford, writing from Sienna in 1639, says: “Galileus never made but
two good glasses, and those were of old Venice glass.” In these best
telescopes, however, the great Florentine had clearly accomplished a
most workmanlike feat. He had brought the focus of his eye lens down to
that usual in modern opera glasses, and has pushed his power about to
the limit for simple lenses thus combined.

The lack of clear and homogeneous glass, the great difficulty
of forming true tools, want of suitable commercial abrasives,
impossibility of buying sheet metals or tubing (except lead), and
default of now familiar methods of centering and testing lenses, made
the production of respectably good instruments a task the difficulty of
which it is hard now to appreciate.

The services of Galileo to the art were of such profound importance,
that his form of instrument may well bear his name, even though his
eyes were not the first that had looked through it. Such, too, was the
judgment of his contemporaries, and it was by the act of his colleagues
in the renowned Acaddemia dei Lincei, through the learned Damiscianus,
that the name “Telescope” was devised and has been handed down to us.

A serious fault of the Galilean telescope was its very small field of
view when of any considerable power. Galileo’s largest instrument had
a field of but 7′15″, less than one quarter the moon’s diameter. The
general reason is plain if one follows the rays through the lenses as
in Fig. 4 where _AB_ is the distant object, _o_ the objective, _e_ the
eye lens, _ab_ the real image in the absence of _e_, and _a′b′_ the
virtual magnified image due to _e_.

It will be at once seen that the axes of the pencils of rays from
all parts of the object, as shown by the heavy lines, act as if they
diverged from the optical center of the objective, but diverging
still more by refraction through the concave eye lens _e_, fall
mostly outside the pupil of the observer’s eye. In fact the field is
approximately measured by the angle subtended by the pupil from the
center of _o_.

To the credit of the Galilean form may be set down the convenient
erect image, a sharp, if small, field somewhat bettered by a partial
compensation of the aberrations of the objective by the concave eye
lens, and good illumination. For a distant object the lenses were
spaced at the difference of their focal lengths, and the magnifying
power was the ratio of these, _f_{o}/f_{e}_.

[Illustration: FIG. 4.—Diagram of Galileo’s Telescope.]

But the difficulty of obtaining high power with a fairly sizeable
field was ultimately fatal and the type now survives only in the
form of opera and field glasses, usually of 2 to 5 power, and in an
occasional negative eye lens for erecting the image in observatory
work. Practically all the modern instruments have achromatic objectives
and commonly achromatic oculars.

[Illustration: FIG. 5.—Diagram of Kepler’s Telescope.]

The necessary step forward was made by Johann Kepler (1571-1630), the
immortal discoverer of the laws of planetary motion. In his _Dioptrice_
(1611) he set forth the astronomical telescope, substantially, save for
the changes brought by achromatism, as it has been used ever since.
His arrangement was that of Fig. 5 in which the letters have the same
significance as in Fig. 4.

There are here three striking differences from the Galilean form.
There is a real image in the front focus of the eye lens _e_, the rays
passing it are refracted inwards instead of outwards, to the great
advantage of the field, and any object placed in the image plane will
be magnified together with the image. The first two points Kepler
fully realized, the third he probably did not, though it is the basis
of the micrometer. The lenses _o_ and _e_ are obviously spaced at the
sum of their focal lengths, and as before the magnifying power is the
ratio of these lengths, the visible image being inverted.

Kepler, so far as known, did not actually use the new telescope, that
honor falling about half a dozen years later, to Christopher Scheiner,
a Jesuit professor of mathematics at Ingolstadt, best known as a very
early and most persistent, not to say verbose, observer of sun spots.
His _Rosa Ursina_ (1630) indicates free use of Kepler’s telescope for
some years previously, in just what size and power is uncertain.[3]
Fontana of Naples also appears to have been early in the field.

 [3] Scheiner also devised a crude parallactic mount which he used
 in his solar observations, probably the first European to grasp the
 principle of the equatorial. It was only near the end of the century
 that Roemer followed his example, and both had been anticipated by
 Chinese instruments with sights.

But the new instrument despite its much larger field and far greater
possibilities of power, brought with it some very serious problems.
With increased power came greatly aggravated trouble from spherical
aberration and chromatic aberration as well, and the additive
aberrations of the eye lens made matters still worse. The earlier
Keplerian instruments were probably rather bad if the drawings of
Fontana from 1629 to 1636 fairly represent them.

If one may judge from the course of developments, the first great
impulse to improvement came with the publication of Descartes’
(1596-1650) study of dioptrics in 1637. Therein was set forth much of
the theory of spherical aberration and astronomers promptly followed
the clues, practical and impractical, thus disclosed.

Without going into the theory of aberrations the fact of importance
to the improvement of the early telescope is that the longitudinal
spherical aberration of any simple lens is directly proportional to its
thickness due to curvature. Hence, other things being equal, the longer
the focus for the same aperture the less the spherical aberration both
absolutely and relatively to the image. Further, although Descartes
knew nothing of chromatic aberration, and the colored fringe about
objects seen through the telescope must then have seemed altogether
mysterious, it, also, was greatly relieved by lengthening the focus.

For the chromatic circle produced by a simple lens of given diameter
has a radial width substantially irrespective of the focal length. But
increasing the focal length increases in exact proportion the size
of the image, correspondingly decreasing the relative effect of the
chromatic error.

Descartes also suggested several designs of lenses which would be
altogether free of spherical aberration, formed with elliptical or
hyperbolic curvature, and for some time fruitless efforts were made to
realize this in practice. It was in fact to be near a century before
anyone successfully figured non-spherical surfaces. It was spherical
quite as much as chromatic aberration that drove astronomers to long
telescopes.

Meanwhile the astronomical telescope fell into better hands than those
of Scheiner. The first fully to grasp its possibilities was William
Gascoigne, a gallant young gentleman of Middleton, Yorkshire, born
about 1620 (some say as early as 1612) and who died fighting on the
King’s side at Marston Moor, July 2, 1644. To him came as early as
1638 the inspiration of utilizing the real focus of the objective for
establishing a telescopic sight.

[Illustration: FIG. 6.—Diagram of Terrestrial Ocular.]

This shortly took the form of a genuine micrometer consisting of a pair
of parallel blades in the focus, moved in opposite directions by a
screw of duplex pitch, with a scale for whole revolutions, and a head
divided into 100 parts for partial revolutions. With this he observed
much from 1638 to 1643, measured the diameters of sun, moon and planets
with a good degree of precision, and laid the foundations of modern
micrometry. He was equipped by 1639 with what was then called a large
telescope.

His untimely death, leaving behind an unpublished treatise on optics,
was a grave loss to science, the more since the manuscript could not be
found, and, swept away by the storms of war, his brilliant work dropped
out of sight for above a score of years.

Meanwhile De Rheita (1597-1660), a Capuchin monk, and an industrious
and capable investigator, had been busy with the telescope, and in
1645 published at Antwerp a somewhat bizarre treatise, dedicated to
Jesus Christ, and containing not a little practical information. De
Rheita had early constructed binoculars, probably quite independently,
had lately been diligently experimenting with Descartes’ hyperbolic
lens, it is needless to say without much success, and was meditating
work on a colossal scale—a glass to magnify 4,000 times.

But his real contribution to optics was the terrestrial ocular. This
as he made it is shown in Fig. 6 where _a b_ is the image formed by
the objective in front of the eye lens r, s and t two equal lenses
separated by their focal lengths and _a′ b′_ the resultant reinverted
image. This form remained in common use until improved by Dolland more
than a century later.

[Illustration: FIG. 7.—Johannes Hevelius.]

A somewhat earlier form ascribed to Father Scheiner had merged the two
lenses forming the inverting system of Fig. 6, into a single lens used
at its conjugate foci.

Closely following De Rheita came Johannes Hevelius (1611-1687) of
Danzig, one of the really important observers of the seventeenth
century. His great treatise _Selenographia_ published in 1647 gives us
the first systematic study of the moon, and a brief but illuminating
account of the instruments of the time and their practical construction.

At this time the Galilean and Keplerian forms of telescope were in
concurrent use and Hevelius gives directions for designing and making
both of them. Apparently the current instruments were not generally
above five or six feet long and from Hevelius’ data would give not
above 30 diameters in the Galilean form. There is mention, however, of
tubes up to 12 feet in length, and of the advantage in clearness and
power of the longer focus plano-convex lens. Paper tubes, evidently
common, are condemned, also those of sheet iron on account of their
weight, and wood was to be preferred for the longer tubes.

Evidently Hevelius had at this time no notion of the effect of the
plano-convex form of lens as such in lessening aberration, but he
mentions a curious form of telescope, actually due to De Rheita, in
which the objective is double, apparently of two plano-convex lenses,
the weaker ahead, and used with a concave eye lens. If properly
proportioned such a doublet would have less than a quarter the
spherical aberration of the equivalent double convex lens.

Hevelius also mentions the earlier form of re-inverting telescope above
referred to, and speaks rather highly of its performance. To judge from
his numerous drawings of the moon made in 1643 and 1644, his telescopes
were much better than those of Scheiner and Fontana, but still woefully
lacking in sharp definition.

Nevertheless the copper plates of the _Selenographia_, representing
every phase of the moon, placed the lunar details with remarkable
accuracy and formed for more than a century the best lunar atlas
available. One acquires an abiding respect for the patience and skill
of these old astronomers in seeing how much they did with means utterly
inadequate.

One may get a fair idea of the size, appearance, and mounting of
telescopes in this early day from Fig. 8, which shows a somewhat
advanced construction credited by Hevelius to a suggestion in
Descartes’ _Dioptrica_. Appearances indicate that the tube was
somewhere about six feet long, approximately two inches in aperture,
and that it had a draw tube for focussing. The offset head of the mount
to allow observing near the zenith is worth an extra glance.

Incidentally Hevelius, with perhaps pardonable pride, also explains the
“Polemoscope,” a little invention of his own, made, he tells us, in
1637. It is nothing else than the first periscope, constructed as shown
in Fig. 9, a tube _c_ with two right angled branches, a fairly long
one _e_ for the objective _f_, a 45° mirror at _g_, another at _a_,
and finally the concave ocular at _b_. It was of modest size, of tubes
1⅔ inch in diameter, the longer tube being 22 inches and the upper
branch 8 inches, a size well suited for trench or parapet.

[Illustration: FIG. 8.—A Seventh Century Astronomer and his Telescope.]

Even in these days of his youth Hevelius had learned much of practical
optics as then known, had devised and was using very rational methods
of observing sun-spots by projection in a darkened room, and gives
perhaps the first useful hints at testing telescopes by such solar
observations and on the planets. He was later to do much in the
development and mounting of long telescopes and in observation,
although, while progressive in other respects, he very curiously never
seemed to grasp the importance of telescopic sights and consistently
refused to use them.

Telescope construction was now to fall into more skillful hands.
Shortly after 1650 Christian Huygens (1629-1695), and his accomplished
brother Constantine awakened to a keen interest in astronomy and
devised new and excellent methods of forming accurate tools and of
grinding and polishing lenses.

[Illustration: FIG. 9.—The first Periscope.]

By 1655 they had completed an instrument of 12 feet focus with which
the study of Saturn was begun, Titan the chief satellite discovered,
and the ring recognized. Pushing further, they constructed a telescope
of 23 feet focal length and 2⅓ inches aperture, with which four
years later Christian Huygens finally solved the mystery of Saturn’s
ring.

Evidently this glass, which bore a power of 100, was of good defining
quality, as attested by a sketch of Mars late in 1695 showing plainly
Syrtis Major, from observation of which Huygens determined the rotation
period to be about 24 hours.

The Huygens brothers were seemingly the first fully to grasp the
advantage of very long focus in cutting down the aberrations, the
aperture being kept moderate. Their usual proportions were about as
indicated above, the aperture being kept somewhere nearly as the square
root of the focus in case of the larger glasses.

In the next two decades the focal length of telescopes was pushed
by all hands to desperate extremes. The Huygens brothers extended
themselves to glasses up to 210 feet focus and built many shorter ones,
a famous example of which, of 6 inches aperture and 123 feet focal
length, presented to the Royal Society, is still in its possession.
Auzout produced even longer telescopes, and Divini and Campani,
in Rome, of whom the last named made Cassini’s telescopes for the
Observatory of Paris, were not far behind. The English makers were
similarly busy, and Hevelius in Danzig was keeping up the record.

[Illustration: FIG. 10.—Christian Huygens.]

Clearly these enormously long telescopes could not well be mounted
in tubes and the users were driven to aerial mountings, in which the
objective was at the upper end of a spar or girder and the eye piece at
the lower. Figure 11 shows an actual construction by Hevelius for an
objective of 150 feet focal length.

In this case the main support was a T beam of wooden planks well braced
together. Additional stiffness was given by light wooden diaphragms
at short intervals with apertures of about 8 inches next to the
objective, and gradually increasing downwards. The whole was lined up
by equalizing tackle in the vertical plane, and spreaders with other
tackle at the joints of the 40foot sections of the main beam. The mast
which supported the whole was nearly 90 feet high.

So unwieldly and inconvenient were these long affairs that, quite apart
from their usual optical imperfections, it is little wonder that they
led to no results commensurate with their size. In fact nearly all the
productive work was done with telescopes from 20 to 35 feet long, with
apertures roughly between 2 and 3 inches.

[Illustration: FIG. 11.—Hevelius’ 150-foot Telescope.]

Dominique Cassini to be sure, scrutinizing Saturn in 1684 with
objectives by Campani, of 100 and 136 feet focus picked up the
satellites Tethys and Dione, but he had previously found Iapetus with
a 17-foot glass, and Rhea with one of 34 feet. The longer glasses
above mentioned had aerial mounts but the smaller ones were in tubes
supported on a sort of ladder tripod. A 20-foot objective, power 90,
gave Cassini the division in Saturn’s ring.

A struggle was still being kept up for the non-spherical curves urged
by Descartes. It is quite evident that Huygens had a go at them,
and Hevelius thought at one time that he had mastered the hyperbolic
figure, but his published drawings give no indication that he had
reduced spherical aberration to any perceptible degree. At this time
the main thing was to get good glass and give it true figure and
polish, in which Huygens and Campani excelled, as the work on Saturn
witnesses.

These were the days of the dawn of popular astronomy and many a
gentleman was aroused to at least a casual interest in observing the
Heavens. Notes Pepys in his immortal _Diary_: “I find Reeves there, it
being a mighty fine bright night, and so upon my leads, though very
sleepy, till one in the morning, looking on the moon and Jupiter, with
this twelve foot glass, and another of six foot, that he hath brought
with him to-night, and the sights mighty pleasant, and one of the
glasses I will buy.”

Little poor Pepys probably saw, by reason of his severe astigmatism,
but astronomy was in the air with the impulse that comes to every
science after a period of brilliant discovery. Another such stimulus
came near the end of the eighteenth century, with the labors of Sir
William Herschel.

Just at this juncture comes one of the interesting episodes of
telescopic history, the ineffectual and abandoned experiments on
reflecting instruments.

[Illustration: FIG. 12.—Gregory’s Diagram of his Telescope.]

In 1663 James Gregory (1638-1675) a famous Scottish mathematician,
published his _Optica Promota_, in which he described the rather
elegant construction which bears his name, a perforated parabolic
mirror with an elliptical mirror forward of the focus returning an
image to the ocular through the perforation. It was convenient in that
it gave an erect image, and it was sound theoretically, and, as the
future proved, practically, but the curves were quite too much for the
contemporary opticians. Figure 12 shows the diagrammatic construction
as published.

The next year Gregory started Reive, a London optician, doubtless the
same mentioned by Pepys, on the construction of a 6 foot telescope.
This rather ambitious effort failed of material success through the
inability of Reive to give the needed figures to the mirrors,[4] and of
it nothing further appears until the ingenious Robert Hooke (1635-1703)
executed in 1674 a Gregorian, apparently without any notable results.
There is a well defined tradition that Gregory himself was using one in
1675, at the time of his death, but the invention then dropped out of
sight.

 [4] He attempted to polish them on cloth, which in itself was
 sufficient to guarantee failure.

No greater influence on the art attended the next attempt at a
reflector, by Isaac Newton (1643-1727). This was an early outcome of
his notable discovery of the dispersion of light by prisms, which led
him to despair of improving refracting telescopes and turned his mind
to reflectors.

Unhappily in an experiment to determine whether refraction and
dispersion were proportional he committed the singular blunder of
raising the refractive index of a water-filled prism to equality
with glass by dissolving sugar of lead in it. Without realizing the
impropriety of thus varying two quite unknown quantities at once in
his crucial experiment, he promptly jumped to the conclusion that
refraction and dispersion varied in exact proportion in all substances,
so that if two prisms or lenses dispersed light to the same extent they
must also equally refract it. It would be interesting to know just how
the fact of his bungling was passed along to posterity. As a naïve
apologist once remarked, it was not to be found in his “_Optics_.” But
Sir David Brewster and Sir John Herschel, both staunch admirers of the
great philosopher, state the fact very positively. If one may hazard a
guess it crept out at Cambridge and was passed along, perhaps to Sir
William Herschel, via the unpublished history of research that is rich
in picturesque details of the mare’s nests of science. At all events a
mistake with a great name behind it carries far, and the result was to
delay the production of the achromatic telescope by some three quarters
of a century.

Turning from refractors he presented to the Royal Society just after
his election as Fellow in 1672, the little six-inch model of his device
which was received with acclamation and then lay on the shelf without
making the slightest impression on the art, for full half a century.

Newton, by dropping the notion of direct view through the tube,
hit upon by far the simplest way of getting the image outside it,
by a plane mirror a little inside focus and inclined at 45°, but
injudiciously abandoned the parabolic mirror of his original paper
on dispersion. His invention therefore as actually made public was
of the combination with a spherical concave mirror of a plane mirror
of elliptical form at 45°, a construction which in later papers he
defended as fully adequate.[5]

 [5] In Fig 13, _A_ is the support of the tube and focussing screw, _B_
 the main mirror, an inch in diameter, _CD_ the oblique mirror, _E_ the
 principal focus, _F_ the eye lens, and _G_ the member from which the
 oblique mirror is carried.

[Illustration: FIG. 13.—Newton’s Model of his Reflector.]

His error in judgment doubtless came from lack of practical
astronomical experience, for he assumed that the whole real trouble
with existing telescopes was chromatic aberration, which in fact
worried the observer little more than the faults due to other causes,
since the very low luminosity toward the ends of the spectrum
enormously lessens the indistinctness due to dispersion.

As a matter of fact the long focus objective of small aperture did very
creditable work, and its errors would not compare unfavorably with
those of a spherical concave mirror of the wide aperture planned by
Newton. Had he actually made one of his telescopes of fair dimensions
and power the definition would infallibly have been wrecked by the
aberrations due to spherical figure.[6]

 [6] In fact a “four foot telescope of Mr. Newton’s invention” brought
 before the Royal Society two weeks after his original paper, proved
 only fair in quality, was returned somewhat improved at the next
 meeting, and then was referred to Mr. Hooke to be perfected as far as
 might be, after which nothing more was heard of it.

[Illustration: FIG. 14.—De Bercé’s sketch of Cassegrain’s Telescope.]

It is quite likely that appreciation of this, and the grave doubts
of both Newton and Huygens as to obtaining a proper parabolic curve
checked further developments. About the beginning of the year 1672
M. Cassegrain communicated to M. de Bercé a design for a reflecting
telescope, which eventually found its way into the _Philosophical
Transactions_ of May in that year, after previous publication in the
_Journal des Sçavans_. Figure 14 shows de Bercé’s rough original
sketch. It differed from Gregory’s construction in that the latter’s
elliptical concave mirror placed outside the main focus, was replaced
by a convex mirror placed inside focus. The image was therefore
inverted.

The inventor is referred to in histories of science as “Cassegrain,
a Frenchman.” He was in fact Sieur Guillaume Cassegrain, sculptor in
the service of Louis Quatorze, modeller and founder of many statues.
In 1666 he was paid 1200 livres for executing a bust of the King
modelled by Bertin, and later made many replicas from the antique for
the decoration of His Majesty’s gardens at Versailles. He disappeared
from the royal records in 1684 and probably died within a year or two
of that date.

At the period here concerned he apparently, like de Bercé, was of
Chartres. Familiar with working bronzes and with the art of the
founder, he was a very likely person to have executed specula. Although
there is no certainty that he actually made a telescope, a contemporary
reference in the _Journal des Sçavans_ speaks of his invention as a
“petite lunette d’approche,” and one does not usually suggest the
dimensions of a thing non-existent. How long he had been working upon
it prior to the period about the beginning of 1672 when he disclosed
the device to de Bercé is unknown.

Probably Newton’s invention was the earlier, but the two were
independent, and it was somewhat ungenerous of Newton to criticise
Cassegrain, as he did, for using spherical mirrors, on the strength of
de Bercé’s very superficial description, when he himself considered the
parabolic needless.

However, nothing further was done, and the devices of Gregory, Newton
and Cassegrain went together into the discard for some fifty years.

These early experiments gave singularly little information about
material for mirrors and methods of working it, so little that those
who followed, even up to Lord Rosse, had to work the problems out
for themselves. We know from his original paper that Newton used
bell-metal, whitened by the addition of arsenic, following the lore of
the alchemists.

These speculative worthies used to alloy copper with arsenic, thinking
that by giving it a whitish cast they had reached a sort of half way
point on the road to silver. Very silly at first thought, but before
the days of chemical analysis, when the essential properties of the
metals were unknown, the way of the scientific experimenter was hard.

What the “steely matter, imployed in London” of which Newton speaks in
an early paper was, we do not know—very likely one of the hard alloys
much richer in tin than is ordinary bell-metal. Nor do we know to what
variety of speculum metal Huygens refers in his correspondence with
Newton.

As to methods of working it Newton only disclosed his scheme of
pitch-polishing some thirty years after this period, while it is
a matter of previous record, that Huygens had been in the habit of
polishing his true tools on pitch from some date unknown. Probably
neither of them originated the practice. Opticians are a peculiarly
secretive folk and shop methods are likely to be kept for a long time
before they leak out or are rediscovered.

Modern speculum metal is substantially a definite compound of four
atoms copper and one tin (SnCu_{4}), practically 68 per cent copper and
32 per cent tin, and is now, as it was in all previous modifications, a
peculiarly mean material to cast and work. Thus exit the reflector.

The long telescope continued to grow longer with only slow improvement
in quality, but the next decade was marked by the introduction of
Huygens’ eyepiece, an immense improvement over the single lens which
had gone before, and with slight modifications in use today.

[Illustration: FIG. 15.—Diagram of Huygens’ Eyepiece.]

This is shown in section in Fig. 15. It consists of a field lens _A_,
plano-convex, and an eye lens _B_ of one-third the focal length, the
two being placed at the difference of their focal lengths apart with
(in later days) a stop half way between them. The eye piece is pushed
inside the main focus until the rays which fall on the field lens focus
through the eye lens.

The great gain from Huygens’ view-point was a very much enlarged
clear field—about a four-fold increase—and in fact the combination is
substantially achromatic, particularly important now when high power
oculars are needed.

Still larger progress was made in giving the objective a better form
with respect to spherical aberration, the “crossed” lens being rather
generally adopted. This form is double convex, and if of ordinary
glass, with the rear radius six times the front radius, and gives even
better results than a plano-convex in its best position-plane side to
the rear. Objectives were rated on focal length for the green rays,
that is, the bright central part of the spectrum, the violet rays of
course falling short and the red running beyond.

To give customary dimensions, a telescope of 3 inches aperture, with
magnifying power of 100, would be of about 30 feet focus with the
violet nearly 6 inches short and the red a similar amount long. It is
vast credit to the early observers that with such slender means they
did so much. But in fact the long telescope had reached a mechanical
_impasse_, so that the last quarter of the seventeenth century and the
first quarter of the next were marked chiefly by the development of
astronomy of position with instruments of modest dimensions.

[Illustration: FIG. 16.—The First Reflector. John Hadley, 1722.]

In due time the new order came and with astounding suddenness. Just
at the end of 1722 James Bradley (1692-1762) measured the diameter of
Venus with an objective of 212 ft. 3 in. focal length; about three
months later John Hadley (1682-1744) presented to the Royal Society
the first reflecting telescope worthy the name, and the old order
practically ended.

John Hadley should in fact be regarded as the real inventor of the
reflector in quite the same sense that Mr. Edison has been held, _de
jure_ and _de facto_, the inventor of the incandescent electric lamp.
Actually Hadley’s case is the stronger of the two, for the only things
which could have been cited against him were abandoned experiments
fifty years old. Moreover he took successfully the essential step at
which Gregory and Newton had stumbled or turned back—parabolizing his
speculum.

The instrument he presented was of approximately 6 inches aperture and
62⅝ inches focal length, which he had made and tested some three
years previously; on a substantial alt-azimuth mount with slow motions.
He used the Newtonian oblique mirror and the instrument was provided
with both convex and concave eye lenses, with magnifications up to
about 230.

The whole arrangement is shown in Fig. 16 which is for the most part
self explanatory. It is worth noting that the speculum is positioned
in the wooden tube by pressing it forward against three equidistant
studs by three corresponding screws at the rear, that a slider moved
by a traversing screw in a wide groove carries the small mirror and
the ocular, that there is a convenient door for access to the mirror,
and also a suitable finder. The motion in altitude is obtained by a
key winding its cord against gravity. That in azimuth is by a roller
support along a horizontal runway carried by an upright, and is
obtained by the key with a cord pull off in one direction, and in the
other, by springs within the main upright, turning a post of which the
head carries cheek pieces on which rest the trunnions of the tube.

A few months later this telescope was carefully tested, by Bradley and
the Rev. J. Pound, against the Huygens objective of 123 feet focus
possessed by the Royal Society, and with altogether satisfactory
results. Hadley’s reflector would show everything which could be
seen by the long instrument, bearing as much power and with equal
definition, though somewhat lessened light. In particular they saw
all five satellites of Saturn, Cassini’s division, which the inventor
himself had seen the previous year even in the northern edge of the
ring beyond the planet, and the shadow of the ring upon the ball.

The casting of the large speculum was far from perfect, with many spots
that failed to take polish, but the figure must have been rather good.
A spherical mirror of these dimensions would give an aberration blur
something like twenty times the width of Cassini’s division, and the
chance of seeing all five satellites with it would be negligibly small.

Further, Hadley presently disclosed to others not only the method he
used in polishing and parabolizing specula, but his method of testing
for true figure by the aberrations disclosed as he worked the figure
away from the sphere—a scheme frequently used even to this day.

The effect of Hadley’s work was profound. Under his guidance others
began to produce well figured mirrors, in particular Molyneux and
Hawksbee; reflecting telescopes became fairly common; and in the
beginning of the next decade James Short, (1710-1768), possessed of
craftsmanship that approached wizardry, not only fully mastered the
art of figuring the paraboloid, but at once took up the Gregorian
construction with its ellipsoidal small mirror, with much success.

His specula were of great relative aperture, F/4 to F/6, and from the
excellent quality of his metal some of them have retained their fine
polish and definition after more than a century. He is said to have
gone even up to 12 inches in diameter. His exact methods of working
died with him. Even his tools he ordered to be destroyed before his
death.

The Cassegrain reflector, properly having a parabolic large mirror and
a hyperbolic small one, seems very rarely to have been made in the
eighteenth century, though one certainly came into the hands of Ramsden
(1735-1800).

Few refractors for astronomical use were made after the advent of the
reflector, which was, and is, however, badly suited for the purposes of
a portable spy-glass, owing to trouble from stray light. The refractor
therefore permanently held its own in this function, despite its length
and uncorrected aberrations.

Relief was near at hand, for hardly had Short started on his notable
career when Chester Moor Hall, Esq. (1704-1771) a gentleman of Essex,
designed and caused to be constructed the first achromatic telescope,
with an objective of crown and flint glass. He is stated to have been
studying the problem for several years, led to it by the erroneous
belief (shared by Gregory long before) that the human eye was an
example of an achromatic instrument.

Be this as it may Hall had his telescopes made by George Bast of
London at least as early as 1733, and according to the best available
evidence several instruments were produced, one of them of above 2
inches aperture on a focal length of about 20 inches (F/8) and further,
subsequently such instruments were made and sold by Bast and other
opticians.

These facts are clear and yet, with knowledge of them among London
workmen as well as among Hall’s friends, the invention made no
impression, until it was again brought to light, and patented, by the
celebrated John Dolland (1706-1761) in the year 1758.

Physical considerations give a clue to this singular neglect. The only
glasses differing materially in dispersion available in Hall’s day
were the ordinary crown, and such flint as was in use in the glass
cutting trade,—what we would now know as a light flint, and far from
homogeneous at that.

[Illustration: _Lodge “Pioneers of Science.”_ FIG. 17.—John Dolland.]

Out of such material it was practically very hard (as the Dollands
quickly found) to make a double objective decently free from spherical
aberration, especially for one working, as Hall quite assuredly did,
by rule of thumb. With the additional handicap of flint full of faults
it is altogether likely that these first achromatics, while embodying
the correct principles, were not good enough to make effective headway
against the cheaper and simpler spy-glass of the time.

Dolland, although in 1753 he strongly supported Newton’s error in a
Royal Society paper against Euler’s belief in achromatism, shifted his
view a couple of years later and after a considerable period of skilful
and well ordered experimenting published his discovery of achromatism
early in 1758, for which a patent was granted him April 19, while in
the same year the Royal Society honored him with the Copley medal. From
that time until his death, late in 1761, he and his son Peter Dolland
(1730-1820) were actively producing achromatic glasses.

The Dollands were admirable craftsmen and their early product was
probably considerably better than were Hall’s objectives but they felt
the lack of suitable flint and soon after John Dolland’s death, about
1765, the son sought relief in the triple objective of which an early
example is shown in Fig. 18, and which, with some modifications, was
his standard form for many years.

[Illustration: FIG. 18.—Peter Dolland’s Triple Objective.]

Other opticians began to make achromatics, and, Peter Dolland having
threatened action for infringement, a petition was brought by 35
opticians of London in 1764 for the annulment of John Dolland’s patent,
alleging that he was not the original inventor but had knowledge of
Chester Moor Hall’s prior work. In the list was George Bast, who in
fact did make Hall’s objectives twenty five years before Dolland, and
also one Robert Rew of Coldbath Fields, who claimed in 1755 to have
informed Dolland of the construction of Hall’s objective.

This was just the time when Dolland came to the right about face on
achromatism, and it may well be that from Rew or elsewhere he may
have learned that a duplex achromatic lens had really been produced.
But his Royal Society paper shows that his result came from honest
investigations, and at worst he is in about the position of Galileo a
century and a half before.

The petition apparently brought no action, perhaps because Peter
Dolland next year sued Champneys, one of the signers, and obtained
judgment. It was in this case that the judge (Lord Camden) delivered
the oft quoted dictum: “It was not the person who locked up his
invention in his scrutoire that ought to profit by a patent for
such invention, but he who brought it forth for the benefit of the
public.[7]”

 [7] Commonly, but it appears erroneously, ascribed to Lord Mansfield.

This was sound equity enough, assuming the facts to be as stated, but
while Hall did not publish the invention admittedly made by him, it had
certainly become known to many. Chester Moor Hall was a substantial and
respected lawyer, a bencher of the Inner Temple, and one is inclined
to think that his alleged concealment was purely constructive, in his
failing to contest Dolland’s claim.

Had he appeared at the trial with his fighting blood up, there is every
reason to believe that he could have established a perfectly good
case of public use quite aside from his proof of technical priority.
However, having clearly lost his own claims through _laches_, he not
improbably was quite content to let the tradesmen fight it out among
themselves. Hall’s telescopes were in fact known to be in existence as
late as 1827.

As the eighteenth century drew toward its ending the reflecting
telescope, chiefly in the Gregorian form, held the field in
astronomical work, the old refractor of many draw tubes was the
spy-glass of popular use, and the newly introduced achromatic was the
instrument of “the exclusive trade.” No glass of suitable quality for
well corrected objectives had been produced, and that available was not
to be had in discs large enough for serious work. A 3-inch objective
was reckoned rather large.




CHAPTER II

THE MODERN TELESCOPE


The chief link between the old and the new, in instrumental as well
as observational astronomy, was Sir William Herschel (1738-1822). In
the first place he carried the figuring of his mirrors to a point not
approached by his predecessors, and second, he taught by example the
immense value of aperture in definition and grasp of light. His life
has never been adequately written, but Miss Clerke’s “_The Herschels
and Modern Astronomy_” is extremely well worth the reading as a record
of achievement that knew not the impossible.

[Illustration: _Miss Clerke’s Herschel & Modern Astronomy_
(_Macmillan_). FIG. 19.—Sir William Herschel.]

He was the son of a capable band-master of Hanover, brought up as a
musician, in a family of exceptional musical abilities, and in 1757
jumped his military responsibilities and emigrated to England, to the
world’s great gain. For nearly a decade he struggled upward in his art,
taking meanwhile every opportunity for self education, not only in the
theory of music but in mathematics and the languages, and in 1767 we
find him settled in fashionable Bath, oboist in a famous orchestra, and
organist of the Octagon Chapel. His abilities brought him many pupils,
and ultimately he became director of the orchestra in which he had
played, and the musical dictator of the famous old resort.

In 1772 came his inspiration in the loan of a 2-foot Gregorian
reflector, and a little casual star-gazing with it. It was the opening
of the kingdom of the skies, and he sought to purchase a telescope of
his own in London, only to find the price too great for his means.
(Even a 2-foot, of 4½ inches aperture, by Short was listed at
five-and-thirty guineas.) Then after some futile attempts at making a
plain refractor he settled down to hard work at casting and polishing
specula.

Although possessed of great mechanical abilities the difficult
technique of the new art long baffled him, and he cast and worked some
200 small discs in the production of his first successful telescopes,
to say nothing of a still greater number in larger sizes in his
immediately subsequent career.

As time went on he scored a larger proportion of successes, but at the
start good figure seems to have been largely fortuitous. Inside of a
couple of years, however, he had mastered something of the art and
turned out a 5-foot instrument which seems to have been of excellent
quality, followed later by a 7-foot (aperture 6¼ inches) even
better, and then by others still bigger.

The best of Herschel’s specula must have been of exquisite figure. His
7-foot was tested at Greenwich against one of Short’s of 9½ inches
aperture much to the latter’s disadvantage. His discovery with the
7-foot, of the “Georgium Sidus” (Uranus) in 1781 won him immediate fame
and recognition, beside spurring him to greater efforts, especially in
the direction of larger apertures, of which he had fully grasped the
importance.

In 1782 he successfully completed a 12-inch speculum of 20 feet focus,
followed in 1788 by an 18-inch of the same length. The previous year he
first arranged his reflector as a “front view” telescope—the so-called
Herschelian. Up to this time he, except for a few Gregorians, had used
Newton’s oblique mirror.

The heavy loss of light (around 40 per cent) in the second reflection
moved him to tilt the main mirror so as to throw the focal point
to the edge of the aperture where one could look downward upon the
image through the ocular as shown in Fig. 20. Here _SS_ is the great
speculum, _O_ the ocular and _i_ the image formed near the rim of the
tube. In itself the tilting would seriously impair the definition, but
Herschel wisely built his telescopes of moderate relative aperture
(F/10 to F/20), so that this difficulty was considerably lessened,
while the saving of light, amounting to nearly a stellar magnitude, was
important.

Meanwhile he was hard at work on his greatest mirror, of 48 inches
clear aperture and 40 feet focal length, the father of the great line
of modern telescopes. It was finished in the summer of 1789. The
speculum was 49½ inches in over-all diameter, 3½ inches thick
and weighed as cast 2118 lbs. The completion of this instrument, which
would rank as large even today, was made notable by the immediate
discovery of two new satellites of Saturn, Enceladus and Mimas.

It also proved of very great value in sweeping for nebulæ, but its
usefulness seems to have been much limited by the flexure of the mirror
under its great weight, and by its rapid tarnishing. It required
repolishing, which meant refiguring, at least every two years, a
prodigious task.[8]

 [8] This was probably due not only to unfavorable climate, but to the
 fact that Herschel, with all his ingenuity, does not appear to have
 mastered the casting difficulty, and was constrained to make his big
 speculum of Cu 75 per cent, Sn 25 per cent, a composition working
 rather easily and taking beautiful, but far from permanent, polish.
 He never seems to have used practically the SnCu_{4} formula, devised
 empirically by Mudge (Phil. Trans. _67_, 298), and in quite general
 use thereafter up to the present time.

[Illustration: FIG. 20.—Herschel’s Front View Telescope.]

It was used as a front view instrument and was arranged as shown in
Fig. 21. Obviously the front view form has against it the mechanical
difficulty of supporting the observer up to quite the full focal length
of the instrument in air, a difficulty vastly increased were the
mount an equatorial one, so that for the great modern reflectors the
Cassegrain form, looked into axially upward, and in length only a third
or a quarter of the principal focus, is almost universal.

As soon as the excellent results obtained by Herschel became generally
known, a large demand arose for his telescopes, which he filled in so
far as he could spare the time from his regular work, and not the
least of his services to science was the distribution of telescopes
of high quality and consequent strong stimulus to general interest in
astronomy.

Two of his instruments, of 4-and 7-feet focus respectively, fell into
the worthy hands of Schröter at Lilienthal and did sterling service in
making his great systematic study of the lunar surface. At the start
even Herschel’s 7-foot telescope brought 200 guineas, and the funds
thus won he promptly turned to research.

[Illustration: _Miss Clerke’s Herschel & Modern Astronomy_
(_Macmillan_). FIG. 21.—Herschel’s Forty-foot Telescope.]

We sometimes think of the late eighteenth century as a time of license
unbounded and the higher life contemned, but Herschel wakened a general
interest in unapplied science that has hardly since been equalled
and never surpassed. Try to picture social and official Washington
rushing to do honor to some astronomer who by luck had found the
trans-Neptunian planet; the diplomatic corps crowding his doors, and
his very way to the Naval Observatory blocked by the limousines of
the curious and admiring, and some idea may be gained of what really
happened to the unassuming music master from Bath who suddenly found
himself famous.

Great as were the advances made by Herschel the reflector was destined
to fall into disuse for many years. The fact was that the specula had
to be refigured, as in the case of the great 40-foot telescope, quite
too often to meet the requirements of the ordinary user, professional
or amateur. Only those capable of doing their own figuring could keep
their instruments conveniently in service.

Sir W. Herschel always had relays of specula at hand for his smaller
instruments, and when his distinguished son, Sir John F. W. Herschel,
went on his famous observing expedition to the Cape of Good Hope in
1834-38 he took along his polishing machine and three specula for his
20-foot telescope. And he needed them indeed, for a surface would
sometimes go bad even in a week, and regularly became quite useless in
2 or 3 months.

Makers who used the harder speculum metal, very brittle and scarcely
to be touched by a file, fared better, and some small mirrors, well
cared for, have held serviceable polish for many years. Many of these
instruments of Herschel’s time, too, were of very admirable performance.

Some of Herschel’s own 7-foot telescopes give evidence of exquisite
figure and he not only commonly used magnifying powers up to some 80
per inch of aperture, a good stiff figure for a telescope old or new,
but went above 2,000, even nearly to 6,000 on one of his 6½-inch
mirrors without losing the roundness of the star image. “Empty
magnification” of course, gaining no detail whatever, but evidence of
good workmanship.

Many years later the Rev. W. R. Dawes, the famous English observer, had
a 5-inch Gregorian, commonly referred to as “The Jewel,” on which he
used 430 diameters, and pushed to 2,000 on Polaris without distortion
of the disc. Comparing it with a 5-foot (approximately 4-inch aperture)
refractor, he reports the Gregorian somewhat inferior in illuminating
power; “But in sharpness of definition, smallness of discs of stars,
and hardness of outline of planets it is superior.” All of which shows
that while methods and material may have improved, the elders did not
in the least lack skill.

The next step forward, and a momentous one, was to be taken in the
achromatic refractor. Its general principles were understood, but clear
and homogeneous glass, particularly flint glass, was not to be had in
pieces of any size. “Optical glass,” as we understand the term, was
unknown.

It is a curious and dramatic fact that to a single man was due not only
the origin of the art but the optical glass industry of the world.
If the capacity for taking infinite pains be genius, then the term
rightfully belongs to Pierre Louis Guinand. He was a Swiss artisan
living in the Canton of Neuchatel near Chaux-de-Fonds, maker of bells
for repeaters, and becoming interested in constructing telescopes
imported some flint glass from England and found it bad.

He thereupon undertook the task of making better, and from 1784 kept
steadily at his experiments, failure only spurring him on to redoubled
efforts. All he could earn at his trade went into his furnaces, until
gradually he won success, and his glass began to be heard of; for by
1799 he was producing flawless discs of flint as much as 6 inches in
diameter.

What is more, to Guinand is probably due the production of the denser,
more highly refractive flints, especially valuable for achromatic
telescopes. The making of optical glass has always been an art rather
than a science. It is one thing to know the exact composition of a
glass and quite another to know in what order and proportion the
ingredients went into the furnace, to what temperature they were
carried, and for how long, and just how the fused mass must be treated
to free the products from bubbles and striæ.

Even today, though much has been learned by scientific investigation
in the past few years, it is far from easy to produce two consecutive
meltings near enough in refractive power to be treated as optically
identical, or to produce large discs optically homogeneous. What
Guinand won by sheer experience was invaluable. He was persuaded in
1805 to move to Munich and eventually to join forces with Fraunhofer,
an association which made both the German optical glass industry and
the modern refractor.

He returned to Switzerland in 1814 and continued to produce perfect
discs of larger and larger dimensions. One set of 12 inches worked up
by Cauchoix in Paris furnished what was for some years the world’s
largest refractor.

Guinaud died in 1824, but his son Henry, moving to Paris, brought
his treasure of practical knowledge to the glass works there, where
it has been handed down, in effect from father to son, gaining
steadily by accretion, through successive firms to the present one of
Parra-Mantois.

Bontemps, one of the early pupils of Henry Guinand, emigrated to
England at the Revolution of 1848 and brought the art to the famous
firm of Chance in Birmingham. Most of its early secrets have long
been open, but the minute teachings of experience are a tremendously
valuable asset even now.

[Illustration: FIG. 22.—Dr. Joseph von Fraunhofer, the Father of
Astrophysics.]

To Fraunhofer, the greatest master of applied optics in the nineteenth
century, is due the astronomical telescope in substantially its
present form. Not only did he become under Guinand’s instruction
extraordinarily skillful in glass making but he practically devised the
art of working it with mathematical precision on an automatic machine,
and the science of correctly designing achromatic objectives.

The form which he originated (Fig. 23) was the first in which the
aberrations were treated with adequate completeness, and, particularly
for small instruments, is unexcelled even now. The curvatures here
shown are extreme, the better to show their relations. The front radius
of the crown is about 2½ times longer than the rear radius, the
front of the flint is slightly flatter than the back of the crown, and
the rear of the flint is only slightly convex.

Fraunhofer’s workmanship was of the utmost exactness and it is not
putting the case too strongly to say that a first class example
of the master’s craft, in good condition, would compare well in
color-correction, definition, and field, with the best modern
instruments.

[Illustration: FIG. 23.]

The work done by the elder Struve at Dorpat with Fraunhofer’s first
large telescope (9.6 inches aperture and 170 inches focal length) tells
the story of its quality, and the Königsberg heliometer, the first of
its class, likewise, while even today some of his smaller instruments
are still doing good service.

It was he who put in practice the now general convention of a relative
aperture of about F/15, and standardized the terrestrial eyepiece into
the design quite widely used today. The improvements since his time
have been relatively slight, due mainly to the recent production of
varieties of optical glass unknown a century ago. Fraunhofer was born
in Straubing, Bavaria, March 6, 1787. Self-educated like Herschel, he
attained to an extraordinary combination of theoretical and practical
knowledge that went far in laying the foundations of astrophysics.

The first mapping of the solar spectrum, the invention of the
diffraction grating and its application to determining the wave
length of light, the first exact investigation of the refraction
and dispersion of glass and other substances, the invention of the
objective prism, and its use in studying the spectra of stars and
planets, the recognition of the correspondence of the sodium lines to
the D lines in the sun, and the earliest suggestion of the diffraction
theory of resolution later worked out by Lord Rayleigh and Professor
Abbé, make a long list of notable achievements.

To these may be added his perfecting of the achromatic telescope, the
equatorial mounting and its clockwork drive, the improvement of the
heliometer, the invention of the stage micrometer, several types of
ocular micrometers, and the automatic ruling engine.

He died at the height of his creative powers June 7, 1826, and lies
buried at Munich under the sublime ascription, by none better earned,
_Approximavit Sidera_.

From Fraunhofer’s time, at the hands of Merz his immediate successor,
Cauchoix in France, and Tully in England, the achromatic refractor
steadily won its way. Reflecting telescopes, despite the sensational
work of Lord Rosse on his 6-foot mirror of 53 feet focus (unequalled
in aperture until the 6-foot of the Dominion Observatory seventy years
later), and the even more successful instrument of Mr. Lassell (4 feet
aperture, 39 feet focus), were passing out of use, for the reason
already noted, that repolishing meant refiguring and the user had to be
at once astronomer and superlatively skilled optician.

These large specula, too, were extremely prone to serious flexure
and could hardly have been used at all except for the equilibrating
levers devised by Thomas Grubb about 1834, and used effectively on the
Rosse instrument. These are in effect a group of upwardly pressing
counterbalanced planes distributing among them the downward component
of the mirror’s weight so as to keep the figure true in any position of
the tube.

Such was the situation in the 50’s of the last century, when the
reflector was quite unexpectedly pushed to the front as a practical
instrument by almost simultaneous activity in Germany and France. The
starting point in each was Liebig’s simple chemical method of silvering
glass, which quickly and easily lays on a thin reflecting film capable
of a beautiful polish.

The honor of technical priority in its application to silvering
telescope specula worked in glass belongs to Dr. Karl August Steinheil
(1801-1870) who produced about the beginning of 1856 an instrument
of 4-inch aperture reported to have given with a power of 100 a
wonderfully good image. The publication was merely from a news item in
the “_Allgemeine Zeitung_” of Augsburg, March 24, 1856, so it is little
wonder that the invention passed for a time unnoticed.

Early the next year, Feb. 16, 1857, working quite independently,
exactly the same thing was brought before the French Academy of
Sciences by another distinguished physicist, Jean Bernard Léon
Foucault, immortal for his proof of the earth’s rotation by the
pendulum experiment, his measurement of the velocity of light, and the
discovery of the electrical eddy currents that bear his name.

[Illustration: FIG. 24.—Dr. Karl August Steinheil. FIG. 25.—Jean
Bernard Léon Foucault. The Inventors of the Silver-on-Glass Reflector.]

To Foucault, chiefly, the world owes the development of the modern
silver-on-glass reflector, for not being a professional optician he
had no hesitation in making public his admirable methods of working
and testing, the latter now universally employed. It is worth noting
that his method of figuring was, physically, exactly what Jesse
Ramsden (1735-1800) had pointed out in 1779, (Phil. Tr. 1779, 427)
geometrically. One of Foucault’s very early instruments mounted
equatorially by Sécrétan is shown in Fig. 26.

[Illustration: FIG. 26.—Early Foucault Reflector.]

The immediate result of the admirable work of Steinheil and Foucault
was the extensive use of the new reflector, and its rapid development
as a convenient and practical instrument, especially in England in
the skillful hands of With, Browning, and Calver. Not the least of
its advantages was its great superiority over the older type in
light-grasp, silver being a better reflector than speculum metal in
the ratio of very nearly 7 to 5. From this time on both refractors and
reflectors have been fully available to the user of telescopes.

In details of construction both have gained somewhat mechanically.
As we have seen, tubes were often of wood, and not uncommonly the
mountings also. At the present time metal work of every kind being more
readily available, tubes and mountings of telescopes of every size are
quite universally of metal, save for the tripod-legs of the portable
instruments. The tubes of the smaller refractors, say 3 to 5 inches in
aperture, are generally of brass, though in high grade instruments this
is rapidly being replaced by aluminum, which saves considerable weight.
Tubes above 5 or 6 inches are commonly of steel, painted or lacquered.
The beautifully polished brass of the smaller tubes, easily damaged
and objectionably shiny, is giving way to a serviceable matt finish
in hard lacquer. Mountings, too, are now more often in iron and steel
or aluminum than in brass, the first named quite universally in the
working parts, for which the aluminum is rather soft.

The typical modern refractor, even of modest size, is a good bit more
of a machine than it looks at first glance. In principle it is outlined
in Fig. 5, in practice it is much more complex in detail and requires
the nicest of workmanship. In fact if one were to take completely apart
a well-made small refractor, including its optical and mechanical parts
one would reckon up some 30 to 40 separate pieces, not counting screws,
all of which must be accurately fitted and assembled if the instrument
is to work properly.

[Illustration: FIG. 27.—Longitudinal Section of Modern Refractor.]

Fig. 27 shows such an instrument in section from end to end, as one
would find it could he lay it open longitudinally.

_A_ is the objective cap covering the objective _B_ in its adjustable
cell _C_, which is squared precisely to the axis of the main tube _D_.
Looking along this one finds the first of the diaphragms, _E_.

These are commonly 3 to 6 in number spaced about equally down the tube,
and are far more important than they look. Their function is not to
narrow the beam of light that reaches the ocular, but to trap light
which might enter the tube obliquely and be reflected from its sides
into the ocular, filling it with stray glare.

No amount of simple blackening will answer the purpose, for even dead
black paint such as opticians use reflects at very oblique incidence
quite 10 to 20 per cent of the beam. The importance of both diaphragms
and thorough blackening has been realized for at least a century and a
half, and one can hardly lay too much stress upon the matter.

The diaphragms should be so proportioned that, when looking up the
tube from the edge of an aperture of just the size and position of
the biggest lens in the largest eyepiece, no part of the edge of the
objective is cut off, and no part of the side of the tube is visible
beyond the nearest diaphragm.

Going further down the tube past a diaphragm or two one comes to
the clamping screws _F_. These serve to hold the instrument to its
mounting. They may be set in separate bases screwed in place on the
inside of the tube, or may be set in the two ends of a lengthwise strap
thus secured. They are placed at the balance point as nearly as may be,
generally nearer the eye end than the objective.

Then, after one or more diaphragms, comes the guide ring _G_, which
steadies the main draw tube _H_, and the rack _I_ by which it is moved
for the focussing in turning the milled head of the pinion _J_. The end
ring _K_ of the main tube furnishes the other bearing of _H_, and both
_G_ and _K_ are commonly recessed for accurately fitted cloth lining
rings _L_, _L_, to give the draw tube the necessary smoothness of
motion.

For the same reason _I_ and _J_ have to be cut and fitted with the
utmost exactness so as to work evenly and without backlash. _H_ is
fitted at its outer end with a slide ring and tube _M_, generally again
cloth lined to steady the sliding eyepiece tube _N_. This is terminated
by the spring collar _O_, in which fits the eyepiece _P_, generally of
the two lens form; and finally comes the eyepiece cap _Q_ set at the
proper distance from the eye lens and with an aperture of carefully
determined size.

One thus gets pretty well down in the alphabet without going much into
the smaller details of construction. Both objective mount and ocular
are somewhat complex in fact, and the former is almost always made
adjustable in instruments of above 3 or 4 inches aperture, as shown in
Fig. 28, the form used by Cooke, the famous maker of York, England.
Unless the optical axis of the objective is true with the tube bad
images result.

[Illustration: FIG. 28.—Adjustable Cell for Objective.]

To the upper end of the tube is fitted a flanged counter-cell _c_, to
an outward flange _f_, tapped for 3 close pairs of adjusting screws as
_s__{1}, _s__{11} spaced at 120° apart. The objective cell itself, _b_,
is recessed for the objective which is held in place by an interior
or exterior ring _d_. The two lenses of the achromatic objective are
usually very slightly separated by spacers, either tiny bits of tinfoil
120° apart, or a very thin ring with its upper edge cut down save at 3
points.

This precaution is to insure that the lenses are quite uniformly
supported instead of touching at uncertain points, and quite usually
the pair as a whole rests below on three corresponding spacers. Of each
pair of adjusting screws one as 1 in the pair _s__{11} is threaded to
push the counter cell out, the adjacent one, 2, to pull it in, so that
when adjustment is made the objective is firmly held. Of the lenses
that form the objective, the concave flint is commonly at the rear and
the convex crown in front.

At the eye end the ocular ordinarily consists of two lenses each
burnished into a brass screw ring, a tube, flange, cap, and diaphragm
arranged as shown in Fig. 29. There are many varieties of ocular as
will presently be shown, but this is a typical form. Figure 30 shows
a complete modern refractor of four inches aperture on a portable
equatorial stand with slow motion in right ascension and diagonal eye
piece.

Reflectors, used in this country less than they deserve, are, when
properly mounted, likewise possessed of many parts. The smaller ones,
such as are likely to come into the reader’s hands, are almost always
in the Newtonian form, with a small oblique mirror to bring the image
outside the tube.

[Illustration: FIG. 29.—The Eye-Piece and its Fittings.]

The Gregorian form has entirely vanished. Its only special merit was
its erect image, which gave it high value as a terrestrial telescope
before the days of achromatics, but from its construction it was almost
impossible to keep the field from being flooded with stray light, and
the achromatic soon displaced it. The Cassegranian construction on
the other hand, shorter and with aberrations much reduced, has proved
important for obtaining long equivalent focus in a short mount, and is
almost universally applied to large reflectors, for which a Newtonian
mirror is also generally provided.

Figure 31 shows in section a typical reflector of the Newtonian form.
Here _A_ is the main tube, fitted near its outer end with a ring _B_
carrying the small elliptical mirror _C_, which is set at 45° to the
axis of the tube. At the bottom of the tube is the parabolic main
mirror _D_, mounted in its cell _E_. Just opposite the 45° small mirror
is a hole in the tube to which is fitted the eye piece mounting _F_,
carrying the eyepiece _G_, fitted to a spring collar _H_, screwed into
a draw tube _I_, sliding in its mounting and brought to focus by the
rack-and-pinion _J_.

[Illustration: FIG. 30.—Portable Equatorial Refractor (Brashear).]

At _K_, _K_, are two rings fixed to the tube and bearing smoothly
against the rings _L L_ rigidly fixed to the bar _M_ carried by the
polar axis of the mount. The whole tube can therefore be rotated about
its axis so as to bring the eye piece into a convenient position for
observation. One or more handles, _N_, are provided for this purpose.

[Illustration: FIG. 31.—Longitudinal Section of Newtonian Reflector.]

Brackets shown in dotted lines at _O_, _O_, carry the usual finder,
and a hinged door _P_ near the lower end of the tube enables one to
remove or replace the close fitting metal cover that protects the
main mirror when not in use. Similarly a cover is fitted to the small
mirror, easily reached from the upper end of the tube. The proportions
here shown are approximately those commonly found in medium sized
instruments, say 7 to 10 inches aperture. The focal ratio is somewhere
about _F_/6, the diagonal mirror is inside of focus by about the
diameter of the main mirror, and its minor axis is from ⅕ to ¼ that
diameter.

[Illustration: FIG. 32.—Reflector with Skeleton Tube (Brashear).]

Note that the tube is not provided with diaphragms. It is merely
blackened as thoroughly as possible, although stray light is quite as
serious here as in a refractor. One could fit diaphragms effectively
only in a tube of much larger diameter than the mirror, which would be
inconvenient in many ways.

A much better way of dealing with the difficulty is shown in Fig. 32 in
which the tube is reduced to a skeleton, a construction common in large
instruments. Nothing is blacker than a clear opening into the darkness
of night, and in addition there can be no localized air currents, which
often injure definition in an ordinary tube.

[Illustration: FIG. 33.]

Instruments by different makers vary somewhat in detail. A good type of
mirror mounting is that shown in Fig. 33, and used for many years past
by Browning, one of the famous English makers. Here the mirror _A_, the
back of which is made accurately plane, is seated in its counter-cell
_B_, of which a wide annulus _F_, _F_, is also a good plane, and is
lightly held in place by a retaining ring. This counter cell rests
in the outer cell _C_ on three equidistant studs regulated by the
concentric push-and-pull adjusting screws _D_, _D_, _E_, _E_. The outer
cell may be solid, or a skeleton for lightness and better equalization
of temperature.

Small specula may be well supported on any flat surface substantial
enough to be thoroughly rigid, with one or more thicknesses of soft,
thick, smooth cloth between, best of all Brussels carpet. Such was the
common method of support in instruments of moderate dimensions prior
to the day of glass specula. Sir John Herschel speaks of thus carrying
specula of more than a hundred-weight, but something akin to Browning’s
plan is generally preferable.

There is also considerable variety in the means used for supporting
the small mirror centrally in the tube. In the early telescopes it was
borne by a single stiff arm which was none too stiff and produced by
diffraction a long diametral flaring ray in the images of bright stars.

A great improvement was introduced by Browning more than a half century
ago, in the support shown in Fig. 34. Here the ring _A_, (_B_, Fig.
31) carries three narrow strips of thin spring steel, _B_, extending
radially inward to a central hub which carries the mirror _D_, on
adjusting screws _E_. Outside the ring the tension screws _C_ enable
the mirror to be accurately centered and held in place. Rarely, the
mirror is replaced by a totally reflecting right angled prism which
saves some light, but unless for small instruments is rather heavy and
hard to obtain of the requisite quality and precision of figure. A
typical modern reflector by Brashear, of 6 inches aperture, is shown in
Fig. 35, complete with circles and driving clock, the latter contained
in the hollow iron pier, an arrangement usual in American-made
instruments.

[Illustration: FIG. 34.—Support of Diagonal Mirror (Browning.)]

Recent reflectors, particularly in this country, have four supporting
strips instead of three, which gives a little added stiffness, and
produces in star images but four diffraction rays instead of the six
produced by the three strip arrangement, each strip giving a diametral
ray.

In some constructions the ring _A_ is arranged to carry the eyepiece
fittings, placed at the very end of the tube and arranged for rotating
about the optical axis of the telescope. This allows the ocular to
be brought to any position without turning the whole tube. In small
instruments a fixed eyepiece can be used without much inconvenience if
located on the north side of the tube (in moderate north latitudes).

Reflectors are easily given a much greater relative aperture than
is practicable in a single achromatic objective. In fact they are
usually given apertures of _F_/5 to _F_/8 and now and then are pushed
to or even below _F_/3. Such mirrors have been successfully used for
photography;[9] and less frequently for visual observation, mounted
in the Cassegranian form, which commonly increases the virtual focal
length at least three or four times. A telescope so arranged, with an
aperture of a foot or more as in some recent examples, makes a very
powerful and compact instrument.

 [9] An _F_/3 mirror of 1_m_ aperture by Zeiss was installed in the
 observatory at Bergedorf in 1911, and a similar one by Schaer is
 mounted at Carre, near Geneva.

[Illustration: FIG. 35.—Small Equatorially Mounted Reflector.]

This is the form commonly adopted for the large reflectors of recent
construction, a type being the 60-inch telescope of the Mount Wilson
Observatory of which the primary focus is 25¼ feet and the ordinary
equivalent focus as a Cassegranian 80 feet.

Comparatively few small reflectors have been made or used in the United
States, although the climatic conditions here are more favorable
than in England, where the reflector originated and has been very
fully developed. The explanation may lie in our smaller number of
non-professional active astronomers who are steadily at observational
work, and can therefore use reflectors to the best advantage.

The relative advantages of refractors and reflectors have long been
a matter of acrimonious dispute. In fact, more of the genuine _odium
theologicum_ has gone into the consideration of this matter than
usually attaches to differences in scientific opinion. A good many
misunderstandings have been due to the fact that until recently few
observers were practically familiar with both instruments, and the
professional astronomer was a little inclined to look on the reflector
as fit only for amateurs. The comparison is somewhat clarified at
present by the fact that the old speculum metal reflector has passed
out of use, and the case now stands as between the ordinary refracting
telescope such as has just been described, and the silver-on-glass
reflector discussed immediately thereafter.

The facts in the case are comparatively simple. Of two telescopes
having the same clear aperture, one a reflector and the other a
refractor, each assumed to be thoroughly well figured, as it can
be in fact today, the theoretical resolving power is the same, for
this is determined merely by the aperture, so that the only possible
difference between the two would be in the residual imperfection in the
performance of the refractor due to its not being perfectly achromatic.
This difference is substantially a negligible one for many, but not
all, purposes.

Likewise, the general definition of the pair, assuming first-class
workmanship, would be equal. Of the two, the single surface of the
mirror is somewhat more difficult to figure with the necessary
precision than is any single surface of the refractor, but reflectors
can be, and are, given so perfect a parabolic figure that the image is
in no wise inferior to that produced by the best refractors, and the
two types of telescopes will stand under favorable circumstances the
same proportional magnifying powers.

The mirror is much more seriously affected by changes of temperature
and by flexure than is the objective, since in the former case the
successive surfaces of the two lenses in the achromatic combination
to a considerable extent compensate each other’s slight changes of
curvature, which act only by still slighter changes of refraction,
while the mirror surface stands alone and any change in curvature
produces double the defect on the reflected ray.

It is therefore necessary, as we shall see presently, to take
particular precautions in working with a reflecting telescope, which
is, so to speak, materially more tender as regards external conditions
than the refractor. As regards light-grasp, the power of rendering
faint objects visible, there is more room for honest variety of
opinion. It was often assumed in earlier days that a reflector was not
much brighter than a refractor of half the aperture, _i.e._, of one
quarter the working area.

This might have been true in the case of an old speculum metal
reflector in bad condition, but is certainly a libel on the
silver-on-glass instrument, which Foucault on the other hand claimed to
be, aperture for aperture, brighter than the refractor. Such a relation
might in fact temporarily exist, but it is far from typical.

The real relation depends merely on the light losses demonstrably
occurring in the two types of telescopes. These are now quite well
known. The losses in a refractor are those due to absorption of light
in the two lenses, plus those due to the four free surfaces of these
lenses. The former item in objectives of moderate size aggregates
hardly more than 2 to 3 per cent. The latter, assuming the polish to be
quite perfect, amount to 18 to 20 per cent of the incident light, for
the glasses commonly used.

The total light transmitted is therefore not over 80 per cent of the
whole, more often somewhat under this figure. For example, a test by
Steinheil of one of Fraunhofer’s refractors gave a transmission of 78
per cent, and other tests show similar results.

The relation between the light transmitted by glass of various
thickness is very simple. If unit thickness transmits m per cent of the
incident light then n units in thickness will pass m^n per cent. Thus
if one half inch passes .98, two inches will transmit .98^4, or .922.
Evidently the bigger the objective the greater the absorptive loss.
If the loss by reflection at a single surface leaves m per cent to be
transmitted then n surfaces will transmit m^n. And m being usually
about .95, the four surfaces of an objective let pass nearly .815, and
the thicker objective as a whole transmits approximately 75 per cent.

As to the reflector the whole relation hinges on the coefficient of
reflection from a silvered surface, under the circumstances of the
comparison.

In the case of a reflecting telescope as a whole, there are commonly
two reflections from silver and if the coefficient of reflection is
m then the total light reflected is m². Now the reflectivity of a
silver-on-glass film has been repeatedly measured. (Chant Ap. J. 21,
211) found values slightly in excess of 95 per cent, Rayleigh (Sci.
Papers 2, 4) got 93.9, Zeiss (Landolt u. Bornstein, Tabellen) about
93.0 for light of average wave length.

Taking the last named value, a double reflection would return
substantially 86.5 per cent of the incident light. No allowance is
here made for any effect of selective reflection, since for the bright
visual rays, which alone we are considering, there is very slight
selective effect. In the photographic case it must be taken into
account, and the absorption in glass becomes a serious factor in the
comparison, amounting for the photographic rays to as much as 30 to 40
per cent in large instruments. Now in comparing reflector and refractor
one must subtract the light stopped by the small mirror and its
supports, commonly from 5 to 7 per cent. One is therefore forced to the
conclusion that with silver coatings fresh and very carefully polished
reflector and refractor will show for equal aperture equal light grasp.

But as things actually go even fresh silver films are quite often below
.90 in reflectivity and in general tarnish rather rapidly, so that in
fact the reflector falls below the refractor by just about the amount
by which the silver films are out of condition. For example Chant (loc.
cit.) found after three months his reflectivity had fallen to .69. A
mirror very badly tarnished by fifteen weeks of exposure to dampness
and dust, uncovered, was found by the writer down to a scant .40.

The line of Fig. 36 shows the relative equivalent apertures of
refractors corresponding to a 10 inch reflector at coefficients of
reflection for a single silvered surface varying from .95 to .50 at
which point the film would be so evidently bad as to require immediate
renewal. The relation is obviously linear when the transmission of the
objective is, as here, assumed constant. The estimates of skilled
observers from actual comparisons fall in well with the line, showing
reflectivities generally around .80 to .85 for well polished films in
good condition.

The long and short of the situation is that a silvered reflector
deteriorates and at intervals varying from a few months to a year or
two depending on situation, climate, and usage, requires repolishing
or replacement of the film. This is a fussy job, but quickly done if
everything goes well.

[Illustration: FIG. 36.—Relative Light-grasp of Reflector and
Refractor.]

As to working field the reflector as ordinarily proportioned is at a
disadvantage chiefly because it works at _F_/5 or _F_/6 instead of
at _F_/15. At equal focal ratios there is no substantial difference
between reflector and refractor in this respect, unless one goes into
special constructions, as in photographic telescopes.

In two items, first cost and convenience in observing, the reflector
has the advantage in the moderate sizes. Roughly, the reflector simply
mounted costs about one half to a quarter the refractor of equal light
grasp and somewhat less resolving power, the discrepancy getting bigger
in large instruments (2 feet aperture and upwards).

As to case of observing, the small refractor is a truly neck-wringing
instrument for altitudes above 45° or thereabouts, just the situation
in which the equivalent reflector is most convenient. In considering
the subject of mounts these relations will appear more clearly.

Practically the man who is observing rather steadily and can give his
telescope a fixed mount can make admirable use of a reflector and will
not find the perhaps yearly or even half yearly re-silvering at all
burdensome after he has acquired the knack—chiefly cleanliness and
attention to detail.

If, like many really enthusiastic amateurs, he can get only an
occasional evening for observing, and from circumstances has to use a
portable mount set up on his lawn, or even roof, when fortune favors
an evening’s work, he will find a refractor always in condition,
easy to set up, and requiring a minimum of time to get into action.
The reflector is much the more tender instrument, with, however, the
invaluable quality of precise achromatism, to compensate for the extra
care it requires for its best performance. It suffers more than the
refractor, as a rule, from scattered light, for imperfect polish of the
film gives a field generally presenting a brighter background than the
field of a good objective. After all the preference depends greatly on
the use to which the telescope is to be put. For astrophysical work
in general, Professor George E. Hale, than whom certainly no one is
better qualified to judge, emphatically endorses the reflector. Most
large observatories are now-a-days equipped with both refractors and
reflectors.




CHAPTER III

OPTICAL GLASS AND ITS WORKING


Glass, one of the most remarkable and useful products of man’s
devising, had an origin now quite lost in the mists of antiquity. It
dates back certainly near a thousand years before the Christian era,
perhaps many centuries more. Respecting its origin there are only
traditions of the place, quite probably Syria, and of the accidental
melting together of sand and soda. The product, sodium silicate,
readily becomes a liquid, i.e., “water-glass,” but the elder Pliny, who
tells the story, recounts the later production of a stable vitreous
body by the addition of a mineral which was probably a magnesia
limestone.

This combination would give a good permanent glass, whether the story
is true or not, and very long before Pliny’s time glass was made in
great variety of composition and color. In fact in default of porcelain
glass was used in Roman times relatively more than now. But without
knowledge of optics there was no need for glass of optical quality,
it was well into the Renaissance before its manufacture had reached a
point where anything of the sort could be made available even in small
pieces, and it is barely over a century since glass-making passed
beyond the crudest empiricism.

Glass is substantially a solid solution of silica with a variety of
metallic oxides, chiefly those of sodium, potassium, calcium and lead,
sometimes magnesium, boron, zinc, barium and others.

By itself silica is too refractory to work easily, though silica
glass has some very valuable properties, and the alkaline oxides in
particular serve as the fluxes in common use. Other oxides are added to
obtain various desired properties, and some impurities may go with them.

The melted mixture is thus a somewhat complex solution containing
frequently half a dozen ingredients. Each has its own natural melting
and vaporizing point, so that while the blend remains fairly uniform
it may tend to lose some constituent while molten, or in cooling to
promote the crystallization of another, if held too near its particular
freezing point. Some combinations are more likely to give trouble from
this cause than others, and while a very wide variety of oxides can
be coerced into solution with silica, a comparatively limited number
produce a homogeneous and colorless glass useful for optical purposes.

Many mixtures entirely suitable for common commercial purposes are
out of the question for lens making, through tendency to surface
deterioration by weathering, lack of homogeneous quality, or
objectionable coloration. A very small amount of iron in the sand used
at the start gives the green tinge familiar in cheap bottles, which
materially decreases the transparency. The bottle maker often adds
oxide of manganese to the mixture, which naturally of itself gives the
glass a pinkish tinge, and so apparently whitens it by compensating the
one absorption by another. The resulting glass looks all right on a
casual glance, but really cuts off a very considerable amount of light.

A further difficulty is that glass differs very much in its degree of
fluidity, and its components sometimes seem to undergo mutual reactions
that evolve persistent fine bubbles, besides reacting with the fireclay
of the melting pot and absorbing impurities from it.

The molten glass is somewhat viscous and far from homogeneous. Its
character suggests thick syrup poured into water, and producing streaks
and eddies of varying density. Imagine such a mixture suddenly frozen,
and you have a good idea of a common condition in glass, transparent,
but full of striæ. These are frequent enough in poor window glass, and
are almost impossible completely to get rid of, especially in optical
glass of some of the most valuable varieties.

The great improvement introduced by Guinand was constant stirring of
the molten mass with a cylinder of fire clay, bringing bubbles to the
surface and keeping the mass thoroughly mixed from its complete fusion
until, very slowly cooling, it became too viscous to stir longer.

The fine art of the process seems to be the exact combination of
temperature, time, and stirring, suitable for each composition of the
glass. There are, too, losses by volatilization during melting, and
even afterwards, that must be reckoned with in the proportions of the
various materials put into the melting, and in the temperatures reached
and maintained.

One cannot deduce accurately the percentage mixture of the raw
materials from an analysis of the glass, and it is notorious that the
product even of the best manufacturers not infrequently fails to run
quite true to type. Therefore the optical properties of each melting
have carefully to be ascertained, and the product listed either as a
very slight variant from its standard type, or as an odd lot, useful,
but quite special in properties. Some of these odd meltings in fact
have optical peculiarities the regular reproduction of which would be
very desirable.

The purity of the materials is of the utmost importance in producing
high grade glass for optical or other purposes. The silica is usually
introduced in the form of the purest of white sand carrying only a few
hundredths of one per cent of impurities in the way of iron, alumina
and alkali. The ordinary alkalis go in preferably as carbonates, which
can be obtained of great purity; although in most commercial glass the
soda is used in the form of “salt-cake,” crude sodium sulphate.

Calcium, magnesium, and barium generally enter the melt as carbonates,
zinc and lead as oxides. Alumina, like iron, is generally an impurity
derived from felspar in the sand, but occasionally enters intentionally
as pure natural felspar, or as chemically prepared hydrate. A few
glasses contain a minute amount of arsenic, generally used in the
form of arsenious acid, and still more rarely other elements enter,
ordinarily as oxides.

Whatever the materials, they are commonly rather fine ground and very
thoroughly mixed, preferably by machinery, before going into the
furnaces. Glass furnaces are in these days commonly gas fired, and
fall into two general classes, those in which the charge is melted
in a huge tank above which the gas flames play, and those in which
the charge is placed in crucibles or pots open or nearly closed,
directly heated by the gas. In the tank furnaces the production is
substantially continuous, the active melting taking place at one end,
where the materials are introduced, while the clear molten glass flows
to the cooler end of the tank or to a cooler compartment, whence it is
withdrawn for working.

The ordinary method of making optical glass is by a modification of
the pot process, each pot being fired separately to permit better
regulation of the temperature.

The pots themselves are of the purest of fire clay, of moderate
capacity, half a ton or so, and arched over to protect the contents
from the direct play of the gases, leaving a side opening sufficient
for charging and stirring.

The fundamental difference between the making of optical glass and the
ordinary commercial varieties lies in the individual treatment of each
charge necessary to secure uniformity and regularity, carried even to
the extent of cooling each melting very slowly in its own pot, which
is finally broken up to recover the contents. The tank furnaces are
under heat week in and week out, may hold several hundred tons, and on
this account cannot so readily be held to exactness of composition and
quality.

The optical glass works, too, is provided with a particularly efficient
set of preheating and annealing kilns, for the heat treatment of pots
and glass must be of the most careful and thorough kind.

The production of a melting of optical glass begins with a very gradual
heating of the pot to a bright red heat in one of the kilns. It is
then transferred to its furnace which has been brought to a similar
temperature, sealed in by slabs of firebrick, leaving its mouth easy of
access, and then the heat is pushed up to near the melting temperature
of the mixture in production, which varies over a rather wide range,
from a moderate white heat to the utmost that a regenerative gas
furnace can conveniently produce. After the heating comes the rather
careful process of charging.

The mixture is added a portion at a time, since the fused material
tends to foam, and the raw material as a solid is more bulky than the
fluid. The chemical reactions as the mass fuses are somewhat complex.
In their simplest form they represent the formation of silicates.

At high temperatures the silica acts as a fairly strong acid, and
decomposes the fused carbonates of sodium and potassium with evolution
of gas. This is the _rationale_ of the fluxing action of such alkaline
substances of rather low melting point. Other mixtures act somewhat
analogously but in a fashion commonly too complex to follow.

The final result is a thick solution, and the chief concern of the
optical glass maker is to keep it homogeneous, free from bubbles,
and as nearly colorless as practicable. To the first two ends the
temperature is pushed up to gain fluidity, and frequently substances
are added (e.g., arsenic) which by volatility or chemical effect tend
to form large bubbles from the entrained gases, capable of clearing
themselves from the fluid where fine bubbles would remain. For the same
purpose is the stirring process.

The stirrer is a hard baked cylinder of fire clay fastened to an iron
bar. First heated in the mouth of the pot, the stirrer is plunged in
the molten glass and given a steady rotating motion, the long bar
being swivelled and furnished with a wooden handle for the workman.
This stirring is kept up pretty steadily while the heat is very slowly
reduced until the mass is too thick to manage, the process taking, for
various mixtures and conditions, from three or four hours to the better
part of a day.

[Illustration: FIG. 37.—Testing Optical Glass in the Rough.]

Then begins the careful and tedious process of cooling. Fairly rapid
until the mass is solid enough to prevent the formation of fresh striæ,
the cooling is continued more slowly, in the furnace or after removal
to the annealing oven, until the crucible is cool enough for handling,
the whole process generally taking a week or more.

Then the real trouble begins. The crucible is broken away and there is
found a more or less cracked mass of glass, sometimes badly broken up,
again furnishing a clear lump weighing some hundreds of pounds. This
glass is then carefully picked over and examined for flaws, striæ and
other imperfections.

These can sometimes be chipped away with more or less breaking up of
the mass. The inspection of the glass in the raw is facilitated by the
scheme shown in elevation Fig. 37. Here _A_ is a tank with parallel
sides of plate glass. In it is placed _B_ the rough block of glass, and
the tank is then filled with a liquid which can be brought to the same
refractive power as the glass, as in Newton’s disastrous experiment.
When equality is reached for, say, yellow light, one can see directly
through the block, the rays no longer being refracted at its surface,
and any interior striæ are readily seen even in a mass a foot or more
thick. Before adding the liquid a ray would be skewed, as _C_, _D_,
_E_, _F_, afterwards it would go straight through; _C_, _D_, _G_, _H_.

The fraction that passes inspection may be found to be from much less
than a quarter to a half of the whole. This good glass is then ready
for the next operation, forming and fine annealing. The final form to
be reached is a disc or block, and the chunks of perfect glass are
heated in a kiln until plastic, and then moulded into the required
shapes, sometimes concave or convex discs suitable for small lenses.

Then the blocks are transferred to a kiln and allowed to cool off very
gradually, for several days or weeks according to the size of the
blocks and the severity of the requirements they must meet. In the
highest class of work the annealing oven has thermostatic control and
close watch is kept by the pyrometer.

It is clear that the chance of getting a large and perfect chunk from
the crucible is far smaller than that of getting fragments of a few
pounds, so that the production of a perfect disc for a large objective
requires both skill and luck. Little wonder therefore that the price of
discs for the manufacture of objectives increases substantially as the
cube of the diameter.

The process of optical glass making as here described is the customary
one, used little changed since the days of Guinand. The great
advances of the last quarter century have been in the production of
new varieties having certain desirable qualities, and in a better
understanding of the conditions that bring a uniform product of high
quality. During the world war the greatly increased demand brought
most extraordinary activity in the manufacture, and especially in the
scientific study of the problems involved, both here and abroad. The
result has been a long step toward quantity production, the discovery
that modifications of the tank process could serve to produce certain
varieties of optical glass of at least fair quality, and great
improvements in the precision and rapidity of annealing.

These last are due to the use of the electric furnace, the study of
the strains during annealing under polarized light, and scientific
pyrometry. It is found that cooling can be much hastened over certain
ranges of temperature, and the total time required very greatly
shortened. It has also been discovered, thanks to captured instruments,
that some of the glasses commonly regarded as almost impossible to
free from bubbles have in fact yielded to improved methods of treatment.

Conventionally optical glass is of two classes, crown and flint.
Originally the former was a simple compound of silica with soda and
potash, sometimes also lime or magnesia, while the latter was rich
in lead oxide and with less of alkali. The crown had a low index of
refraction and small dispersion, the flint a high index and strong
dispersion. Crown glass was the material of general use, while the
flint glass was the variety used in cut glass manufacture by reason of
its brilliancy due to the qualities just noted.

[Illustration: FIG. 38.—The Index of Refraction.]

The refractive index is the ratio between the sine of the angle of
incidence on a lens surface and that of the angle of refraction in
passing the surface. Fig. 38 shows the relation of the incident and
refracted rays in passing from air into the glass lens surface _L_, and
the sines of the angles which determine n, the conventional symbol for
the index of refraction. Here _i_ is the angle of incidence and _r_
the angle of refraction i.e. n = _s_/_s′_. The indices of refraction
are usually given for specific colors representing certain lines
in the spectrum, commonly _A_¹, the potassium line in the extreme
red, _C_ the red line due to hydrogen, _D_ the sodium line, _F_ the
blue hydrogen line and _G′_ the blue-violet line hydrogen line, and
are distinguished as n_{_c_}, n_{_d_}, n_{_f_}, etc. The standard
dispersion (dn) for visual rays is given as between _C_ and _F_, while
the standard refractivity is taken for _D_, in the bright yellow part
of the spectrum. (Note. For the convenience of those who are rusty on
their trigonometry, Fig. 39 shows the simpler trigonometric functions
of an angle. Thus the sine of the angle _A_ is, numerically, the length
of the radius divided into the length of the line dropped from the end
of the radius to the horizontal base line, i.e. _bc_/_Ob_, the tangent
is _da_/_Ob_, and the cosine _Oc_/_Ob_.)

Ordinarily the index of refraction of the crown was taken as about
3/2, that of the flint as about 8/5. As time has gone on and
especially since the new glasses from the Jena works were introduced
about 35 years ago, one cannot define crowns and flints in any such
simple fashion, for there are crowns of high index and flints of low
dispersion.

[Illustration: FIG.39.—The Simple Trigonometric Functions of an Angle.]

The following table gives the optical data and chemical analyses of
a few typical optical glasses. The list includes common crowns and
flints, a typical baryta crown and light flint, and a telescope crown
and flint for the better achromatization of objectives, as developed at
the Jena works.

The thing most conspicuous here as distinguishing crowns from flints
is that the latter have greater relative dispersion in the blue, the
former in the red end of the spectrum, as shown by the bracketed
ratios. This as we shall see is of serious consequence in making
achromatic objectives. In general, too, the values of ν for flints are
much lower than for crowns, and the indices of refraction themselves
commonly higher.

As we have just seen, glass comes to the optician in blocks or discs,
for miscellaneous use the former, three or four inches square and an
inch think, more or less; for telescope making the latter. The discs
are commonly some ten percent greater in diameter than the finished
objective for which they are intended, and in thickness from 1/8
to 1/10 the diameter. They are commonly well annealed and given a
preliminary polish on both sides to facilitate close inspection.

                  CHARACTERISTICS OF OPTICAL GLASSES

 ---------------+--------+--------+------+--------------------------+
                |        |        |      |        Bracketed         |
                |        |        |      |        numbers are       |
                |        |   dn   |      |      proportions of dn   |
     Glass      |  n__d_ | -----  |  ν   +--------+--------+--------+
                |        | (F-C)  |      |  D-A´  |   F-D  |  G´-F  |
                |        |        |      |  ----  |  ----  |  ----  |
                |        |        |      |   dn   |   dn   |   dn   |
 ---------------+--------+--------+------+--------+--------+--------+
 Boro-silicate  | 1.5069 | .00813 | 62.3 | .00529 | .00569 | .00457 |
   crown        |        |        |      | (.651) | (.701) | (.562) |
 Zinco-silicate | 1.5170 | .00859 | 60.2 | .00555 | .00605 | .00485 |
  (hard) crown  |        |        |      | (.646) | (.704) | (.565) |
 Dense baryta   | 1.5899 | .00970 | 60.8 | .00621 | .00683 | .00546 |
   crown        |        |        |      | (.640) | (.704) | (.563) |
 Baryta light   | 1.5718 | .01133 | 50.4 | .00706 | .00803 | .00660 |
    flint       |        |        |      | (.623) | (.709) | (.582) |
 Common light   | 1.5710 | .01327 | 43.0 | .00819 | .00943 | .00791 |
   flint        |        |        |      | (.617) | (.710) | (.596) |
 Common dense   | 1.6116 | .01638 | 37.3 | .00995 | .01170 | .00991 |
   flint        |        |        |      | (.607) | (.714) | (.607) |
 Very dense     | 1.6489 | .01919 | 33.8 | .01152 | .01372 | .01180 |
   flint        |        |        |      | (.600) | (.714) | (.615) |
 Densest flint  | 1.7541 | .02743 | 27.5 | .01607 | .01974 | .01730 |
                |        |        |      | (.585) | (.720) | (.630) |
 [*]Telescope   | 1.5285 | .00866 | 61.0 | .00557 | .00610 | .00493 |
  crown         |        |        |      | (.643) | (.705) | (.570) |
 [*]Telescope   | 1.5286 | .01025 | 51.6 | .00654 | .00723 | .00591 |
   flint        |        |        |      | (.638) | (.705) | (.576) |

 [* Optical data close approximations only.]

 +------------------------------------------------------------------------
 |
 |              Analysis of glasses in percentages
 |
 +----+----+---+----+----+----+----+----+----+----+----+----+----+----+----
 | Si |B_2 |   |    |    |K_2 |Na_2|    |AL_2|As_2|As_2|Fe_2|Mn_2|Sb_2|
 | O_2| O_3|ZnO| PbO| BaO| O  | O  |CaO | O_3| O_5| O_3| O_3| O_3| O_3| MgO
 |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
 +----+----+---+----+----+----+----+----+----+----+----+----+----+----+----
 |74.8| 5.9| --| -- | -- |7.11|11.3| -- | .75| -- | .06| -- | .06|    |
 |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
 |65.4| 2.5|2.0| -- | 9.6|15.0| 5.0| -- | -- | -- | .4 | -- | .1 |    |
 |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
 |37.5|15.0| --| -- |41.0| -- |    | -- |5.0 | 1.5|    |    |    |    |
 |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
 |51.7| -- |7.0|10.0|20.0| 9.5| 1.5| -- | -- | .30|    |    |    |    |
 |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
 |54.3| 1.5| --|33.0| -- | 8.0| 3.0| -- | -- | .20|    |    |    |    |
 |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
 |54.8| -- | --|37.0| -- | 5.8|  .8| .60| .4 | -- | -- | .70| -- | -- | .20
 |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
 |40.0| -- | --|52.6| -- | 6.5|  .5| -- | -- | .30| -- | -- | .09|    |
 |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
 |29.3| -- | --|67.5| -- | 3.0|  --| -- | -- | -- | .20| -- | .04|    |
 |    |    |   |    |    |    |    |    |    |    |    | ---^--- |    |
 |55.2| -- | --| -- |22.0| 5.7| 7.5|5.9 | -- | -- | -- |   3.7   |    |
 |    |    |   |    |    |    |    |    |    |    |    |         |    |
 |59.9|12.7| --| -- | -- | 5.1| 3.5| -- | -- | -- | -- |   2.7   |16.1|
 |    |    |   |    |    |    |    |    |    |    |    |         |    |
 +----+----+---+----+----+----+----+----+----+----+----+---------+----+----

The first step toward the telescope is the testing of these discs
of glass, first for the presence or absence of striæ and other
imperfections; second, for the perfection of the annealing. The maker
has usually looked out for all the grosser imperfections before the
discs left his works, but a much closer inspection is needed in order
to make the best use of the glass.

[Illustration: FIG. 40.—Testing Glass for Striæ.]

Bad striæ are of course seen easily, as they would be in a window pane,
but such gross imperfections are often in reality less damaging than
the apparently slighter ones which must be searched for. The simplest
test is to focus a good telescope on an artificial star, remove the
eyepiece and bring the eye into its place.

When the eye is in focus the whole aperture of the objective is
uniformly filled with light, and if the disc to be tested be placed
in front of it, any inequality in refraction will announce itself by
an inequality of illumination. A rough judgment as to the seriousness
of the defect may be formed from the area affected and the amount by
which it affects the local intensity of illumination. Fig. 40 shows the
arrangement for the test, _A_ being the eye, _B_ the objective and _C_
the disc. The artificial star is conveniently made by setting a black
bottle in the sun a hundred feet or so away and getting the reflection
from its shoulder.

[Illustration: FIG. 41.—The Mirror Test for Striæ.]

A somewhat more delicate test, very commonly used, is shown in Fig.
41. Here _A_ is a truly spherical mirror silvered on the front. At _B_
very close to its centre of curvature is placed a lamp with a screen in
front of it perforated with a hole 1/32 inch or so in diameter.

The rays reflected from the mirror come back quite exactly upon
themselves and when the eye is placed at _C_, their reflected focus,
the whole mirror _A_ is uniformly lighted just as the lens was in Fig.
40, with the incidental advantage that it is much easier and cheaper to
obtain a spherical mirror for testing a sizeable disc than an objective
of similar size and quality. Now placing the disc _D_ in front of the
mirror, the light passing twice through it shows up the slightest stria
or other imperfection as a streak or spot in the field. Its place is
obvious and can be at once marked on the glass, but its exact position
in the substance of the disc is not so obvious.

To determine this, which may indicate that the fault can be ground out
in shaping the lens, a modification of the first test serves well, as
indeed it does for the general examination of large discs. Instead of
using a distant artificial star and a telescope, one uses the lamp and
screen, or even a candle flame ten feet or more away and a condensing
lens of rather short focus, which may or may not be achromatic, so
that the eye will get into its focus conveniently while the lens is
held in the hand. Fig. 42 shows the arrangement. Here _A_ is the eye,
_B_ the condensing lens, _C_ the disc and _D_ the source of light. The
condensing lens may be held on either side of the disc as convenience
suggests, and either disc or lens may be moved. The operation is
substantially the examination of a large disc piecemeal, instead of all
at once by the use of a big objective or mirror.

[Illustration: FIG. 42.—Locating Striæ in the Substance of a Disc.]

Now when a stria has been noted mark its location as to the surface,
and, moving the eye a little, look for parallax of the fault with
respect to the surface mark. If it appears to shift try a mark on the
opposite surface in the same way. Comparison of the two inspections
will show about where the fault lies with respect to the surfaces,
and therefore what is the chance of working it out. Sometimes a look
edgewise of the disc will help in the diagnosis.

Numerous barely detectable striæ are usually worse than one or two
conspicuous ones, for the latter frequently throw the light they
transmit so wide of the focus that it does not affect the image, which
could be greatly damaged by slight blurs of light that just miss focus.

Given a disc that passes well the tests for striæ and the like the next
step is to examine the perfection of the annealing, which in its larger
aspect is revealed by an examination in polarized light.

[Illustration: FIG. 43.—Testing a Disc in Polarized Light.]

For this purpose the disc is set up against a frame placed on table or
floor with a good exposure to skylight behind it, and inclined about
35° from the vertical. Behind it is laid a flat shiny surface to serve
as polarizer. Black enamel cloth smoothly laid, a glass plate backed
with black paint, or even a smooth board painted with asphalt paint
will answer excellently. Then holding a Nicol prism before the eye and
looking perpendicular to the face of the disc, rotate the prism on its
axis. Fig. 43 shows the arrangement, _A_ being the eye, _B_ the Nicol,
_C_ the disc, and _D_ the polarizer behind it.

If annealing has left no strain the only effect of rotating the Nicol
will be to change the field from bright to dark and back again as if
the disc were not there. Generally a pattern in the form of a somewhat
hazy Maltese cross will appear, with its arms crossing the disc,
growing darker and lighter alternately as the Nicol is turned.

If the cross is strongly marked but symmetrical and well centered the
annealing is fair—better as the cross is fainter and hazier—altogether
bad if colors show plainly or if the cross is decentered or distorted.
The test is extremely sensitive, so that holding a finger on the
surface of the disc may produce local strain that will show as a faint
cloudy spot.

A disc free of striæ and noticeable annealing strains is usually, but
not invariably, good, for too frequent reheating in the moulding or
annealing process occasionally leaves the glass slightly altered, the
effect extending, at worst, to the crystallization or devitrification
to which reference has been made.

Given a good pair of discs the first step towards fashioning them into
an objective is roughing to the approximate form desired. As a guide
to the shaping of the necessary curves, templets must be made from the
designed curves of the objective as precisely as possible. These are
laid out by striking the necessary radii with beam compass or pivoted
wire and scribing the curve on thin steel, brass, zinc or glass. The
two last are the easier to work since they break closely to form.

From these templets the roughing tools are turned up, commonly from
cast iron, and with these, supplied with carborundum or even sand, and
water, the discs, bearing against the revolving tool, are ground to the
general shape required. They are then secured to a slowly revolving
table, bearing edgewise against a revolving grindstone, and ground
truly circular and of the proper final diameter.

At this point begins the really careful work of fine grinding, which
must bring the lens very close to its exact final shape. Here again
tools of cast iron, or sometimes brass, are used, very precisely
brought to shape according to the templets. They are grooved on the
face to facilitate the even distribution of the abrasive, emery or
fine carborundum, and the work is generally done on a special grinding
machine, which moves the tool over the firmly supported disc in a
complicated series of strokes imitating more or less closely the
strokes found to be most effective in hand polishing.

In general terms the operator in handwork at this task supports the
disc on a firm vertical post, by cementing it to a suitable holder, and
then moves the tool over it in a series of straight or oval strokes,
meanwhile walking around the post. A skilful operator watches the
progress of his work, varies the length and position of his strokes
accordingly, and, despite the unavoidable wear on the tool, can both
keep its figure true and impart a true figure to the glass.

[Illustration: FIG. 44.—Dr. Draper’s Polishing Machine.]

The polishing machine, of which a type used by Dr. Draper is shown
in Fig. 44, produces a similar motion, the disc slowly revolving and
the rather small tool moving over it in oval strokes kept off the
center. More often the tool is of approximately the same diameter as
the disc under it. The general character of the motion is evident
from the construction. The disc _a_ is chucked by _c c′_ on the bed,
turned by the post _d_ and worm wheel _e_. This is operated from the
pulleys, _i_, _g_, which drive through _k_, the crank _m_, adjustable
in throw by the nuts _n_, _n′_, and in position of tool by the clamps
_r_, _r_. The motion may be considerably varied by adjustment of the
machine, always keeping the stroke from repeating on the same part of
the disc, by making the period of the revolution and of the stroke
incommensurable so far as may be. Even in spectacle grinding machines
the stroke may repeat only once in hundreds of times, and even this
frequency in a big objective would, if followed in the polishing, leave
tool marks which could be detected in the final testing.

In the fine grinding, especially near the end of the process, the
templets do not give sufficient precision in testing the curves, and
recourse is had to the spherometer, by which measurements down to about
1/100000 inch can be consistently made.

The next stage of operations is polishing, which transforms the grey
translucency of the fine ground lens into the clear and brilliant
surface which at last permits rigorous optical tests to be used for the
final finish of the lens. This polishing is done generally on the fine
grinding machine but with a very different tool and with rouge of the
utmost fineness.

The polishing tool is in any case ground true and is then faced with a
somewhat yielding material to carry the charge of rouge. Cheap lenses
are commonly worked on a cloth polisher, a texture similar to billiard
cloth being suitable, or sometimes on paper worked dry.

With care either may produce a fairly good surface, with, however, a
tendency to polish out the minute hollows left by grinding rather than
to cut a true surface clear down to their bottoms. Hence cloth or paper
is likely to leave microscopic inequalities apparently polished, and
this may be sufficient to scatter over the field a very perceptible
amount of light which should go to forming the image. All first class
objectives and mirrors are in fact polished on optician’s pitch. This
is not the ordinary pitch of commerce but a substance of various
composition, sometimes an asphaltic compound, again on a base of tar,
or of resin brought to the right consistency by turpentine.

Whatever the exact composition, the fundamental property is that
the material, apparently fairly hard and even brittle when cold, is
actually somewhat plastic to continued pressure. Sealing wax has
something of this quality, for a stick which may readily be broken will
yet bend under its own weight if supported at the ends.

If the fine grinding process has been properly carried out the lens has
received its correct form as nearly as gauges and the spherometer can
determine it. The next step is to polish the surface as brilliantly
and evenly as possible. To this end advantage is taken of the plastic
quality already mentioned, that the glass may form its own tool.

The base of the tool may be anything convenient, metal, glass or even
wood. Its working surface is made as nearly of the right curvature as
practicable and it is then coated with warm pitch to a thickness of an
eighth of an inch more or less, either continuously or in squares, and
while still slightly warm the tool is placed against the fine ground
disc, the exact shape of which it takes.

When cold the pitch surface can easily be cut out into squares or
symmetrically pitted with a suitable tool, at once facilitating the
distribution of the rouge and water that serves for polishing, and
permitting delicate adjustment of the working curvature in a way about
to be described.

Fig. 45 shows the squared surface of the tool as it would be used for
polishing a plane or very slightly convex or concave surface. Supplied
with the thin abrasive paste, it is allowed to settle, cold, into its
final contact with the glass, and then the process of polishing by hand
or machine is started.

The action of the tool must be uniform to avoid changing the shape of
the lens. It can be regulated as it was in the grinding, by varying the
length and character of the stroke, but even more delicately by varying
the extent of surface covered by the pitch actually working on the
glass.

[Illustration: FIG. 45.—Tool for Flat Surface.]

[Illustration: FIG. 46.—Tool for Concave Surface.]

This is done by channeling or boring away pitch near the rim or center
of the tool as the case may be. Fig. 46 shows a tool which has been
thus treated so that the squares are progressively smaller near the
periphery. Such a spacing tends to produce a concave surface from a
flat tool or to increase the concavity from a curved one. Trimming down
the squares towards the centre produces the opposite result.

Broadly, the principle is that the tool cuts the more in the areas
where the contact surfaces are the greater. This is not wholly by
reason of greater abrading surface, but also because where the contact
is greater in area the pitch settles less, from the diminished
pressure, thus increasing the effective contact.

Clearly the effect of trimming away is correlated with the form and
length of stroke, and the temper of the pitch, and in fact it requires
the wisdom of the serpent to combine these various factors so as to
produce the perfectly uniform and regular action required in polishing.
Now and then, at brief intervals, the operation is stopped to supply
rouge and to avoid changing the conditions by the heat of friction.
Especially must heating be looked out for in hand polishing of lenses
which is often done with the glass uppermost for easier inspection of
the work.

Polishing, if the fine grinding has been judiciously done is, for
moderate sized surfaces, a matter of only a few hours. It proceeds
quite slowly at first while the hills are being ground down and then
rather suddenly comes up brilliantly as the polisher reaches the
bottoms of the valleys. Large lenses and mirrors may require many days.

Now begins the final and extraordinarily delicate process of figuring.
The lens or mirror has its appointed form as nearly as the most precise
mechanical methods can tell—say down to one or two hundred-thousandths
of an inch. From the optical standpoint the result may be thoroughly
bad, for an error of a few millionths of an inch may be serious in the
final performance.

The periphery may be by such an amount longer or shorter in radius
than it should be, or there may be an intermediate zone that has
gone astray. In case of a mirror the original polishing is generally
intended to leave a spherical surface which must be converted into
a paraboloidal one by a change in curvature totalling only a few
hundred-thousandths of an inch and seriously affected by much smaller
variations.

The figuring is done in a fashion very similar to the polishing. The
first step is to find out by optical tests such as are described in
Chapter IX the location of the errors existing after the polishing, and
once found, they must be eliminated by patient and cautious work on the
surface.

Every optical expert has his own favorite methods of working out the
figure. If there is a hollow zone the whole surface must be worked
down to its level by repolishing; if, on the other hand, there is an
annular hump, one may repolish with stroke and tool-face adapted to cut
it down, or one may cautiously polish it out until it merges with the
general level.

Polishing is commonly done with tools of approximately the size of
the work, but in figuring there is great difference of practice, some
expert workers depending entirely on manipulation of a full sized
tool, others working locally with small polishers, even with the ball
of the thumb, in removing slight aberrations. In small work where the
glass can be depended on for homogeneity and the tools are easily kept
true the former method is the usual one, but in big objectives the
latter is often easier and may successfully reach faults otherwise very
difficult to eliminate.

Among well known makers of telescopes the Clarks and their equally
skilled successors the Lundins, father and son, developed the art
of local retouching to a point little short of wizardry; the late
Dr. Brashear depended almost entirely on the adroitly used polishing
machine; Sir Howard Grubb uses local correction in certain cases,
and in general the cautiously modified polisher; while some of the
Continental experts are reported to have developed the local method
very thoroughly.

The truth probably is that the particular error in hand should
determine the method of attack and that its success depends entirely
on the skill of the operator. As to the perfection of the objectives
figured in either way, no systematic difference due to the method of
figuring can be detected by the most delicate tests.

In any case the figuring operation is long and tedious, especially in
large work where problems of supporting to avoid flexure arise, where
temperature effects on tool and glass involve long delays between tests
and correction, and where in the last resort non-spherical surfaces
must often be resorted to in bringing the image to its final perfection.

The final test of goodness is performance, a clean round image without
a trace of spherical or zonal aberration and the color correction the
best the glasses will allow. Constant and rigorous testing must be
applied all through the process of figuring, and the result seems to
depend on a combination of experience, intuition and tactual expertness
rarely united in any one person.

Sir Howard Grubb, in a paper to be commended to anyone interested in
objectives, once forcibly said: “I may safely say that I have never
finished any objective over 10 inches diameter, in the working of which
I did not meet with some new experience, some new set of conditions
which I had not met before, and which had then to be met by special and
newly devised arrangements.”

The making of reflecting telescopes is not much easier since although
only one surface has to be worked, that one has to be figured with
extraordinary care, flexure has to be guarded against at every stage
of the working, and afterwards, temperature change is a busy foe,
while testing for correct figure, the surface being non-spherical, is
considerably more troublesome.

An expert can make a good mirror with far less actual labor than an
objective of similar aperture, but when one reads Dr. Henry Draper’s
statement that in spite of knowing at first hand the methods and
grinding machines of Lord Rosse and Mr. Lassell, he ground over a
hundred mirrors, and spent three years of time, before he could get a
correct figure with reasonable facility, one certainly gains a high
respect for the skill acquired.

This chapter is necessarily sketchy and not in the least intended to
give the reader a complete account of technical glass manufacture,
far less of the intricate and almost incommunicable art of making
objectives and mirrors. It may however lead to a better understanding
of the difference between the optical glass industry and the
fabrication of commercial glass, and lead the reader to a fuller
realization of how fine a work of art is a finished objective or mirror
as compared with the crude efforts of the early makers or the hasty
bungling of too many of their successors.

For further details on making, properties and working of optical glass
see:

 HOVESTADT: “Jenaer Glas.”

 ROSENHAIN: “Glass Manufacture.”

 SIR HOWARD GRUBB: “Telescopic Objectives and Mirrors: Their
 Preparation and Testing.” Nature _34_, 85.

 DR. HENRY DRAPER: “On the Construction of a Silvered Glass Telescope.”
 (Smithsonian Contributions to Knowledge, Vol. 34.)

 G. W. RITCHEY: On the Modern Reflecting Telescope and the Making and
 Testing of Optical Mirrors. (Smithsonian Contributions to Knowledge,
 Vol. 34.)

 LORD RAYLEIGH: Polishing of Glass Surfaces. (Proc. Opt. Convention,
 1905, p. 73.)

 BOTTONE: “Lens Making for Amateurs.”




CHAPTER IV

THE PROPERTIES OF OBJECTIVES AND MIRRORS


The path of the rays through an ordinary telescope has been shown in
Fig. 5. In principle all the rays from a point in the distant object
should unite precisely in a corresponding point in the image which is
viewed by the eyepiece. Practically it takes very careful design and
construction of the objective to make them meet in such orderly fashion
even over an angular space of a single degree, and the wider the view
required the more difficult the construction. We have spoken in the
account of the early workers of their struggles to avoid chromatic and
spherical aberrations, and it is chiefly these that still, in less
measure, worry their successors.

[Illustration: FIG. 47.—Chromatic Aberration of Convex Lens.]

The first named is due to the fact that a prism does not bend light of
all colors equally, but spreads them out into a spectrum; red refracted
the least, violet the most. Since a lens may be regarded as an
assemblage of prisms, of small angle near the centre and greater near
the edge, it must on the whole and all over bend the blue and violet
rays to meet on the axis nearer the rear surface than the corresponding
red rays, as shown in Fig. 47. Here the incident ray _a_ is split up by
the prismatic effect of the lens, the red coming to a focus at _r_, the
violet at _v_.

One can readily see this chromatic aberration by covering up most of a
common reading glass with his hand and looking through the edge portion
at a bright light, which will be spread out into a colored band.

If the lens is concave the violet rays will still be the more bent,
but now outwards, as shown in Fig. 48. The incident ray _a′_ is split
up and the violet is bent toward _v_, proceeding as if coming straight
from a virtual focus _v′_ in front of the lens, and nearer it than the
corresponding red focus _r′_. Evidently if we could combine a convex
lens, bending the violet inward too much, with a concave one, bending
it outward too much, the two opposite variations might compensate each
other so that red and violet would come to the same focus—which is the
principle of the achromatic objective.

[Illustration: FIG. 48.—Chromatic Aberration of Concave Lens.]

If the refractive powers of the lenses were exactly proportional to
their dispersive powers, as Newton erroneously thought, it is evident
that the concave lens would pitch all the rays outwards to an amount
which would annul both the chromatic variation and the total refraction
of the convex lens, leaving the pair without power to bring anything
to a focus. Fortunately flint glass as compared with crown glass has
nearly double the dispersion between red and violet, and only about 20%
greater refractive power for the intermediate yellow ray.

Hence, the prismatic dispersive effect being proportional to the total
curvature of the lens, the chromatic aberration of a crown glass
lens will be cured by a concave flint lens of about half the total
curvature, and, the refractions being about as 5 to 6, of ⅗ the total
power.

Since the “power” of any lens is the reciprocal of its focal length,
a crown glass convex lens of focal length 3, and a concave flint lens
of focal length 5 (negative) will form an approximately achromatic
combination. The power of the combination will be the algebraic sum of
the powers of the components so that the focal length of the pair will
be about 5/2 that of the crown lens with which we started.

To be more precise the condition of achromatism is

  Σρδn + Σρ′δn′ = 0

where ρ is the reciprocal of a radius and δn, or δn′, is the difference
in refractive index between the rays chosen to be brought to exact
focus together, as the red and the blue or violet.

This conventional equation simply states that the sum of the
reciprocals of the radii of the crown lens multiplied by the dispersion
of the crown, must equal the corresponding quantity for the flint lens
if the two total dispersions are to annul each other, leaving the
combination achromatic. Whatever glass is used the power of a lens made
of it is

  P( = 1/_f_) = Σρ(n - 1)

so that it will be seen that, other things being equal, a glass of high
index of refraction tends to give moderate curves in an objective.
Also, referring to the condition of achromatism, the greater the
difference in dispersion between the two glasses the less curvatures
will be required for a given focal length, a condition advantageous for
various reasons.

The determination of achromatism for any pair of glasses and focal
length is greatly facilitated by employing the auxiliary quantity ν
which is tabulated in all lists of optical glass as a short cut to a
somewhat less manageable algebraic expression. Using this we can figure
achromatism for unity focal length at once,

  P = ν/(ν-ν′) P′ = ν′/(ν-ν′) ν = (n_{_D_}-1)/δn

being the powers of the leading and following lenses respectively.
The combined lens will bring the rays of the two chosen colors, as
red and blue, to focus at the same point on the axis. It does not
necessarily give to the red and blue images of an object the same exact
size. Failure in this respect is known as chromatic difference of
magnification, but the fault is small and may generally be neglected in
telescope objectives.

We have now seen how an objective may be made achromatic and of
determinate focal length, but the solution is in terms of the sums of
the respective curvatures of the crown and flint lenses, and gives no
information about the radii of the individual surfaces. The relation
between these is all-important in the final performance.

[Illustration: FIG. 49.—Spherical Aberration of Convex Lens.]

For in a convex lens with spherical surfaces the rays striking near the
edge, of whatever color, are pitched inwards too much compared with
rays striking the more moderate curvatures near the axis, as shown in
Fig. 49. The ray _a′ b′_ thus comes to a focus shorter than the ray _a
b_.

This constitutes the fault of spherical aberration, which the
old astronomers, following the suggestions of Descartes, tried
ineffectually to cure by forming lenses with non-spherical surfaces.

[Illustration: FIG. 50.—Spherical Aberration of Concave Lens.]

Fig. 50 suggests the remedy, for the outer ray _a″_ is pitched out
toward _b″_ as if it came from a focal point _c″_, while the ray
nearer the center _a″′_ is much less bent toward _b″′_ as if it came
from _c″′_. The spherical aberrations of a concave lens therefore,
being opposite to those of a convex lens, the two must, at least to a
certain extent, compensate each other as when combined in an achromatic
objective.

So in fact they do, and, if the curves that go to make up the total
curvatures of the two are properly chosen, the total spherical
aberration can be made negligibly small, at least on and near the
axis. Taking into account this condition, therefore, at once gives
us a clue to the distribution of the total curvatures and hence to
the radii of the two lenses. Spherical aberration, however, involves
not only the curvatures but the indices of refraction, so that exact
correction depends in part on the choice of glasses wherewith to obtain
achromatization.

In amount spherical aberration varies with the square of the aperture
and inversely with the cube of the focal length i.e. with a²/f³. It is
reckoned as + when, as in Fig. 49, the rim rays come to the shorter
focus, as-, when they come to the longer focus.

In any event, since the spherical aberration of a lens may be varied in
above the ratio of 4:1, for the same total power, merely by changing
the ratio of the radii, it is evident that the two lenses being fairly
correct in total curvature might be given considerable variations in
curvature and still mutually annul the axial spherical aberration.

Such is in fact the case, so that to get determinate forms for
the lenses one must introduce some further condition or make some
assumption that will pin down the separate curvatures to some definite
relations. The requirement may be entirely arbitrary, but in working
out the theory of objectives has usually been chosen to give the lens
some real or hypothetical additional advantage.

The commonest arbitrary requirement is that the crown glass lens
shall be equiconvex, merely to avoid making an extra tool. This fixes
one pair of radii, and the flint lens is then given the required
compensating aberration choosing the easiest form to make. This results
in the objective of Fig. 51.

[Illustration: FIG. 51.—Objectives with Equiconvex Crown.]

Probably nine tenths of all objectives are of this general form,
equiconvex crown and nearly or quite plano-concave flint. The inside
radii may be the same, in which case the lenses should be cemented,
or they may differ slightly in either direction as _a_, Fig. 51
with the front of the flint less curved than the rear of the crown,
and _b_ where the flint has the sharper curve. The resulting lens if
ordinary glasses are chosen gives excellent correction of the spherical
aberration on the axis, but not much away from it, yielding a rather
narrow sharp field. Only a few exceptional combinations of glasses
relieve this situation materially.

The identity of the inner radii so that the surfaces can be cemented
is known historically as Clairault’s condition, and since it fixes two
curvatures at identity somewhat limits the choice of glasses, while to
get proper corrections demands quite wide variations in the contact
radii for comparatively small variations in the optical constants of
the glass.

When two adjacent curves are identical they should be cemented,
otherwise rays reflected from say the third surface of Fig. 51 will be
reflected again from the second surface, and passing through the rear
lens in almost the path of the original ray will come to nearly the
same focus, producing a troublesome “ghost.” Hence the curvatures of
the second and third surfaces when not cemented are varied one way or
the other by two or three per cent, enough to throw the twice reflected
rays far out of focus.

In this case, as in most others, the analytical expression for the
fundamental curvature to be determined turns up in the form of a
quadratic equation, so that the result takes the form a ± b and there
are two sets of radii that meet the requirements. Of these the one
presenting the gentler curves is ordinarily chosen. Fig. 52 _a_ and
_c_ shows the two cemented forms, thus related, for a common pair of
crown and flint glasses, both cleanly corrected for chromatic and axial
spherical aberration.

Nearly a century ago Sir John Herschel proposed another defining
condition, that the spherical aberration should be removed both for
parallel incident rays and for those proceeding from a nearer point
on the axis, say ten or more times the focal length in front of the
objective. This condition had little practical value in itself, and its
chief merit was that it approximated one that became of real importance
if the second point were taken far enough away.

[Illustration: FIG. 52.—Allied Forms of Cemented Objectives.]

A little later Gauss suggested that the spherical aberration should be
annulled for two different colors, much as the chromatic aberration is
treated. And, being a mathematical wizard, he succeeded in working out
the very intricate theory, which resulted in an objective approximately
of the form shown in Fig. 53.

It does not give a wide field but is valuable for spectroscopic work,
where keen definition in all colors is essential. Troublesome to
compute, and difficult to mount and center, the type has not been much
used, though there are fine examples of about 9½ inches aperture at
Princeton, Utrecht, and Copenhagen, and a few smaller ones elsewhere,
chiefly for spectroscopic use.

It was Fraunhofer who found and applied the determining condition of
the highest practical value for most purposes. This condition was
absence of _coma_, the comet shaped blur generally seen in the outer
portions of a wide field.

It is due to the fact that parallel oblique rays passing through
the opposite rims of the lens and through points near its center do
not commonly come to the same focus, and it practically is akin to
a spherical aberration for oblique rays which greatly reduces the
extent of the sharp field. It is reckoned + when the blur points
outwards,-when it points inwards, and is directly proportional to the
tangent of the obliquity and the square of the aperture, and inversely
to the square of the focal length i.e. it varies with a²tan(u)/f².

[Illustration: FIG. 53.—Gaussian Objective.]

Just how Fraunhofer solved the problem is quite unknown, but solve it
he did, and very completely, as he indicates in one of his later papers
in which he speaks of his objective as reducing all the aberrations
to a minimum, and as Seidel proved 30 years later in the analysis of
one of Fraunhofer’s objectives. Very probably he worked by tracing
axial and oblique rays through the objective form by trigonometrical
computation, thus finding his way to a standard form for the glasses he
used.[10]

 [10] More recently his condition proves to be quite the exact
 equivalent of Abbé’s _sine condition_ which states that the sine of
 the angle made with the optical axis by a ray entering the objective
 from a given axial point shall bear a uniform ratio to the sine of the
 corresponding angle of emergence, whatever the point of incidence.
 For parallel rays along the axis this reduces to the requirement that
 the sines of the angles of emergence shall be proportional to the
 respective distances of the incident rays from the axis.

Fraunhofer’s objective, of which Fig. 54_a_ is an example worked by
modern formulæ for the sine condition, gives very exact corrections
over a field of 2°-3° when the glasses are suitably chosen and hence is
invaluable for any work requiring a wide angle of view.

With certain combinations of glasses the coma-free condition may
be combined successfully with Clairault’s, although ordinarily
the coma-free form falls between the two forms clear of spherical
aberration, as in Fig. 52, _b_, which has its oblique rays well
compensated but retains serious axial faults.

[Illustration: FIG. 54.—The Fraunhofer Types.]

Fraunhofer’s objective has for all advantageous combinations of glasses
the front radius of the flint longer than the rear radius of the
crown hence the two must be separated by spacers at the edge, which
in small lenses in simple cells is slightly inconvenient. However,
the common attempt to simplify mounting by making the front flint
radius the shorter almost invariably violates the sine condition and
reduces the sharp field, fortunately not a very serious matter for most
astronomical work.

The only material objection to the Fraunhofer type is the strong
curvature of the rear radius of the crown which gives a form somewhat
susceptible to flexure in large objectives. This is met in the
flint-ahead form, developed essentially by Steinheil, and used in most
of the objectives of his famous firm. Fig. 54_b_ shows the flint-ahead
objective corresponding to Fig. 54_a_. Obviously its curves are
mechanically rather resistant to flexure.[11]

 [11] It is interesting to note that in computing Fig. 54_a_ for the
 sine condition, the other root of the quadratic gave roughly the
 Gaussian form of Fig. 53.

[Illustration: FIG. 55.—Clark Objective.]

Mechanical considerations are not unimportant in large objectives, and
Fig. 55, a highly useful form introduced by the Clarks and used in
recent years for all their big lenses, is a case in point. Here there
is an interval of about the proportion shown between the crown and
flint components.

This secures effective ventilation allowing the lenses to come quickly
to their steady temperature, and enables the inner surfaces to be
cleaned readily and freed of moisture. Optically it lessens the
deviation from the sine condition otherwise practically inseparable
from the equiconvex crown, reduces the chromatic difference of
spherical aberration, and gives an easy way of controlling the color
correction by slightly varying the separation of the lenses.

One further special case is worth noting, that of annulling the
spherical aberration for rays passing through the lens in both
directions. By proper choice of glass and curvatures this can be
accomplished to a close approximation and the resulting form is shown
in Fig. 56. The front of the crown is notably flat and the rear of
the flint conspicuously curved, the shape in fact being intermediate
between Figs. 52_b_ and 52_c_. The type is useful in reading telescopes
and the like, and for some spectroscopic applications.

[Illustration: FIG. 56.—Corrected in Both Directions.]

There are two well known forms of aberration not yet considered;
astigmatism and curvature of field. The former is due to the fact that
when the path of the rays is away from the axis, as from an extended
object, those coming from a line radial to the axis, and those from a
line tangent to a circle about the axis, do not come to the same focus.
The net result is that the axial and tangential elements are brought to
focus in two coaxial surfaces touching at the axis and departing more
and more widely from each other as they depart from it. Both surfaces
have considerable curvature, that for tangential lines being the
sharper.

It is possible by suitable choice of glasses and their curvatures
to bring both image surfaces together into an approximate plane for
a moderate angular space about the axis without seriously damaging
the corrections for chromatic and spherical aberration. To do this
generally requires at least three lenses, and photographic objectives
thus designed (_anastigmats_) may give a substantially flat field over
a total angle of 50° to 60° with corrections perfect from the ordinary
photographic standpoint.

If one demands the rigorous precision of corrections called for in
astronomical work, the possible angle is very much reduced. Few
astrographic lenses cover more than a 10° or 15° field, and the wider
the relative aperture the harder it is to get an anastigmatically flat
field free of material errors. Astigmatism is rarely noticeable in
ordinary telescopes, but is sometimes conspicuous in eyepieces.

Curvature of field results from the tendency of oblique rays in
objectives, otherwise well corrected, to come to shorter focus than
axial rays, from their more considerable refraction resulting from
greatly increased angles of incidence. This applies to both the
astigmatic image surfaces, which are concave toward the objective in
all ordinary cases.

Fortunately both these faults are negligible near the axis. They are
both proportional to tan²{u}/f where u is the obliquity to the axis
and f the focal length; turn up with serious effect in wide angled
lenses such as are used in photography, but may generally be forgotten
in telescopes of the ordinary _F_ ratios, like _F_/12 to _F_/16. So
also one may commonly forget a group of residual aberrations of higher
orders, but below about _F_/8 look out for trouble. Objectives of
wider aperture require a very careful choice of special glasses or
the sub-division of the curvatures by the use of three or more lenses
instead of two. Fig. 57 shows a cemented triplet of Steinheil’s design,
with a crown lens between two flints. Such triplets are made up to
about 4 inches diameter and of apertures ranging from _F_/4 to _F_/5.

[Illustration: FIG. 57.—Steinheil Triple Objective.]

[Illustration: FIG. 58.—Tolles Quadruple Objective.]

In cases of demand for extreme relative aperture, objectives composed
of four cemented elements have now and then been produced. An example
is shown in Fig. 58, a four-part objective of 1 inch aperture made
by Tolles years ago for a small hand telescope. Its performance,
although it worked at _F_/4, was reported to be excellent even up to 75
diameters.

The main difficulty with these objectives of high aperture is the
relatively great curvature of field due to short focal length which
prevents full utilization of the improved corrections off the axis.

Distortion is similarly due to the fact that magnification is not quite
the same for rays passing at different distances from the axis. It
varies in general with the cube of the distance from the axis, and is
usually negligible save in photographic telescopes, ordinary visual
fields being too small to show it conspicuously.

Distortion is most readily avoided by adopting the form of a
symmetrical doublet of at least four lenses as in common photographic
use. No simple achromatic pair gives a field wholly free of distortion
and also of the ordinary aberrations, except very near the axis, and
in measuring plates taken with such simple objectives corrections for
distortion are generally required.

At times it becomes necessary to depart somewhat from the objective
form which theoretically gives the least aberrations in order to
meet some specific requirement. Luckily one may modify the ratios of
the curves very perceptibly without serious results. The aberrations
produced come on gradually and not by jumps.

[Illustration: FIG. 59.—“Bent” Objective.]

A case in point is that of the so-called “bent” objective in which the
curvatures are all changed symmetrically, as if one had put his fingers
on the periphery and his thumbs on the centre of the whole affair, and
had sprung it noticeably one way or the other.

The corrections in general are slightly deteriorated but the field may
be in effect materially flattened and improved. An extreme case is the
photographic landscape lens. Figure 59 is an actual example from a
telescope where low power and very large angular view were required.
The objective was first designed from carefully chosen glass to meet
accurately the sine condition. Even so the field, which covered an
apparent angle of fully 40°, fell off seriously at the edge.

Bearing in mind the rest of the system, the objective was then “bent”
into the form given by the dotted lines, and the telescope then showed
beautiful definition clear to the periphery of the field, without any
visible loss in the centre.

This spurious flattening cannot be pushed far without getting into
trouble for it does not cure the astigmatic difference of focus, but
it is sometimes very useful. Practically curvature of field is an
outstanding error that cannot be remedied in objectives required to
stand high magnifying powers, except by going to the anastigmatic forms
similar to those used in photography.[12]

 [12] The curvature of the image is the thing which sets a limit to
 shortening the relative focus, as already noted, for the astigmatic
 image surfaces as we have seen, fall rapidly apart away from the
 axis, and both curvatures are considerable. The tangential is the
 greater, corresponding roughly to a radius notably less than ⅓ the
 focal length, while the radial fits a radius of less than ⅔ this
 length with all ordinary glasses, given forms correcting the ordinary
 aberrations. The curves are concave towards the objective except in
 “anastigmats” and some objectives having bad aberrations otherwise.
 Their approximate curvatures assuming a semiangular aperture for an
 achromatic objective not over say 5°, have been shown to be, to focus
 unity

 ρ_{r} = 1 + (1/(ν-ν′)(ν/n - ν′/n′)),
 and ρ_{t} = 3 + 1/(ν-ν′)(ν/n - ν′/n′)

 ρ_r and ρ_t being the respective reciprocals of the radii. The
 surfaces are really somewhat egg shaped rather than spherical as one
 departs from the axis.

Aside from curvature the chief residual error in objectives is
imperfection of achromatism. This arises from the fact that crown and
flint glasses do not disperse the various colors quite in the same
ratio. The crown gives slightly disproportionate importance to the
red end of the spectrum, the flint to the violet end—the so-called
“irrationality of dispersion.”

Hence if a pair of lenses match up accurately for two chosen colors
like those represented by the C and F lines, they will fail of mutual
compensation elsewhere. Figure 60 shows the situation. Here the spectra
from crown and flint glasses are brought to exactly the same extent
between the C and F lines, which serve as landmarks.

Clearly if two prisms or lenses are thus adjusted to the same
refractions for C and F, the light passing through the combination will
still be slightly colored in virtue of the differences elsewhere in the
spectrum. These residual color differences produce what is known as the
“secondary spectrum.”

What this does in the case of an achromatic lens may be clearly seen
from the figure; C and F having exactly the same refractions in the
flint and crown, come to the same focus. For D, the yellow line of
sodium, the flint lens refracts a shade the less, hence is not quite
powerful enough to balance the crown, which therefore brings D to a
focus a little shorter than C and F. On the other hand for A′ and G′,
the flint refracts a bit more than the crown, overbalances it and
brings these red and violet rays to a focus a little longer than the
joint C and F focus.

[Illustration: FIG. 60.—Irrationality of Dispersion.]

The difference for D is quite small, roughly about 1/2000 of the focal
length, while the red runs long by nearly three times that amount,
the violet by about four. Towards the H line the difference increases
rapidly and in large telescopes the actual range of focus for the
various colors amounts to several inches.

This difficulty cannot be avoided by any choice among ordinary pairs of
glasses, which are nearly alike in the matter of secondary spectrum.
In the latter part of the last century determined efforts were made to
produce glasses that would give more nearly an equal run of dispersion,
at first by English experimenters, and then with final success by
Schott and Abbé at Jena.

Both crown and flint had to be quite abnormal in composition,
especially the latter, and the pair were of very nearly the same
refractive index and with small difference in the quantity ν which
we have seen determines the general amount of curvature. Moreover it
proved to be extremely hard to get the crown quite homogeneous and
it is listed by Schott with the reservation that it is not free from
bubbles and striæ.

Nevertheless the new glasses reduce the secondary spectrum greatly, to
about ¼ of its ordinary value, in the average. It is difficult to
get rid of the spherical aberration, however, from the sharp curves
required and the small difference between the glasses, and it seems to
be impracticable on this account to go to greater aperture than about
_F_/20.

Figure 61 shows the deeply curved form necessary even at half the
relative aperture usable with common glasses. At _F_/20 the secondary
spectrum from the latter is not conspicuous and Roe (Pop. Ast. _18_,
193), testing side by side a small Steinheil of the new glasses, and a
Clark of the old, of almost identical size and focal ratio, found no
difference in their practical performance.

Another attack on the same problem was more successfully made by H. D.
Taylor. Realizing the difficulty found with a doublet objective of even
the best matched of the new glasses, he adopted the plan of getting a
flint of exactly the right dispersion by averaging the dispersions of a
properly selected pair of flints formed into lenses of the appropriate
relative curvatures.

[Illustration: FIG. 61.—Apochromatic Doublet.]

[Illustration: FIG. 62.—Apochromatic Triplet.]

The resulting form of objective is made, especially, by Cooke of York,
and also by Continental makers, and carries the name of “photo-visual”
since the exactness of corrections is carried well into the violet,
so that one can see and photograph at the same focus. The residual
chromatic error is very small, not above 1/8 to 1/10 the ordinary
secondary spectrum.

By this construction it is practicable to increase the aperture to
_F_/12 or _F_/10 while still retaining moderate curvatures and reducing
the residual spherical aberration. There are a round dozen triplet
forms possible, of which the best, adopted by Taylor, is shown in Fig.
62. It has the duplex flint ahead—first a baryta light flint, then a
borosilicate flint, and to the rear a special light crown. The two
latter glasses have been under some suspicion as to permanence, but the
difficulty has of late years been reported as remedied. Be that as it
may, neither doublets nor triplets with reduced secondary spectrum have
come into any large use for astronomical purposes. Their increased
cost is considerable,[13] their aperture even in the triplet, rather
small for astrophotography, and their achromatism is still lacking the
perfection reached by a mirror.

 [13] The doublet costs about one and a half times, and the triplet
 more than twice the price of an ordinary achromatic of the same
 aperture.

The matter of achromatism is further complicated by the fact that
objectives are usually over-achromatized to compensate for the
chromatic errors in the eyepiece, and especially in the eye. As a
general rule an outstanding error in any part of an optical system can
be more or less perfectly balanced by an opposite error anywhere else
in the system—the particular point chosen being a matter of convenience
with respect to other corrections.

The eye being quite uncorrected for color the image produced even by
a reflector is likely to show a colored fringe if at all bright, the
more conspicuous as the relative aperture of the pupil increases. For
low power eyepieces the emerging ray may quite fill a wide pupil and
then the chromatic error is troublesome. Hence it has been the custom
of skilled opticians, from the time of Fraunhofer, who probably started
the practice, to overdo the correction of the objective just a little
to balance the fault of the eye.

What actually happens is shown in Fig. 63, which gives the results
of achromatization as practiced by some of the world’s adepts. The
shortest focus is in the yellow green, not far from the line D. The
longest is in the violet, and F, instead of coinciding in focus with
C as it is conventionally supposed to do, actually coincides with the
deep and faint red near the line marked B. Hence the visible effect
is to lengthen the focus for blue enough to make up for the tendency
of the eye in the other direction. The resulting image then should
show no conspicuous rim of red or blue. The actual adjustment of
the color correction is almost wholly a matter of skilled judgment
but Fig. 63 shows that of the great makers to be quite uniform. The
smallest overcorrection is found in the Grubb objective, the largest
in the Fraunhofer. The differences seem to be due mainly to individual
variations of opinion as to what diameter of pupil should be taken as
typical for the eye.

The common practice is to get the best possible adjustment for a fairly
high power, corresponding to a beam hardly 1/64 inch in diameter
entering the pupil.

In any case the bigger the pencil of rays utilized by the eye, i.e.,
the lower the power, the more overcorrection must be provided, so that
telescopes intended, like comet seekers, for regular use with low
powers must be designed accordingly, either as respects objective or
ocular.

[Illustration: FIG. 63.—Achromatization Curves by Various Makers.
1. Fraunhofer 2. Clark 3. Steinheil 4. Hastings-Brashear 5. Grubb ]

The differences concerned in this chromatic correction for power are by
no means negligible in observing, and an objective actually conforming
to the C to F correction assumed in tables of optical glass would
produce a decidedly unpleasant impression when used with various
powers on bright objects. And the values for ν implied in the actual
color correction are not immaterial in computing the best form for a
proposed objective.

1 is from Franunhofer’s own hands, the instrument of 9.6 inches
aperture and 170 inches focus in the Berlin Observatory.

2 The Clark refractor of the Lowell Observatory, 24 inches aperture and
386 inches focal length. This is of the usual Clark form, crown ahead,
with lenses separated by about ⅙ of their diameter.

3 is a Steinheil refractor at Potsdam of 5.3 inches aperture, and 85
inches focus.

4 is from the fine equatorial at Johns Hopkins University, designed by
Professor Hastings and executed by Brashear.

The objective was designed with special reference to minimizing the
spherical aberration not only for one chosen wave length but for all
others, has the flint lens ahead, aperture 9.4 inches, focal length 142
inches, and the lenses separated by ¼ inch in the final adjustment of
the corrections.

5 is from the Potsdam equatorial by Grubb, 8.5 inches aperture 124
inches focus.

The great similarity of the color curves is evident at a glance, the
differences due to variations in the glass being on the whole much less
significant than those resulting from the adjustment for power.

Really very little can be done to the color correction without going to
the new special glasses, the use of which involves other difficulties,
and leaves the matter of adjustment for power quite in the air, to be
brought down by special eye pieces. Now and then a melting of glass has
a run of dispersion somewhat more favorable than usual, but there is
small chance of getting large discs of special characteristics, and the
maker has to take his chance, minute differences in chromatic quality
being far less important than uniformity and good annealing.

Regarding the aberrations of mirrors something has been said in Chap.
I, but it may be well here to show the practical side of the matter by
a few simple illustrations.

Figure 64 shows the simplest form of concave mirror—a spherical
surface, in this instance of 90° aperture, the better to show its
properties. If light proceeded radially outward from _C_, the center of
curvature of the surface, evidently any ray would strike the surface
perpendicularly as at _a_ and would be turned squarely back upon
itself, passing again through the center of curvature as indicated in
the figure.

A ray, however, proceeding parallel to the axis and striking the
surface as at _bb_ will be deflected by twice the angle of incidence as
is the case with all reflected rays. But this angle is measured by the
radius _Cb_ from the center of curvature and the reflected ray makes an
angle _CbF_ with the radius, equal to _FCb_. For points very near the
axis _bF_, therefore, equals _FC_, and substantially also equals _cF_.
Thus rays near the axis and parallel to it meet at _F_ the focus half,
way from _c_ to _C_. The equivalent focal length of a spherical concave
mirror of small aperture is therefore half its radius of curvature.

[Illustration: FIG. 64.—Reflection from Concave Spherical Mirror.]

But obviously for large angles of incidence these convenient equalities
do not hold. As the upper half of the figure shows, the ray parallel
to the axis and incident on the mirror 45° away at _e_ is turned
straight down, for it falls upon a surface inclined to it by 45° and
is therefore deflected by 90°, cutting the axis far inside the nominal
focus, at _d_. Following up other rays nearer the axis it appears that
there is no longer a focal point but a cusp-like focal surface, known
to geometrical optics as a caustic and permitting no well defined image.

A paraboloidal reflecting surface as in Fig. 65 has the property
of bringing to a single point focus all rays parallel to its axis
while quite failing of uniting rays proceeding from any point on its
axis, since its curvature is changing all the way out from vertex
to periphery. Here the parallel rays _a_, _a_, _a_, _a_ meeting
the surface are reflected to the focus _F_, while in a perfectly
symmetrical way the prolongation of these rays _a′_, _a′_, _a′_, _a′_
if incident on the convex surface of the paraboloid would be reflected
in _R_, _R′_, _R″_ _R″′_ just as if they proceeded from the same focus
_F_.

The difference between the spherical and parabolic curves is well shown
in Fig. 66. Here are sections of the former, and in dotted lines of
the latter. The difference points the moral. The parabola falls away
toward the periphery and hence pushes outward the marginal rays. But
it is of relatively sharper curvature near the center and pulls in the
central to meet the marginal portion. In the actual construction of
parabolic mirrors one always starts with a sphere which is easy to test
for precision of figure at its center of curvature. Then the surface
may be modified into a paraboloid lessening the curvature towards the
periphery, or by increasing the curvature toward the center starting in
this case with a sphere of a bit longer radius as in Fig. 66a.

[Illustration: FIG. 65.—Reflection from Paraboloid.]

[Illustration: FIG. 66_a_. FIG. 66_b_.
Variation of Paraboloid from Sphere.]

Practice differs in this respect, either process leading to the same
result. In any case the departure from the spherical curve is very
slight—a few hundred thousandths or at most ten thousandths of an inch
depending on the size and relative focus of the mirror.

Yet this small variation makes all the difference between admirable and
hopelessly bad definition. However the work is done it is guided by
frequent testing, until the performance shows that a truly parabolic
figure has been reached. Its attainment is a matter of skilled judgment
and experience.

The weak point of the parabolic mirror is in dealing with rays coming
in parallel but oblique to the axis. Figure 67 shows the situation
plainly enough. The reflected rays _a′_, _a″_ no longer meet in a
point at the focus _F_ but inside the focus for parallel rays, at _f_
forming a surface of aberration. The practical effect is that the image
rapidly deteriorates as the star passes away from the axis, taking on
an oval character that suggests a bad case of astigmatism with serious
complications from coma, which in fact is substantially the case.

[Illustration: FIG. 67.—Aberration of Parabolic Mirror.]

Even when the angular aperture is very small the focal surface is
nevertheless a sphere of radius equal to one half the focal length, and
the aberrations off the axis increase approximately as the square of
the relative aperture, and directly as the angular distance from the
axis.

The even tolerably sharp field of the mirror is therefore generally
small, rarely over 30′ of arc as mirrors are customarily proportioned.
At the relative aperture usual with refractors, say F/15, the sharp
fields of the two are quite comparable in extent. The most effective
help for the usual aberrations[14] of the mirror is the adoption of the
Cassegrain form, by all odds the most convenient for large instruments,
with a hyperboloid secondary mirror.

 [14] A very useful treatment of the aberrations of parabolic mirrors
 by Poor is in Ap. J. 7, 114. In this is given a table of the maximum
 dimension of a star disc off the axis in reflectors of various
 apertures. This table condenses to the closely approximate formula

 a = lld/f²

 where a is the aberrational diameter of the star disc, in seconds of
 arc, d the distance from the axis in minutes of arc, f the denominator
 of the F ratio (F/8 &c.) and 11, a constant. Obviously the separating
 power of a telescope (see Chap. X) being substantially 4.″56/D where
 D is the diameter of objective or mirror in inches, the separating
 power will be impaired when a > 4.″56/D. In the photographic
 case the critical quantity is not 4.″56/D, but the maximum image
 diameter tolerable for the purpose in hand. mirror is the adoption
 of the Cassegrain form, by all odds the most convenient for large
 instruments, with a hyperboloidal secondary mirror.

The hyperboloid is a curve of very interesting optical properties. Just
as a spherical mirror returns again rays proceeding from its center of
curvature without aberration, and the paraboloid sends from its focus
a parallel axial beam free of aberration, or returns such a beam to an
exact focus again, so a hyperboloid, Fig. 68, sends out a divergent
beam free from aberration or brings it, returning, to an exact focus.

Such a beam _a_, _a_, _a_, in fact behaves as if it came from and
returned to a virtual conjugate focus _F′_ on the other side of the
hyperbolic surface. And if the convex side be reflecting, converging
rays _R_, _R_′, _R″_, falling upon it at _P_, _P′_, _P″_, as if headed
for the virtual focus _F_, will actually be reflected to _F′_, now a
real focus.

This surface being convex its aberrations off the axis are of opposite
sign to those due to a concave surface, and can in part at least, be
made to compensate the aberrations of a parabolic main mirror. The
rationale of the operation appears from comparison of Figs. 67 and 68.

[Illustration: FIG. 68.—Reflection from Hyperboloid.]

In the former the oblique rays _a_, _a′_ are pitched too sharply down.
When reflected from the convex surface of Fig. 68 as a converging beam
along _R_, _R′_, _R″_, they can nevertheless, if the hyperbola be
properly proportioned, be brought down to focus at _F′_ conjugate to
_F_, their approximate mutual point of convergence.

Evidently, however, this compensation cannot be complete over a wide
angle, when _F′_ spreads into a surface, and the net result is that
while the total aberrations are materially reduced there is some
residual coma together with some increase of curvature of field, and
distortion. Here just as in the parabolizing of the large speculum
the construction is substantially empirical, guided in the case of a
skilled operator by a sort of insight derived from experience.

Starting from a substantially spherical convexity of very nearly the
required curvature the figure is gradually modified as in the earlier
example until test with the truly parabolic mirror shows a flawless
image for the combination. The truth is that no conic surface of
revolution save the sphere can be ground to true figure by any rigorous
geometrical method. The result must depend on the skill with which one
by machine or hand can gauge minute departures from the sphere.

Attempts have been made by the late Professor Schwarzchild and others
to improve the corrections of reflectors so as to increase the field
but they demand either very difficult curvatures imposed on both
mirrors, or the interposition of lenses, and have thus far reached no
practical result.


REFERENCES

  SCHWARZCHILD: Untersuchungen 2, Geom., Opt. II.
  SAMPSON _Observatory 36_, 248.
  CODDINGTON: “Reflexion and Refraction of Light.”
  HERSCHEL: “Light.”
  TAYLOR: “Applied Optics.”
  SOUTHALL: “Geometrical Optics.”
  MARTIN: _Ann. Sci. de l’Ecole Normale_, 1877, Supplement.
  MOSER: _Zeit. f._ Instrumentenkunde, 1887.
  HARTING: _Zeit. f. Inst._, 1899.
  HARTING: _Zeit. f. Inst._, 1898.
  VON HOEGH: _Zeit. f. Inst._, 1899.
  STEINHEIL & VOIT: “Applied Optics.”
  COLLECTED RESEARCHES, National Physical Laboratory, Vol. 14.
  GLEICHEN: “Lehrbuch d. Geometrische Optik.”

NOTE.—In dealing with optical formulæ look out for the algebraic signs.
Writers vary in their conventions regarding them and it sometimes is
as difficult to learn how to apply a formula as to derive it from the
start. Also, especially in optical patents, look out for camouflage,
as omitting to specify an optical constant, giving examples involving
glasses not produced by any manufacturer, and even specifying curves
leading to absurd properties. It is a good idea to check up the
achromatization and focal length before getting too trustful of a
numerical design.




CHAPTER V

MOUNTINGS


A steady and convenient mounting is just as necessary to the successful
use of the telescope as is a good objective. No satisfactory
observations for any purpose can be made with a telescope unsteadily
mounted and not provided with adjustments enabling it to be moved
smoothly and easily in following a celestial object.

Broadly, telescope mounts may be divided into two general classes,
alt-azimuth and equatorial. The former class is, as its name suggests,
arranged to be turned in azimuth about a vertical axis, and in altitude
about a horizontal axis. Such a mounting may be made of extreme
simplicity, but obviously it requires two motions in order to follow up
any object in the field, for the apparent motion of the heavenly bodies
is in circles about the celestial pole as an axis, and consequently
inclined from the vertical by the latitude of the place of observation.

Pointing a telescope with motions about a vertical and horizontal axis
only, therefore means that, as a star moves in its apparent path, it
will drift away from the telescope both in azimuth and in altitude, and
require to be followed by a double motion.

Alt-azimuth mounts may be divided into three general groups according
to their construction. The first and simplest of them is the
pillar-and-claw stand shown in Figure 69. This consists of a vertical
pillar supported on a strong tripod, usually of brass or iron, and
provided at its top with a long conical bearing carrying at its upper
extremity a hinged joint, bearing a bar to which the telescope is
screwed as shown in the illustration.

If properly made the upper joint comprises a circular plate carrying
the bar and held between two cheek pieces with means for taking up
wear, and providing just enough friction to permit of easy adjustment
of the telescope, which can be swung in altitude from near the zenith
to the horizon or below, and turned around its vertical axis in any
direction.

When well made a stand of this kind is steady and smooth working,
readily capable of carrying a telescope up to about 3 inches aperture.
It needs for its proper use a firm sub-support for the three strong
hinged legs of the pillar. This is conveniently made as a very solid
stool with spreading legs, or a plank of sufficient size may be firmly
bolted to a well set post.

[Illustration: FIG. 69.—Table Mount with Slow Motion.]

Thus arranged the mount is a very serviceable one for small
instruments. Its stability, however, depends on the base upon which
it is set. The writer once unwisely attempted to gain convenience by
removing the legs of the stand and screwing its body firmly upon a very
substantial tripod. The result was a complete failure in steadiness,
owing to the rather long lever arm furnished by the height of the
pillar; and the instrument, which had been admirably steady originally,
vibrated abominably when touched for focussing.

The particular stand here shown is furnished with a rack motion in
altitude which is a considerable convenience in following. More
rarely adjustable steadying rods attached to the objective end of the
instrument are brought down to its base, but for a telescope large
enough to require this a better mount is generally desirable.

Now and then an alt-azimuth head of just the sort used in the
pillar-and-claw stand is actually fitted on a tall tripod, but such an
arrangement is usually found only in cheap instruments and for such
tripod mountings other fittings are desirable.

[Illustration: FIG. 70.—Alt-azimuth Mount, Clark Type T.]

The second form of alt-azimuth mount, is altogether of more substantial
construction. The vertical axis, usually tapered and carefully ground
in its bearings, carries an oblique fork in which the telescope tube is
carried on trunnions for its vertical motion. The inclination of the
forked head enables the telescope to be pointed directly toward the
zenith and the whole mount forms the head of a well made tripod.

Figure 70 shows an excellent type of this form of mount as used
for the Clark Type T telescope, designed for both terrestrial and
astronomical observation. In this particular arrangement the telescope
lies in an aluminum cradle carried on the trunnions, from which it can
be readily removed by loosening the thumb screws and opening the cradle.

[Illustration: FIG. 71.—Alt-azimuth with Full Slow Motions.]

It can also be set longitudinally for balance in the cradle if any
attachments are to be placed upon either end. Here the adjustment for
the height of the instrument is provided both in the spread of the
tripod and in the adjustable legs. So mounted a telescope of 3 or 4
inches aperture is easily handled and capable of rendering very good
service either for terrestrial or celestial work.

Indeed the Clarks have made instruments up to 6 inches aperture,
mounted for special service in this simple manner. For celestial use
where fairly high powers may be required this or any similar mount can
be readily furnished with slow motions either in azimuth or altitude or
both.

Figure 71 shows a 4¼ inch telescope and mount by Zeiss thus
equipped. Some alt-azimuth mounts are also provided with a vertical
rack motion to bring the telescope to a convenient height without
disturbing the tripod. A good alt-azimuth mount such as is shown in
Figs. 70 and 71 is by no means to be despised for use with telescopes
of 3 or 4 inch aperture.

The sole inconvenience to be considered is that of the two motions
required in following. With well fitted slow motions this is not really
serious for ordinary observing with moderate powers, for one can work
very comfortably up to powers of 150 or 200 diameters keeping the
object easily in view; but with the higher powers in which the field is
very small, only a few minutes of arc, the double motion becomes rather
a nuisance and it is extremely inconvenient even with low powers in
sweeping for an object the place of which is not exactly known.

There are in fact two distinct kinds of following necessary in
astronomical observations. First, the mere keeping of the object
somewhere in the field, and second, holding it somewhat rigorously in
position, as in making close observations of detail or micrometrical
measurements. When this finer following is necessary the sooner one
gets away from alt-azimuth mounts the better.

Still another form of alt-azimuth mount is shown in Fig. 72 applied for
a Newtonian reflector of 6 or 8 inches aperture. Here the overhung fork
carrying the tube on trunnions is supported on a stout fixed tripod, to
which it is pivoted at the front, and it is provided at the rear with a
firm bearing on a sector borne by the tripod.

At the front a rod with sliding coarse, and screw fine, adjustment
provides the necessary motion in altitude. The whole fork is swung
about its pivot over the sector bearing by a cross screw turned by a
rod with a universal joint.

This mount strongly suggests the original one of Hadley, Fig. 16, and
is most firm and serviceable. A reflector thus mounted is remarkably
convenient in that the eyepiece is always in a most accessible
position, the view always horizontal, and the adjustments always within
easy reach of the observer.

[Illustration: FIG. 72.—Alt-azimuth Newtonian Reflector.]

Whenever it is necessary to follow an object closely, as in using
a micrometer and some other auxiliaries, the alt-azimuth mount is
troublesome and some modification adjustable by a single motion,
preferably made automatic by clockwork, becomes necessary.

The first step in this direction is a very simple one indeed. Suppose
one were to tilt the azimuth axis so that it pointed to the celestial
pole, about which all the stars appear to revolve. Then evidently
the telescope being once pointed, a star could be followed merely by
turning the tube about this tilted axis. Of course one could not easily
reach some objects near the pole without, perhaps, fouling the mount,
but in general the sky is within reach and a single motion follows the
star, very easily if the original mount had a slow motion in azimuth.

This is in fact the simplest form of equatorial mount, sometimes
called parallactic. Figure 73 shows the principle applied to a small
reflector. An oblique block with its angle adjusted to the co-latitude
of the place drops the vertical axis into line with the pole, and the
major part of the celestial vault is then within easy reach.

It may be regarded as the transition step from the alt-azimuth to
the true equatorial. It is rarely used for refractors, and the first
attempt at a real equatorial mount was in fact made by James Short F.
R. S. in mounting some of his small Gregorians.[15] As a matter of
record this is shown, from Short’s own paper before the Royal Society
in 1749, in Fig. 74.

 [15] Instruments with a polar axis were used by Scheiner as early
 as 1627; by Roemer about three quarters of a century later, and
 previously had been employed, using sights rather than telescopes, by
 the Chinese; but these were far from being equatorials in the modern
 sense.

[Illustration: FIG. 73.—Parallactic Mount for Reflector.]

A glance shows a stand apparently most complicated, but closer
examination discloses that it is merely an equatorial on a table
stand with a sweep in declination over a very wide arc, and quite
complete arrangements for setting to the exact latitude and azimuth.
The particular instrument shown was of 4 inches aperture and about 18
inches long and was one of several produced by Short at about this
epoch.

[Illustration: FIG. 74.—Short’s Equatorial Mount.]

In the instrument as shown there is first an azimuth circle _A A_
supported on a base _B B B B_ having levelling screws in the feet.
Immediately under the azimuth circle is mounted a compass needle for
approximate orientation, and the circle is adjustable by a tangent
screw _C_.

Carried by the azimuth circle on a bearing supported by four pillars
is a latitude circle _D D_ for the adjustment of the polar axis, with
a slow motion screw _E_. The latitude circle carries a right ascension
circle _F F_, with a slow motion _G_, and this in turn carries on four
pillars the declination circle _H H_, and its axis adjustable by the
slow motion _K_.

To this declination circle is secured the Gregorian reflector _L L_
which serves as the observing telescope. All the circles are provided
with verniers as well as slow motions. And the instrument is, so to
speak, a universal one for all the purposes of an equatorial, and when
the polar axis is set vertical equally adapted for use as a transit
instrument, theodolite, azimuth instrument, or level, since the circles
are provided with suitable levels.

This mount was really a very neat and complete piece of work for the
purpose intended, although scarcely suitable for mounting any but a
small instrument. A very similar construction was used later by Ramsden
for a small refractor.

It is obvious that the reach of the telescope when used as an
equatorial is somewhat limited in the mount just described. In modern
constructions the telescope is so mounted that it may be turned readily
to any part of the sky, although often the polar axis must be swung
through 180° in order to pass freely from the extreme southern to the
extreme northern heavens.

The two motions necessary are those in right ascension to follow the
heavenly bodies in their apparent course, and in declination to reach
an object at any particular angular distance from the pole.

There are always provided adjustments in azimuth and for latitude over
at least a small arc, but these adjustments are altogether rudimentary
as compared with the wide sweep given by Short.

The fundamental construction of the equatorial involves two axes
working at right angles positioned like a capital T.

The upright of the T is the polar axis, fitted to a sleeve and bearing
the cross of the T, which is hollow and provides the bearing for the
declination axis, which again carries at right angles to itself the
tube of the telescope.

When the sleeve which carries the upright of the T points to the pole
the telescope tube can evidently be swung to cover an object at any
altitude, and can then be turned on its polar axis so as to follow
that object in its apparent diurnal motion. The front fork of a bicycle
set at the proper angle with a cross axis replacing the handle bars has
more than once done good service

[Illustration: FIG. 75.—Section of Modern Equatorial.]

in an emergency. Figure 75 shows in section a modern equatorial mount
for a medium sized telescope.

The mounting shown in Fig. 75, by Zeiss, is thoroughly typical of
recent practice in instruments of moderate size. The general form of
this equatorial comes straight down to us from Fraunhofer’s mounting
of the Dorpat instrument. It consists essentially of two axes crossed
exactly at right angles.

P, the polar axis, is aligned exactly with the pole, and is supported
on a hollow iron pier provided at its top with the latitude block L to
which the bearings of P are bolted. D the declination axis supports the
telescope tube T.

The tube is counterpoised as regards the polar axis by the weight a,
and as regards the declination axis by the weights b b. At A, the upper
section of the pier can be set in exact azimuth by adjusting screws,
and at the base of the lower section the screws at B. B. allow some
adjustment in latitude. To such mere rudiments are the azimuth and
altitude circles of Short’s mount reduced.

At the upper end of the polar axis is fitted the gear wheel g, driven
by a worm from the clockwork at C to follow the stars in their course.
At the lower end of the same axis is the hour circle h, graduated for
right ascension, and a hand wheel for quick adjustment in R. A.

At d is the declination circle, which is read, and set, by the
telescope t with a right angled prism at its upper end, which saves the
observer from leaving the eye piece for small changes.

F is the usual finder, which should be applied to every telescope of 3
inches aperture and above. It should be of low power, with the largest
practicable field, and has commonly an aperture ¼ or ⅕ that of the
main objective, big enough to pick up readily objects to be examined
and by its coarse cross wires to bring them neatly into the field. At m
and n are the clamping screws for the right ascension and declination
axes respectively, while o and p control the respective tangent screws
for fine adjustment in R. A. and Dec. after the axes are clamped. This
mount has really all the mechanical refinements needed in much larger
instruments and represents the class of permanently mounted telescopes
used in a fixed observatory.

The ordinary small telescope is provided with a mount of the same
general type but much simpler and, since it is not in a fixed
observatory, has more liberal adjustments in azimuth and altitude
to provide for changes of location. Figure 76 shows in some detail
the admirable portable equatorial mounting used by the Clarks for
instruments up to about 5 or 6 inches aperture.

Five inches is practically the dividing line between portable and fixed
telescopes. In fact a 5 inch telescope of standard construction with
equatorial mounting is actually too heavy for practical portability
on a tripod stand. The Clarks have turned out really portable
instruments of this aperture, of relatively short focus and with
aluminum tube fitted to the mounting standard for a 4 inch telescope,
but the ordinary 5 inch equipment of the usual focal length deserves a
permanent placement.

In this mount the short tapered polar axis P is socketed between the
cheeks A, and tightened in any required position by the hand screws B.
The stout declination axis D bears the telescope and the counterweight
C. Setting circles in R. A. and Dec., p and d respectively, are carried
on the two axes, and each axis has a worm wheel and tangent screw
operated by a universal joint to give the necessary slow motion.

[Illustration: FIG. 76.—Clark Adjustable Equatorial Mount.]

The worm wheels carry their respective axes through friction bearings
and the counter poising is so exact that the instrument can be quickly
swung to any part of the sky and the slow motion picked up on the
instant. The wide sweep of the polar axis allows immediate conversion
into an alt-azimuth for terrestrial use, or adjustment for any
latitude. A graduated latitude arc is customarily engraved on one of
the check pieces to facilitate this adjustment.

Ordinarily portable equatorials on tripod mounts are not provided
with circles, and have only a single slow motion, that in R. A. A
declination circle, however, facilitates setting up the instrument
accurately and is convenient for locating an object to be swept for in
R. A. which must often be done if one has not sidereal time at hand. In
Fig. 76 a thumb screw underneath the tripod head unclamps the mount so
that it may be at once adjusted in azimuth without shifting the tripod.

As a rule American stands for fixed equatorials have the clock drive
enclosed in the hollow pillar which carries the equatorial head
as shown in the reflector of Fig. 35, and in the Clark mount for
refractors of medium size shown in Fig. 77. Here a neat quadrangular
pillar carries an equatorial mounting in principle very much like Fig.
76, but big enough to carry telescopes of 8 to 10 inches aperture.
It has universal adjustment in latitude, so that it can be used in
either hemisphere, the clock and its driving weight are enclosed in the
pillar and slow motions are provided for finding in R. A. and Dec. The
adjustment in azimuth is made by moving the pillar on its base-plate,
which is bolted to the pier. The convenient connections for accurate
following and the powerful clock make the mount especially good for
photographic telescopes of moderate size and the whole equipment is
most convenient and workmanlike. It is worth noting that the circles
are provided with graduations that are plain rather than minute, in
accordance with modern practice. In these days of celestial photography
equatorials are seldom used for determining positions except with the
micrometer, and graduated circles therefore, primarily used merely for
finding, should be, above all things, easy to read.

All portable mounts are merely simplifications of the observatory type
of Fig. 75, which, with the addition of various labor saving devices is
applied to nearly all large refractors and to many reflectors as well.

There is a modified equatorial mount sometimes known as the “English”
equatorial in which the polar axis is long and supported on two piers
differing enough in height to give the proper latitude angle, the
declination axis being about midway of the polar axis. A bit of the
sky is cut off by the taller pier, and the type is not especially
advantageous unless in supporting a very heavy instrument, too heavy to
be readily overhung in the usual way.

[Illustration: FIG. 77.—Universal Observatory Mount (Clark 9-inch).]

In such case some form of the “English” mounting is very important to
securing freedom from flexure and thereby the perfection of driving
in R. A. so important to photographic work. The 72 inch Dominion
Observatory reflector and the 100 inch Hooker telescope at Mt. Wilson
are thus mounted, the former on a counterpoised declination axis
crosswise the polar axis, the original “English” type; the latter on
trunnions within a long closed fork which carries the polar bearings at
its ends.

[Illustration: FIG. 78.—English Equatorial Mount (Hooker 100-inch
Telescope).]

Figure 78 shows the latter instrument, of 100 inches clear aperture
and of 42 feet principal focal length, increased to 135 feet when used
as a Cassegrainian. It is the immense stability of this mount that has
enabled it to carry the long cross girder bearing the interferometer
recently used in measuring the diameters of the stars. Note the
mercury-flotation drum at each end of the polar axis. The mirrors were
figured by the skillful hands of Mr. Ritchey.

[Illustration: FIG. 79.—English Equatorial Mount (72-inch Dominion
Observatory Telescope).]

Figure 79 gives in outline the proportions and mounting of the
beautiful instrument in service at the Dominion Observatory, near
Victoria, B. C. The mirror and its auxiliaries were figured by Brashear
and the very elegant mounting was by Warner and Swasey. The main mirror
is of 30 feet principal focus. The 20 inch hyperboloidal mirror extends
the focus as a Cassagrainian to 108 feet. The mechanical stability
of these English mounts for very large instruments has been amply
demonstrated by this, as by the Hooker 100 inch reflector. They suffer
less from flexure than the Fraunhofer mount where great weights are
to be carried, although the latter is more convenient and generally
useful for instruments of moderate size. It is hard to say too much of
the mechanical skill that has made these two colossal telescopes so
completely successful as instruments of research.

[Illustration: FIG. 80.—Astrographic Mount with Bent Pier.]

The inconvenience of having to swing the telescope tube to clear the
pier at certain points in the R. A. following is often a serious
nuisance in photographic work requiring long exposures, and may waste
valuable time in visual work. Several recent forms of equatorial mount
have therefore been devised to allow the telescope complete freedom of
revolution in R. A., swinging clear of everything.

One such form is shown in Fig. 80 which is a standard astrographic
mount for a Brashear doublet and guiding telescope. The pier is
strongly overhung in the direction of the polar axis far enough to
allow the instrument to follow through for any required period, even
to resuming operations on another night without a shift of working
position.

[Illustration: FIG. 81.—Open Fork Mounting.]

Another form, even simpler and found to be extremely satisfactory even
for rather large instruments, is the open polar fork mount. Here the
polar axis of an ordinary form is continued by a wide and stiff casting
in the form of a fork within which the tube is carried on substantial
trunnions, giving it complete freedom of motion.

The open fork mount in its simplest form, carrying a heliostat mirror,
is shown in Fig. 81. Here _A_ is the fork, _B_ the polar axis, carried
on an adjustable sector for variation in latitude, _C_ the declination
axis carrying the mirror _D_ in its cell, _E_ the slow motion in
declination, and _F_ that in R. A. Both axes can be unclamped for quick
motion and the R. A. axis can readily be driven by clock or electric
motor.

The resemblance to the fully developed English equatorial mount of
Fig. 78 is obvious, but the present arrangement gives entirely free
swing to a short instrument, is conveniently adjustable, and altogether
workmanlike. It can easily carry a short focus celestial camera up to 6
or 8 inches aperture or a reflector of 4 or 5 feet focal length.

In Fig. 173, Chap. X a pair of these same mounts are shown at Harvard
Observatory. The nearer one, carrying a celestial camera, is exposed
to view. It is provided with a slow motion and clamp in declination,
and with an electric drive in R. A., quickly unclamped for swinging the
camera. It works very smoothly, its weight is taken by a very simple
self adjusting thrust bearing at the lower end of the polar axis, and
altogether it is about the simplest and cheapest equatorial mount of
first class quality that can be devised for carrying instruments of
moderate length.

Several others are in use at the Harvard Observatory and very similar
ones of a larger growth carry the 24 inch Newtonian reflector there
used for stellar photography and the 16 inch Metcalf photographic
doublet.

[Illustration: FIG. 82.—Mounting of Mt. Wilson 60-inch Reflector.]

[Illustration: FIG. 83.—The 60-inch as Cassegrainian, F = 100′.]

In fact the open fork mount, which was developed by the late Dr.
Common, is very well suited to the mounting of big reflectors. It was
first adapted by him to his 3 ft. reflector and later used for his
two 5 ft. mirrors, and more recently for the 5 ft. instrument at Mt.
Wilson, and a good many others of recent make. Dr. Common in order
to secure the easiest possible motion in R. A. devised the plan of
floating most of the weight assumed by the polar axis in mercury.

Figure 82 is, diagrammatically, this fork mount as worked out by
Ritchey for the 5′ Mt. Wilson reflector. Here A is the lattice tube, B
the polar axis, C the fork and D the hollow steel drum which floats the
axis in the mercury trough E. The great mirror is here shown worked as
a simple Newtonian of 25 ft. focal length. As a matter of fact it is
used much of the time as a Cassegranian.

To this end the upper section of tube carrying the oblique mirror is
removed and a shorter tube carrying any one of three hyperboloidal
mirrors is put in its place. Fig. 83 is the normal arrangement for
visual or photographic work on the long focus, 100 ft. The dotted lines
show the path of the rays and it will be noticed that the great mirror
is not perforated as in the usual Cassegrainian construction, but that
the rays are brought out by a diagonal flat.

Figure 84 is a similar arrangement used for stellar spectroscopy with
a small flat and an equivalent focus of 80 ft. In Fig. 85 a radically
different scheme is carried out. The hyperboloidal mirror now used
gives an equivalent focus of 150 ft., and the auxiliary flat is
arranged to turn on an axis parallel to the declination axis so as to
send the reflected beam down the hollow polar axis into a spectrograph
vault below the southern end of the axis. Obviously one cannot work
near the pole with this arrangement but only through some 75° as
indicated by the dotted lines. The fork mount is not at all universal
for reflectors, as has already been seen, and Cassegrainian of moderate
size are very commonly mounted exactly like refractors.

[Illustration: FIG. 84.—The 60-inch as Cassegrainian, F = 80′.]

[Illustration: FIG. 85.—The 60-inch as Polar Cassegrainian, F = 150′.]

We now come to a group of mounts which have in common the fundamental
idea of a fixed eyepiece, and incidentally better protection of the
observer against the rigors of long winter nights when the seeing
may be at its best but the efficiency of the observer is greatly
diminished by discomfort. Some of the arrangements are also of value in
facilitating the use of long focus objectives and mirrors and escaping
the cost of the large domes which otherwise would be required.

Perhaps the earliest example of the class is found in Caroline
Herschel’s comet seeker, shown in Fig. 86. This was a Newtonian
reflector of about 6 inches aperture mounted in a fashion that is
almost self explanatory. It was, like all Herschel’s telescopes, an
alt-azimuth but instead of being pivoted in altitude about the mirror
or the center of gravity of the whole tube, it was pivoted on the
eyepiece location and the tube was counterbalanced as shown so that it
could be very easily adjusted in altitude while the whole frame turned
in azimuth about a vertical post.

Thus the observer could stand or sit at ease sweeping in a vertical
circle, and merely had to move around the post as the azimuth was
changed. The arrangement is not without advantages, and was many years
later adopted with modifications of detail by Dr. J. W. Draper for
the famous instrument with which he advanced so notably the art of
celestial photography.

The same fundamental idea of freeing the observer from continual
climbing about to reach the eyepiece has been carried out in various
equatorially mounted comet seekers. A very good example of the type
is a big comet seeker by Zeiss, shown in Fig. 87. The fundamental
principle is that the ocular is at the intersection of the polar and
declination axis, the telescope tube being overhung well beyond the
north end of the former and counterbalanced on the latter. The observer
can therefore sit in his swivel chair and without stirring from it
sweep rapidly over a very wide expanse of sky.

This particular instrument is probably the largest of regular comet
seekers, 8 inches in clear aperture and 52½ inches focal length
with a triple objective to ensure the necessary corrections in
using so great a relative aperture. In this figure 1 is the base
with corrections in altitude and azimuth, 2 the counterpoise of the
whole telescope on its base, 3 the polar axis and R. A. circle, 4
the overhung declination axis and its circle, 5 the counterpoise in
declination, 6 the polar counterpoise, and 7 the main telescope tube.
The handwheel shown merely operates the gear for revolving the dome
without leaving the observing chair.

The next step beyond the eyepiece fixed in general position is so
to locate it that the observer can be thoroughly protected without
including the optical parts of the telescope in such wise as to injure
their performance.

One cannot successfully observe through an open window on account of
the air currents due to temperature differences, and in an observatory
dome, unheated as it is, must wait after the shutter is opened until
the temperature is fairly steadied.

Except for these comet seekers practically all of the class make use of
one or two auxiliary reflections to bring the image into the required
direction, and in general the field of possible view is somewhat
curtailed by the mounting. This is less of a disadvantage than it would
appear at first thought, for, to begin with, observations within 20°
of the horizon or thereabouts are generally unsatisfactory, and the
advantages of a stable and convenient long focus instrument are so
notable as for many purposes quite to outweigh some loss of sky-space.

[Illustration: FIG. 86.—Caroline Herschel’s Comet Seeker.]

The simplest of the fixed eyepiece group is the polar telescope of
which the rudiments are well shown in Fig. 88, a mount described by Sir
Howard Grubb in 1880, and an example of which was installed a little
later in the Crawford Observatory in Cork. Here the polar axis A is
the main tube of the telescope, and in front of the objective B, is
held in a fork the declination cradle and mirror C, by which any object
within a wide sweep of declination can be brought into the field and
held there by hand or clockwork through rotating the polar tube.

[Illustration: FIG. 87.—Mounting of Large Comet Seeker.]

Looked at from another slant it is a polar heliostat, of which the
telescope forms the driving axis in R. A. The whole mount was a
substantial casting on wheels which ran on a pair of rails. For use the
instrument was rolled to a specially arranged window and through it
until over its regular bearings on a pier just outside.

A few turns of the wheel D lowered it upon these, and the back of the
frame then closed the opening in the wall leaving the instrument in the
open, and the eye end inside the room. The example first built was of
only 4 inches aperture but proved its case admirably as a most useful
and convenient instrument.

This mount with various others of the fixed eyepiece class may be
regarded as derived from the horizontal photoheliographs used at the
1874 transit of Venus and subsequently at many total solar eclipses.
Given an equatorially mounted heliostat like Fig. 81 and it is evident
that the beam from it may be turned into a horizontal telescope placed
in the meridian, (or for that matter in any convenient direction) and
held there by rotation of the mirror in R. A., but also in declination,
save in the case where the beam travels along the extension of the
polar axis.

[Illustration: FIG. 88.—Grubb’s Original Polar Telescope.]

For the brief exposure periods originally needed and the slow variation
of the sun in declination this heliostatic telescope was easily kept
in adjustment. The original instruments were of 5 inches aperture and
40 ft. focal length, and the 7 inch heliostat mirror was provided with
ordinary equatorial clockwork. Set up with the telescope pointing along
the polar axis no continuous variation in declination is needed and the
clock drive holds the field steadily, as in any other equatorial.

Figure 89 shows diagrammatically the 12 inch polar telescope used for
more than twenty years past at the Harvard Observatory. The mount was
designed by Mr. W. P. Gerrish of the Harvard staff and contains many
ingenious features. Unlike Fig. 88 this is a fixed mount, with the
eye-end comfortably housed in a room on the second floor of the main
observatory building, and the lower bearing on a substantial pier to
the southward.

[Illustration: FIG. 89.—Diagram of Gerrish Polar Telescope.]

In the figure, _A_ is the eye end, _B_ the main tube with the objective
at its lower end and prolonged by a fork supported by the bearing _C_
and _D_ is the declination mirror sending the beam upward. The whole
is rotated in R. A. by an electric clock drive, and all the necessary
adjustments are made from the eye end.

A view of the exterior is shown in Fig. 90, with the mirror and
objective uncovered. The rocking arm at the objective end, operated by
a small winch beside the ocular, swings clear both mirror and objective
caps in a few seconds, and the telescope is then ready for use. Its
focal length is 16 ft. 10 inches and it gives a sweep in declination of
approximately 80°. It gives excellent definition and has proved a most
useful instrument.

A second polar telescope was set up at the Harvard Observatory station
in Mandeville, Jamaica, in the autumn of 1900. This was intended
primarily for lunar photography and was provided with a 12 inch
objective of 135 ft. 4 inches focal length and an 18 inch heliostat
with electric clock drive.

[Illustration: FIG. 90.—Gerrish Polar Telescope, Harvard Observatory.]

Inasmuch as all instruments of this class necessarily rotate the image
as the mirror turns, the tail-piece of this telescope is also mounted
for rotation by a similar drive so that the image is stationary on the
plate both in position and orientation. As Mandeville is in N. lat. 18°
01′ the telescope is conveniently near the horizontal. The observatory
of Yale University has a large instrument of this class, of 50 feet
focal length, with a 15-inch photographic objective and a 10-inch
visual guiding objective working together from the same heliostat.

Despite its simplicity and convenience the polar telescope has an
obvious defect in its very modest sweep in declination, only to be
increased by the use of an exceptionally large mirror. It is not
therefore remarkable that the first serious attempt at a fixed eyepiece
instrument for general use turned to a different construction even at
the cost of an additional reflection.

This was the _equatorial coudé_ devised by M. Loewy of the Paris
Observatory in 1882. (Fig. 91.) In the diagram A is the main tube
which forms the polar axis, and B the eye end under shelter, with all
accessories at the observer’s hand. But the tube is broken by the box
casing C containing a mirror rigidly supported at 45° to the axis of
the main tube and of the side tube D, which is counterbalanced and is
in effect a hollow declination axis carrying the objective E at its
outer end.

[Illustration: FIG. 91.—Diagram of Equatorial Coudé.]

In lieu of the telescope tube usually carried on this declination
axis we have the 45° mirror, F, turning in a sleeve concentric with
the objective, which, having a lateral aperture, virtually gives the
objectives a full sweep in declination, save as the upper pier cuts it
off. The whole instrument is clock driven in R. A., and has the usual
circles and slow motions all handily manipulated from the eye end.

The _equatorial coudé_ is undeniably complicated and costly, but
as constructed by Henry Frères it actually performs admirably even
under severe tests, and has been several times duplicated in French
observatories. The first _coudé_ erected was of 10½ inches aperture
and was soon followed by one of 23.6 inches aperture and 59 ft. focus,
which is the largest yet built.

Still another mounting suggestive of both the polar telescope and the
_coudé_ is due to Sir Howard Grubb, Fig. 92. Here as in the _coudé_
the upper part of the polar axis, _A_, is the telescope tube which
leads into a solid casing _B_, about which a substantial fork, _C_, is
pivoted. This fork is the extension of the side tube _D_, which carries
the objective, and thus has free swing in declination through an angle
limited by the roof of the observing room above, and the proximity of
the horizon below.

Its useful swing, as in the polar telescope, is limited by the
dimensions of the mirror _E_, which receives the cone of rays from the
objective and turns it up the polar tube to the eyepiece. This mirror
is geared to turn at half the rate of the tube _D_ so that the angle _D
E A_ is continually bisected.

[Illustration: FIG. 92.—Grubb Modified Coudé.]

In point of fact the sole gain in this construction is the reduction
in the size of mirror required, by reason of the diminished size of
the cone of rays when it reaches the mirror. The plan has been very
successfully worked out in the fine astrographic telescope of the
Cambridge Observatory of 12½ inches aperture and 19.3 ft. focal
length.

As in the other instruments of this general class the adjustments are
all conveniently made from the eye end. The Cambridge instrument has a
triple photo-visual objective of the form designed by Mr. H. D. Taylor
and the side tube, when not in use, is turned down to the horizontal
and covered in by a low wheeled housing carried on a track. The sky
space covered is from 15° above the pole to near the horizontal.

It is obvious that various polar and _coudé_ forms of reflector
are quite practicable and indeed one such arrangement is shown in
connection with the 60 inch Mt. Wilson reflector, but we are here
concerned only with the chief types of mounting which have actually
proved their usefulness. None of the arrangements which require the
use of additional large reflecting surfaces are exempt from danger of
impaired definition. Only superlatively fine workmanship and skill in
mounting can save them from distortion and astigmatism due to flexure
and warping of the mirrors, and such troubles have not infrequently
been encountered.

To a somewhat variant type belong several valuable constructions which
utilize in the auxiliary reflecting system the cœlostat rather than
the polar heliostat or its equivalent. The cœlostat is simply a plane
mirror mounted with its plane fixed in that of a polar axis which
rotates once in 48 hours, i.e., at half the apparent rate of the stars.

[Illustration: FIG. 93.—Diagram of Snow Horizontal Telescope.]

A telescope pointed at such a mirror will hold the stars motionless
in its field as if the firmament were halted à la Joshua. But if a
change of view is wanted the telescope must be shifted in altitude or
azimuth or both. This is altogether inconvenient, so that as a matter
of practice a second plane mirror is used to turn the steady beam from
the cœlostat into any desired direction.

By thus shifting the mirror instead of the telescope, the latter can be
permanently fixed in the most convenient location, at the cost of some
added expense and loss of light. Further, the image does not rotate as
in case of the polar heliostat, which is often an advantage.

An admirable type of the fixed telescope thus constituted is the Snow
telescope at Mt. Wilson (Cont. from the Solar Obs. #2, Hale). Fig.
93 from this paper shows the equipment in plan and elevation. The
topography of the mountain top made it desirable to lay out the axis of
the building 15° E. of N. and sloping downward 5° toward the N.

At the right hand end of the figure is shown the cœlostat pier, 29 ft.
high at its S end. This pier carries the cœlostat mirror proper, 30
inches in diameter, on rails _a a_ accurately E. and W. to allow for
sliding the instrument so that its field may clear the secondary mirror
of 24 inches diameter which is on an alt-azimuth fork mounting and also
slides on rails _b b_.

The telescope here is a pair of parabolic mirrors each of 24 inches
aperture and of 60 ft. and 145 ft. focus respectively. The beam from
the secondary cœlostat mirror passes first through the spectrographic
laboratory shown to the left of the main pier, and in through a long
and narrow shelter house to one of these mirrors; the one of longest
focus on longitudinal focussing rails _e e_, the other on similar rails
_c c_, with provision for sliding sidewise at _d_ to clear the way for
the longer beam.

The ocular end of this remarkable telescope is the spectrographic
laboratory where the beam can be turned into the permanently mounted
instruments, for the details of which the original paper should be
consulted. The purpose of this brief description is merely to show the
beautiful facility with which a cœlostatic telescope may be adapted to
astrophysical work. Obviously an objective could be put in the cœlostat
beam for any purpose for which it might be desirable.

Such in fact is the arrangement of the tower telescopes at the Mt.
Wilson Observatory. In these instruments we have the ordinary cœlostat
arrangement turned on end for the sake of getting the chief optical
parts well above the ground where, removed from the heated surface,
the definition is generally improved. To be sure the focus is at or
near the ground level, but the upward air currents cause much less
disturbance than the crosswise ones in the Snow telescope.

The head of the first tower telescope is shown in Fig. 94.[16] A is the
cœlostat mirror proper 17 inches in diameter and 12 inches thick, B
the secondary mirror 12¾ inches in the shorter axis of the ellipse,
22¼ inches in the longer, and also 12 inches thick. C is the 12
inch objective of 60 ft. focus, and D the focussing gear worked by a
steel ribbon from below.

 [16] Contributions from the Solar Obs. #23, Hale, which should be seen
 for details.

[Illustration: FIG. 94.—Head of 60-inch Tower Telescope.]

This instrument being for solar research the mirrors are arranged for
convenient working with the sun fairly low on either horizon where the
definition is at its best, and can be shifted accordingly, to the same
end as in the Snow telescope. There is also provision for shifting the
objective laterally at a uniform rate from below, to provide for the
use of the apparatus as spectro-heliograph.

The tower is of the windmill type and proved to be fairly steady
in spite of its height, high winds being rare on Mt. Wilson. The
great thickness of the mirrors in the effort to escape distortion
deserves notice. They actually proved to be too thick to give thermal
conductivity sufficient to prevent distortion.

[Illustration: FIG. 95.—Porter’s Polar Reflector.]

In the later 150′ tower telescope the mirrors are relatively less
thick, and a very interesting modification has been introduced in
the tower, in that it consists of a lattice member for member within
another exterior lattice, so that the open structure is retained, while
each member that supports the optical parts is shielded from the wind
and sudden temperature change by its corresponding outer sheath.

Still another form of mounting to give the observer access to a fixed
eyepiece under shelter is found in the ingenious polar reflector by
Mr. Russell W. Porter of which an example with main mirror of 16
inches diameter and 15 ft. 6 inches focal length was erected by him
a few years ago. Fig. 95 is entirely descriptive of the arrangement
which from Mr. Porter’s account seems to have worked extremely well.
The chief difficulty encountered was condensation of moisture on the
mirrors, which in some climates is very difficult to prevent.

[Illustration: FIG. 96.—Diagram of Hartness Turret Telescope.]

It is interesting to note that Mr. Porter’s first plan was to use the
instrument as a Herschelian with its focus thrown below the siderostat
at _F′_, but the tilting of the mirror, which was worked at F/11.6,
produced excessive astigmatism of the images, and the plan was
abandoned in favor of the Newtonian form shown in the figure. At F/25
or thereabouts the earlier scheme would probably have succeeded well.

Still another fixed eyepiece telescope of daring and successful design
is the turret telescope of the Hon. J. E. Hartness of which the
inventor erected a fine example of 10 inch aperture at Springfield,
Vermont. The telescope is in this case a refractor, and the feature of
the mount is that the polar axis is expanded into a turret within which
the observer sits comfortably, looking into the ocular which lies in
the divided declination axis and is supplied from a reflecting prism in
the main beam from the objective

Figure 96 shows a diagram of the mount and observatory. Here _a_ is the
polar turret, _bb_ the bearings of the declination axis, _c_ the main
tube, d its support, and _e_ the ocular end. Optically the telescope is
merely an ordinary refractor used with a right angled prism a little
larger and further up the tube than usual. The turret is entered
in this instance from below, through a tunnel from the inventor’s
residence. The telescope as shown in Fig. 96 has a 10 inch Brashear
objective of fine optical quality, and the light is turned into the
ocular tube by a right angled prism only 2¾ inches in the face. This
is an entirely practicable size for a reflecting prism and the light
lost is not materially in excess of that lost in the ordinary “star
diagonal” so necessary for the observation of stars near the zenith in
an ordinary equatorial. The only obvious difficulty of the construction
is the support of the very large polar axis. Being an accomplished
mechanical engineer, Mr. Hartness worked out the details of this design
very successfully although the moving parts weighed some 2 tons. The
ocular is not absolutely fixed with reference to the observer but is
always conveniently placed, and the performance of the instrument is
reported as excellent in every respect, while the sheltering of the
observer from the rigors of a Vermont winter is altogether admirable.
Figure 97 shows the complete observatory as it stands. Obviously the
higher the latitude the easier is this particular construction, which
lends itself readily to large instruments and has the additional
advantage of freeing the observer from the insect pests which are
extremely troublesome in warm weather over a large part of the world.

This running account of mountings makes no claim at completeness. It
merely shows the devices in common use and some which point the way to
further progress. The main requirements in a mount are steadiness, and
smoothness of motion. Even an alt-azimuth mount with its need of two
motions, if smooth working and steady, is preferable to a shaky and
jerky equatorial.

Remember that the Herschels did immortal work without equatorial
mountings, and used high powers at that. A clock driven equatorial is
a great convenience and practically indispensable for the photographic
work that makes so large a part of modern astronomy, but for eye
observations one gets on very fairly without the clock.

[Illustration: FIG. 97.—Hartness Turret Observatory from the N. E.]

Circles arc a necessity in all but the small telescopes used on
portable tripods, otherwise much time will be wasted in finding. In any
event do not skimp on the finder, which should be of ample aperture and
wide field, say ¼ the aperture of the main objective, and 3° to 5°
in field. Superior definition is needless, light, and sky room enough
to locate objects quickly being the fundamental requisites.

As a final word see that all the adjustments are within easy reach from
the eyepiece, since an object once lost from a high power ocular often
proves troublesome to locate again.


REFERENCES

  CHAMBERS’ Astronomy, Vol. II.
  F. L. O. WADSWORTH: _Ap. J._, =5=, 132. Ranyard’s mounts for
    reflectors.
  G. W. RITCHEY: _Ap. J._, =5=, 143. Supporting large specula.
  G. E. HALE: Cont. Solar Obs. # 2. The “Snow” horizontal telescope.
  G. E. HALE: Cont. Solar Obs. # 23. The 60 ft. tower telescope.
  J. W. DRAPER: Smithsonian Contrib. =34=. Mounting of his large
    reflector.
  G. W. RITCHEY: Smithsonian Contrib. =35=. Mounting of the Mt. Wilson
    60 inch reflector.
  SIR H. GRUBB: Tr. Roy. Dublin Soc. Ser. 2. =3=. Polar Telescopes.
  SIR R. S. BALL: _M. N._ =59=, 152. Photographic polar telescope.
  A. A. COMMON: Mem. R. A. S., =46=, 173. Mounting of his 3 ft.
    reflector.
  R. W. PORTER: _Pop. Ast._, =24=, 308. Polar reflecting telescope.
  JAMES HARTNESS: _Trans. A. S. M. E._, 1911, Turret Telescope.
  SIR DAVID GILL: Enc. Brit., 11th Ed. Telescope. Admirable summary of
    mounts.




CHAPTER VI

EYE PIECES


The eyepiece of a telescope is merely an instrument for magnifying
the image produced by the objective or mirror. If one looks through a
telescope without its eyepiece, drawing the eye back from the focus to
its ordinary distance of distinct vision, the image is clearly seen as
if suspended in air, or it can be received on a bit of ground glass.

It appears larger or smaller than the object seen by the naked eye, in
proportion as the focal length of the objective is larger or smaller
than the distance to which the eye has to drop back to see the image
clearly.

This real image, the quality of which depends on the exactness of
correction of the objective or mirror, is then to be magnified so much
as may be desirable, by the eyepiece of the instrument. In broad terms,
then, the eyepiece is a simple microscope applied to the image of an
object instead of the object itself.

And looking at the matter in the simplest way the magnifying power of
any simple lens depends on the focal length of that lens compared with
the ordinary seeing distance of the eye. If this be taken at 10 inches
as it often conventionally is, then a lens of 1 inch focus brings clear
vision down to an inch from the object, increases the apparent angle
covered by the object 10 times and hence gives a magnifying power of 10.

But if the objective has a focal length of 100 inches the image, as we
have just seen, is already magnified 10 times as the naked eye sees it,
hence with an objective of 100 inches focus and a 1 inch eyepiece the
total magnification is 100 diameters. And this expresses the general
law, for if we took the normal seeing distance of the naked eye at some
other value than 10 inches, say 12½ inches then we should have to
reckon the image as magnified by 8 times so far as the objective inches
is concerned, but 12½ times due to the 1 inch eyepiece, and so
forth. Thus the magnifying power of any eyepiece is F/f where F is the
focal length of the objective or mirror and f that of the eyepiece.
The focal distance of the eye quite drops out of the reckoning.

All these facts appear very quickly if one explores the image from an
objective with a slip of ground glass and a pocket lens. An ordinary
camera tells the same story. A distant object which covers 1° will
cover on the ground glass 1° reckoned on a radius equal to the focal
length of the lens. If this is equal to the ordinary distance of clear
vision, an eye at the same distance will see the image (or the distant
object) covering the same 1°.

The geometry of the situation is as follows: Let _o_ Fig. 5, Chap.
1, be the objective. This lens, as in an ordinary camera, forms an
inverted image of an object A B at its focus, as at _a b_, and for
any point, as _a_, of the image there is a corresponding point of the
object lying on the straight line from A to that point through the
center, _c_, of the objective.

A pair of rays 1, 2, diverging from the object point A pass through
rim and center of _o_ respectively and meet in A. After crossing at
this point they fall on the eye lens _e_, and if _a_ is nearly in the
principal focus of _e_, the rays 1 and 2 will emerge substantially
parallel so that the eye will unite them to form a clear image.

Now if F is the focal length of _o_, and f that of _a_, the object
forming the image subtends at the center of the objective, o, an angle
_A c B_, and for a distant object this will be sensibly the angle under
which the eye sees the same object.

If L is the half linear dimension of the image, the eye sees half the
object covering the angle whose tangent is L/F. Similarly half the
image _ab_ is seen through the eye lens _e_ as covering a half angle
whose tangent is L/f. Since the magnifying power of the combination,
m, is directly as the ratio of increase in this tangent of the visual
angle, which measures the image dimension

  m = F/f, as before

Further, as all the light which comes in parallel through the whole
opening of the objective forms a single conical beam concentrating into
a focus and then diverging to enter the eye lens, the diameter of the
cone coming through the eye lens must bear the same relation to the
diameter of _o_, that f does to F.

Any less diameter of _e_ will cut off part of the emerging light; any
more will show an emergent beam smaller than the eye lens, which is
generally the case. Hence if we call p the diameter of the bright
pencil of light which we see coming through the eye lens then for that
particular eye lens,

m = _o_/p

That is, f = pF/_o_ which is quite the easiest way of measuring the
focal length of an eyepiece.

Point the telescope toward the clear sky, focusing for a distant object
so that the emergent pencil is sharply defined at the ocular, and then
measure its diameter by the help of a fine scale and a pocket lens,
taking care that scale and emergent pencil are simultaneously in sharp
focus and show no parallax as the eye is shifted a bit. This bright
circle of the emerging beam is actually the projection by the eye lens
of the focal image of the objective aperture.

This method of measuring power is easy and rather accurate. But it
leads to trouble if the measured diameter of the objective is in
fact contracted by a stop anywhere along the path of the beam, as
occasionally happens. Examine the telescope carefully with reference to
this point before thus testing the power.[17]

 [17] A more precise method, depending on an actual measurement of the
 angle subtended by the diameter of the eyepiece diaphragm as seen
 through the eye end of the ocular and its comparison with the same
 angular diameter reckoned from the objective, is given by Schaeberle.
 M. N. =43=, 297.

The eye lens of Fig. 5 is a simple double convex one, such as was used
by Christopher Scheiner and his contemporaries. With a first class
objective or mirror the simple eye lens such as is shown in Fig. 98a
is by no means to be despised even now. Sir William Herschel always
preferred it for high powers, and speaks with evident contempt of
observers who sacrificed its advantages to gain a bigger field of view.
Let us try to fathom the reason for his vigorously expressed opinion,
strongly backed up by experienced observers like the late T. W. Webb
and Mr. W. F. Denning.

First of all a single lens saves about 10% of the light. Each surface
of glass through which light passes transmits 95 to 96% of that light,
so that a single lens transmits approximately 90%, two lenses 81%
and so on. This loss may be enough to determine the visibility of an
object. Sir Wm. Herschel found that faint objects invisible with the
ordinary two lens eyepiece came to view with the single lens.

Probably the actual loss is less serious than its effect on seeing
conditions. The loss is due substantially to reflection at the
surfaces, and the light thus reflected is scattered close to, or
into, the eye and produces stray light in the field which injures the
contrast by which faint objects become visible.

In some eyepieces the form of the surfaces is such that reflected light
is strongly concentrated where the eye sees it, forming a “ghost”
quite bright enough greatly to interfere with the vision of delicate
contrasts.

The single lens has a very small sharp field, hardly 10° in angular
extent, the image falling off rapidly in quality as it departs from the
axis. If plano-convex, as is the eye lens of common two-lens oculars,
it works best with the curved side to the eye, i.e., reversed from
its usual position, the spherical aberration being much less in this
position.

[Illustration: FIG. 98.—Simple Oculars.]

Herschel’s report of better definition with a single lens than with an
ordinary two lens ocular speaks ill for the quality of the latter then
available. Of course the single lens gives some chromatic aberration,
generally of small account with the narrow pencils of light used in
high powers.

A somewhat better form of eye lens occasionally used is the so-called
Coddington lens, really devised by Sir David Brewster. This, Fig. 98b,
is derived from a glass sphere with a thick equatorial belt removed
and a groove cut down centrally leaving a diameter of less than half
the radius of the sphere. The focus is, for ordinary crown glass, 3/2
the radius of the sphere, and the field is a little improved over the
simple lens, but it falls off rather rapidly, with considerable color
toward the edge.

The obvious step toward fuller correction of the aberrations while
retaining the advantages of the simple lens is to make the ocular
achromatic, like a minute objective, thus correcting at once the
chromatic and spherical aberrations over a reasonably large field. As
the components are cemented the loss of light at their common surface
is negligible. Figure 98c shows such a lens. If correctly designed it
gives an admirably sharp field of 15° to 20°, colorless and with very
little distortion, and is well adapted for high powers.

[Illustration: _a_   _b_
FIG. 99.—Triple Cemented Oculars.]

Still better results in field and orthoscopy can be attained by
going to a triple cemented lens, similar to the objective of Fig.
57. Triplets thus constituted are made abroad by Zeiss, Steinheil
and others, while in this country an admirable triplet designed by
Professor Hastings is made by Bausch & Lomb.

[Illustration: FIG. 100.—Path of Rays Through Huygenian Ocular.]

Such lenses give a beautifully flat and sharp field over an angle of
20° to 30°, quite colorless and orthoscopic. Fig. 99_a_, a form used
by Steinheil, is an excellent example of the construction and a most
useful ocular. The late R. B. Tolles made such triplets, even down to
⅛ inch focus, which gave admirable results.

A highly specialized form of triplet is the so-called monocentric of
Steinheil Fig. 99_b_. Its peculiarity is less in the fact that all the
curves are struck from the same center than in the great thickness
of the front flint and the crown, which, as in some photographic
lenses, give added facilities for flattening the field and eliminating
distortion.

The monocentric eyepiece has a high reputation for keen definition
and is admirably achromatic and orthoscopic. The sharp field is about
32°, rather the largest given by any of the cemented combinations.
All these optically single lenses are quite free of ghosts, reduce
scattered light to a minimum, and leave little to be desired in precise
definition. The weak point of the whole tribe is the small field,
which, despite Herschel’s opinion, is a real disadvantage for certain
kinds of work and wastes the observer’s time unless his facilities for
close setting are more than usually good.

Hence the general use of oculars of the two lens types, all of
them giving relatively wide fields, some of them faultless also in
definition and orthoscopy. The earliest form, Fig. 100, is the very
useful and common one used by Huygens and bearing his name, though
perhaps independently devised by Campani of Rome. Probably four out of
five astronomical eyepieces belong to this class.

The Huygenian ocular accomplishes two useful results—first, it gives a
wider sharp field than any single lens, and second it compensates the
chromatic aberration, which otherwise must be removed by a composite
lens. It usually consists of a plano-convex lens, convex side toward
the objective, which is brought inside the objective focus and forms
an image in the plane of a rear diaphragm, and a similar eye lens of
shorter focus by which this image is examined.

Fig. 100 shows the course of the rays—_A_ being the field lens, _B_
the diaphragm and _C_ the eye lens. Let _1_, _2_, be rays which are
incident near the margin of _A_. Each, in passing through the lens, is
dispersed, the blue being more refracted than the red. Both rays come
to a general focus at _B_, and, crossing, diverge slightly towards _C_.

But, on reaching _C_, ray _1_, that was nearer the margin and the more
refracted because in a zone of greater pitch, now falls on _C_ the
nearer its center, and is less refracted than ray _2_ which strikes _C_
nearer the rim. If the curvatures of _A_ and _C_ are properly related
_1_ and _2_ emerge from _C_ parallel to each other and thus unite in
forming a distinct image.

Now follow through the two branches of _l_ marked _l_r_, and _l_v_, the
red and violet components. Ray _l_v_, the more refrangible, strikes
_C_ nearer the center, and is the less refracted, emerging from _C_
substantially parallel with its mate _l_r_, hence blending the red and
violet images, if, being of the same glass, _A_ and _C_ have suitably
related focal lengths and separation.

As a matter of fact the condition for this chromatic compensation is

 d = (f + f′)/2

where d is the distance between the lenses and f, f′, their respective
focal lengths. If this condition of achromatism be combined with
that of equal refraction at _A_ and _C_, favorable to minimizing
the spherical aberration, we find f = 3f′ and d = 2f′. This is the
conventional Huygenian ocular with an eye lens ⅓ the focus of the
field lens, spaced at double the focus of the eye lens, with the
diaphragm midway.

In practice the ratio of foci varies from 1:3 to 1:2 or even 1:1.5, the
exact figure varying with the amount of overcorrection in the objective
and under-correction in the eye that has to be dealt with, while the
value of d should be adjusted by actual trial on the telescope to
obtain the best color correction practicable. One cannot use any chance
ocular and expect the finest results.

[Illustration: FIG. 101_a_.—Airy and Mittenzuey Oculars.]

The Huygenian eyepieces are often referred to as “negative” inasmuch
as they cannot be used directly as magnifiers, although dealing
effectively with an image rather than an object. The statement is
also often made that they cannot be used with cross wires. This is
incorrect, for while there is noticeable distortion toward the edge of
the wide field, to say nothing of astigmatism, in and near the center
of the field the situation is a good deal better.

Central cross wires in the plane of the diaphragm are entirely suitable
for alignment of the instrument, and over a moderate extent of field
the distortion is so small that a micrometer scale in the plane of
the diaphragm gives very good approximate measurements, and indeed is
widely used in microscopy.

It should be noted that the achromatism of this type of eyepiece is
compensatory rather than real. One cannot at the same time bring the
images of various colors to the same size, and also to the same plane.
As failure in the latter respect is comparatively unimportant, the
Huygenian eyepiece is adjusted so far to compensate the paths of the
various rays as to bring the colored images to the same size, and in
point of fact the result is very good.

The field of the conventional form of Huygenian ocular is fully 40°,
and the definition, particularly centrally, is very excellent. There
are no perceptible ghosts produced, and while some 10% of light is lost
by reflection in the extra lens it is diffused in the general field
and is damaging only as it injures the contrast of faint objects. The
theory of the Huygenian eyepiece was elaborately given by Littrow,
(Memoirs R. A. S. Vol. 4, p. 599), wherein the somewhat intricate
geometry of the situation is fully discussed.

Various modifications of the Huygenian type have been devised and used.
Figure 101_a_ is the Airy form devised as a result of a somewhat full
mathematical investigation by Sir George Airy, later Astronomer Royal.
Its peculiarity lies in the form of the lenses which preserve the usual
3:1 ratio of focal lengths. The field lens is a positive meniscus with
a noticeable amount of concavity in the rear face while the eye lens
is a “crossed” lens, the outer curvature being about ⅙ of the inner
curvature. The marginal field in this ocular is a little better than in
the conventional Huygenian.

[Illustration: FIG. 101_b_.—Airy and Mittenzwey Oculars.]

A commoner modification now-a-days is the Mittenzwey form, Fig. 101_b_.
This is usually made with 2:1 ratio of focal lengths, and the field
lens still a meniscus, but less conspicuously concave than in the
Airy form. The eye lens is the usual plano-convex. It is widely used,
especially abroad, and gives perhaps as large available field as any
ocular yet devised, approximately 50°, with pretty good definition out
to the margin.

Finally, we come to the solid eyepiece Fig. 102_a_, devised by the late
R. B. Tolies nearly three quarters of a century ago, and and often
made by him both for telescopes and microscopes. It is practically
a Huygenian eyepiece made out of a single cylinder of glass with a
curvature ratio of 1½:1 between the eye and the field lens. A groove
is cut around the long lens at about ⅓ its length from the vertex of
the field end. This serves as a stop, reducing the diameter of the
lens to about one-half its focal length.

It is in fact a Huygenian eyepiece free from the loss of light in the
usual construction. It gives a wide field, more extensive than in the
ordinary form, with exquisite definition. It is really a most admirable
form of eyepiece which should be used far more than is now the case.
The late Dr. Brashear is on record as believing that all negative
eyepieces less than ¾ inch focus should be made in this form.

[Illustration: _a_   _b_
FIG. 102.—Tolles’ Solid and Compensated Oculars.]

So far as the writer can ascertain the only reason that it is not
more used is that it is somewhat more difficult to construct than the
two lens form, for its curvatures and length must be very accurately
adjusted. It is consequently unpopular with the constructing optician
in spite of its conspicuous merits. It gives no ghosts, and the faint
reflection at the eye end is widely spread so that if the exterior of
the cylinder is well blackened, as it should be, it gives exceptional
freedom from stray light. Still another variety of the Huygenian
ocular sometimes useful is analogous to the compensating eyepiece used
in microscopy. If, as commonly is the case, a telescope objective is
over-corrected for color to correct for the chromatism of the eye in
low powers, the high powers show strong over correction, the blue focus
being longer than the red, and the blue image therefore the larger.

If now the field lens of the ocular be made of heavy flint glass and
the separation of the lenses suitably adjusted, the stronger refraction
of the field lens for the blue pulls up the blue focus and brings its
image to substantially the dimensions of the red, so that the eye lens
performs as if there were no overcorrection of the objective.

The writer has experimented with an ocular of this sort as shown
in Fig. 102_b_ and finds that the color correction is, as might be
expected, greatly improved over a Mittenzwey ocular of the same focus
(⅕ inch). There would be material advantage in thus varying the
ocular color correction to suit the power.

In the Huyghenian eyepiece the equivalent focal length F is given by,

 F = 2ff′/(f + f′)

where f and f′ are the focal lengths of the field and eye lenses
respectively. This assumes the normal spacing, d, of half the sum of
the focal lengths, not always adhered to by constructors. The perfectly
general case, as for any two combined lenses is,

 F = ff_{1}/(f + f_{1}-d)

[Illustration: FIG. 103.—Path of Rays Through Ramsden Ocular.]

To obtain a flatter field, and particularly one free from distortion
the construction devised by Ramsden is commonly used. This consists,
Fig. 103, of two plano convex lenses of equal focal length, placed with
their plane faces outward, at a distance equal to, or somewhat less
than, their common focal length. The former spacing is the one which
gives the best achromatic compensation since as before the condition
for achromatism is

 d = ½(f + f′)

When thus spaced the plane surface of the field lens is exactly in the
focus of the eye lens, the combined focus F is the same as that of
either lens, since as just shown in any additive combination of two
lenses

 F = ff′/(f + f′-d)

and while the field is flat and colorless, every speck of dust on the
field lens is offensively in view.

It is therefore usual to make this ocular in the form suggested by
Airy, in which something of the achromatic correction is sacrificed to
obviate this difficulty, and to obtain a better balance of the residual
aberrations. The path of the rays is shown in Fig. 103. The lenses _A_
and _B_ are of the same focal length but are now spaced at ⅔ of this
length apart.

The two neighboring rays _1_, _2_, coming through the objective from
the distant object meet at the objective focus in a point, _a_, of the
image plane _a b_. Thence, diverging, they are so refracted by _A_
and _B_ as to leave the latter substantially parallel so that both
appear to proceed from the point c, of the image plane _c_, _d_, in the
principal focus of _B_.

From the ordinary equation for the combination, F = ¾ f. The
combination focusses ¼ f back of the principal focus of the
objective, and the position of the eye is ¼ F back of the eye lens,
which is another reason for shortening the lens spacing. At longer
spacing the eye distance is inconveniently reduced.

Thus constituted, the Ramsden ocular, known as “positive” from its
capability for use as a magnifier of actual objects, gives a good flat
field free from distortion over a field of nearly 35° and at some loss
of definition a little more. It is the form most commonly used for
micrometer work.

In all optical instruments the aberrations increase as one departs from
the axis, so that angular field is rather a loose term depending on the
maximum aberrations that can be tolerated.[18]

 [18] The angular field a is defined by

 tan ½a = γ/F

 where γ is, numerically, the radius of the field sharp enough for the
 purpose in hand, and F the effective focal length of the ocular.

Of the Ramsden ocular there are many modifications. Sometimes f and f′
are made unequal or there is departure from the simple plano-convex
form. More often the lenses are made achromatic, thus getting rid
of the very perceptible color in the simpler form and materially
helping the definition. Figure 104_a_ shows such an achromatic ocular
as made by Steinheil. The general arrangement is as in the ordinary
Ramsden, but the sharp field is slightly enlarged, a good 36°, and the
definition is improved quite noticeably.

A somewhat analogous form, but considerably modified in detail, is
the Kellner ocular, Fig. 104_b_. It was devised by an optician of that
name, of Wetzlar, who exploited it some three quarters of a century
since in a little brochure entitled “Das orthoskopische Okular,” as
notable a blast of “hot air” as ever came from a modern publicity agent.

As made today the Kellner ocular consists of a field lens which is
commonly plano-convex, plano side out, but sometimes crossed or even
equiconvex, combined with a considerably smaller eye lens which is
an over-corrected achromatic. The focal length of the field lens is
approximately 7/4 F, that of the eye lens 4/3 F, separated by about ¾
F.

This ocular has its front focal plane very near the field lens,
sometimes even within its substance, and a rather short eye distance,
but it gives admirable definition and a usable field of very great
extent, colorless and orthoscopic to the edge. The writer has one of
2⅝″ focus, with an achromatic triplet as eye lens, which gives an
admirable field of quite 50°.

[Illustration: FIG. 104.—Achromatic and Kellner Oculars.]

The Kellner is decidedly valuable as a wide field positive ocular, but
it has in common with the two just previously described a sometimes
unpleasant ghost of bright objects. This arises from light reflected
from the inner surface of the field lens, and back again by the front
surface to a focus. This focus commonly lies not far back of the field
lens and quite too near to the focus of the eye lens for comfort. It
should be watched for in going after faint objects with oculars of the
types noted.

A decidedly better form of positive ocular is the modern orthoscopic
as made by Steinheil and Zeiss, Fig. 105_a_. It consists of a triple
achromatic field lens, a dense flint between two crowns, with a
plano-convex eye lens of much shorter focus (⅓ to ½) almost in
contact on its convex side.

The field triplet is heavily over-corrected for color, the front focal
plane is nearly ½ F ahead of the front vertex of the field lens, and
the eye distance is notably greater than in the Kellner. The field
is above 40°, beautifully flat, sharp, and orthoscopic, free of
troublesome ghosts. On the whole the writer is inclined to rate it as
the best of two-lens oculars.

There should also here be mentioned a very useful long relief ocular,
often used for artillery sights, and shown in Fig. 105_b_. It consists
like Fig. 104_a_, of a pair of achromatic lenses, but they are placed
with the crowns almost in contact and are frequently used with a simple
plano convex field lens of much longer focus, to render the combination
more fully orthoscopic.

The field, especially with the field lens, is wide, quite 40° as
apparent angle for the whole instrument, and the eye distance is
roughly equal to the focal length. It is a form of ocular that might
be very advantageously used in finders, where one often has to assume
uncomfortable angles of view, and long relief is valuable.

[Illustration: _a_   _b_
FIG. 105.—Orthoscopic and Long Relief Oculars.]

Whatever the apparent angular field of an ocular may be, the real
angular field of view is obtained by dividing the apparent field by the
magnifying power. Thus the author’s big Kellner, just mentioned, gives
a power of 20 with the objective for which it was designed, hence a
real field of 2½°, while a second, power 65, gives a real field of
hardly 0°40′, the apparent field in this case being a trifle over 40°.
There is no escaping this relation, so that high power always implies
small field.

The limit of apparent field is due to increasing errors away from the
axis, strong curvature of the field, and particularly astigmatism in
the outer zones. The eye itself can take in only about 40° so that more
than this, while attainable, can only be utilized by peering around the
marginal field.

For low powers the usable field is helped out by the accommodation of
the eye, but in oculars of short focus the curvature of field is the
limiting factor. The radius of curvature of the image is, in a single
lens approximately 3/2 F, and in the common two lens forms about ¾ F.

In considering this matter Conrady has shown (M. N. _78_ 445) that for
a total field of 40° the sharpness of field fails at a focal length
of about 1 inch for normal power of accommodation. The best achromatic
combinations reduce this limit to about ½ inch.

At focal lengths below this the sharpest field is obtainable only with
reduced aperture. There is an interesting possibility of building an
anastigmatic ocular on the lines of the modern photographic lens, which
Conrady suggests, but the need of wide field in high powers is hardly
pressing enough to stimulate research.

[Illustration: FIG. 106.—Ordinary Terrestrial Ocular.]

Finally we may pass to the very simple adjunct of most small
telescopes, the terrestrial ocular which inverts the image and shows
the landscape right side up. Whatever its exact form it consists of
an inverting system which erects the inverted image produced by the
objective alone, and an eyepiece for viewing this erected image. In its
common form it is composed of four plano-convex lenses arranged as in
Fig. 106. Here A and B for the inverting pair and C and D a modified
Huygenian ocular. The image from the objective is formed in the front
focus of AB which is practically an inverted ocular, and the erected
image is formed in the usual way between C and D.

The apparent field is fairly good, about 35°, and while slightly
better corrections can be gained by using lenses of specially adjusted
curvatures, as Airy has shown, these are seldom applied. The chief
objection to this erecting system is its length, some ten times its
equivalent focus. Now and then to save light and gain field, the
erector is a single cemented combination and the ocular like Fig. 99_a_
or Fig. 102_a_. Fig. 107 shows a terrestrial eyepiece so arranged,
from an example by the late R. B. Tolles. When carefully designed an
apparent field of 40° or more can be secured, with great brilliancy,
and the length of the erecting system is moderate.

Very much akin in principle is the eyepiece microscope, such as is made
by Zeiss to give variable power and a convenient position of the eye
in connection with filar micrometers, Fig. 108. It is provided with
a focussing collar and its draw tube allows varying power just as in
case of an ordinary microscope. In fact eyepiece microscopes have long
been now and then used to advantage for high powers. They are easier on
the eye, and give greater eye distance than the exceedingly small eye
lenses of short focus oculars, and using a solid eyepiece and single
lens objective lose no more light than an ordinary Huygenian ocular.
The erect resultant image is occasionally a convenience in astronomical
use.

[Illustration: FIG. 107.—Tolles Triplet Inverting System.]

[Illustration: FIG. 108.—Microscope as Ocular.]

[Illustration: FIG. 109.—“Davon” Instrument.]

Quite analogous to the eyepiece microscope is the so-called “Davon”
micro-telescope. Originally developed as an attachment for the substage
of a microscope to give large images of objects at a little distance
it has grown also into a separate hand telescope, monocular or
binocular, for general purposes. The attachment thus developed is shown
complete in Fig. 109. D is merely a well corrected objective set in a
mount provided with ample stops. The image is viewed by an ordinary
microscope or special eyepiece microscope A, as the case may be,
furnished with rack focussing at A′ and assembled with the objective by
means of the carefully centered coupling C.

It furnishes a compact and powerful instrument, very suitable for
terrestrial or minor astronomical uses, like the Tolles’ short-focus
hand telescopes already mentioned. When properly designed telescopes
of this sort give nearly the field of prism glasses, weigh much less
and lose far less light for the same effective power and aperture. They
also have under fairly high powers rather the advantage in the matter
of definition, other things being equal.




CHAPTER VII

HAND TELESCOPES AND BINOCULARS


The hand telescope finds comparatively little use in observing
celestial bodies. It is usually quite too small for any except very
limited applications, and cannot be given sufficient power without
being difficult to keep steady except by the aid of a fixed mounting.
Still, for certain work, especially the observation of variable
stars, it finds useful purpose if sufficiently compact and of good
light-gathering power.

There is most decidedly a limit to the magnifying power which can be
given to an instrument held in the hand without making the outfit too
unsteady to be serviceable. Anything beyond 8 to 10 diameters is highly
troublesome, and requires a rudimentary mount or at least steadying the
hand against something in order to observe with comfort.

The longer the instrument the more difficult it is to manage, and
the best results with hand telescopes are to be obtained with short
instruments of relatively large diameter and low power. The ordinary
field glass of Galilean type comes immediately to mind and in fact the
field glass is and has been much used. As ordinarily constructed it is
optically rather crude for astronomical purposes. The objectives are
rarely well figured or accurately centered and a bright star usually
appears as a wobbly flare rather than a point.

Furthermore the field is generally small, and of quite uneven
illumination from centre to periphery, so that great caution has to
be exercised in judging the brightness of a star, according to its
position in the field. The lens diameter possible with a field glass
of ordinary construction is limited by the limited distance between
the eyes, which must be well centered on the eyepieces to obtain clear
vision.

The inter-pupillary distance is generally a scant 2½ inches so that
the clear aperture of one of the objectives of a field glass is rarely
carried up to 2 inches. The best field glasses have each objective
a triple cemented lens, and the concave lenses also triplets, the
arrangement of parts being that shown in Fig. 110. Glasses of this sort
rarely have a magnifying power above 5.

In selecting a field glass with the idea of using it on the sky try it
on a bright star, real or artificial, and if the image with careful
focussing does not pull down to a pretty small and uniform point take
no further interest in the instrument.

[Illustration: FIG. 110.—Optical Parts of Field Glass.]

The advantage of a binocular instrument is popularly much exaggerated.
It gives a somewhat delusive appearance of brilliancy and clearness
which is psychological rather than physical. During the late war a
very careful research was made at the instance of the United States
Government to determine the actual value of a binocular field glass
against a monocular one of exactly the same type, the latter being
cheaper, lighter, and in many respects much handier.

The difference found in point of actual seeing all sorts of objects
under varying conditions of illumination was so small as to be
practically negligible. An increase of less than 5 per cent in
magnifying power enabled one to see with the monocular instrument
everything that could be seen with the binocular, equally well, and it
is altogether probable that in the matter of seeing fine detail the
difference would be even less than in general use, since it is not
altogether easy to get the two sides of a binocular working together
efficiently or to keep them so afterwards.

There has been, therefore, a definite field for monocular hand
telescopes of good quality and moderate power and such are manufactured
by some of the best Continental makers. Such instruments have
sometimes been shortened by building them on the exact principle of
the telephoto lens, which gives a relatively large image with a short
camera extension.

[Illustration: FIG. 111.—Steinheil Shortened Telescope.]

A much shortened telescope, as made by Steinheil for solar photographic
purposes, is shown in Fig. 111. This instrument with a total length
of about 2 feet and a clear aperture of 2⅜ inches gives a solar
image of ½ inch diameter, corresponding to an ordinary glass of
more than double that total length. Quite the same principle has been
applied to terrestrial telescopes by the same maker, giving again an
equivalent focus of about double the length of the whole instrument.
This identical principle has often been used in the so-called Barlow
lens, a negative lens placed between objective and eyepiece and
giving increased magnification with small increase of length; also
photographic enlargers of substantially similar function have found
considerable use.

A highly efficient hand telescope for astronomical purposes might be
constructed along this line, the great shortening of the instrument
making it possible to use somewhat higher powers than the ordinary
without too much loss of steadiness. There is also constructed a
binocular for strictly astronomical use consisting of a pair of small
hand comet-seekers.

One of these little instruments is shown in Fig. 112. It has a
clear diameter of objectives of 1⅜ inch, magnification of 5, and
a brilliant and even field of 7½° aperture. The objectives are
triplets like Fig. 57, already referred to, the oculars achromatic
doublets of the type of Fig. 104_a_.

With the exception of these specialized astronomical field glasses
the most useful and generally available hand instrument is the prism
glass now in very general use. It is based on reversal of the image
by internal total reflection in two prisms having their reflecting
surfaces perpendicular each to the other. The rudiments of the process
lie in the simple reversion prism shown in diagram in Fig. 113.

[Illustration: FIG. 112.—Astronomical Binocular.]

This is nothing more nor less than a right angled glass prism set with
its hypothenuse face parallel and with its sides at 45° to the optical
axis of the instrument. Rays falling upon one of its refracting faces
at an angle of 45° are refracted upon the hypothenuse face, are there
totally reflected and emerge from the second face of the prism parallel
to their original course.

Inspection of Fig. 113 shows that an element like A B perpendicular to
the plane of the hypothenuse face is inverted by the total reflection
so that it takes the position A′ B′. It is equally clear that an
element exactly perpendicular to A B will be reflected from the
hypothenuse face flatwise as it were, and will emerge without its ends
being reversed so that the net effect of this single reflection is to
invert the image without reversing it laterally at the same time.

On the other hand if a second prism be placed behind the first, flat
upon its side, with its hypothenuse face occupying a plane exactly
perpendicular to that of the first prism, the line A′B′ will be
refracted, totally reflected and refracted again out of the prism
without a second inversion, while a line perpendicular to A′B′ will be
refracted endwise on the hypothenuse face of the second prism and will
be inverted as was the line A B at the start.

[Illustration: FIG. 113.—Reversion Prism.]

Consequently two prisms thus placed will completely invert the image,
producing exactly the same effect as the ordinary inverting system Fig.
106. The simple reversion prism is useful as furnishing a means, when
placed over an eye lens, and rotated, of revolving the image on itself,
a procedure occasionally convenient, especially in stellar photometry.
The two prisms together constitute a true inverting system and have
been utilized in that function, but they give a rather small angular
field and have never come into a material amount of use. The exact
effect of this combination, known historically as Dove’s prisms, is
shown plainly in Fig. 114.

The first actual prismatic inverting system was due to M. Porro, who
invented it about the middle of the last century, and later brought it
out commercially under the name of “Lunette à Napoleon Troisiéme,” as a
glass for military purposes.

[Illustration: FIG. 114.—Dove’s Prisms.]

[Illustration: FIG. 115.—Porro’s Prism System.]

The prism system of this striking form of instrument is shown in Fig.
115. It was composed of three right angle prisms _A_, _B_, and _C_. _A_
presented a cathetus face to the objective and _B_ a cathetus face to
the ocular. Obviously a vertical element brought in along _a_ from the
objective would be reflected at the hypothenuse face _b_, to a position
at right angles to the original one, would enter the hypothenuse face
of _C_ and thence after two reflections at _c_ and _d_ flatwise and
without change of direction would emerge, enter the lower cathetus face
of _B_ and by reflection at the hypothenuse face _e_ of _B_ would be
turned another 90° making a complete reversion as regards up and down
at the eye placed at _f_. An element initially at right angles to the
one just considered would enter _A_, be reflected flatwise, in the
faces of _C_ be twice reflected endwise, thereby completely inverting
it, and would again be reflected flatwise from the hypothenuse face
of _C_, thereby effecting, as the path of the rays indicated plainly
shows, a complete inversion of the image. Focussing was very simply
attained by a screw motion affecting the prism _C_ and the whole affair
was in a small flat case, the external appearance and size of which is
indicated in Fig. 116.

[Illustration: FIG. 116.—Lunette à Napoleon Troisiéme.]

[Illustration: FIG. 117.—Porro’s First Form of Prisms.]

From ocular to objective the length was about an inch and a half. It
was of 10 power and took in a field of 45 yards at a distance of 1000
yards. Here for the first time we find a prismatic inverting system of
strictly modern type. And it is interesting to note that if one had
wished to make a binocular “Lunette à Napoleon Troisiéme” he would
inevitably have produced an instrument with enhanced stereoscopic
effect like the modern prism field glass by the mere effort to dodge
the observer’s nose. Somewhat earlier M. Porro had arranged his prisms
in the present conventional form of Fig. 117, where two right angle
prisms have their faces positioned in parallel planes, but turned
around by 90° as in Fig. 114. The ray traced through this conventional
system shows that exactly the same inversion occurs here as in the
original Porro construction, and this form is the one which has been
most commonly used for prismatic inversion and is conveniently known as
Porro’s first form, it actually having been antecedent in principle and
practice to the “Lunette à Napoleon Troisiéme.” The original published
description of Porro’s work, translated from “Cosmos” Vol. 2, p. 222
(1852) et seq. is here annexed as it sets forth the origin of the
modern prism glass in unmistakable terms.

_Cosmos, Vol. 2_, p. 222.—“We have wished for some time to make known
to our readers the precious advantages of the “longue-vue cornet” or
télémetre of M. Porro. Ordinary spyglasses or terrestrial telescopes
of small dimensions are at least 30 or 40 cm. long when extended to
give distinct vision of distant objects. The length is considerably
reduced by substituting for a fixed tube multiple tubes sliding into
each other. But the drawing out which this substitution necessitates is
a somewhat grave inconvenience; one cannot point the telescope without
arranging it and losing time.

For a long time we have wished it were possible to have the power
of viewing distant objects, with telescopes very short and without
draw. M. Porro’s “longue-vue cornet” seems to us to solve completely
this difficult and important problem. Its construction rests upon an
exceedingly ingenious artifice which literally folds triply the axis
of the telescope and the luminous ray so that by this fact alone the
length of the instrument is reduced by two-thirds.

Let us try to give an idea of this construction: Behind the telescope
objective M. Porro places a rectangular isosceles prism of which the
hypothenuse is perpendicular to the optic axis. The luminous rays
from the object fall upon the rectangular faces of this prism, are
twice totally reflected, and return upon themselves parallel to their
original direction: half way to the point where they would form the
image of the object, they are arrested by a second prism entirely
similar to the first, which returns them to their original direction
and sends them to the eyepiece through which we observe the real image.
If the rectangular faces of the second prism were parallel to the
faces of the first, this real image would be inverted—the telescope
would be an astronomical and not a terrestrial telescope. But M. Porro
being an optician eminently dextrous, well divined that to effect the
reinversion it sufficed to place the rectangular faces of the second
prism perpendicular to the corresponding faces of the first by turning
them a quarter revolution upon themselves.

In effect, a quarter revolution of a reflecting surface is a half
revolution for the image, and a half revolution of the image evidently
carries the bottom to the top and the right to the left, effecting a
complete inversion. As the image is thus _redressed_ independently of
the eyepiece one can evidently view it with a simple two-lens ocular
which decreases still further the length of the telescope so that it
is finally reduced to about a quarter of that of a telescope of equal
magnifying power, field and clearness.

The new telescope is then a true pocket telescope even with a
magnifying power of 10 or 15. Its dimensions in length and bulk are
those of a field glass usually magnifying only 4 to 6 times. The more
draws, the more bother,—it here suffices to turn a little thumbscrew to
find in an instant the point of sharpest vision.

In brilliancy necessarily cut down a little, not by the double total
reflection, which as is well known does not lose light, but by the
quadruple passage across the substance of the two prisms, the cornet
in sharpness and amplification of the images can compare with the
best hunting telescopes of the celebrated optician Ploessl of Vienna.
M. Porro has constructed upon the same principles a marine telescope
only 15 c.m. long with an objective of 40 m.m. aperture which replaces
an ordinary marine glass 70 c.m. long. He has done still better,—a
telescope only 30 c.m. long carries a 60 m.m. objective and can be made
by turns a day and a night glass, by substituting by a simple movement
of the hand and without dismounting anything, one ocular for the other.
Its brilliancy and magnification of a dozen times with the night
ocular, of twenty-five times with the day ocular, permits observing
without difficulty the eclipses of the satellites of Jupiter.

This is evidently immense progress. One of the most illustrious
of German physicists, M. Dove of Berlin, gave in 1851 the name of
reversion prism to the combination of two prisms placed normally one
behind the other so that their corresponding faces were perpendicular.
He presented this disposition as an important new discovery made by
himself. He doubtless did not know that M. Porro, who deserves all the
honor of this charming application, had realized it long before him.”

A little later M. Porro produced what is commonly referred to as
Porro’s second form, which is derived directly from annexing _A_ Fig.
115 to the corresponding half of _C_ as a single prism, the other half
of _B_ being similarly annexed to the prism _C_, thus forming two
sphenoid prisms, such as are shown in Fig. 118 which may be mounted
separately or may have their faces cemented together to save loss of
light by reflections. The sphenoid prisms have had the reputation of
being much more difficult to construct than the plain right angled
prisms of the other forms shown. In point of fact they are not
particularly difficult to make and the best inverting eye pieces for
telescopes are now constructed with sphenoid prisms like those just
described.

[Illustration: FIG. 118.—Porro’s Second Form.]

[Illustration: FIG. 119.—Clark Prismatic Eyepiece.]

This particular arrangement lends itself very readily to a fairly
compact and symmetrical mounting, as is well shown in Fig. 119 which
is the terrestrial prismatic eyepiece as constructed by the Alvan
Clark corporation for application to various astronomical telescopes
of their manufacture. A glance at the cut shows the compactness of
the arrangement, which actually shortens the linear distance between
objective and ocular by the amount of the path of the ray through the
prisms instead of lengthening the distance as in the common terrestrial
eyepiece.

The field moreover is much larger than that attainable by a
construction like Fig. 110, extending to something over 40°, and there
is no strong tendency for the illumination or definition to fall off
near the edge of the field.

In the practical construction of prism field glasses the two right
angled prisms are usually separated by a moderate space as in Porro’s
original instruments so as to shorten the actual length of the prism
telescope by folding the ray upon itself as in Fig. 120, which is a
typical modern binocular of this class.

[Illustration: FIG. 120.—Section of Prism Binocular.]

The path of the rays is plainly shown and the manner in which the
prisms fold up the total focal length of the objective is quite
obvious. The added stereoscopic effect obtained by the arrangement of
the two sides of the instrument is practically a very material gain.
It gives admirable modelling of the visible field, a perception of
distance which is at least very noticeable and a certain power of
penetration, as through a mass of underbrush, which results from the
objectives to a certain extent seeing around small objects so that
one or the other of them gives an image of something beyond. For near
objects there is some exaggeration of stereoscopic effect but on the
whole for terrestrial use the net gain is decidedly in evidence.

A well made prism binocular is an extremely useful instrument for
observation of the heavens, provided the objectives are of fair size,
and the prisms big enough to receive the whole beam from the objective,
and well executed enough to give a thoroughly good image with a flat
field.

The weak points of the prism glass are great loss of light through
reflection at the usual 10 air-glass surfaces and the general presence
of annoying ghosts of bright objects in the field. Most such binoculars
have Kellner eyepieces which are peculiarly bad, as we have seen, with
respect to reflected images, and present the plane surface of the last
prism to the plane front of the field lens. Recently some constructors
have utilized the orthoscopic eyepiece, Figure 105_a_, as a substitute
with great advantage in the matter of reflections.

The loss of light in the prism glass is really a serious matter,
between reflection at the surfaces and absorption in the thick masses
of glass necessary in the prisms. If of any size the transmitted light
is not much over one-half of that received, very seldom above 60%.
If the instrument is properly designed the apparent field is in the
neighborhood of 45°, substantially flat and fairly evenly illuminated.
Warning should here be given however that many binoculars are on the
market in which the field is far from flat and equally far from being
uniform.

In many instances the prisms are too small to take the whole bundle of
rays from the objective back to the image plane without cutting down
the marginal light considerably. Even when the field is apparently
quite flat this fault of uneven illumination may exist, and in a glass
for astronomical uses it is highly objectionable.

Before picking out a binocular for a study of the sky make very careful
trial of the field with respect to flatness and clean definition of
objects up to the very edge. Then judge as accurately as you may of the
uniformity of illumination, if possible by observation on two stars
about the radius of the field apart. It should be possible to observe
them in any part of the field without detectable change in their
apparent brilliancy.

If the objectives are easily removable unscrew one of them to obtain a
clear idea as to the actual size of the prisms.[19] Look out, too, for
ghosts of bright stars.

 [19] There are binoculars on the market which are to outward
 appearance prism glasses, but which are really ordinary opera glasses
 mounted with intent to deceive, sometimes bearing a slight variation
 on the name of some well known maker.

The objectives of prism glasses usually run from ¾ inch to 1½ inch
in diameter, and the powers from 6 to 12. The bigger the objectives the
better, provided the prisms are of ample size, while higher power than
6 or 8 is generally unnecessary and disadvantageous. Occasional glasses
of magnifying power 12 to 20 or more are to be found but such powers
are inconveniently great for an instrument used without support. Do not
forget that a first class monocular prism glass is extremely convenient
and satisfactory in use, to say nothing of being considerably less in
price than the instrument for two eyes. A monocular prism glass, by
the way, makes an admirable finder when fitted with coarse cross lines
in the eyepiece. It is particularly well suited to small telescopes
without circles.

[Illustration: FIG. 121.—Binocular with Extreme Stereoscopic Effect.]

Numerous modifications of Porro’s inverting prisms have been made
adapting them to different specific purposes. Of these a single
familiar example will suffice as showing the way in which the Porro
prism system can be treated by mere rearrangement of the prismatic
elements. In Fig. 121 is shown a special Zeiss binocular capable of
extreme stereoscopic effect. It is formed of two Porro prism telescopes
with the rays brought into the objectives at right angles to the axis
of the instrument by a right angled prism external to the objective.

The apertures of these prisms appear pointing forward in the cut. As
shown they are in a position of maximum stereoscopic effect.

Being hinged the tubes can be swung up from the horizontal position,
in which latter the objectives are separated by something like eight
times the interocular distance. The stereoscopic effect with the tubes
horizontal is of course greatly exaggerated so that it enables one to
form a fair judgment as to the relative position of somewhat distant
objects, a feature useful in locating shell bursts.

The optical structure of one of the pair of telescopes is shown in Fig.
122 in which the course of the entering ray can be traced through the
exterior prism of the objective and the remainder of the reversing
train and thence through the eyepiece. This prism erecting system is
obviously derived from the “Lunette à Napoleon Troisiéme” by bringing
down the prism _B_ upon the corresponding half _A_ and cementing it
thereto, meanwhile placing the objective immediately under _A_.

One occasionally meets prismatic inverting systems differing
considerably from the Porro forms. Perhaps the best known of these is
the so called roof prism due to Prof. Abbé, Fig. 123, and occasionally
useful in that the entering and emerging rays lie in the same straight
line, thus forming a direct vision system. Looking at it as we did at
the Porro system a vertical element in front of the prism is reversed
in reflection from the two surfaces a and b, while a corresponding
horizontal element is reflected flatwise so far as these are concerned,
but is turned end for end by reflection at the roof surfaces c and d,
thus giving complete inversion.

In practice the prism is made as shown, in three parts, two of them
right angled prisms, the third containing the roof surfaces. The
extreme precision required in figuring the roof forms a considerable
obstacle to the production of such prisms in quantity and while
they have found convenient use in certain special instruments like
gunsights, where direct vision is useful, they are not extensively
employed for general purposes, although both monocular and binocular
instruments have been constructed by their aid.

[Illustration: FIG. 122.—Path of Ray in Fig. 121.]

[Illustration: FIG. 123.—Abbé Roof Prism.]

One other variety of prism involving the roof principle has found some
application in field glasses manufactured by the firm of Hensoldt. The
prism form used is shown in Fig. 124. This like other forms of roof
prism is less easy to make than the conventional Porro type. Numerous
inverting and laterally reflecting prisms are in use for specific
purposes. Some of them are highly ingenious and remarkably well adapted
for their use, but hardly can be said to form a material portion of
telescope practice. They belong rather to the technique of special
instruments like gunsights and periscopes, while some of them have been
devised chiefly as ingenious substitutes for the simpler Porro forms.

Most prism telescopes both monocular and binocular are generally made
on one or the other of the Porro forms. This is particularly true
of the large binoculars which are occasionally constructed. Porro’s
second form with the sphenoid prisms seems to be best adapted to cases
where shortening of the instrument is not a paramount consideration.
For example, some Zeiss short focus telescopes are regularly made in
binocular form, and supplied with inverting systems composed of two
sphenoid prisms, and with oculars constructed on the exact principle
of the triple nose-piece of a microscope, so that three powers are
immediately available to the observer.

[Illustration: FIG. 124.—Hensoldt Prism.]

Still less commonly binocular telescopes of considerable aperture
are constructed, primarily for astronomical use, being provided with
prismatic inversion for terrestrial employment, but more particularly
in order to gain by the lateral displacement of a Porro system the
space necessary for two objectives of considerable size. As we have
already seen, the practical diameter of objectives in a binocular
is limited to a trifle over 2 inches unless space is so gained. The
largest prismatic binocular as yet constructed is one made years ago
by the Clarks, of 6¼ inches objective aperture and 92¼ inches
focal length. So big and powerful an instrument obviously would give
admirable binocular views of the heavens and so accurately was it
constructed that the reports of its performance were exceedingly good.
The same firm has made a good many similar binoculars of 3 inch and
above, of which a typical example of 4 inch aperture and 60 inch focal
length is shown in Fig. 125. In this case the erecting systems were
of Porro’s first form, and were provided with Kellner oculars of very
wide field. These binoculars constructions in instruments of such size,
however well made and agreeable for terrestrial observation, hardly
justify the expense for purely astronomical use.

[Illustration: FIG. 125.—Clark 4″ Binocular Telescope.]




CHAPTER VIII

ACCESSORIES


Aside from the ordinary equipment of oculars various accessories
form an important part of the observer’s equipment, their number and
character depending on the instrument in use and the purposes to which
it is devoted.

[Illustration: FIG. 126.—Star Diagonal.]

First in general usefulness are several special forms of eyepiece
equipment supplementary to the usual oculars. At the head of the list
is the ordinary star diagonal for the easier viewing of objects near
the zenith here shown in Fig. 126. It is merely a tube, _A_, fitting
the draw tube of the telescope, with a slotted side tube _B_, at a
right angle, into which the ordinary ocular fits, and a right angled
prism _C_ with its two faces perpendicular respectively to the axes of
the main and side tubes, and the hypothenuse face at 45° to each. The
beam coming down the tube is totally reflected at this face and brought
to focus at the ocular. The lower end of the tube is closed by a cap to
exclude dust.

One looks, by help of this, horizontally at zenith stars, or, if
observing objects at rather high altitude, views them at a comfortable
angle downward. The prism must be very accurately made to avoid injury
to the definition, but loses only about 10% of the light, and adds
greatly to the comfort of observing.

Of almost equal importance is the solar diagonal devised by Sir John
Herschel, Fig. 127. Here the tube structure _A_, _B_, is quite the
same as in Fig. 126 but the right angled prism is replaced by a simple
elliptical prism _C_ of small angle, 10° or less, with its upper face
accurately plane and at 45° to the axes of the tubes, resting on a
lining tube _D_ cut off as shown. In viewing the sun only about 5% of
the light (and heat) is reflected at this upper surface to form the
image at the eye piece.

[Illustration: FIG. 127.—Solar Diagonal.]

Any reflection from the lower polished surface is turned aside out
of the field, while the remainder of the radiation passes through
the prism _C_ and is concentrated below it. To prevent scorching the
observer the lower end of the tube is capped at _E_, but the cap has
side perforations to provide circulation for the heated air. Using such
a prism, the remnant of light reflected can be readily toned down by a
neutral tinted glass over the ocular.

In the telescopes of 3 inches and less aperture, and ordinary focal
ratio, a plane parallel disc of very dark glass over the ocular gives
sufficient protection to the eye. This glass is preferably of neutral
tint, and commonly is a scant 1/16 inch thick. Some observers prefer
other tints than neutral. A green and a red glass superimposed give
good results and so does a disc of the deepest shade of the so-called
Noviweld glass, which is similar in effect.

With an aperture as large as 3 inches a pair of superimposed dark
glasses is worth while, for the two will not break simultaneously from
the heat and there will be time to get the eye away in safety. A broken
sunshade is likely to cost the observer a permanent scotoma, blindness
in a small area of the retina which will neither get better nor worse
as time goes on.

Above 3 inches aperture the solar prism should be used or, if one cares
to go to fully double the cost, there is nothing more comfortable to
employ in solar observation than the polarizing eye piece, Fig. 128.
This shows schematically the arrangement of the device. It depends on
the fact that a ray of light falling on a surface of common glass at an
angle of incidence of approximately 57° is polarized by the reflection
so that while it is freely reflected if it falls again on a surface
parallel to the first, it is absorbed if it falls at the same incidence
on a surface at right angles to the first.

[Illustration: FIG. 128.—Diagram of Polarizing Eyepiece.]

Thus in Fig. 128 the incident beam from the telescope falls on the
black glass surface _a_ at 57° incidence, is again reflected from the
parallel mirror _b_, and then passed on, parallel to its original
path, to the lower pair of mirrors _c_, _d_. The purpose of the
second reflection is to polarize the residual light which through the
convergence of the rays was incompletely polarized at the first.

The lower pair of mirrors _c_, _d_, again twice reflect the light at
the polarizing angle, and, in the position shown, pass it on to the
ocular diminished only by the four reflections. But if the second pair
of mirrors be rotated together about a line parallel to _b c_ as an
axis the transmitted light begins to fade out, and when they have been
turned 90°, so that their planes are inclined 90° to _a_ and _b_ (= 33°
to the plane of the paper), the light is substantially extinguished.

Thus by merely turning the second pair of mirrors the solar image can
be reduced in brilliancy to any extent whatever, without modifying its
color in any way. The typical form given to the polarizing eyepiece is
similar to Fig. 129. Here _t__2 is the box containing the polarizing
mirrors, _a b_, fitted to the draw tube, but for obvious reasons
eccentric with it, _t__1 is the rotating box containing the “analysing”
mirrors _c_, _d_, and _a_ is the ocular turning with it.

Sometimes the polarizing mirrors are actually a pair of Herschel prisms
as in Fig. 126, facing each other, thus getting rid of much of the
heat. Otherwise the whole set of mirrors is of black glass to avoid
back reflections. In simpler constructions single mirrors are used as
polarizer and analyser, and in fact there are many variations on the
polarizing solar eyepiece involving about the same principles.

[Illustration: FIG. 129.—Polarizing Solar Eyepiece.]

In any solar eyepiece a set of small diaphragms with holes from perhaps
1/64 inch up are useful in cutting down the general glare from the
surface outside of that under scrutiny. These may be dropped upon the
regular diaphragm of the ocular or conveniently arranged in a revolving
diaphragm like that used with the older photographic lenses.

The measurement of celestial objects has developed a large group of
important auxiliaries in the micrometers of very varied forms. The
simplest needs little description, since it consists merely of a plane
parallel disc of glass fitting in the focus of a positive ocular,
and etched with a network of uniform squares, forming a reticulated
micrometer by which the distance of one object from another can be
estimated.

It can be readily calibrated by measuring a known distance or noting
the time required for an equatorial star to drift across the squares
parallel to one set of lines. It gives merely a useful approximation,
and accurate measures must be turned over to more precise instruments.

[Illustration: FIG. 130.—Diagram of Ring Micrometer.]

The ring micrometer due, like so much other valuable apparatus, to
Fraunhofer, is convenient and widely used for determining positions.
It consists, as shown in Fig. 130, of an accurately turned opaque
ring, generally of thin steel, cemented to a plane parallel glass or
otherwise suspended in the center of the eyepiece field. The whole
ring is generally half to two thirds the width of the field and has a
moderate radial width so that both the ingress and the egress of a star
can be conveniently timed.

It depends wholly on the measurement of time as the stars to be
compared drift across the ring while the telescope is fixed, and while
a clock or chronometer operating a sounder is a desirable adjunct
one can do pretty well with a couple of stop watches since only
differential times are required.

For full directions as to its use consult Loomis’ Practical Astronomy,
a book which should be in the library of every one who has the least
interest in celestial observations. Suffice it to say here that
the ring micrometer is very simple in use, and the computation of
the results is quite easy. In Fig. 130 F is the edge of the field,
R the ring, and _a b_, _a′b′_, the paths of the stars _s_ and _s′_,
the former well into the field, the latter just within the ring. The
necessary data comprise the time taken by each star to transverse
the ring, and the radius of the ring in angular measure, whence the
difference in R. A. or Dec, can be obtained.[20]

 [20] r the radius of the ring, is given by, r = (15/2)(t′-t) cos Dec.,
 t′-t being the seconds taken for transit.

Difference of R. A. = ½ (t′-t)½ (T′-T) where (T′-T) is the time
taken for transit of second star. To obtain differences of declination
one declination should be known at least approximately, and the second
estimated from its relative position in the ring or otherwise. Then
with these tentative values proceed as follows.

Put x = angle _aob_ and _x_′ = angle _a′o′b′_

Also let d  = approximate declination of _s_ and
         d′ = approximate declination of _s′_

Then sin x = (15/2r) cos d (T′-T)

     sin x′ = (15/2r) cos d′ (t′-t) and finally

Difference of Dec. = r (cos x′-cos x), when both arcs are on the same
side of center of ring. If on opposite sides, Diff. = r (cos x′ + cos
x).

[Illustration: _Chamber’s “Astronomy”_ (_Clarendon Press_).
FIG. 131.—Double Image Micrometer. (_Courtesy of The Clarendon Press._)]

There is also now and then used a square bar micrometer, consisting of
an opaque square set with a diagonal in the line of diurnal motion.
It is used in much the same way as the ring, and the reductions are
substantially the same. It has some points of convenience but is
little used, probably on account of the great difficulty of accurate
construction and the requirement, for advantageous use, that the
telescope should be on a well adjusted equatorial stand.[21] The ring
micrometer works reasonably well on any kind of steady mount, requires
no illumination of the field and is in permanent working adjustment.

 [21] (For full discussion of this instrument see Chandler, Mem. Amer.
 Acad. Arts & Sci. 1885, p. 158).

Still another type of micrometer capable of use without a clock-drive
is the double image instrument. In its usual form it is based on the
principle that if a lens is cut in two along a diameter and the halves
are slightly displaced along the cut all objects will be seen double,
each half of the lens forming its own set of images.

Conversely, if one choses two objects in the united field these can be
brought together by sliding the halves of the lens as before, and the
extent of the movement needed measures the distance between them. Any
lens in the optical system can be thus used, from the objective to the
eyepiece. Fig. 131 shows a very simple double image micrometer devised
by Browning many years ago. Here the lens divided is a so-called Barlow
lens, a weak achromatic negative lens sometimes used like a telephoto
lens to lengthen the focus and hence vary the power of a telescope.

This lens is shown at A with the halves widely separated by the double
threaded micrometer screw B, which carries them apart symmetrically.
The ocular proper is shown at C.

Double image micrometers are now mainly of historical interest, and
the principle survives chiefly in the heliometer, a telescope with the
objective divided, and provided with sliding mechanism of the highest
refinement. The special function of the heliometer is the direct
micrometric measurement of stellar distances too great to be within the
practicable range of a filar micrometer—distances for example up to
1½° or even more.

The observations with the heliometer are somewhat laborious and demand
rather intricate corrections, but are capable of great precision. (See
Sir David Gill’s article “Heliometer” in the Enc. Brit. 11th Ed.). At
the present day celestial photography, with micrometric measurement
of the resulting plates, has gone far in rendering needless visual
measurements of distances above a very few minutes of arc, so that
it is somewhat doubtful whether a large heliometer would again be
constructed.

[Illustration: FIG. 132.—Filar Micrometer. (_Courtesy of J. B.
Lippincott Co._)]

The astronomer’s real arm of precision is the filar micrometer. This
is shown in outline in Fig. 132, the ocular and the plate that carries
it being removed so as to display the working parts. It consists of a
main frame aa, carrying a slide bb, which is moved by the screws and
milled head B. The slide bb carries the vertical spider line mm, and
usually one or more horizontal spider lines, line mm is the so-called
fixed thread of the micrometer, movable only as a convenience to avoid
shifting the telescope.

On bb moves the micrometer slide cc, carrying the movable spider line
nn and the comb which records, with mm as reference line, the whole
revolutions of the micrometer screw C. The ocular sometimes has a
sliding motion of its own on cc, to get it positioned to the best
advantage. In use one star is set upon mm by the screw B and then C is
turned until nn bisects the other star.

Then the exact turns and fraction of a turn can be read off on the comb
and divided head of C, and reduced to angular measure by the known
constant of the micrometer, usually determined by the time of passage
of a nearly equatorial star along the horizontal thread when mm, nn,
are at a definite setting

apart. (Then r = (15(t′-t) cos d)/N where r is the value of a
revolution in seconds of arc, N the revolutions apart of mm, nn, and t
and d as heretofore.)

Very generally the whole system of slides is fitted to a graduated
circle, to which the fixed horizontal thread is diametral. Then by
turning the micrometer until the horizontal threads cut the two objects
under comparison, their position angle with reference to a graduated
circle can be read off. This angle is conventionally counted from 0° to
360° from north around through east.

[Illustration: FIG. 133.—Filar Position Micrometer.]

Figure 133 shows the micrometer constructed by the Clarks for their
24 inch equatorial of the Lowell Observatory. Here A is the head of
the main micrometer screw of which the whole turns are reckoned on the
counter H in lieu of the comb of Fig. 132. B is the traversing screw
for the fixed wire system, C the clamping screw of the position circle,
D its setting pinion, E the rack motion for shifting the ocular, F
the reading glass for the position circle, and G the little electric
lamp for bright wire illumination. The parts correspond quite exactly
with the diagram of Fig. 132 but the instrument is far more elegant in
design than the earlier forms of micrometer and fortunately rid of the
oil lamps that were once in general use. A small electric lamp with
reflector throws a little light on the spider lines—just enough to show
them distinctly. Or sometimes a faint light is thus diffused in the
field against which the spider lines show dark.

Commonly either type of illumination can be used and modified as
occasion requires. The filar micrometer is seldom used on small
telescopes, since to work easily with it the instrument should be
permanently mounted and clock-driven. Good work was done by some of the
early observers without these aids, but at the cost of infinite pains
and much loss of time.

The clock drive is in fact a most important adjunct of the telescope
when used for other purposes than ordinary visual observations, though
for simple seeing a smooth working slow motion in R. A. answers well.
The driving clock from the horological view-point is rudimentary. It
consists essentially of a weight-driven, or sometimes spring-driven,
drum, turning by a simple gear connection a worm which engages a
carefully cut gear wheel on the polar axis, while prevented from
running away by gearing up to a fast running fly-ball governor, which
applies friction to hold the clockwork down to its rate if the speed
rises by a minute amount. There is no pendulum in the ordinary sense,
the regularity depending on the uniformity of the total friction—that
due to the drive plus that applied by the governor.

Figure 134 shows a simple and entirely typical driving clock by Warner
& Swasey. Here A is the main drum with its winding gear at B, C is the
bevel gear, which is driven from another carried by A, and serves to
turn the worm shaft D; E marks the fly balls driven by the multiplying
gearing plainly visible. The governor acts at a predetermined rotation
speed to lift the spinning friction disc F against its fixed mate,
which can be adjusted by the screw G.

The fly-balls can be slightly shifted in effective position to complete
the regulation. These simple clocks, of which there are many species
differing mainly in the details of the friction device, are capable of
excellent precision if the work of driving the telescope is kept light.

For large and heavy instruments, particularly if used for photographic
work where great precision is required, it is difficult to keep the
variations of the driving friction within the range of compensation
furnished by the governor friction alone, and in such case recourse
is often taken to constructions in which the fly balls act as relay
to an electrically controlled brake, or in which the driving power is
supplied by an electric motor suitably governed either continuously
or periodically. For such work independent hand guiding mechanism is
provided to supplement the clockwork. For equatorials of the smallest
sizes, say 3 to 4 inches aperture, spring operated driving clocks are
occasionally used. The general plan of operation is quite similar to
the common weight driven forms, and where the weights to be carried are
not excessive such clocks do good work and serve a very useful purpose.

[Illustration: FIG. 134.—Typical Driving Clock. (_Courtesy of The
Clarendon Press._)]

An excellent type of the simple spring driving clock is shown in
Fig. 136 as constructed by Zeiss. Here 1 is the winding gear, 2 the
friction governor, and 3 the regulating gear. It will be seen that the
friction studs are carried by the fly balls themselves, somewhat as in
Fraunhofers’ construction a century since, and the regulation is very
easily and quickly made by adjusting the height of the conical friction
surface above the balls.

For heavier work the same makers generally use a powerful weight driven
train with four fly-balls and electric seconds control, sometimes with
the addition of electric motor slow motions to adjust for R. A. in both
directions.

[Illustration: FIG. 135.—Clark Driving Clock.]

Figure 135 is a rather powerful clock of analogous form by the Clarks.
It differs a little in its mechanism and especially in the friction
gear in which the bearing disc is picked up by a delicately set latch
and carried just long enough to effect the regulation. It is really
remarkable that clockworks of so simple character as these should
perform as well as experience shows that they do. In a few instances
clocks have depended on air-fans for their regulating force, something
after the manner of the driving gear of a phonograph, but though rather
successful for light work they have found little favor in the task
of driving equatorials. An excellent type of a second genus is the
pendulum controlled driving clock due to Sir David Gill. This has a
powerful weight-driven train with the usual fly-ball governor. But the
friction gear is controlled by a contact-making seconds pendulum in the
manner shown diagrammatically in Fig. 137. Two light leather tipped
rods each controlled by an electro magnet act upon an auxiliary brake
disc carried by the governor spindle which is set for normal speed with
one brake rod bearing lightly on it. Exciting the corresponding magnet
relieves the pressure and accelerates the clock, while exciting the
other adds braking effect and slows it.

[Illustration: FIG. 136.—Spring Operated Driving Clock.]

In Fig. 137 is shown from the original paper, (M. N. Nov., 1873), the
very ingenious selective control mechanism. At P is suspended the
contact-making seconds-pendulum making momentary contact by the pin Q
with a mercury globule at R. Upon a spindle of the clock which turns
once a second is fixed a vulcanite disc γ, δ, ε, σ. This has a rim of
silver broken at the points γ, δ, ε, σ, by ivory spacers covering 3° of
circumference. On each side of this disc is another, smaller, and with
a complete silver rim. One, ηθ, is shown, connected with the contact
spring V; its mate η′θ′, on the other side contacts with U, while a
third contact K bears on the larger disc.

The pair of segments σ, γ, and δ, ε, are connected to η θ, the other
pair of segments to η′ θ′. Now suppose the discs turning with the
arrows: If K rests on one of the insulated points when the pendulum
throws the battery C Z into circuit nothing happens. If the disc is
gaining on the pendulum, K, instead of resting on γ as shown will
contact with segment γ, σ, and actuate a relay via V, exciting the
appropriate brake magnet.

[Illustration: FIG. 137.—Sir David Gill’s Electric Control.]

If the disc is losing, K contacts with segment γ, δ, and current
will pass via η′θ′ and U to a relay that operates the other brake
magnet and lets the clock accelerate. A fourth disc (not shown) on
the same spindle is entirely insulated on its edge except at points
corresponding to γ and ε, and with a contact spring like K.

If the disc is neither gaining nor losing when the pendulum makes
contact, current flows via this fourth disc and sets the relay on
the mid-point ready to act when needed. This clock is the prototype
of divers electrically-braked driving clocks with pendulum control,
and proved beautifully precise in action, like various kindred devices
constructed since, though the whole genus is somewhat expensive and
intricate.

The modern tendency in driving apparatus for telescopes, particularly
large instruments, is to utilize an electric motor for the source of
power, using a clock mechanism merely for the purpose of accurately
regulating the rate of the motor. We thus have the driving clock in
its simplest form as a purely mechanical device worked by a sensitive
fly-ball governor. The next important type is that in which the clock
drive is precisely regulated by a pendulum clock, the necessary
governing power being applied electrically as in Fig. 137 or sometimes
mechanically.

Finally we come to the type now under consideration where the
instrument itself is motor driven and the function of the clock is
that of regulating the motor. A very good example of such a drive is
the Gerrish apparatus used for practically all the instruments at the
various Harvard observatory stations, and which has proved extremely
successful even for the most trying work of celestial photography.
The schematic arrangement of the apparatus is shown in Fig. 138. Here
an electric motor shown in diagram in 1, Fig. 138, is geared down to
approximately the proper speed for turning the right ascension axis of
the telescope. It is supplied with current either from a battery or
in practice from the electric supply which may be at hand. This motor
is operated on a 110 volt circuit which supplies current through the
switch 2 which is controlled by the low voltage clock circuit running
through the magnet 3. The clock circuit can be closed and opened at two
points, one controlled by the seconds pendulum 5, the other at 7 by the
stud on the timing wheel geared to the motor for one revolution per
second. There is also a shunt around the pendulum break, closed by the
magnet switch at 6. This switch is mechanically connected to the switch
2 by the rod 4, so that the pair open and close together.

The control operates as follows: Starting with the motor at rest, the
clock circuit is switched on, switches 2, 6 being open and 7 closed.
At the first beat of the pendulum 2, 6 closes and the current, shunted
across the loop containing 5, holds 2 closed until the motor has
started and broken the clock circuit at the timer. The fly-wheel
carries on until the pendulum again closes the power circuit via 2,
6, and current stays on the motor until the timer has completed its
revolution.

This goes on as the motor speeds up, the periodic power supply being
shortened as the timer breaks it earlier owing to the acceleration,
until the motor comes to its steady speed at which the power is applied
just long enough to maintain uniformity. If the motor for any cause
tends to overspeed the cut-off is earlier, while slowing down produces
a longer power-period bringing the speed back to normal. The power
period is generally ¼ to ½ second. The power supplied to the motor
is very small even in the example here shown, only 1 ampere at 110
volts.

[Illustration: FIG. 138.—Diagram of Gerrish Electric Control.]

The actual proportion of a revolution during which current is supplied
the motor is therefore rigorously determined by the clock pendulum,
and the motor is selected so that its revolutions are exactly timed
to this clock pendulum which has no work to do other than the circuit
closing, and can hence be regulated to keep accurate time. The small
fly-wheel (9), the weight of which is carefully adjusted with respect
to the general amount of work to be done, attached to the motor shaft,
effectively steadies its action during the process of government.
This Gerrish type has been variously modified in detail to suit the
instruments to which it has been applied, always following however the
same fundamental principles.

[Illustration: FIG. 139.—Gerrish Drive on 24 inch Reflector.]

An admirable example of the application of this drive is shown in Fig.
139, the 24 inch reflector at the Harvard Observatory. The mount is
a massive open fork, and the motor drive is seen on the right of the
mount. There are here two motors, ordinary fan motors in size. The
right hand motor carries the fly-wheel and runs steadily on under the
pendulum control. The other, connected to the same differential gear as
the driving motor, serves merely for independent regulation and can be
run in either direction by the observer to speed or slow the motion in
R. A. These examples of clock drive are merely typical of those which
have proved to be successful in use for various service, light and
heavy. There are almost innumerable variations on clocks constructed on
one or another of the general lines here indicated, so many variations
in fact that one almost might say there are few driving clocks which
are not in some degree special.

The tendency at present is for large instruments very distinctly toward
a motor-driven mechanism operating on the right ascension axis, and
governed in one of a considerable variety of ways by an actual clock
pendulum. For smaller instruments the old mechanical clock, often
fitted with electric brake gear and now and then pendulum regulated, is
capable of very excellent work.

The principle of the spectroscope is rudimentarily simple, in the
familiar decomposition of white light into rainbow colors by a prism.
One gets the phenomena neatly by holding a narrow slit in a large piece
of cardboard at arms length and looking at it through a prism held with
its edge parallel to the slit. If the light were not white but of a
mixture of definite colors each color present would be represented by
a separate image of the slit instead of the images being merged into a
continuous colored band.

With the sun as source the continuous spectrum is crossed by the dark
lines first mapped by Fraunhofer, each representing the absorption by
a relatively cool exterior layer of some substance that at a higher
temperature below gives a bright line in exactly the same position.

The actual construction of the astronomical spectroscope varies greatly
according to its use. In observations on the sun the distant slit is
brought nearer for convenience by placing it in the focus of a small
objective pointed toward the prisms (the collimator) and the spectrum
is viewed by a telescope of moderate magnifying power to disclose more
of detail. Also, since there is extremely bright light available, very
great dispersion can be used, obtained by several or many prisms, so
that the spectrum is both fairly wide, (the length of the slit) and
extremely long.

In trying to get the spectrum of a star the source is a point,
equivalent to an extremely minute length of a very narrow slit.
Therefore no actual slit is necessary and the chief trouble is to get
the spectrum wide enough and bright enough to examine.

The simplest form of stellar spectroscope and the one in most common
use with small telescopes is the ocular spectroscope arranged much like
Fig. 140. This fits into the eye tube of a telescope and the McClean
form made by Browning of London consists of an ordinary casing with
screw collar _B_, a cylindrical lens _C_, a direct vision prism _c_,
_f_, _c_, and an eye-cap _A_.

The draw tube is focussed on the star image as with any other ocular,
and the light is delivered through _C_ to the prism face nearly
parallel, and thence goes to the eye, after dispersion by the prism.
This consists of a central prism, _f_, of large angle, made of
extremely dense flint, to which are cemented a pair of prisms of light
crown _c_, _c_, with their bases turned away from that of _f_.

We have already seen that the dispersions of glasses vary very much
more than their refractions so that with proper choice of materials and
angles the refraction of _f_ is entirely compensated for some chosen
part of the spectrum, while its dispersion quite overpowers that of the
crown prisms and gives a fairly long available spectrum.

The cylindrical lens _C_ merely serves to stretch out the tiny round
star image into a short line thereby giving the resulting spectrum
width enough to examine comfortably. The weak cylindrical lens is
sometimes slipped over the eye end of the prisms to give the needed
width of spectrum instead of putting it ahead of the prisms.

A small instrument of this kind used with a telescope of 3 inches to 5
inches aperture gives a fairly good view of the spectra of starts above
second or third magnitude, the qualities of tolerably bright comets and
nebulæ and so forth. The visibility of stellar spectra varies greatly
according to their type, those with heavy broad bands being easy to
observe, while for the same stellar magnitude spectra with many fine
lines may be quite beyond examination. Nevertheless a little ocular
spectroscope enables one to see many things well worth the trouble of
observing.

[Illustration: FIG. 140.—McClean Ocular Spectroscope.]

With the larger instruments, say 6 or 8 inches, one can well take
advantage of the greater light to use a spectroscope with a slit, which
gives somewhat sharper definition and also an opportunity to measure
the spectrum produced.

An excellent type of such an instrument is that shown in Fig. 141,
due to Professor Abbé. The construction is analogous to Fig. 140. The
ocular is a Huyghenian one with the slit mechanism (controlled by a
milled head) at A in the usual place of the diaphragm. The slit is
therefore in the focus of the eye lens, which serves as collimating
lens. Above is the direct vision system J with the usual prisms which
are slightly adjustable laterally by the screw P and spring Q.

At N is a tiny transparent scale of wave lengths illuminated by a faint
light reflected from the mirror O, and in the focus of the little lens
R, which transfers it by reflection from the front face of the prism
to the eye, alongside the edge of the spectrum. One therefore sees the
spectrum marked off by a bright line wave-length scale.

[Illustration: FIG. 141.—Abbé Ocular Spectroscope.]

The pivot K and clamp L enable the whole to be swung side-wise so that
one can look through the widened slit, locate the star, close the slit
accurately upon it and swing on the prisms. M is the clamp in position
angle. Sometimes a comparison prism is added, together with suitable
means for throwing in spectra of gases or metals alongside that of
the star, though these refinements are more generally reserved for
instruments of higher dispersion.

To win the advantage of accurate centering of the star in the field
gained by the swing-out of the spectroscope in Fig. 141 simple
instruments like Fig. 140 are sometimes mounted with an ordinary ocular
in a double nose-piece like that used for microscope objectives, so
that either can be used at will.

Any ordinary pocket spectroscope, with or without scale or a comparison
prism over part of the slit, can in fact be fitted to an adapter and
used with the star focussed on the slit and a cylindrical lens, if
necessary, as an eye-cap.

Such slit spectroscopes readily give the characteristics of stellar
spectra and those of the brighter nebulæ or of comets. They enable one
to identify the more typical lines and compare them with terrestrial
sources, and save for solar work are about all the amateur observer
finds use for.

For serious research a good deal more of an instrument is required,
with a large telescope to collect the light, and means for
photographing the spectra for permanent record. The cumulative effect
of prolonged exposures makes it possible easily to record spectra
much too faint to see with the same aperture, and exposures are often
extended to many hours.

Spectroscopes for such use commonly employ dense flint prisms of about
60° refracting angle and refractive index of about 1.65, one, two, or
three of these being fitted to the instrument as occasion requires.
A fine example by Brashear is shown in Fig. 142, arranged for visual
work on the 24 inch Lowell refractor. Here A is the slit, B the prism
box, C the observing telescope, D the micrometer ocular with electric
lamp for illuminating the wires, and E the link motion that keeps the
prism faces at equal angles with collimator and observing telescope
when the angle between these is changed to observe different parts of
the spectrum. This precaution is necessary to maintain the best of
definition.

When photographs are to be taken the observing telescope is unscrewed
and a photographic lens and camera put in its place. If the brightness
of the object permits, three prisms are installed, turning the beam
180° into a camera braced to the same frame alongside the slit.

For purely photographic work, too, the objective prism used by
Fraunhofer for the earliest observation of stellar spectra is in wide
use. It is a prism fitted in front of the objective with its refracting
faces making equal angles with the telescope and the region to be
observed, respectively. Its great advantages are small loss of light
and the ability to photograph many spectra at once, for all the stars
in the clear field of the instrument leave their images spread out into
spectra upon the photographic plate.

Figure 143 shows such an objective prism mounted in front of an
astrographic objective. The prism is rotatable into any azimuth about
the axis of the objective and by the scale i and clamping screw r can
have its refracting face adjusted with respect to that axis to the
best position for photographing any part of the spectrum. Such an
arrangement is typical of those used for small instruments say from 3
inches to 6 inches aperture.

[Illustration: FIG. 142.—Typical Stellar Spectroscope.]

For larger objectives the prism is usually of decidedly smaller angle,
and, if the light warrants high dispersion, several prisms in tandem
are used. The objective prism does its best work when applied to true
photographic objectives of the portrait lens type which yield a fairly
large field. It is by means of big instruments of such sort that the
spectra for the magnificent Draper Catalogue have been secured by the
Harvard Observatory, mostly at the Arequipa station. In photographing
with the objective prism the spectra are commonly given the necessary
width for convenient examination by changing just a trifle the rate of
the driving clock so that there is a slight and gradual drift in R. A.
The refracting edge of the prism being turned parallel to the diurnal
motion this drift very gradually and uniformly widens the spectrum to
the extent of a few minutes of arc during the whole exposure.

When one comes to solar spectroscopy one meets an entirely different
situation. In stellar work the difficulty is to get enough light, and
the tendency is toward large objectives of relatively short focal
length and spectroscopes of moderate dispersion. In solar studies there
is ample light, and the main thing is to get an image big enough to be
scrutinized in detail with very great dispersion.

[Illustration: FIG. 143.—Simple Objective Prism.]

Especially is this true in the study of the chromospheric flames
that rim the solar disc and blaze over its surface. To examine these
effectively the spectroscope should have immense dispersion with a
minimum amount of stray light in the field to interfere with vision of
delicate details.

In using a spectroscope like Fig. 142, if one turned the slit toward
the landscape, the instrument being removed from the telescope and the
slit opened wide, he could plainly see its various features, refracted
through the prism, and appearing in such color as corresponded to
the part of the spectrum in the line of the observing telescope. In
other words one sees refracted images quite distinctly in spite of the
bending of the rays. With high dispersion the image seen is practically
monochromatic.

Now if one puts the spectroscope in place, brings the solar image
tangent to the slit and then cautiously opens the slit, he sees the
bright continuous spectrum of the sky close to the sun, plus any light
of the particular color for which the observing telescope is set, which
may proceed from the edge of the solar disc. Thus, if the setting is
for the red line of hydrogen (C), one sees the hydrogen glow that plays
in fiery pillars of cloud about the sun’s limb quite plainly through
the opened slit, on a background of light streaming from the adjacent
sky. To see most clearly one must use great dispersion to spread this
background out into insignificance, must keep other stray light out of
the field, and limit his view to the opened slit.

[Illustration: FIG. 144.—Diagram of Evershed Solar Spectroscope.]

To these ends early solar spectroscopes had many prisms in tandem,
up to a dozen or so, kept in proper relation by complicated linkages
analogous to the simple one shown in Fig. 142. Details can be found
in almost any astronomical work of 40 years ago. They were highly
effective in giving dispersion but neither improved the definition nor
cut out light reflected back and forth from their many surfaces.

Of late simpler constructions have come into use of which an excellent
type is the spectroscope designed by Mr. Evershed and shown in diagram
in Fig. 144. Here the path of the rays is from the slit through the
collimator objective, then through a very powerful direct vision
system, giving a dispersion of 30° through the visible spectrum, then
by reflection from the mirror through a second such system, and thence
to the observing telescope. The mirror is rotated to get various parts
of the spectrum into view, and the micrometer screw that turns it gives
means for making accurate measurement of wave lengths.

There are but five reflecting surfaces in the prism system (for the
cemented prism surfaces do not count for much) as against more than
20 in one of the older instruments of similar power, and as in other
direct vision systems the spectrum lines are substantially straight
instead of being strongly curved as with multiple single prisms. The
result is the light, compact, and powerful spectroscope shown complete
in Fig. 145, equally well fitted for observing the sun’s prominences
and the detailed spectrum from his surface.

[Illustration: FIG. 145.—Evershed Solar Spectroscope.]

In most of the solar spectroscopes made at the present time the prisms
are replaced by a diffraction grating. The original gratings made by
Fraunhofer were made of wire. Two parallel screws of extremely fine
thread formed two opposite sides of a brass frame. A very fine wire was
then wound over these screws, made fast by solder on one side of each,
and then cut away on the other, so as to leave a grating of parallel
wires with clear spaces between.

Today the grating is generally ruled by an automatic ruling engine
upon a polished plate of speculum metal. The diamond point carried by
the engine cuts very smooth and fine parallel furrows, commonly from
10,000 to 20,000 to the inch. The spaces between the furrows reflect
brilliantly and produce diffraction spectra.[22]

 [22] For the principle of diffraction spectra see Baly, Spectroscopy;
 Kayser, Handbuch d. Specktroskoie or any of the larger textbooks of
 physics.

When a grating is used instead of prisms the instrument is commonly
set up as shown in Fig. 146. Here _A_ is the collimator with slit upon
which the solar image light falls, _B_ is the observing telescope, and
_C_ the grating set in a rotatable mount with a fine threaded tangent
screw to bring any line accurately upon the cross wires of the ocular.

[Illustration: FIG. 146.—Diagram of Grating Spectroscope.]

The grating gives a series of spectra on each side of the slit,
violet ends toward the slit, and with deviations proportional to 1,
2, 3, 4, etc., times the wave length of the line considered. The
spectra therefore overlap, the ultra violet of the second order being
superimposed on the extreme red of the first order and so on. Colored
screens over the slit or ocular are used to get the overlying spectra
out of the way.

The grating spectroscopes are very advantageous in furnishing a wide
range of available dispersions, and in giving less stray light than
a prism train of equal power. The spectra moreover are very nearly
“normal,” _i.e._, the position of each line is proportional to its
wave length instead of the blue being disproportionately long as in
prismatic spectra.

In examining solar prominences the widened slit of a grating
spectroscope shows them foreshortened or stretched to an amount
depending on the angular position of the grating, but the effect is
easily reckoned.[23]

 [23] The effect on the observed height of a prominence is h = h′ sin
 c/sin t, where h is the real height, h′ the apparent height, c the
 angle made by the grating face with the collimator, and t that with
 the telescope (Fig. 146).

If the slit is nearly closed one sees merely a thin line, irregularly
bright according to the shape of the prominence; a shift of the slit
with respect to the solar image shows a new irregular section of the
prominence in the same monochromatic light.

These simple phenomena form the basis of one of the most important
instruments of solar study—the spectro-heliograph. This was devised
almost simultaneously by G. E. Hale and M. Deslandres about 30 years
ago, and enables photographs of the sun to be taken in monochromatic
light, showing not only the prominences of the limb but glowing masses
of gas scattered all over the surface.

The principle of the instrument is very simple. The collimator of a
powerful grating spectroscope is provided with a slit the full length
of the solar diameter, arranged to slide smoothly on a ball-bearing
carriage clear across the solar disc. Just in front of the photographic
plate set in the focus of the camera lens is another narrow sliding
slit, which, like a focal plane shutter, exposes strip after strip of
the plate.

The two slits are geared together by a system of levers or otherwise
so that they move at exactly the same uniform rate of speed. Thus
when the front slit is letting through a monochromatic section of
a prominence on the sun’s limb the plate-slit is at an exactly
corresponding position. When the front slit is exactly across the sun’s
center so is the plate slit, at each element of movement exposing a
line of the plate to the monochromatic image from the moving front
slit. The grating can of course be turned to put any required line
into action but it usually is set for the K line (calcium), which is
photographically very brilliant and shows bright masses of floating
vapor all over the sun’s surface.

Figure 147 shows an early and simple type of Professor Hale’s
instrument. Here A is the collimator with its sliding slit, B the
photographic telescope with its corresponding slide and C the lever
system which connects the slides in perfectly uniform alignment.
The source of power is a very accurately regulated water pressure
cylinder mounted parallel with the collimator. The result is a complete
photograph of the sun taken in monochromatic light of exactly defined
wave length and showing the precise distribution of the glowing vapor
of the corresponding substance.

Since the spectro-heliograph of Fig. 147, which shows the principle
remarkably well, there have been made many modifications, in particular
for adapting the scheme to the great horizontal and vertical fixed
telescopes now in use. (For details of these see Cont. from the Solar
Obs. Mt. Wilson, Nos. 3, 4, 23, and others). The chief difficulty
always is to secure entirely smooth and uniform motion of the two
moving elements.

[Illustration: FIG. 147.—Hale’s Spectro-heliograph (Early Form).]

So great and interesting a branch of astronomy is the study of variable
stars that some form of photometer should be part of the equipment of
every telescope in serious use for celestial observation. An immense
amount of useful work has been done by Argelander’s systematic method
of eye observation, but it is far from being precise enough to disclose
many of the most important features of variability.

The conventional way of reckoning by stellar magnitudes is conducive to
loose measurements, since each magnitude of difference implies a light
ratio of which the log is 0.4, _i.e._, each magnitude is 2.512 times
brighter than the following one. As a result of this way of reckoning
the light of a star of mag. 9.9 differs from one of mag. 10.0 not by
one per cent but by about nine. Hence to grasp light variations of
small order one must be able to measure far below 0.1^_m_.

[Illustration: FIG. 148.-Double Image Stellar Photometer.]

The ordinary laboratory photometer enables one to compare light sources
of anywhere near similar color to a probable error of well under 0.1
per cent, but it allows a comparison between sharply defined juxtaposed
fields from the two illuminants, a condition much more favorable to
precision than the comparison of two points of light, even if fairly
near together.

Stellar photometers may in principle be divided into three classes. (1)
Those in which two actual stars are brought into the same field and
compared by varying the light from one or both in a known degree. (2)
Those which bring a real star into the field alongside an artificial
star, and again bring the two to equality by a known variation,
usually comparing two or more stars via the same artificial star;
(3) those which measure the light of a star by a definite method of
extinguishing it entirely or just to the verge of disappearance in a
known progression. Of each class there are divers varieties. The type
of the first class may be taken as the late Professor E. C. Pickering’s
polarizing photometer. Its optical principle is shown in Fig. 148. Here
the brightness of two neighboring objects is compared by polarizing
at 90° apart the light received from each and reducing the resulting
images to equality by an analyzing Nicol prism. The photometer is
fully described, with, several other polarizing instruments, in H. A.
Vol. II from which Fig. 148 is taken.

A is a Nicol prism inserted in the ocular _B_, which revolves carrying
with it a divided circle _C_ read against the index _D_. In the tube
_E_ which fits the eye end of the telescope, is placed the double
image quartz prism _F_ capable of sliding either way without rotation
by pulling the cord _G_. With the objects to be compared in the same
field, two images of each appear. By turning the analyzing Nicol the
fainter image of the brighter can always be reduced to equality with
the brighter image of the fainter, and the amount of rotation measures
the required ratio of brightness.[24] This instrument works well for
objects near enough to be in the same field of view. The distance
between the images can be adjusted by sliding the prism _F_ back and
forth, but the available range of view is limited to a small fraction
of a degree in ordinary telescopes.

 [24] If A be the brightness of one object and B that of the other, α
 the reading of the index when one image disappears and β the reading
 when the two images are equal then A/B = tan²(α-β). There are
 four positions of the Nicol, 90° apart, for which equality can be
 established, and usually all are read and the mean taken. (H. A. II,
 1.)

The meridian photometer was designed to avoid this small scope. The
photometric device is substantially the same as in Fig. 148. The
objects compared are brought into the field by two exactly similar
objectives placed at a small angle so that the images, after passing
the double image prism, are substantially in coincidence. In front of
each of the objectives is a mirror. The instrument points in the east
and west line and the mirrors are at 45° with its axis. One brings
Polaris into the field, the other by a motion of rotation about the
telescope axis can bring any object in or close to the meridian into
the field alongside Polaris. The images are then compared precisely
as in the preceding instance.[25] There are suitable adjustments for
bringing the images into the positions required.

 [25] For full description and method see H. A. Vol. 14, also Miss
 Furness’ admirable “Introduction to the Study of Variable Stars,” p.
 122, et seq. Some modifications are described in H. A. Vol. 23. These
 direct comparison photometers give results subject to some annoying
 small corrections, but a vast amount of valuable work has been done
 with them in the Harvard Photometry.

The various forms of photometer using an artificial star as
intermediary in the comparison of real stars differ chiefly in the
method of varying the light in a determinate measure. Rather the best
known is the Zöllner instrument shown in diagram in Fig. 149. Here
_A_ is the eye end of the main telescope tube. Across it at an angle
of 45° is thrown a piece of plane parallel glass _B_ which serves to
reflect to the focus the beam from down the side tube, _C_, forming the
artificial star.

[Illustration: FIG. 149.—Zöllner Photometer Diagram.]

At the end of this tube is a small hole or more often a diaphragm
perforated with several very small holes any of which can be brought
into the axis of the tube. Beyond at _D_, is the source of light,
originally a lamp flame, now generally a small incandescent lamp, with
a ground glass disc or surface uniformly to diffuse the light.

Within the tube _C_ lie three Nicol prisms _n_, _n__{1}, _n__{2}.
Of these _n_, is fixed with respect to the mirror B and forms the
analyser, which _n__{1} and _n__{2} turn together forming the
polarizing system. Between _n_1_ and _n_2_ is a quartz plate _e_ cut
perpendicular to the crystal axis. The color of the light transmitted
by such a plate in polarized light varies through a wide range.
By turning the Nicol _n_2_ therefore, the color of the beam which
forms the artificial star can be made to match the real star under
examination, and then by turning the whole system _n_2_, _E_, _n_1_,
reading the rotation on the divided circle at _F_, the real star can be
matched in intensity by the artificial one.

[Illustration: FIG. 150.—Wedge Photometer.]

This is viewed via the lens _G_ and two tiny points of light appear
in the field of the ocular due respectively to reflection from the
front and back of the mirror _B_, the latter slightly fainter than
the former. Alongside or between these the real star image can be
brought for a comparison, and by turning the polarizer through an angle
α the images can be equalized with the real image. Then a similar
comparison is made with a reference star. If A be the brightness of the
former and B of the latter then

A/B = sin²α/sin²ββ

The Zöllner photometer was at first set up as an alt-azimuth instrument
with a small objective and rotation in altitude about the axis _C_.
Since the general use of electric lamps instead of the inconvenient
flame it is often fitted to the eye end of an equatorial.

Another very useful instrument is the modern wedge photometer, closely
resembling the Zöllner in some respects but with a very different
method of varying the light; devised by the late Professor E. C.
Pickering. It is shown somewhat in diagram in Fig. 150. Here as before
O is the eye end of the tube, B the plane parallel reflector, C the
side tube, L the source of light D the diaphragm and A the lens forming
the artificial star by projecting the hole in the diaphragm. In actual
practice the diameter of such hole is 1/100 inch or less.

[Illustration: FIG. 151.—Simple Polarizing Photometer.]

The light varying device W is a “photographic wedge” set in a frame
which is graduated on the edge and moved in front of the aperture by a
rack and pinion at R. There are beside colored and shade glasses for
use as occasion requires. The “photographic wedge” is merely a strip
of fine grained photographic plate given an evenly graduated exposure
from end to end, developed, and sealed under a cover glass. Its
absorption is permanent, non-selective as to color, and it can be made
to shade off from a barely perceptible density to any required opacity.
Sometimes a wedge of neutral tinted glass is used in its stead.

Before using such a “wedge photometer” the wedge must be accurately
calibrated by observation of real or artificial stars of known
difference in brightness. This is a task demanding much care and is
well described, together with the whole instrument by Parkhurst (Ap.
J. 13, 249). The great difficulty with all instruments of this general
type is the formation of an artificial star the image of which shall
very closely resemble the image of the real star in appearance and
color.

Obviously either the real or artificial star, or both, may be varied
in intensity by wedge or Nicols, and a very serviceable modification
of the Zöllner instrument, with this in mind was recently described by
Shook (Pop. Ast. 27, 595) and is shown in diagram in Fig. 151. Here A
is the tube which fits the ordinary eyepiece sleeve. E is a side tube
into which is fitted the extension D with a fitting H at its outer
end into which sets the lamp tube G. This carries on a base plug F a
small flash light bulb run by a couple of dry cells. At O is placed
a little brass diaphragm perforated with a minute hole. Between this
and the lamp is a disc of diffusing glass or paper. A Nicol prism is
set a little ahead of O, and a lens L focusses the perforation at the
principal focus of the telescope after reflection from the diagonal
glass M, as in the preceding examples. I is an ordinary eyepiece over
which is a rotatable Nicol N with a position circle K. At P is a third
Nicol in the path of the rays from the real star, thereby increasing
the convenient range of the instrument. The original paper gives the
details of construction as well as the methods of working. Obviously
the same general arrangement could be used for a wedge photometer using
the wedge on either real or artificial star or both.

The third type of visual photometer depends on reducing the light of
the star observed until it just disappears. This plan was extensively
employed by Professor Pritchard of Oxford some 40 years ago. He used
a sliding wedge of dark glass, carefully calibrated, and compared two
stars by noting the point on the wedge at which each was extinguished.
A photographic wedge may be used in exactly the same way.

Another device to the same end depends on reducing the aperture of the
telescope by a “cat’s eye,” an iris diaphragm, or similar means until
the star is no longer visible or just disappearing. The great objection
to such methods is the extremely variable sensitivity of the eye under
varying stimulus of light.

The most that can be said for the extinction photometer is that in
skillful and experienced hands like Pritchard’s it has sometimes given
much more consistent readings than would be expected. It is now and
then very convenient for quick approximation but by no courtesy can
it be considered an instrument of precision either in astronomical or
other photometry.[26]

 [26] The general order of precision attained by astronomical
 photometers is shown in the discovery, photographically, by
 Hertzsprung in 1911, that Polaris, used as a standard magnitude for
 many years, is actually a variable. Its period is very near to four
 days, its photographic amplitude 0.17 and its visual amplitude about
 0.1, _i.e._, a variation of ± 5 per cent in the light was submerged in
 the observational uncertainties, although once known it was traced out
 in the accumulated data without great difficulty.

The photometer question should not be closed without referring the
reader to the methods of physical photometry as developed by Stebbins,
Guthnick and others. The first of these depends on the use of the
selenium cell in which the electrical resistance falls on exposure
of the selenium to light. The device is not one adapted to casual
use, and requires very careful nursing to give the best results, but
these are of an order of precision beyond anything yet reached with an
astronomical visual photometer. Settings come down to variations of
something like 2 per cent, and variations in stellar light entirely
escaping previous methods become obvious.

The photoelectric cell depends on the lowering of the apparent electric
resistance of a layer of rarified inert gas between a platinum grid and
an electrode of metallic potassium or other alkali metal when light
falls on that electrode. The rate of transmission of electricity is
very exactly proportional to the illumination, and can be best measured
by a very sensitive electrometer. The results are extraordinarily
consistent, and the theoretical “probable error” is very small, though
here, as elsewhere, “probable error” is a rather meaningless term
apt to lead to a false presumption of exactness. Again the apparatus
is somewhat intricate and delicate, but gives a precision of working
if anything a little better than that of the selenium cell, quite
certainly below 1 per cent.

Neither instrument constitutes an attachment to the ordinary
telescope of modest size which can be successfully used for ordinary
photometry, and both require reduction of results to the basis
of visual effect.[27] But both offer great promise in detecting
minute variations of light and have done admirable work. For a good
fundamental description of the selenium cell photometer see Stebbins,
Ap. J. =32=, 185 and for the photoelectric method see Guthnick A. N.
=196=, 357 also A. F. and F. A. Lindemann, M. N. =39=, 343. The volume
by Miss Furness already referred to gives some interesting details of
both.

 [27] Such apparatus is essentially appurtenant to large instruments
 only, say of not less than 12″ aperture and preferably much more. The
 eye is enormously more sensitive as a detector of radiant energy than
 any device of human contrivance, and thus small telescopes can be well
 used for visual photometry, the bigger instruments having then merely
 the advantage of reaching fainter stars.




CHAPTER IX

THE CARE AND TESTING OF TELESCOPES


A word at the start concerning the choice and purchase of telescopes.
The question of refractors vs. reflectors has been already considered.
The outcome of the case depends on how much and how often you are
likely to use the instrument, and just what you want it for. For casual
observations and occasional use—all that most busy buyers of telescopes
can expect—the refractor has a decided advantage in convenience. If
one has leisure for frequent observations, and particularly if he can
give his telescope a permanent mount, and is going in for serious work,
he will do well not to dismiss the idea of a reflector without due
deliberation.

In any case it is good policy to procure an instrument from one of
the best makers. And if you do not buy directly of the actual maker
it is best to deal with his accredited agents. In other words avoid
telescopes casually picked up in the optical trade unless you chance to
have facilities for thorough testing under competent guidance before
purchase. No better telescopes are made than can be had from the best
American makers. A few British and German makers are quite in the same
class. So few high grade French telescopes reach this country as to
cause a rather common, but actually unjust,[28] belief that there are
none.

 [28] E. g., the beautiful astrographic and other objectives turned out
 by the brothers Henry.

If economy must be enforced it is much wiser to try to pick up a used
instrument of first class manufacture than to chance a new one at a
low price. Now and then a maker of very ordinary repute may turn out
a good instrument, but the fact is one to be proved—not assumed. Age
and use do not seriously deteriorate a telescope if it has been given
proper care. Some of Fraunhofer’s are still doing good service after a
century, and occasionally an instrument from one of the great makers
comes into the market at a real bargain. It may drift back to the maker
for resale, or turn up at any optician’s shop, and in any case is
better worth looking at than an equally cheap new telescope.

The condition of the tube and stand cuts little figure if they are
mechanically in good shape. Most of the older high grade instruments
were of brass, beautifully finished and lacquered, and nothing looks
worse after hard usage. It is essential that the fitting of the parts
should be accurate and that the focussing rack should work with the
utmost smoothness. A fault just here, however, can be remedied at
small cost. The mount, whatever its character, should be likewise
smooth working and without a trace of shakiness, unless one figures on
throwing it away.

As to the objective, it demands very careful examination before a
real test of its optical qualities. The objective with its cell
should be taken out and closely scrutinized in a strong light after
the superficial dust has been removed with a camel’s hair brush or
by wiping very gently with the soft Japanese “lens paper” used by
opticians.

One is likely to find plenty to look at; spots, finger marks, obvious
scratches, and what is worse a network of superficial scratches, or a
surface with patches looking like very fine pitting. These last two
defects imply the need of repolishing the affected surface, which means
also more or less refiguring. Ordinary brownish spots and finger marks
can usually be removed with little trouble.

The layman, so to speak, is often warned never to remove the cell from
a telescope but he might as well learn the simpler adjustments first as
last. In taking off a cell the main thing is to see what one is about
and to proceed in an orderly manner. If the whole cell unscrews, as
often is the case in small instruments, the only precaution required is
to put a pencil mark on the cell and its seat so that it can be screwed
back to where it started.

If as is more usual the cell fits on with three pairs of screws, one of
each pair will form an abutment against which its mate pulls the cell.
A pencil mark locating the position of the head of each of the pulling
screws enables one to back them out and replace them without shifting
the cell.

The first inspection will generally tell whether the objective is
worth further trouble or not. If all surfaces save the front are in
good condition it may pay to send the objective to the maker for
repolishing. If more than one surface is in bad shape reworking hardly
pays unless the lens can be had for a nominal figure. In buying a used
instrument from its original source these precautions are needless
as the maker can be trusted to stand back of his own and to put it in
first class condition.

However, granted that the objective stands well the inspection for
superficial defects, it should then be given a real test for figure
and color correction, bearing in mind that objectives, even from first
class makers, may now and then show slightly faulty corrections, while
those from comparatively unknown sources may now and then turn out
well. In this matter of necessary testing old and new glasses are quite
on all fours save that one may safely trust the maker with a well
earned reputation to make right any imperfections. Cleansing other than
dusting off and cautiously wiping with damp and then dry lens paper
requires removal of the lenses from their cell which demands real care.

With a promising looking objective, old or new, the first test to be
applied is the artificial star—artificial rather than natural since
the former stays put and can be used by day or by night. For day use
the “star” is merely the bright reflection of the sun from a sharply
curved surface—the shoulder of a small round bottle, a spherical flask
silvered on the inside, a small silvered ball such as is used for
Christmas tree decoration, a bicycle ball, or a glass “alley” dear to
the heart of the small boy.

The object, whatever it is, should be set up in the sun against a dark
background distant say 40 or 50 times the focal length of the objective
to be tested. The writer rather likes a silvered ball cemented to a
big sheet of black cardboard. At night a pin hole say 1/32 inch or
less in diameter through cardboard or better, tinfoil, with a flame,
or better a gas filled incandescent lamp behind it, answers well. The
latter requires rather careful adjustment that the projected area of
the closely coiled little filament may properly fill the pinhole just
in front of it.

Now if one sets up the telescope and focusses it approximately with a
low power the star can be accurately centered in the field. Then if
the eyepiece is removed, the tube racked in a bit, and the eye brought
into the focus of the objective, one can inspect the objective for
striæ. If these are absent the field will be uniformly bright all
over. Not infrequently however one will see a field like Fig. 152 or
Fig. 153. The former is the appearance of a 4 inch objective that the
author recently got his eye upon. The latter shows typical striæ of
the ordinary sort. An objective of glass as bad as shown in Fig. 152
gives no hope of astronomical usefulness, and should be relegated to
the porch of a seashore cottage. Figure 153 may represent a condition
practically harmless though undesirable.

The next step is a really critical examination of the focal image.
Using a moderately high power ocular, magnifying say 50 to the inch of
aperture, the star should be brought to the sharpest focus possible
and the image closely examined. If the objective is good and in
adjustment this image should be a very small spot of light, perfectly
round, softening very slightly in its brilliancy toward the edge,
and surrounded by two or three thin, sharp, rings of light, exactly
circular and with well defined dark spaces separating them.

[Illustration: FIG. 152.—A Bad Case of Striæ.]

[Illustration: FIG. 153.—Ordinary Striæ.]

Often from the trembling of the air the rings will seem shaky and
broken, but still well centered on the star-disc. The general
appearance is that shown in Fig. 154.[29]

 [29] This and several of the subsequent figures are taken from quite
 the best account of testing objectives: “On the Adjustment and Testing
 of Telescope Objectives.” T. Cooke & Sons, York, 1891, a little
 brochure unhappily long since out of print. A new edition is just now,
 1922, announced.

[Illustration: FIG. 154.—A First Class Star Image.]

Instead, several very different appearances may turn up. First, the
bright diffraction rings may be visible only on one side of the central
disc, which may itself be drawn out in the same direction. Second, the
best image obtainable may be fairly sharp but angular or irregular
instead of round or oval and perhaps with a hazy flare on one side.
Third, it may be impossible to get a really sharp focus anywhere, the
image being a mere blob of light with nothing definite about it.

One should be very sure that the eyepiece is clean and without fault
before proceeding further. As to the first point a bit of lens paper
made into a tiny swab on a sliver of soft wood will be of service, and
the surfaces should be inspected with a pocket lens in a good light to
make sure that the cleaning has been thorough. Turning the ocular round
will show whether any apparent defects of the image turn with it.

In the first case mentioned the next step is to rack the ocular gently
out when the star image will expand into a more or less concentric
series of bright interference rings separated by dark spaces, half a
dozen or so resulting from a rather small movement out of focus. If
these rings are out of round and eccentric like Fig. 155 one has a
clear case of failure of the objective to be square with the tube, so
that the ocular looks at the image askew.

[Illustration: FIG. 155.—Effect of Objective Askew.]

In the ordinary forms of objective this means that the side of the
objective toward the brighter and less expanded part of the ring system
is too near the ocular. This can be remedied by pushing that side
of the objective outwards a trifle. Easing off the pulling screw on
that side and slightly tightening the abutment screw makes the needed
correction, which can be lessened if over done at the first trial,
until the ring system is accurately centered. It is a rather fussy job
but not at all difficult if one remembers to proceed cautiously and to
use the screw driver gently.

[Illustration: FIG. 156.—Effect of Flaws in Objective.]

In the second case, racking out the ocular a little gives a ring
system which exaggerates just the defects of the image. The faults may
be due to mechanical strain of the objective in its cell, which is
easily cured, or to strains or flaws in the glass itself, which are
irremediable. Therefore one should, with the plane of the objective
horizontal, loosen the retaining ring that holds the lenses, without
disturbing them, and then set it back in gentle contact and try the out
of focus rings once more. If there is no marked improvement the fault
lies in the glass and no more time should be wasted on that particular
objective. Fig. 156 is a typical example of this fault.

In dealing with case three it is well to give the lens a chance by
relieving it of any such mechanical strains, for now and then they will
apparently utterly ruin the definition, but the prognosis is very bad
unless the objective has been most brutally mishandled.

In any case failure to give a sharply defined focus in a very definite
plane is a warning that the lens (or mirror) is rather bad. In testing
a reflector some pains must be taken at the start with both the main
and the secondary mirror. Using an artificial star as before, one
should focus and look sharply to the symmetry of the image, taking
care to leave the instrument in observing position and screened from
the sun for an hour or two before testing. Reflectors are much more
sensitive to temperature than refractors and take longer to settle
down to stability of figure. With a well mounted telescope of either
sort a star at fair altitude on a fine night gives even better testing
conditions than an artificial star, (Polaris is good in northern
latitudes) but one may have a long wait.

If the reflector is of good figure and well adjusted, the star image,
in focus or out, has quite the same appearance as in a refractor except
that with a bright star in focus one sees a thin sharp cross of light
centered on the image, rather faint but perfectly distinct. This is
due to the diffraction effect of the four thin strips that support the
small mirror, and fades as the star is put out of focus.

The rings then appear as usual, but also a black disc due to the
shadowing of the small mirror. Fig. 157 shows the extra-focal image of
a real or artificial star when the mirror is well centered, and the
star in the middle of the field. There only are the rings round and
concentric with the mirror spot. The rings go out of round and the spot
out of center for very small departure from the middle of the field
when the mirror is of large relative aperture—F/5 or F/6.

[Illustration: FIG. 157.—Extra-focal Image from Reflector.]

If the star image shows flare or oval out-of-focus rings when central
of the field, one or both mirrors probably need adjustment. Before
laying the trouble to imperfect figure, the mirrors should be adjusted,
the small one first as the most likely source of trouble. The side of
the mirror toward which the flare or the expanded side of the ring
system projects should be slightly pushed away from the ocular. (Note
that owing to the reflection this movement is the reverse of that
required with a refractor.)

If the lack of symmetry persists one may as well get down to first
principles and center the mirrors at once. Perhaps the easiest plan is
to prepare a disc of white cardboard exactly the size of the mirror
with concentric circles laid out upon it and an eighth inch hole in the
center. Taking out the ocular and putting a half inch stop in its place
one can stand back, lining up the stop with the draw tube, and see
whether the small mirror looks perfectly round and is concentric with
the reflected circles. If not, a touch of the adjusting screws will be
needed.

Then with a fine pointed brush dot the center of the mirror itself
through the hole, with white paint. Then, removing the card, one will
see this dot accurately centered in the small mirror if the large one
is in adjustment, and it remains as a permanent reference point. If
the dot be eccentric it can be treated as before, but by the adjusting
screws of the large mirror.

The final adjustment can then be made by getting a slightly extra-focal
star image fairly in the center of the field with a rather high power
and making the system concentric as before described. This sounds a
bit complicated but it really is not. If the large mirror is not in
place, its counter cell may well be centered and levelled by help of a
plumb line from the center of the small mirror and a steel square, as a
starting point, the small mirror having been centered as nearly as may
be by measurement.[30]

 [30] Sometimes with ever so careful centering the ring system in the
 middle of the field is still eccentric with respect to the small
 mirror, showing that the axis of the parabola is not perpendicular to
 the general face of the mirror. This can usually be remedied by the
 adjusting screws of the main mirror as described, but now and then
 it is necessary actually to move over the small mirror into the real
 optical axis. Draper (loc. cit.) gives some experiences of this sort.

So much for the general adjustment of the objective or mirror. Its
actual quality is shown only on careful examination.

As a starting point one may take the extra-focal system of rings given
by an objective or mirror after proper centering. If the spherical
aberration has thoroughly removed the appearance of the rings when
expanded so that six or eight are visible should be like Fig. 158. The
center should be a sharply defined bright point and surrounding it, and
exactly concentric, should be the interference rings, truly circular
and gradually increasing in intensity outwards, the last being very
noticeably the strongest.

One can best make the test when looking through a yellow glass screen
which removes the somewhat confusing flare due to imperfect achromatism
and makes the appearances inside and outside focus closely similar.
Just inside or outside of focus the appearance should be that of Fig.
159 for a perfectly corrected objective or mirror.

[Illustration: FIG. 158.—Correct Extra-focal Image.]

Sometimes an objective will be found in which one edge of the focussed
star image is notably red and the opposite one tinted with greenish or
bluish, showing unsymmetrical coloring, still more obvious when the
image is put a little out of focus. This means that the optical centers
of crown and flint are out of line from careless edging of the lenses
or very bad fitting. The case is bad enough to justify trying the only
remedy available outside the optician’s workshop—rotating one lens upon
the other and thus trying the pair in different relative azimuths.

The initial positions of the pair must be marked plainly, care must be
taken not to displace the spacers 120° apart often found at the edges
of the lenses, and the various positions must be tried in an orderly
manner. One not infrequently finds a position in which the fault is
negligible or disappears altogether, which point should be at once
marked for reference.

[Illustration: FIG. 159.—Correct Image Just Out of Focus.]

In case there is uncorrected spherical aberration there is departure
from regular gradation of brightness in the rings. If there is a “short
edge,” _i.e._, + spherical aberration, so that rays from the outer
zone come to a focus too short, the edge ring will look too strong
within focus, and the inner rings relatively weak; with this appearance
reversed outside focus. A “long edge” _i.e._, - spherical aberration,
shows the opposite condition, edge rings too strong outside focus and
too weak within. Both are rather common faults. The “long edge” effect
is shown in Figs. 160 and 161, as taken quite close to focus.

It takes a rather sharp eye and considerable experience to detect small
amounts of spherical aberration; perhaps the best way of judging is
in quickly passing from just inside to just outside focus and back
again, using a yellow screen and watching very closely for variations
in brightness. Truth to tell a small amount of residual aberration,
like that of Fig. 160, is not a serious matter as regards actual
performance—it hurts the telescopist’s feelings much more than the
quality of his images.

[Illustration: FIG. 160.—Spherical Aberration Just Inside Focus.]

[Illustration: FIG. 161.—Spherical Aberration Just Outside Focus.]

A much graver fault is zonal aberration, where some intermediate
zone of objective or mirror comes to a focus too long or too short,
generally damaging the definition rather seriously, depending on the
amount of variation in focus of the faulty zone. A typical case is
shown in Fig. 162 taken within focus. Here two zones are abnormally
strong showing, just as in the case of simple spherical aberration,
too short focus. Outside of focus the intensities would change places,
the outer and midway zones and center being heavy, and the strong
zones of Fig. 162 weak. These zonal aberrations are easily detected
and are rather common both in objectives and mirrors, though rarely as
conspicuous as in Fig. 162.

Another failing is the appearance of astigmatism, which, broadly, is
due to a refracting or reflecting surface which is not a surface of
revolution and therefore behaves differently for rays incident in
different planes around its optical axis. In its commonest form the
surface reflects or refracts more strongly along one plane than along
another at right angles to it. Hence the two have different foci and
there is no point focus at all, but two line foci at right angles.
Figs. 163 and 164 illustrate this fault, the former being taken inside
and the latter outside focus, under fairly high power. If a star image
is oval and the major axis of this oval has turned through 90° when one
passes to the other side of focus, astigmatism is somewhere present.

As more than half of humanity is astigmatic, through fault of the eye,
one should twist the axis of the eyes some 90° around the axis of the
telescope and look again. If the axis of the oval has turned with the
eyes a visit to the oculist is in order. If not, it is worth while
rotating the ocular. If the oval does not turn with it that particular
telescope requires reworking before it can be of much use.

This astigmatism due to fault of figure must not be confused with the
astigmatic difference of the image surfaces referred to in Chapter IV
which is zero on the axis and not of material importance in ordinary
telescopes. Astigmatism of figure on the contrary is bad everywhere and
always. It should be especially looked out for in reflecting surfaces,
curved or plane, since it is a common result of flexure.

Passing on now from these simple tests for figure, chromatic aberration
has to be examined. Nothing is better than an artificial star formed
by the sun in daylight, for the preliminary investigation. At night
Polaris is advantageous for this as for other tests.

[Illustration: FIG. 162.—A Case of Zonal Aberration.]

[Illustration: FIG. 163.—Astigmatism Inside Focus.]

[Illustration: FIG. 164.—Astigmatism Outside Focus.]

The achromatization curves, Fig. 163, really tell the whole story
of what is to be seen. When the telescope is carefully focussed for
the bright part of the spectrum, getting the sharpest star image
attainable, the central disc, small and clean, should be yellowish
white, seen under a power of 60 or 70 per inch of aperture.

But the red and blue rays have a longer focus and hence rim the image
with a narrow purplish circle varying slightly in hue according to the
character of the achromatization. Pushing the ocular a little inside,
focus, the red somewhat overbalances the blue and the purple shades
toward the red. Pulling out the ocular very slightly one brings the
deep red into focus as a minute central red point, just as the image
begins to expand a little. Further outside focus a bluish or purplish
flare fills the center of the field, while around it lies a greenish
circle due to the rays from the middle of the secondary spectrum
expanding from their shorter focus.

In an under-corrected objective this red point is brighter and the
fringe about the image, focussed or within focus, is conspicuously
reddish. Heavy overcorrection gives a strong bluish fringe and the red
point is dull or absent. With a low power ocular, unless it be given a
color correction of its own, any properly corrected objective will seem
under-corrected as already explained.

The color correction can also be well examined by using an ocular
spectroscope like Fig. 140, with the cylindrical lens removed.
Examining the focussed star image thus, the spectrum is a narrow line
for the middle color of the secondary spectrum, widening equally
at F and B, and expanding into a sort of brush at the violet end.
Conversely, when moved outside focus until the width is reduced to a
narrow line at F and B, the widening toward the yellow and green shows
very clearly the nature and extent of the secondary spectrum. In this
way too, the actual foci for the several colors can easily be measured.

The exact nature of the color correction is somewhat a matter of taste
and of the uses for which the telescope is designed, but most observers
agree in the desirability of the B-F correction commonly used as best
balancing the errors of eye and ocular. With reflectors, achromatic or
even over-corrected oculars are desirable. The phenomena in testing a
telescope for color vary with the class of star observed—the solar type
is a good average. Trying a telescope on α Lyræ emphasizes unduly
the blue phases, while α Orionis would overdo the red.

The simple tests on star discs in and out of focus here described are
ample for all ordinary purposes, and a glass which passes them well is
beyond question an admirably figured one. The tests are not however
quantitative, and it takes an experienced eye to pick out quickly minor
errors, which are somewhat irregular. One sometimes finds the ring
system excellent but a sort of haze in the field, making the contrasts
poor—bad polish or dirt, but figure good.

A test found very useful by constructors or those with laboratory
facilities is the knife edge test, worked out chiefly by Foucault and
widely used in examining specula. It consists in principle of setting
up the mirror so as to bring the rays to the sharpest possible focus.
For instance in a spherical mirror a lamp shining through a pin hole is
placed in the centre of curvature, and the reflected image is brought
just alongside it where it can be inspected by eye or eyepiece. In
Fig. 165 all the rays which emanate from the pinhole _b_ and fall on
the mirror a are brought quite exactly to focus at _c_. The eye placed
close to _c_ will see, if the mirror surface is perfect, a uniform disc
of light from the mirror.

[Illustration: FIG. 165.—The Principle of the Foucault Test.]

If now a knife edge like _d_, say a safety razor blade, be very
gradually pushed through the focus the light will be cut off in a
perfectly uniform manner—no zone or local spot going first. If some
error in the surface at any point causes the reflected ray to miss the
focus and cross ahead of or behind it as in the ray _bef_, then the
knife edge will catch it first or last as the case may be, and the spot
_e_ will be first darkened or remain bright after the light elsewhere
is extinguished.

[Illustration: FIG. 166.—Foucault Test of Parabolic Mirror.]

One may thus explore the surface piecemeal and detect not only zones
but slight variations in the same zone with great precision. In case of
a parabolic mirror as in Fig. 166 the test is made at the focus by aid
of the auxiliary plane mirror, and a diagonal as shown, the pinhole and
knife edge being arranged quite as before. A very good description of
the practical use of the knife edge test may be found in the papers of
Dr. Draper and Mr. Ritchey already cited.

It is also applied to refractors, in which case monochromatic light had
better be used, and enables the experimenter to detect even the almost
infinitesimal markings sometimes left by the polishing tool, to say
nothing of slight variations in local figure which are continually lost
in the general illumination about the field when one uses the star test
in the ordinary manner.

The set-up for the knife edge experiments should be very steady and
smooth working to secure precise results, and it therefore is not
generally used save in the technique of figuring mirrors, where it is
invaluable. With micrometer motions on the knife edge, crosswise and
longitudinally, one can make a very exact diagnosis of errors of figure
or flexure.

A still more delicate method of examining the perfection of figuring
is found in the Hartmann test. (Zeit. fur Instk., 1904, 1909). This is
essentially a photographic test, comparing the effect of the individual
zones of the objective inside and outside of focus. Not only are the
effects of the zones compared but also the effects of different parts
of the same zone, so that any lack of symmetry in performance can be at
once found and measured.

The Hartmann test is shown diagrammatically in Fig. 167. The objective
is set up for observing a natural or artificial star. Just in front
of it is placed an opaque screen perforated with holes, as shown in
section by Fig. 167, where A is the perforated screen. The diameters
of the holes are about 1/20 the diameter of the objective as the test
is generally applied, and there are usually four holes 90° apart for
each zone. And such holes are not all in one line, but are distributed
symmetrically about the screen, care being taken that each zone shall
be represented by holes separated radially and also tangentially,
corresponding to the pairs of elements in the two astigmatic image
surfaces, an arrangement which enables the astigmatism as well as
figure to be investigated.

[Illustration: FIG. 167.—The Principle of the Hartmann Test.]

The arrangement of holes actually found useful is shown in Hartmann’s
original papers, and also in a very important paper by Plaskett (Ap.
J. _25_ 195) which contains the best account in English of Hartmann’s
methods and their application. Now each hole in the screen transmits
a pencil of light through the objective at the corresponding point,
and each pencil comes to a focus and then diverges, the foci being
distributed somewhere in the vicinity of what one may regard as the
principal focus, _B_. For instance in Fig. 167 are shown five pairs
of apertures _a_, _a′_, _b_, _b′_, etc., in five different zones.
Now if a photographic plate be exposed a few inches inside focus as
at C each pencil from an aperture in the screen will be represented
by a dot on the photograph, at such distance from the axis and from
the corresponding dot on the other side of the axis as the respective
inclinations of the pencils of light may determine.

Similarly a plate exposed at approximately equal distance on the other
side of the general focus, as at _D_, will show a pattern of dots due
to the distribution of the several rays at a point beyond focus. Now
if all the pencils from the several apertures met at a common focus in
_B_, the two patterns on the plates _C_ and _D_ would be exactly alike
and for equal distance away from focus of exactly the same size. In
general the patterns will not exactly correspond, and the differences
measured with the micrometer show just how much any ray in question has
departed from meeting at an exact common focus with its fellows.

For instance in the cut it will be observed that the rays _e_ and _a′_
focus barely beyond _C_ and by the time they reach _D_ are well spread
apart. The relative distance of the dots upon these corresponding
plates, with the distance between the plates, shows exactly at what
point between _C_ and _D_ these particular rays actually did cross and
come to a focus.

Determining this is merely a matter of measuring up similar triangles,
for the path of the rays is straight. Similarly inspection will show
that the rays _d_ and _d′_ meet a little short of _B_, and measurement
of their respective records on the plates _C_ and _D_ would show the
existence of a zone intermediate in focus between the focus of _e,e′_
and the general focus at _B_. The exact departure of this zone from
correct focus can therefore be at once measured.

A little further examination discloses the fact that the outer zone
represented by the rays _a,b_, and _a′,b′_ has not quite the same focus
at the two extremities of the same diameter of the objective. In other
words the lens is a little bit flatter at one end of this diameter
than it is at the other, so that the rays here have considerably
longer focus than they should, a fault by no means unknown although
fortunately not very common.

It will be seen that the variations between the two screen patterns on
_C_ and _D_, together with the difference between them, give accurately
the performance of each point of the objective represented by an
aperture in the screen. And similar investigations by substantially
the same method may be extended to the astigmatic variations, to the
general color correction, and to the difference in the aberrations for
the several colors. The original papers cited should be consulted for
the details of applying this very precise and interesting test.

It gives an invaluable record of the detailed corrections of an
objective, and while it is one with which the ordinary observer has
little concern there are times when nothing else can give with equal
precision the necessary record of performance. There are divers other
tests used for one purpose or another in examining objectives and
mirrors, but those here described are ample for nearly all practical
purposes, and indeed the first two commonly disclose all that it is
necessary to know.

Now and then one has to deal with an objective which is unmitigatedly
dirty. It can be given a casual preliminary cleaning in the way already
mentioned, but sometimes even this will not leave it in condition for
testing. Then one must get down to the bottom of things and make a
thorough job of it.

The chief point to remember in undertaking this is that the thing which
one is cleaning is glass, and very easy to scratch if one rubs dust
into it, but quite easy to clean if one is careful. The second thing to
be remembered is that once cleaned it must be replaced as it was before
and not in some other manner.

The possessor of a dirty objective is generally advised to take it
to the maker or some reliable optician. If the maker is handy, or an
optician of large experience in dealing with telescope objectives is
available, the advice is good, but there is no difficulty whatever in
cleaning an objective with the exercise of that ordinary care which the
user of a telescope may be reasonably expected to possess.

It is a fussy job, but not difficult, and the best advice as to how to
clean a telescope objective is to “tub” it, literally, if beyond the
stage where the superficial wiping described is sufficient.

To go about the task one first sets down the objective in its cell on
a horizontal surface and removes the screws that hold in the retaining
ring, or unscrews the ring itself as the case may be. This leaves the
cell and objective with the latter uppermost and free to be taken
out. Prepare on a table a pad of anything soft, a little smaller than
the objective, topping the pad with soft and clean old cloth; then,
raising up the cell at an edge, slip the two thumbs under it and lay
the fingers lightly on the outer lens of the objective, then invert the
whole affair upon the pad and lift off the cell, leaving the objective
on its soft bed.

Before anything else is done the edge of the objective should be marked
with a hard lead pencil on the edge of both the component lenses,
making two well defined v’s with their points touching. Also, if, as
usual, there are three small separators between the edges of the flint
and crown lenses, mark the position of each of these 1, 2, 3, with the
same pencil.

Forming another convenient pad of something soft, lift off the upper
lens, take out the three separators and lay them in order on a sheet of
paper without turning them upside down. Mark alongside each, the serial
number denoting its position. Then when these spacers, if in good
condition, are put back, they will go back in the same place rightside
up, and the objective itself will go back into place unchanged.

Now have at hand a wooden or fibre tub or basin which has been
thoroughly washed out with soap and water and wiped dry. Half fill it
with water slightly lukewarm and with a good mild toilet soap, shaving
soap for example, with clean hands and very soft clean cloth, go at
one of the lenses and give it a thorough washing. After this it should
be rinsed very thoroughly and wiped dry. As to material for wiping,
the main thing is that it must be soft and free from dust that will
scratch. Old handkerchiefs serve a good turn.

Dr. Brashear years ago in describing this process recommended cheese
cloth. The present day material that goes under this name is far from
being as soft at the start as it ought to be, and only the best quality
of it should be used, and then only after very thorough soaking,
rinsing and drying. The very soft towels used for cleaning cut glass,
if washed thoroughly clean and kept free from dust, answer perfectly
well. The cheese cloth has the advantage of being comparatively cheap
so that it can be thrown away after use. Whatever the cloth, it should
be kept, after thorough washing and drying, in a closed jar.

Rinsing the lens thoroughly and wiping it clean and dry is the main
second stage of cleansing. It sometimes will be found to be badly
spotted in a way which this washing will not remove. Sometimes the
spotting will yield to alcohol carefully rubbed on with soft absorbent
cotton or a bunch of lens paper.

If alcohol fails the condition of the surface is such as to justify
trying more strenuous means. Nitric acid of moderate strength rubbed on
with a swab of absorbent cotton will sometimes clear up the spotting.
If this treatment be used it should be followed up with a 10 per cent
solution of pure caustic potash or moderately strong c.p. ammonia and
then by very thorough rinsing. Glass will stand without risk cautious
application of both acid and alkali, but the former better than the
latter.

Then a final rinsing and drying is in order. Many operators use a final
washing with alcohol of at least 90 per cent strength which is allowed
to evaporate with little or no wiping. Alcohol denatured with methyl
alcohol serves well if strong enough but beware denatured alcohol of
unknown composition. Others have used petroleum naphtha and things of
that sort. At the present time these commercial petroleum products are
extremely uncertain in quality, like gasoline, being obtained, Heaven
knows how, from the breaking down of heavier petroleum products.

If pure petroleum ether can be obtained it answers quite as well as
alcohol, but unless the volatile fluid is pure it may leave streaks.
Ordinarily neither has to be used, as after the proper wiping the glass
comes perfectly clean. This done the glass can be replaced on the pad
whence it came and its mate put through the same process.

Flint glass is more liable to spot than the crown, but the crown is
by no means immune against the deterioration of the surface, perhaps
incipient devitrification, and during the war many objectives “went
blind” from unexplained action of this character. As a rule the soap
and water treatment applied with care leaves even a pretty hard looking
specimen of objective in fairly good condition except for the scratches
which previous users have put upon it.

Then if the spacing pieces, usually of tinfoil, are not torn or
corroded they can be put back into place, the one lens superimposed
upon the other, and the pair put back into the cell by dropping it
gently over them and re-inverting the whole, taking care this time to
have soft cloth or lens paper under the fingers. Then the retaining
ring can be put into place again and the objective is ready for testing
or use as the case may be.

If the spacers are corroded or damaged it may be necessary to replace
them with very thin tinfoil cut the same size and shape, leaving
however a little extra length to turn down over the edge of the lower
lens. They are fastened in place on the extreme edge only by the merest
touch of mucilage, shellac or Canada balsam, whichever comes to hand.
The one important thing is that the spacers should be entirely free of
the sticky material where they lap over the edge of the lens to perform
the separation. This lap is generally not over 1/16 of an inch, not
enough to show at the outside of the objective when it is in its cell.
When the upper lens is lightly pressed down into place, after the gum
or shellac is dry, all the projecting portion can be trimmed away with
a sharp pen-knife leaving simply the spacers in the appointed places
from which the original ones were removed.

Some little space has been given to this matter of cleaning objectives,
as in many situations objectives accumulate dirt rather rapidly and it
is highly desirable for the user to learn how to perform the simple but
careful task of cleansing them.

In ordinary use, when dirt beyond the reach of mere dusting with a
camel’s hair brush has stuck itself to the exterior of an objective, a
succession of tufts of absorbent cotton or wads of lens paper at first
dampened with pure water or alcohol and then followed lightly, after
the visible dirt has been gently mopped up, by careful wiping with the
same materials, will keep the exterior surface in good condition, the
process being just that suggested in the beginning of this chapter as
the ordinary cleaning up preparatory to a thorough examination.

The main thing to be avoided in the care of a telescope, aside from
rough usage generally, is getting the objective wet and then letting
it take its chances of drying. In many climates dew is a very serious
enemy and the customary dew cap three or four diameters long, bright
on the outside and blackened within, is of very great service in
lessening the deposit of dew upon the glass. Also the dew cap keeps out
much stray light that might otherwise do mischief by brightening the
general field. In fact its function as a light-trap is very important
especially if it is materially larger in diameter than the objective
and provided with stops.

The finder should be similarly protected, otherwise it will
mysteriously go blind in the middle of an evening’s work due to a heavy
deposit of moisture on the objective. The effect is an onset of dimness
and bad definition which is altogether obnoxious.

As regards the metal parts of a telescope they should be treated like
the metal parts of any other machine, while the moving parts require
from time to time a little touch of sperm or similar oil like every
other surface where friction may occur.

The old fashioned highly polished and lacquered brass tube was
practically impossible to keep looking respectably well provided it
was really used to any considerable extent. About the most that could
be done to it was dusting when dusty, and cautiously and promptly
wiping off any condensed moisture. The more modern lacquered tubes
require very little care and if they get in really bad condition can be
relacquered without much expense or difficulty.

Wooden tubes, occasionally found in old instruments, demand the
treatment which is accorded to other highly finished wooden things,
occasional rubbing with oil or furniture polish according to the
character of the original surface. Painted tubes may occasionally
require a fresh coat, which it does not require great skill to
administer. If the surface of wooden tripods comes to be in bad shape
it needs the oil or polish which would be accorded to other well
finished wooden articles.

Mountings are usually painted or lacquered and either surface can be
renewed eventually at no great trouble. Bright parts may be lightly
touched with oil as an ordinary rust preventive.

Reflecting telescopes are considerably more troublesome to keep in
order than refractors owing to the tender nature of the silvered
surface. It may remain in good condition with fairly steady use for
several years or it may go bad in a few months or a few weeks. The
latter is not an unusual figure in telescopes used about a city where
smoke is plentiful. The main thing is to prevent the deposit of dew on
the mirror, or getting it wet in any other way, for in drying off the
drops almost invariably leave spots.

Many schemes have been proposed for the prevention of injury to the
mirror surface. A close fitting metal cover, employed whenever the
mirror is not in use, has given good results in many places. Where
conditions are extreme this is sometimes lined with a layer of dry
absorbent cotton coming fairly down upon the mirror surface, and if
this muffler is dry, clean, and a little warmer than the mirror when
put on, it seems to be fairly effective. Preferably the mirror should
be kept, when not in use, at a little higher temperature than the
surrounding air so that dew will not tend to deposit upon it.

As to actual protective measures the only thing that seems to be
really efficient is a very thin coating of lacquer, first tried by
Perot at the Paris Observatory. The author some ten years since took
up the problem in protecting some laboratory mirrors against fumes
and moisture and found that the highest grade of white lacquer, such
as is used for the coating of fine silverware in the trade, answered
admirably if diluted with six or eight volumes of the thinner sold
with such commercial lacquers. It is best to thin the lacquer to the
requisite amount and then filter.

If now a liberal amount of the mixture is poured upon the mirror
surface after careful dusting, swished quickly around, and the mirror
is then immediately turned up on edge to drain and dry, a very thin
layer of lacquer will be left upon it, only a fraction of a wave length
thick, so that it shows broad areas of interference colors.

Treated in this way and kept dry the coating will protect the
brilliancy of the silver for a good many months even under rather
unfavorable circumstances. After trying out the scheme rather
thoroughly the treatment was applied to the 24 inch reflector of the
Harvard Observatory and has been in use ever since. The author applied
the first coating in the spring of 1913, and since that time it has
only been necessary to resilver perhaps once in six months as against
about as many weeks previously.

The lacquer used in this case was the so-called “Lastina” lacquer made
by the Egyptian Lacquer Company of New York, but there are doubtless
others of similar grade in the market. It is a collodion lacquer and
in recent years it has proved desirable to use as a thinner straight
commercial amylacetate rather than the thinner usually provided with
the lacquer, perhaps owing to the fact that difficulty of obtaining
materials during the war may have caused, as in so many other cases,
substitutions which, while perfectly good for the original purpose did
not answer so well under the extreme conditions required in preserving
telescope mirrors.

The lacquer coating when thinned to the extent here recommended does
not apparently in any way deteriorate the definition as some years of
regular work at Harvard have shown. Some experimenters have, however,
found difficulty, quite certainly owing to using too thick a lacquer.
The endurance of a lacquer coating where the mirror is kept free from
moisture, and its power to hold the original brilliancy of the surface
is very extraordinary.

The writer took out and tested one laboratory mirror coated seven years
before, and kept in a dry place, and found the reflecting power still
a little above .70, despite the fact that the coating was so dry as
to be almost powdery when touched with a tuft of cotton. At the start
the mirror had seen some little use unprotected and its reflection
coefficient was probably around .80. If the silver coating is thick
as it can be conveniently made, on a well coated mirror, the coat of
lacquer, when tarnish has begun, can be washed off with amylacetate and
tufts of cotton until the surface is practically clear of it, and the
silver itself repolished by the ordinary method and relacquered.

There are many silvering processes in use and which one should be
chosen for re-silvering a mirror, big or little, is quite largely a
matter of individual taste, and more particularly experience. The two
most used in this country are those of Dr. Brashear and Mr. Lundin,
head of the Alvan Clark Corporation, and both have been thoroughly
tried out by these experienced makers of big mirrors.

The two processes differ in several important particulars but both
seem to work very successfully. The fundamental thing in using either
of them is that the glass surface to be silvered should be chemically
clean. The old silver, if a mirror is being resilvered, is removed with
strong nitric acid which is very thoroughly rinsed off after every
trace of silver has been removed. Sometimes a second treatment with
nitric acid may advantageously follow the first with more rinsing.
The acid should be followed by a 10 per cent solution of c.p. caustic
potash (some operators use c.p. ammonia as easier to clear away) rinsed
off with the utmost thoroughness.

On general principles the last rinsing should be with distilled water
and the glass surface should not be allowed to dry between this rinsing
and starting the silvering process, but the whole mirror should be kept
under water until the time for silvering. In Dr. Brashear’s process the
following two solutions are made up; first the reducing solution as
follows:

Rock candy, 20 parts by weight.

Strong nitric acid (spec. gr. 1.22), 1 part.

Alcohol, 20 parts.

Distilled water, 200 parts.

This improves by keeping and if this preparation has to be hurried the
acid, sugar and distilled water should be boiled together and then the
alcohol added after the solution is cooled.

Second, make up the silvering solution in three distinct portions;
first the silver solution proper as follows:

  1. 2 parts silver nitrate. 20 parts distilled water.
  Second, the alkali solution as follows:
  2. 1⅓ parts c.p. caustic potash. 20 parts distilled water.
  Third, the reserve silver solution as follows:
  3. ¼ part silver nitrate. 16 parts distilled water.

The working solution of silver is then prepared thus: Gradually add
to the silver solution No. 1 the strongest ammonia, slowly and with
constant stirring. At first the solution will turn dark brown and then
it will gradually clear up. Ammonia should be added only just to the
point necessary to clear the solution.

Then add No. 2, the alkali solution. Again the mixture will turn dark
brown and must be cautiously cleared once more with ammonia until it is
straw colored but clear of precipitate. Finally add No. 3, the reserve
solution, very cautiously with stirring until the solution grows
darker and begins to show traces of suspended matter which will not
stir out. Then filter the whole through absorbent cotton to free it of
precipitate and it is ready for use. One is then ready for the actual
silvering.

Now there are two ways of working the process, with the mirror face
up, or face down. The former is advantageous in allowing better
inspection of the surface as it forms, and also it permits the mirror
of a telescope to be silvered without removing it from the cell, as was
in fact done habitually in case of the big reflector of the Alleghany
Observatory where the conditions were such as to demand re-silvering
once a month. The solution was kept in motion during the process by
rocking the telescope as a whole.

When silvering face up the mirror is made to form the bottom of the
silvering vessel, being fitted with a wrapping of strong paraffined
or waxed paper or cloth, wound several times around the rim of the
mirror and carried up perhaps half the thickness of the mirror to
form a retainer for the silvering solution. This band is firmly tied
around the edge of the mirror making a water tight joint. Ritchey uses
a copper band fitted to the edge of the mirror and drawn tight by
screws, and finishes making tight with paraffin and a warm iron.

In silvering face down the mirror is suspended a little distance above
the bottom of a shallow dish, preferably of earthen ware, containing
the solution. Various means are used for supporting it. Thus cleats
across the back cemented on with hard optician’s pitch answer well for
small mirrors, and sometimes special provision is made for holding the
mirror by the extreme edge in clamps.

Silvering face down is in some respects less convenient but does free
the operator from the very serious trouble of the heavy sediment which
is deposited from the rather strong silver solution. This is the
essential difficulty of the Brashear process in silvering face up. The
trouble may be remedied by very gentle swabbing of the surface under
the liquid with absorbent cotton, from the time when the silver coating
begins fairly to form until it is completed.

The Brashear process is most successfully worked at a temperature
between 65° and 70° F. and some experience is required to determine the
exact proportion of the reducing solution to be added to the silvering
solution. Ritchey advises such quantity of the reducing solution as
contains of sugar one-half the total weight of the silver nitrate used.
The total amount of solution after mixing should cover the mirror about
an inch deep. Too much increases the trouble from sediment and fails to
give a clean coating. The requisite quantity of reducing solution is
poured into the silvering solution and then immediately, if the mirror
is face up, fairly upon it, without draining it of the water under
which it has been standing.

If silvering face down the face will have been immersed in a thin
layer of distilled water and the mixed solutions are poured into the
dish. In either case the solution is rocked and kept moving pretty
thoroughly until the process is completed which will take about five
minutes. If silvering is continued too long there is likelihood of an
inferior whitish outer surface which will not polish well, but short of
this point the thicker the coat the better, since a thick coat stands
reburnishing where a thin one does not and moreover the thin one may be
thin enough to transmit some valuable light.

When the silvering is done the solution should be rapidly poured off,
the edging removed or the mirror lifted out of the solution, rinsed
off first with tap water and then with distilled, and swabbed gently
to clear the remaining sediment. Then the mirror can be set up on edge
to dry. A final flowing with alcohol and the use of a fan hastens the
process.

In Lundin’s method the initial cleaning process is the same but after
the nitric acid has been thoroughly rinsed off the surface is gently
but thoroughly rubbed with a saturated solution of tin chloride,
applied with a wad of absorbent cotton. After the careful rubbing the
tin chloride solution must be washed off with the utmost thoroughness,
preferably with moderately warm water. It is just as important to get
off the tin chloride completely, as it is to clean completely the
mirror surface by its use. Otherwise streaks may be left where the
silvering will not take well.

When the job has been properly done one can wet the whole surface with
a film of water and it will stay wet even when the surface is slightly
tilted. As in the Brashear process the mirror must be kept covered with
water. Mr. Lundin always silvers large mirrors face up, and forms the
dish by wrapping around the edge of the mirror a strip of bandage cloth
soaked in melted beeswax and smoothed off by pulling it while still hot
between metal rods to secure even distribution of the wax so as to make
a water tight joint. This rim of cloth is tied firmly around the edge
of the mirror and the strings then wet to draw them still tighter.

Meanwhile the water should cover the mirror by ¾ of an inch or more.
It is to be noted that in the Lundin process ordinary water is usually
found just as efficient as distilled water, but it is hardly safe to
assume that such is the case, without trying it out on a sample of
glass.

There are then prepared two solutions, a silver solution,

2.16 parts silver nitrate (see King, Pop. Ast =30=, 93)

100 parts water.

and a reducing solution,

4 parts Merck’s formaldehyde

20 parts water.

This latter quantity is used for each 100 parts of the above silver
solution, and the whole quantity made up is determined by the amount of
liquid necessary to cover the mirror as just described.

The silver solution is cautiously and completely cleared up by strong
ammonia as in the Brashear process. The silver and reducing solutions
are then mixed, the water covering the mirror poured quickly off, and
the silvering solution immediately poured on. The mirror should then be
gently rocked and the silver coating carefully watched as it forms.

As the operation is completed somewhat coarse black grains of sediment
will form and when these begin to be in evidence the solution should
be poured off, the mirror rinsed in running water, the edging removed
while the mirror is still rinsing and finally the sediment very gently
swabbed off with wet absorbent cotton. Then the mirror can be set up to
dry.

The Lundin process uses a considerably weaker silver solution than the
Brashear process, is a good deal more cleanly while in action, and
is by experienced workers said to perform best at a materially lower
temperature than the Brashear process, with the mirror, however, always
slightly warmer than the solution. Some workers have had good results
by omitting the tin chloride solution and cleaning up the surface
by the more ordinary methods. In the Lundin process the solution is
sufficiently clear for the density acquired by the silver coating to be
roughly judged by holding an incandescent lamp under the mirror. A good
coating should show at most only the faintest possible outline of the
filament, even of a gas filled lamp.

Whichever process of silvering is employed, and both work well, the
final burnishing of the mirror after it is thoroughly dry is performed
in the same way, starting by tying up a very soft ball of absorbent
cotton in the softest of chamois skin.

This burnisher is used at first without any addition, simply to smooth
and condense the film by going over it with quick, short, and gentle
circular strokes until the entire surface has been thoroughly cleaned
and begins to show a tendency to take polish. Then a very little of the
finest optical rouge should be put on to the same, or better another,
rubber, and the mirror gone steadily over in a similar way until it
comes to a brilliant polish.

A good deal of care should be taken in performing this operation to
avoid the settling of dust upon the surface since scratches will
inevitably result. Great pains should also be taken not to take any
chance of breathing on the mirror or in any other way getting the
surface in the slightest degree damp. Otherwise it will not come to a
decent polish.

Numerous other directions for silvering will be found in the
literature, and all of them have been successfully worked at one time
or another. The fundamental basis of the whole process is less in the
particular formula used than in the most scrupulous care in cleaning
the mirror and keeping it clean until the silvering is completed. Also
a good bit of experience is required to enable one to perform the
operation so as to obtain a uniform and dense deposit.




CHAPTER X

SETTING UP AND HOUSING THE TELESCOPE


In regard to getting a telescope into action and giving it suitable
protection, two entirely different situations present themselves. The
first relates to portable instruments or those on temporary mounts,
the second to instruments of position. As respects the two, the
former ordinarily implies general use for observational purposes, the
latter at least the possibility of measurements of precision, and a
mount usually fitted with circles and with a driving clock. Portable
telescopes may have either alt-azimuth or equatorial mounting, while
those permanently set up are now quite universally equatorials.

Portable telescopes are commonly small, ranging from about 2½ inches
to about 5 inches in aperture. The former is the smallest that can
fairly be considered for celestial observations. If thoroughly good and
well mounted even this is capable of real usefulness, while the five
inch telescope if built and equipped in the usual way, is quite the
heaviest that can be rated as portable, and deserves a fixed mount.

Setting up an alt-azimuth is the simplest possible matter. If on a
regular tripod it is merely taken out and the tripod roughly levelled
so that the axis in azimuth is approximately vertical. Now and then one
sets it deliberately askew so that it may be possible to pass quickly
between two objects at somewhat different altitudes by swinging on the
azimuth axis.

If one is dealing with a table tripod like Fig. 69 it should merely be
set on any level and solid support that may be at hand, the main thing
being to get it placed so that one may look through it conveniently.
This is a grave problem in the case of all small refractors, which
present their oculars in every sort of unreachable and uncomfortable
position.

Of course a diagonal eyepiece promises a way out of the difficulty,
but with small apertures one hesitates to lose the light, and often
something of definition, and the observer must pretty nearly stand
on his head to use the finder. With well adjusted circles, such
are commonly found on a fixed mount, location of objects is easy.
On a portable set-up perhaps the easiest remedy is a pair of well
aligned coarse sights near the objective end of the tube and therefore
within reach when it is pointed zenith-ward. The writer has found a
low, armless, cheap splint rocker, such as is sold for piazza use,
invaluable under these painful circumstances, and can cordially
recommend it.

Even better is an observing box and a flat cushion. The box is merely a
coverless affair of any smooth ⅞ inch stuff firmly nailed or screwed
together, and of three unequal dimensions, giving three available
heights on which to sit or stand. The dimensions originally suggested
by Chambers (_Handbook of Astronomy_, II, 215) were 21 × 12 × 15
inches, but the writer finds 18 × 10 × 14 inches a better combination.

The fact is that the ordinary stock telescope tripod is rather too high
for sitting, and too low for standing, comfortably. A somewhat stubby
tripod is advantageous both in point of steadiness and in accessibility
of the eyepiece when one is observing within 30° of the zenith, where
the seeing is at its best; and a sitting position gives a much greater
range of convenient upward vision than a standing one.

When an equatorial mount is in use one faces the question of adjustment
in its broadest aspect. Again two totally different situations arise in
using the telescope. First is the ordinary course of visual observation
for all general purposes, in which no precise measurements of position
or dimensions are involved.

Here exact following is not necessary, a clock drive is convenient
rather than at all indispensable, and even circles one may get along
without at the cost of a little time. Such is the usual situation with
portable equatorials. One does not then need to adjust them to the
pole with extreme precision, but merely well enough to insure easy
following; otherwise one is hardly better off than with an alt-azimuth.

In a totally different class falls the instrument with which one
undertakes regular micrometric work, or enters upon an extended
spectroscopic program or the use of precise photometric apparatus, to
say nothing of photography. In such cases a permanent mount is almost
imperative, the adjustments must be made with all the exactitude
practicable, one finds great need of circles, and the lack of a clock
drive is a serious handicap or worse.

Moreover in this latter case one usually has, and needs, some sort of
timepiece regulated to sidereal time, without which a right ascension
circle is of very little use.

In broad terms, then, one has to deal, first; with a telescope on a
portable mount, with or without position circles, generally lacking
both sidereal clock and driving clock, and located where convenience
dictates; second, with a telescope on a fixed mount in a permanent
location, commonly with circles and clock, and with some sort of
permanent housing.

Let us suppose then that one is equipped with a 5 inch instrument like
Fig. 168, having either the tripod mount, or the fixed pillar mount
shown alongside it; how shall it be set up, and, if on the fixed mount,
how sheltered?

In getting an equatorial into action the fundamental thing is to place
the optical axis of the telescope exactly parallel to the polar axis
of the mount and to point the latter as nearly as possible at the
celestial pole.

The conventional adjustments of an equatorial telescope are as follows:

1. Adjust polar axis to altitude of pole.

2. Adjust index of declination circle.

3. Adjust polar axis to the meridian.

4. Adjust optical axis perpendicular to declination axis.

5. Adjust declination axis perpendicular to polar axis.

6. Adjust index of right ascension circle, and

7. Adjust optical axis of finder parallel to that of telescope.

Now let us take the simplest and commonest case, the adjustment of
a portable equatorial on a tripod mount, when the instrument has a
finder but neither circles nor driving clock. Adjustments 2 and 6
automatically drop out of sight, 5 vanishes for lack of any means to
make the adjustment, and on a mount made with high precision, like the
one before us, 4 is negligible for any purpose to which our instrument
is applicable.

Adjustments 1, 3 and 7 are left and these should be performed in the
order 7, 1, 3, for sake of simplicity. To begin with the finder has
cross-wires in the focus of its eyepiece, and the next step is to
provide the telescope itself with similar cross-wires.

These can readily be made, if not provided, by cutting out a disc of
cardboard to fit snugly either the spring collar just in front of
a positive eyepiece or the eyepiece itself at the diaphragm, if an
ordinary Huygenian. Rule two diametral lines on the circle struck for
cutting the cardboard, crossing at the center, cut out the central
aperture, and then very carefully stretch over it, guided by the
diametral lines, two very fine threads or wires made fast with wax or
shellac.

[Illustration: FIG. 168.—Clark 5-inch with Tripod and Pier.]

Now pointing the telescope at the most distant well defined object in
view, rotate the spring collar or ocular, when, if the crossing of the
threads is central, their intersection should stay on the object. If
not shift a thread cautiously until the error is corrected.

Keeping the intersection set on the object by clamping the tube, one
turns attention to the finder. Either the whole tube is adjustable
in its supports or the cross-wires are capable of adjustment by
screws just in front of the eyepiece. In either case finder tube or
cross-wires should be shifted until the latter bear squarely upon the
object which is in line with the cross threads of the main telescope.
Then the adjusting screws should be tightened, and the finder is in
correct alignment.

As to adjustments 1 and 3, in default of circles the ordinary
astronomical methods are not available, but a pretty close
approximation can be made by levelling. A good machinist’s level is
quite sensitive and reliable. The writer has one picked out of stock at
a hardware shop that is plainly sensitive to 2′ of arc, although the
whole affair is but four inches long.

Most mounts like the one of Fig. 168 have a mark ruled on the support
of the polar axis and a latitude scale on one of the cheek pieces.
Adjustment of the polar axis to the correct altitude is then made by
placing the level on the declination axis, or any other convenient
place, bringing it to a level, and then adjusting the tripod until the
equatorial head can be revolved without disturbing this level. Then
set the polar axis to the correct latitude and adjustment number 1 is
complete for the purpose in hand.

Lacking a latitude scale, it is good judgment to mark out the latitude
by the help of the level and a paper protractor. To do this level the
polar axis to the horizontal, level the telescope tube also, and clamp
it in declination to maintain it parallel. Then fix the protractor to
a bit of wood tied or screwed to the telescope support, drop a thin
thread plumb line from a pin driven into the wood, the declination axis
being still clamped, note the protractor reading, and then raise the
polar axis by the amount of the latitude.

Next, with a knife blade scratch a conspicuous reference line on the
sleeve of the polar axis and its support so that when the equatorial
head is again levelled carefully you can set approximately to the
latitude at once.

Now comes adjustment 3, the alignment of the polar axis to the
meridian. One can get it approximately by setting the telescope tube
roughly parallel with the polar axis and, sighting along it, shifting
the equatorial head in azimuth until the tube points to the pole star.
Then several methods of bettering the adjustment are available.

At the present date Polaris is quite nearly 1° 07′ from the true pole
and describes a circle of that radius about it every 24 hours. To get
the correct place of the pole with reference to Polaris one must have
at least an approximate knowledge of the place of that star in its
little orbit, technically its hour-angle. With a little knowledge of
the stars this can be told off in the skies almost as easily as one
reckons time on a clock. Fig. 169 is, in fact, the face of the cosmic
clock, with a huge sweeping hour hand that he who runs may read.

[Illustration: FIG. 169.—The Cosmic Clock.]

It is a clock in some respects curious; it has a twenty-four hour face
like some clocks and watches designed for Continental railway time; the
hour hand revolves backward, (“counter-clockwise”) and it stands in the
vertical not at noon, but at 1.20 Star Time. The two stars which mark
the tip and the reverse end of the hour hand are delta Cassiopeæ and
zeta Ursæ Majoris respectively. The first is the star that marks the
bend in the back of the great “chair,” the second (Mizar), the star
which is next to the end of the “dipper” handle.

One or the other is above the horizon anywhere in the northern
hemisphere. Further, the line joining these two stars passes almost
exactly through the celestial pole, and also very nearly through
Polaris, which lies between the pole and δ Cassiopeæ. Consequently if
you want to know the hour-angle of Polaris just glance at the clock and
note where on the face δ Cassiopeæ stands, between the vertical which
is XXIV o’clock, and the horizontal, which is VI (east) or XVIII (west)
o’clock.

You can readily estimate its position to the nearest half hour, and
knowing that the great hour hand is vertical (δ Cassiopeæ up) at I^h
20^m or (ζ Ursæ Majoris up) at XIII^h 20^m, you can make a fairly close
estimate of the sidereal time.

A little experience enables one to make excellent use of the clock
in locating celestial objects, and knowledge of the approximate hour
angle of Polaris thus observed can be turned to immediate use in making
adjustment 3. To this end slip into the plane of the finder cross wires
a circular stop of metal or paper having a radius of approximately 1°
15′ which means a diameter of 0.52 inch per foot of focal length.

Then, leaving the telescope clamped in declination as it was after
adjustment 1, turn it in azimuth across the pole until the pole star
enters the field which, if the finder inverts it will do on the other
side of the center; i.e. if it stands at IV to the naked eye it will
enter the field apparently from the XVI o’clock quarter. When just
comfortably inside the field, the axis of the telescope is pointing
substantially at the pole.

It is better to get Polaris in view before slipping in the stop and if
it is clearly coming in too high or too low shift the altitude of the
polar axis a trifle to correct the error. This approximate setting can
be made even with the smallest finder and on any night worth an attempt
at observation.

With a finder of an inch or more aperture a very quick and quite
accurate setting to the meridian can be made by the use of Fig. 170,
which is a chart of all stars of 8 mag. or brighter within 1° 30′ of
the pole. There are only three stars besides Polaris at all conspicuous
in this region, one quite close to Polaris, the other two forming with
it the triangle marked on the chart. These two are, to the left, a
star of magnitude 6.4 designated B. D. 88 112, and to the right one of
magnitude 7.0, B. D. 89 13.

The position of the pole for the rest of the century is marked on the
vertical arrow and with the stars in the field of the finder one can
set the cross wires on the pole, the instrument remaining clamped in
declination, within a very few minutes of arc, quite closely enough
for any ordinary use of a portable mount. All this could be done even
better with the telescope itself, but it is very rare to find an
eyepiece with sufficient field.

[Illustration: FIG. 170.—The Pole among the Stars.]

At all events the effect of any error likely to be made in these
adjustments is not serious for the purpose in hand, since if one makes
an error of a minute of arc in the setting the resulting displacement
of a star in the field will even in the most unfavorable case reach
this full amount only after 6 hours following. I.e. with any given
eyepiece an error of adjustment equal to the radius of the field will
still permit following a star for an hour or two before it drifts
inconveniently wide of the center.

Considerable space has been devoted to these easy approximations in
setting up, since the directions commonly given require circles and
often a clock drive.

In some cases one has to set up a portable equatorial where from
necessity for clear sky space, Polaris is not visible. The best plan
then is to set up with great care where Polaris can be seen, paying
especial attention to the levelling. Then establish two meridian marks
on stakes at a convenient distance by turning the telescope 180° on its
declination axis and sighting through it in both directions. Now with
a surveyor’s tape transfer the meridian line East or West as the case
may be until it can be used where there is clear sky room.

Few observers near a city can get good sky room, from the interference
of houses, trees or blazing street lamps, and the telescope must often
be moved from one site to another to reach different fields. In such
case it is wise to take the very first step toward giving the telescope
a local habitation by establishing a definite placement for the tripod.

To this end the three legs should be firmly linked together by chains
that will not stretch—leg directly to leg, and not to a common
junction. Then see to it that each leg has a strong and moderately
sharp metal point, and, the three points of support being thus
definitely fixed, establish the old reliable point-slot-plane bearing
as follows:

Lay out at the site (or sites) giving the desired clear view, a circle
scratched on the ground of such size that the three legs of your tripod
may rest approximately on its periphery. Then lay out on the circle
three points 120° apart. At each point sink a short post 12 to 18
inches long and of any convenient diameter, well tarred, and firmly set
with the top levelled off quite closely horizontal.

To the top of each bolt a square or round of brass or iron about half
an inch thick. The whole arrangement is indicated in diagram in Fig.
171. In _a_ sink a conical depression such as is made by drilling
nearly through with a 1 inch twist drill. The angle here should be a
little broader than the point on the tripod leg. In _b_ have planed a V
shaped groove of equally broad angle set with its axis pointing to the
conical hole in _a_. Leave the surface of _c_ a horizontal plane.

Now if you set a tripod leg in _a_, another in the slot at _b_ and
the third on _c_, the tripod will come in every instance to the same
level and orientation. So, if you set up your equatorial carefully in
the first place and leave the head clamped in azimuth, you can take it
in and replace it at any time still in adjustment as exact as at the
start. And if it is necessary to shift from one location to another you
can do it without delay still holding accurate adjustment of the polar
axis to the pole, and avoiding the need of readjustment.

In case the instrument has a declination circle the original set-up
becomes even simpler. One has only to level the tripod, either with
or without the equatorial head in place, and then to set the polar
axis either vertical or horizontal, levelling the tube with it either
by placing the level across the objective cell perpendicular to the
declination axis, or laying it along the tube when horizontal.

[Illustration: FIG. 171.—A Permanent Foothold for the Tripod.]

Then, reading the declination circle, one can set off the co-atitude
or latitude as the case may be and, leaving the telescope clamped in
declination, lower or raise the polar axis until the tube levels to
the horizontal. When the mount does not permit wide adjustment and has
no latitude scale one is driven to laying out a latitude templet and,
placing a straight edge under the equatorial head, or suspending a
plumb line from the axis itself, setting it mechanically to latitude.

Now suppose we are dealing with the same instrument, but are planning
to plant it permanently in position on its pillar mount. It is now
worth while to make the adjustments quite exactly, and to spend some
time about it. The pillar is commonly assembled by well set bolts on a
brick or concrete pier. The preliminary steps are as already described.

The pillar is levelled across the top, the equatorial head, which turns
upon it in azimuth, is levelled as before, the adjustment being made
by metal wedges under the pillar or by levelling screws in the mount
if there are any. Then the latitude is set off by the scale, or by
the declination circle, and the polar axis turned to the approximate
meridian as already described.

There is likely to be an outstanding error of a few minutes of arc
which should in a permanent mount be reduced as far as practicable. At
the start adjust the declination of the optical axis of the telescope
to that of the polar axis. This is done in the manner suggested by Fig.
172.

Here _p_ is the polar axis and _d_ the declination axis. Now if one
sights, using the cross wires, through the telescope a star near the
meridian, i.e., one that is changing in declination quite slowly,
starting from the position _A_ with the telescope _E_. of the polar
axes, and turns it over 180° into the position _B_, _W_. of the polar
axis, the prolongation of the line of sight, _b_, will fall below _a_,
when as here the telescope points too high in the _A_ position.

[Illustration: FIG. 172.—Aligning the Optical Axis.]

In other words the apparent altitude of the star will change by twice
the angle between _A_ and _p_. Read both altitudes on the declination
circle and split the difference with the slow motion as precisely as
the graduation of the declination circle permits.

The telescope will probably not now point exactly at the star, but as
the tube is swung from the _A_ to the _B_ position and back the visible
stars will describe arcs of circles which should be nearly concentric
with the field as defined by the stop in the eyepiece. If not, a very
slight touch on the declination slow motion one way or the other will
make them do so to a sufficient exactness, especially if a rather high
power eyepiece is used.

The optical axis of the telescope is now parallel to the polar axis,
but the latter may be slightly out of position in spite of the
preliminary adjustment. Now reverting to the polar field of Fig. 170,
swing from position _A_ to _B_ and back again, correcting any remaining
eccentricity of the star arcs around the pole by cautious shifting
of the polar axis, leaving the telescope clamped in declination. The
first centering is around the pole of the instrument, the second around
the celestial pole by help of a half dozen small stars within a half
degree on both sides of it, magnitudes 9 and 10, easily visible in a 3”
or 4” telescope, using the larger field of the finder for the coarse
adjustment.

If the divided circles read to single minutes or closer, which they
generally do not on instruments of moderate size, one can use the
readings to set the polar axis and the declination circle, and to make
the other adjustments as well.

In default of this help, the declination circle adjustment may be set
to read 90° when the optical axis is brought parallel to the polar
axis, and after the adjustment of the latter is complete, the R. A.
circle can be set by swinging up the telescope in the meridian and
watching for the transit of any star of known R. A. over the central
cross wire, at which moment the circle should be clamped to the R. A.
thus defined.

Two possible adjustments are left, the perpendicularity of the polar
and declination axes, and that of the optical axis to the declination
axis. As a rule there is no provision for either of these, which are
supposed to have been carried out by the maker. The latter adjustment
if of any moment will disclose itself as a lateral wobble in trying
to complete the adjustment of optical axis to polar axis. It can be
remedied by a liner of tinfoil or even paper under one end of the
tube’s bearing on its cradle. Adjustment of the former is strictly a
job for the maker.

For details of the rigorous adjustments on the larger instruments the
reader will do well to consult Loomis’ _Practical Astronomy_ page 28
and following.[31] The adjustments here considered are those which can
be effectively made without driving clock, finely divided circles,
or exact knowledge of sidereal time. The first and last of these
auxiliaries, however, properly belong with an instrument as large as
Fig. 168, on a fixed mount.

 [31] See also two valuable papers by Sir Howard Grubb, _The
 Observatory_, Vol. VII, pp. 9, 43. Also in Jour. Roy. Ast. Soc.
 Canada, Dec., 1921, Jan. 1922.

There are several rather elegant methods of adjusting the polar axis
to the pole which depend on the use of special graticules in the
eyepiece, or on auxiliary devices applied to the telescope, the general
principle being automatically to provide for setting off the distance
between Polaris and the pole at the proper hour angle. A beautifully
simple one is that of Gerrish (_Pop. Ast._ =29=, 283).

The simple plan here outlined will generally, however, prove sufficient
for ordinary purposes and where high precision is necessary one has to
turn to the more conventional astronomical methods.

If one gives his telescope a permanent footing such as is shown in Fig.
171 adjustment has rarely to be repeated. With a pillar mount such as
we have just now been considering the instrument itself can be taken in
doors and replaced with very slight risk of disturbing its setting, but
some provision must be made for sheltering the mount.

A tarpaulin is sometimes recommended and indeed answers well,
particularly if a bag of rubber sheeting is drawn loosely over the
mount first. Better still is a box cover of copper or galvanized iron
set over the mount and closely fitting well down over a base clamped to
the pillar with a gasket to close the joint.

But the fact is when one is dealing with a fine instrument like Fig.
168 of as much as 5 inches aperture, the question of a permanent
housing (call it observatory if you like) at once comes up and will not
down.

It is of course always more convenient to have the telescope
permanently in place and ready for action. Some observers feel that
working conditions are better with the telescope in the open, but most
prefer a shelter from the wind, even if but partial, and the protection
of a covering, however slight, in severe weather.

In the last resort the question is mainly one of climate. Where nights,
otherwise of the best seeing quality, are generally windless or with
breezes so slight that the tube does not quiver a telescope in the
open, however protected between times, works perfectly well.

In other regions the clearest nights are apt to be those of a steady
gentle wind producing great uniformity of conditions at the expense
of occasional vibration of the instrument and of discomfort to the
observer. Hence one finds all sorts of practice, varied too, by the
inevitable question of expense.

The simplest possible housing is to provide for the fixed instrument
a moveable cover which can be lifted or slid quite out of the way
leaving the telescope in the open air, exposed to wind, but free from
the disturbing air currents that play around the opening of a dome.
Shelters of this cheap and simple sort have been long in use both for
small and large instruments.

[Illustration: FIG. 173.—The Simplest of Telescope Housings.]

For example several small astrographic instruments in the Harvard
equipment are mounted as shown in Fig. 173. Here are two fork mounts,
each on a short pier, and covered in by galvanized iron hoods made in
two parts, a vertical door which swings down, as in the camera of the
foreground, and the hood proper, hinged to the base plate and free to
swing down when the rear door is unlocked and opened. A little to the
rear is a similar astrographic camera with the hood closed. It is all
very simple, cheap, and effective for an instrument not exceeding say
two or three feet in focal length.

A very similar scheme has been successfully tried on reflectors as
shown in Fig. 174. The instrument shown is a Browning equatorial of
8½ inches aperture. The cover is arranged to open after the manner
of Fig. 173 and the plan proved very effective, preserving much greater
uniformity of conditions and hence permitting better definition than in
case of a similar instrument peering through the open shutter of a dome.

Such a contrivance gets unwieldly in case of a refractor on account of
the more considerable height of the pier and the length of the tube
itself. But a modification of it may be made to serve exceedingly well
in climates where working in the open is advantageous. A good example
is the equatorial of the Harvard Observatory station at Mandeville,
Jamaica, which has been thus housed for some twenty years, as shown in
Fig. 175.

This 11 inch refractor, used mainly on planetary detail, is located
alongside the polar telescope of 12 inches aperture and 135 feet 4
inches focal length used for making a photographic atlas of the moon
and on other special problems. The housing, just big enough to take in
the equatorial with the tube turned low, opens on the south side and
then can be rolled northward on its track, into the position shown,
where it is well clear of the instrument, which is then ready for use.

[Illustration: FIG. 174.—Cover for Small Reflector.]

The climate of Jamaica, albeit extremely damp, affords remarkably
good seeing during a large part of the year, and permits use of the
telescope quite in the open without inconvenience to the observer. The
success of this and all similar housing plans depends on the local
climate more than on anything else—chiefly on wind during the hours
of good seeing. An instrument quite uncovered suffers from gusts far
more than one housed under a dome, which is really the sum of the whole
matter, save that a dome to a slight extent does shelter the observer
in extremely cold weather.

Even very large reflectors can be housed in similar fashion if suitably
mounted. For example in Fig. 176 is shown the 36 inch aperture
reflector of the late Dr. Common, which was fitted with an open fork
equatorial mounting. Here the telescope itself, with its short pier and
forked polar axis, is shown in dotted lines.

[Illustration: FIG. 175.—Sliding Housing for 11-inch Refractor.]

Built about it is a combined housing and observing stand rotatable on
wheels _T_ about a circular track _R_. The housing consists of low
corrugated metal sides and ends, here shown partly broken away, of
dimensions just comfortably sufficient to take in the telescope when
the housing is rotated to the north and south position, and the tube
turned down nearly flat southward. A well braced track _WW_ extends
back along the top of the side housing and well to the rear. On this
track rolls the roof of the housing _X,X,X_, with a shelter door at the
front end.

[Illustration: FIG. 176.—Sliding Housing for a Big Reflector.]

The members _U_ constitute a framing which supports at once the housing
and the observing platform, to which access is had by a ladder, _Z_,
provided with a counterbalanced observing seat. The instrument is
put into action by clearing the door at the end of the roof, running
the roof back to the position shown in the dotted lines, raising the
tube, and then revolving the whole housing into whatever position is
necessary to permit the proper setting of the tube.

[Illustration: FIG. 177.—Sliding Roof Observatory.]

This arrangement worked well but was found a bit troublesome owing to
wind and weather. With a skeleton tube and in a favorable climate the
plan would succeed admirably providing an excellent shelter for a large
telescope at very low cost.

Since a fork mount allows the tube to lie flat, such an instrument, up
to say 8 or 10 inches aperture can be excellently protected by covers
fitting snugly upon a base and light enough to lift off as a whole.

The successful use of all these shelters however depends on climatic
conditions. They require circumstances allowing observation in the
open, as with tripod mounts, and afford no protection from wind or
cold. Complete protection for the observer cannot be had, except by
some of the devices shown in Chapter V, but conditions can be improved
by permanent placement in an observatory, simple or elaborate, as the
builder may wish.

The word observatory may sound formidable, but a modest one can be
provided at less expense than a garage for the humblest motor car.
The chief difference in the economic situation is that not even the
most derided car can be picked up and carried into the back hall for
shelter, and it really ought not to be left out in the weather.

The next stage of evolution is the telescope house with a sliding roof
in one or more sections—ordinarily two. In this case the building
itself is a simple square structure large enough to accommodate the
instrument with maneuvering room around it. The side walls are carried
merely high enough to give clearance to the tube when turned nearly
flat and to give head room to the observer. The roof laps with a close
joint in the middle and each half rolls on a track supported beyond the
ends of the building by an out-rigger arranged in any convenient manner.

When the telescope is in use the roof sections are displaced enough
to give an ample clear space for observing, often wide open as shown
in Fig. 177, which is the house of the 16 inch Metcalf photographic
doublet at the Harvard Observatory. This instrument is in an open fork
mount like that shown in Fig. 139.

The sliding roof type is on the whole the simplest structure that can
be regarded as an observatory in the sense of giving some shelter to
the observer as well as the instrument. It gives ample sky room for
practical purposes even to an instrument with a fork mount, since in
most localities the seeing within 30° or so of the horizon is decidedly
bad. If view nearer the horizon is needed it can readily be secured by
building up the pier a bit.

Numberless modifications of the sliding roof type will suggest
themselves on a little study. One rather interesting one is used in
the housing of the 24 inch reflector of the Harvard Observatory, 11
feet 3 inches in focal length, the same of which the drive in its
original dome is shown in Fig. 139. As now arranged the lower part
of the observatory remains while the upper works are quite similar
in principle to the housing of Dr. Common’s 3 foot reflector of Fig.
176. The cover open is shown in Fig. 178. It will be seen that on the
north side of the observatory there is an out-rigger on which the top
housing slides clear of the low revolving turret which gives access to
the ocular fitting used generally to carry the plate holder, and the
eyepiece for following when required.

The tube cannot be brought to the horizontal, but it easily commands
all the sky-space that can advantageously be used in this situation,
and the protection given the telescope when not in use is very
complete. To close the observatory the tube is brought north and south
and turned low and the sliding roof is then run back into its fixed
position. The turret is very easily turned by hand.

[Illustration: FIG. 178.—Turret Housing of the 24-inch Harvard
Reflector.]

Of course for steady work with the maximum shelter for observer
obtainable without turning to highly special types of housing, the
familiar dome is the astronomer’s main reliance. It is in the larger
sizes usually framed in steel and covered with wood, externally
sheathed in copper or steel. Sometimes in smaller domes felt covered
with rubberoid serves a good purpose, and painted canvas is now and
then used, with wooden framing.

But even the smallest dome of conventional construction is heavy
and rather expensive, and for home talent offers many difficulties,
especially with respect to the shutter and shutter opening. A
hemisphere is neither easy to frame nor to cover, and the curved
sliding shutter is especially troublesome.

[Illustration: FIG. 179.—The Original “Romsey” Observatory.]

Hence for small observatories other forms of revolving roof are
desirable, and quite the easiest and cheapest contrivance is that
embodied in the “Romsey” type of observatory, devised half a century
ago by that accomplished amateur the Rev. E. L. Berthon, vicar of
Romsey. The feature of his construction is an unsymmetrical peak in the
revolving roof which permits the ordinary shutter to be replaced by a
hinged shutter like the skylight in a roof, exposing the sky beyond the
zenith when open, and closing down over a coaming to form a water tight
joint.

Berthon’s original description of his observatory, which accommodated a
9¼ inch reflector, may be found in Vol. 14 of the _English Mechanic
and World of Science_ whence Fig. 179 is taken. In this plate Fig. 1
shows the complete elevation and Fig. 2 the ground plan, each to a
scale of a eighth of an inch to the foot. In the plan, _A,A_, are the
main joists, _P_ the pier for the telescope, T that for the transit,
and _C_ the clock. Figs. 3, 4, and 5 are of details. In the last named
_A_ is a rafter, _b_ the base ring, _c_ the plate, _d_ one of the sash
rollers carrying the roof, and _e_ a lateral guide roller holding the
roof in place.

The structure can readily be built without the transit shelter, and in
fact now-a-days most observers find it easier to pick up their time by
wireless. The main bearing ring is cut out of ordinary ⅞ inch board,
in ten or a dozen, or more, sections according to convenience, done in
duplicate, joints lapping, and put very firmly together with screws set
up hard. Sometimes 3 layers are thus used.

The roof in the original “Romsey” observatory was of painted canvas,
but rubberoid or galvanized iron lined with roofing paper answers well.
The shutter can be made single or double in width, and counterbalanced
if necessary. The framing may be of posts set in the ground as here
shown, or with sills resting on a foundation, and the walls of any
construction—matched boards of any kind, cement on wire lath, hollow
tile, or concrete blocks.

Chambers’ _Handbook of Astronomy_ Vol. II contains quite complete
details of the “Romsey” type of observatory and is easier to get at
than the original description.

A very neat adaptation of the plan is shown in Fig. 180, of which
a description may be found in _Popular Astronomy_ =28=, 183. This
observatory was about 9 feet in diameter, to house a 4 inch telescope,
and was provided with a rough concrete foundation on which was built a
circular wall 6 feet high of hollow glazed tile, well levelled on top.
To this was secured a ring plate built up in two layers, carrying two
circles of wooden strips with a couple of inches space between them for
a runway. In this ran 6 two-inch truck castors secured to a similar
ring plate on which was built up the frame of the “dome” arranged as
shown. Altogether a very neat and workmanlike affair, in this case
built largely by the owner but permitting construction at very small
expense almost anywhere. Another interesting modification of the same
general plan in the same volume just cited is shown in Fig. 181. This
is also for a 4 inch refractor and the dome proper is but 8 feet 4
inches in diameter. Like the preceding structure the foundation is of
concrete but the walls are framed in spruce and sheathed in matched
boards with a “beaver-board” lining.

[Illustration: FIG. 180.—A More Substantial “Romsey” Type.]

The ring plate is three-ply, 12 sections to the layer, and its mate on
which the dome is assembled is similarly formed, though left with the
figure of a dodecagon to match the dome. The weight is carried on four
rubber tired truck rollers, and there are lateral guide rollers on the
plan of those in Fig. 179.

The dome itself however, is wholly of galvanized iron, in 12 gores
joined with standing seams, turned, riveted, and soldered. There is a
short shutter at the zenith sliding back upon a frame, while the main
shutter is removed from the outside by handles.

[Illustration: FIG. 181.—Detail of Light Metal Dome for Small
Observatory.]

Observatories of the Romsey or allied types can be erected at very
moderate cost, varying considerably from place to place, but running
at present say from $200 to $600, and big enough to shelter refractors
of 4 to 6 inches aperture. The revolving roofs will range from 9 to 12
feet in diameter. If reflectors are in use, those of about double these
apertures can be accommodated since the reflector is ordinarily much
the shorter for equal aperture.

The sliding roof, not to say the sliding shelter, forms of housing cost
somewhat less, depending on the construction adopted. Going to brick
may double the figures quoted, but such solidity is generally quite
needless, though it is highly desirable that the cover of a valuable
instrument should be fire-proof and not easily broken open. The
stealing of objectives and accessories is not unknown, and vandalism
is a risk not to be forgotten. But to even the matter up, housing a
telescope is rather an easy thing to accomplish, and as a matter of
fact for the price of a very modest motor car one can both buy and
house an instrument big enough to be of genuine service.




CHAPTER XI

SEEING AND MAGNIFICATION


Few things are more generally disappointing than one’s first glimpse
of the Heavens through a telescope. The novice is fed up with maps of
Mars as a great disc full of intricate markings, and he generally sees
a little wriggling ball of light with no more visible detail than an
egg. It is almost impossible to believe that, at a fair opposition,
Mars under the power of even the smallest astronomical telescope really
looks as big as the full moon. Again, one looks at a double star
to see not two brilliant little discs resplendent in color, but an
indeterminate flicker void of shape and hue.

The fact is, that most of the time over most of the world seeing
conditions are bad, so that the telescope does not have a fair chance,
and on the whole the bigger the telescope the worse the chance. One
famous English astronomer, possessed of a fine refractor that would be
reckoned large even now-a-days, averred that he had seen but one first
class night in fifteen years past.

The case is really much less bad than this implies, for even in rather
unfavorable climates many a night, at some o’clock or other, will
furnish an hour or two of pretty good seeing, while now and then,
without any apparent connection with the previous state of the weather,
a night will turn up when the pictures in the popular astronomies come
true, the stars shrink to steady points set in clean cut rings, and no
available power seems too high.

One can get a good idea of the true inwardness of bad seeing by trying
to read a newspaper through an opera glass across a hot stove. If the
actual movements in the atmosphere could be made visible they would
present a strange scene of turbulence—rushing currents taking devious
courses up and around obstacles, slowly moving whirlpools, upward
slants such as gulls hug on the quarter of a liner, great downward
rushes dreaded by the aviator, and over it all incessant ripples in
every direction.

And movements of air are usually associated with changes of
temperature, as over the stove, varying the refraction and contorting
the rays that come from a distant star until the image is quite ruined.

The condition for excellence of definition is that the atmosphere
through which we see shall be homogeneous, whatever its temperature,
humidity, or general trend of movement. Irregular refraction is
the thing to be feared, particularly if the variations are sudden
and frequent. Hence the common troubles near the ground and about
buildings, especially where there are roofs and chimneys to radiate
heat—even in and about an observatory dome.

Professor W. H. Pickering, who has had a varied experience in
climatic idiosyncrasies, gives the Northern Atlantic seaboard the bad
preëminence of having the worst observing conditions of any region
within his knowledge. The author cheerfully concurs, yet now and
then, quite often after midnight, the air steadies and, if the other
conditions are good, definition becomes fairly respectable, sometimes
even excellent.

Temperature and humidity as such, seem to make little difference, and a
steady breeze unless it shakes the instrument is relatively harmless.
Hence we find the most admirable definition in situations as widely
different as the Harvard station at Mandeville, Jamaica; Flagstaff,
Arizona 7000 feet up and snow bound in winter; Italy, and Egypt. The
first named is warm and with very heavy rainfall and dew, the second
dry with rather large seasonal variation of temperature, and the others
temperate and hot respectively.

Perhaps the most striking evidence of the importance of uniformity
was noted by Evershed at an Indian station where good conditions
immediately followed the flooding of the rice fields with its tendency
to stabilize the temperature. Mountain stations may be good as at
Flagstaff, Mt. Hamilton, or Mt. Wilson, or very bad as Pike’s Peak
proved to be, probably owing to local conditions.

In fact much of the trouble comes from nearby sources, atmospheric
waves and ripples rather than large movements, ripples indeed often
small compared with the aperture of the telescope and sometimes in or
not far outside of the tube itself.

Aside from these difficulties, there are still others which have to do
with the transparency of the atmosphere with respect to its suspended
matter. This does not affect the definition as such, but it cuts down
the light to a degree that may interfere seriously with the observation
of faint stars and nebulæ. The smoke near a city aggravates the
situation, but in particular it depends on general weather conditions
which may be persistent or merely temporary.

Often seeing conditions may be admirable save for this lack of
transparency in the atmosphere, so that study of the moon, of planetary
markings and even of double stars, not too faint, may go on quite
unimpeded. The actual loss of light may reach however a magnitude or
more, while the sky is quite cloudless and without a trace of fog or
noticeable haziness by day.

There have been a good many nights the past year (1921) when Alcor
(80 Ursæ Majoris) the tiny neighbor of Mizar, very nearly of the 4th
magnitude, has been barely or not at all visible while the seeing
otherwise was respectably good. Ordinarily stars of 6^_m_ should be
visible in a really clear night, and in a brilliant winter sky in the
temperate zones, or in the clear air of the tropics, a good many eyes
will do better than this, reaching 6^_m_.5 or even 7^_m_, occasionally
a bit more.

The relation of air waves and such like irregularities to telescopic
vision was rather thoroughly investigated by Douglass more than twenty
years ago (Pop. Ast. =6=, 193) with very interesting results. In
substance, from careful observation with telescopes from 4 inches up
to 24 inches aperture, he found that the real trouble came from what
one may call ripples, disturbances from say 4 inches wave length down
to ¾ inch or less. Long waves are rare and relatively unimportant
since their general effect is to cause shifting of the image as a whole
rather than the destruction of detail which accompanies the shorter
waves.

This rippling of the air is probably associated with the contact
displacements in air currents such as on a big scale become visible
in cloud forms. Clearly ripples, marked as they are by difference
of refraction, located in front of a telescope objective, produce
different focal lengths for different parts of the objective and render
a clean and stable image quite out of the question.

In rough terms Douglass found that waves of greater length than half
the aperture did not materially deteriorate the image, although they
did shift it as a whole, while waves of length less than one third the
aperture did serious mischief to the definition, the greater as the
ripples were shorter, and the image itself more minute in dimension or
detail.

Hence there are times when decreasing the aperture of an objective by
a stop improves the seeing considerably by increasing the relative
length of the air waves. Such is in fact found to be the case in
practical observing, especially when the seeing with a large aperture
is decidedly poor. In other words one may often gain more by increased
steadiness than he loses by lessened “resolving power,” the result
depending somewhat on the class of observation which chances to be
under way.

And this brings us, willy-nilly, to the somewhat abstruse matter of
resolving power, depending fundamentally upon the theory of diffraction
of light, and practically upon a good many other things that modify the
character of the diffraction pattern, or the actual visibility of its
elements.

When light shines through a hole or a slit the light waves are bent at
the margins and the several sets, eventually overlapping, interfere
with each other so as to produce a pattern of bright and dark elements
depending on the size and shape of the aperture, and distributed about
a central bright image of that aperture. One gets the effect well in
looking through an open umbrella at a distant street light. The outer
images of the pattern are fainter and fainter as they get away from the
central image.

Without burdening the reader for the moment with details to be
considered presently, the effect in telescopic vision is that a star
of real angular diameter quite negligible, perhaps 0.″001 of arc, is
represented by an image under perfect conditions like Fig. 154, of
quite perceptible diameter, surrounded by a system of rings, faint but
clear-cut, diminishing in intensity outwards. When the seeing is bad no
rings are visible and the central disc is a mere bright blur several
times larger than it ought to be.

The varying appearance of the star image is a very good index of the
quality of the seeing, so that, having a clear indication of this
appearance, two astronomers in different parts of the world can gain a
definite idea of each other’s relative seeing conditions. To this end
a standard scale of seeing, due largely to the efforts of Prof. W. H.
Pickering, has come into rather common use. (H. A. =61= 29). It is as
follows, based on observations with a 5 inch telescope.


STANDARD SCALE OF SEEING

1. Image usually about twice the diameter of the third ring.

2. Image occasionally twice the diameter of the third ring.

3. Image of about the same diameter as the third ring, and brighter at
the centre.

4. Disc often visible, arcs (of rings) sometimes seen on brighter stars.

5. Disc always visible, arcs frequently seen on brighter stars.

6. Disc always visible, short arcs constantly seen.

7. Disc sometimes sharply defined, (_a_) long arcs. (_b_) Rings
complete.

8. Disc always sharply defined, (_a_) long arcs. (_b_) Rings complete
all in motion.

9. Rings, (_a_) Inner ring stationary, (_b_) Outer rings momentarily
stationary.

10. Rings all stationary, (_a_) Detail between the rings sometimes
moving. (_b_) No detail between the rings.

The first three scale numbers indicate very bad seeing; the next two,
poor; the next two, good; and the last three, excellent. One can
get some idea of the extreme badness of scale divisions 1, 2, 3, in
realizing that the third bright diffraction ring is nearly 4 times the
diameter of the proper star-disc.

It must be noted that for a given condition of atmosphere the seeing
with a large instrument ranks lower on the scale than with a small one,
since as already explained the usual air ripples are of dimensions that
might affect a 5 inch aperture imperceptibly and a 15 inch aperture
very seriously.

Douglass (loc. cit.) made a careful comparison of seeing conditions for
apertures up to 24 inches and found a systematic difference of 2 or 3
scale numbers between 4 or 6 inches aperture, and 18 or 24 inches. With
the smallest aperture the image showed merely bodily motion due to air
waves that produced serious injury to the image in the large apertures,
as might be expected.

There is likewise a great difference in the average quality of seeing
as between stars near the zenith and those toward the horizon, due
again to the greater opportunity for atmospheric disturbances in the
latter case. Pickering’s experiments (loc. cit.) show a difference
of nearly 3 scale divisions between say 20° and 70° elevation. This
difference, which is important, is well shown in Fig. 182, taken from
his report.

The three lower curves were from Cambridge observations, the others
obtained at various Jamaica stations. They clearly show the systematic
regional differences, as well as the rapid falling off in definition
below altitude 40°, which points the importance of making provision for
comfortable observing above this altitude.

[Illustration: FIG. 182.—Variation of Seeing with Altitude.]

[Illustration: FIG. 183.—Airy’s Diffraction Pattern.]

The relation of the diffraction pattern as disclosed in the moments
of best seeing to its theoretical form is a very interesting one. The
diffraction through a theoretically perfect objective was worked out
many years ago by Sir George Airy who calculated the exact distribution
of the light in the central disc and the surrounding rings.

This is shown from the centre outwards in Fig. 183, in which the
ordinates of the curve represent relative intensities while the
abscissæ represent to an arbitrary scale the distances from the axis.
It will be at once noticed that the star image, brilliant at its
centre, sinks, first rapidly and then more slowly, to a minimum and
then very gradually rises to the maximum of the first bright ring, then
as slowly sinks again to increase for the second ring and so on.

[Illustration: FIG. 184.—Diffraction Solid for a Star.]

For unity brightness in the centre of the star disc the maximum
brightness of the first ring is 0.017, of the second 0.004 and the
third 0.0016. The rings are equidistant and the star disc has a radius
substantially equal to the distance between rings. One’s vision does
not follow down to zero the intensities of the rings or of the margin
of the disc, so that the latter has an apparent diameter materially
less than the diameter to the first diffraction minimum, and the rings
themselves look sharper and thinner than the figure would show, even
were the horizontal scale much diminished. The eye does not descend in
the presence of bright areas to its final threshold of perception.

One gains a somewhat vivid idea of the situation by passing to three
dimensions as in Fig. 184, the “diffraction solid” for a star, a
conception due to M. André (Mem. de l’Acad. de Lyon =30=, 49). Here
the solid represents in volume the whole light received and the height
taken at any point, the intensity at that point.

A cross section at any point shows the apparent diameter of the disc,
its distance to the apex the remaining intensity, and the volume above
the section the remaining total light. Substantially 85% of the total
light belongs to the central cone, for the theoretical distribution.

Granting that the eye can distinguish from the background of the sky,
in presence of a bright point, only light above a certain intensity,
one readily sees why the discs of faint stars look small, and why shade
glasses are sometimes useful in wiping out the marginal intensities
of the solid. There are physiological factors that alter profoundly
the appearance of the actual star image, despite the fact that the
theoretical diffraction image for the aperture is independent of the
star’s magnitude.

Practically the general reduction of illumination in the fainter stars
cuts down the apparent diameters of their discs, and reduces the number
of rings visible against the background of the sky.

The scale of the diffraction system determines the resolving power of
the telescope. This scale is given in Airy’s original paper (Cambr.
Phil. Trans. =1834= p. 283), from which the angle α to any maximum or
minimum in the ring system is defined by

sin α = _n_λ/_R_

in which λ is numerically the wave length of any light considered and
_R_ is the radius of the objective.

We therefore see that the ring system varies in dimension inversely
with the aperture of the objective and directly with the wave length
considered. Hence the bigger the objective the smaller the disc and
its surrounding ring system; and the greater the wave length, i.e. the
redder the light, the bigger the diffraction system. Evidently there
should be color in the rings but it very seldom shows on account of the
faintness of the illumination.

Now the factor _n_= is for the first dark ring 0.61, and for the
first bright ring 0.81, as computed from Airy’s general theory, and
therefore if we reckon that two stars will be seen as separate when
the central disc of one falls on the first dark ring of the other the
angular distance will be

Sinα = 0.61 λ/_R_′

and, taking λ at the brightest part of the spectrum i.e., about 560
μμ, in the yellow green, with α taken for sin α, we can compute this
assumed separating power for any aperture. Thus 560 μμ being very
nearly 1/45,500 inch, and assuming a 5 inch telescope, the instrument
should on this basis show as double two stars whose centres are
separated by 1.″1 of arc.

In actual fact one can do somewhat better than this, showing that
the visible diameter of the central disc is in effect less than the
diameter indicated by the diffraction pattern, owing to the reasons
already stated. Evidently the brightness of the star is a factor in the
situation since if very bright the disc gains apparent size, and when
very faint there is sufficient difficulty in seeing one star, let alone
a pair.

The most thorough investigation of this matter of resolving power was
made by the Rev. W. R. Dawes many years ago (Mem. R.A.S. =35=, 158).
His study included years of observation with telescopes of different
sizes, and his final result was to establish what has since been known
as “Dawes’ Limit.”

To sum up Dawes’ results he established the fact that on the average a
one inch aperture would enable one to separate two 6th magnitude stars
the centers of which were separated by 4.56″. Or, to generalize from
this basis, the separating power of any telescope is for very nearly
equal stars, moderately bright, 4″.56/_A_ where _A_ is the aperture of
the telescope in inches.

Many years of experience have emphasized the usefulness of this
approximate rule, but that it is only approximate must be candidly
admitted. It is a limit decidedly under that just assigned on the basis
of the theory of diffraction for the central bright wave-lengths of
the spectrum. Attempts have been made to square the two figures by
assuming in the diffraction theory a wave length of 1/55,000 inch, but
this figure corresponds to a point well up into the blue, of so low
luminosity that it is of no importance whatever in the visual use of a
telescope.

The fact is that the visibility of two neighboring bright points as
distinct, depends on a complex of physical and physiological factors,
the exact relations of which have never been unravelled. To start with
we have the principles of diffraction as just explained, which define
the relation of the stellar disc to the center of the first dark ring,
but we know that under no circumstances can one see the disc out to
this limit, since vision fails to take cognizance of the faint rim of
the image. The apparent diameter of the diffraction solid therefore
corresponds to a section taken some distance above the base, the exact
point depending on the sensitiveness of the particular observer’s eye,
the actual brilliancy of the center of the disc, and the corresponding
factors for the neighboring star.

[Illustration: FIG. 185.—Diffraction Solid for a Disc.]

Under favorable circumstances one would not go far amiss in taking the
visible diameter of the disc at about half that reckoned to the center
of the first dark ring. This figure in fact corresponds to what has
been shown to be within the grasp of a good observer under favorable
conditions, as we shall presently see.

On the other hand, if the stars are decidedly bright there is increase
of apparent diameter of the disc due to the phenomenon known as
irradiation, the spreading of light about its true image on the retina
which corresponds quite closely to the halation produced by a bright
spot on a photographic plate.

If, on the contrary, the stars are very faint the total amount of
light available is not sufficient to make contrast over and above the
background sufficient to disclose the two points as separate, while if
the pair is very unequal the brighter one will produce sufficient glare
to quite over-power the light from the smaller one so that the eye
misses it entirely.

A striking case of this is found in the companion to Sirius, an
extremely difficult object for ordinary telescopes although the
distance to the companion is about 10.6″ and its magnitude is 8.4,
making a superlatively easy double for the very smallest telescope
save for the overpowering effect of the light of the large star.
Another notoriously difficult object for small telescopes is δ Cygni, a
beautiful double of which the smaller component falls unpleasantly near
the first diffraction maximum of the primary in which it is apt to be
lost.

“Dawes’ Limit” is therefore subject to many qualifying factors. Lewis,
in the papers already referred to (Obs. =37=, 378) did an admirable
piece of investigation in going through the double star work of about
two score trained observers working with telescopes all the way from 4
inches to 36 inches aperture.

From this accumulation of data several striking facts stand out. First
there is great difference between individual observers working with
telescopes of similar aperture as respects their agreement with “Dawes’
Limit,” showing the effect of variation in the physiological factors as
well as instrumental ones.

Second, there is also a very large difference between the facility of
observing equal bright pairs and equal faint pairs, or unequal pairs of
any kind, again emphasizing the physiological as well as the physical
factors.

Finally, there is most unmistakable difference between small and large
apertures in their capacity to work up to or past the standard of
“Dawes’Limit.” The smaller telescopes are clearly the more efficient
as would be anticipated from the facts just pointed out regarding the
different effect of the ordinary and inescapable atmospheric waves on
small and large instruments.

The big telescopes are unquestionably as good optically speaking as
the small ones but under the ordinary working conditions, even as good
as those a double star observer seeks, the smaller aperture by reason
of less disturbance from atmospheric factors does relatively much the
better work, however good the big instrument may be under exceptional
conditions.

This is admirably shown by the discussion of the beautiful work of the
late Mr. Burnham, than whom probably no better observer of doubles has
been known to astronomy. His records of discovery with telescopes of
6, 9.4, 12, 18½ and 36 inches show the relative ease of working to
the theoretical limit with instruments not seriously upset by ordinary
atmospheric waves.

With the 6 inch aperture Burnham reached in the average 0.53 of Dawes’
limit, quite near the rough figure just suggested, and he also fell
well inside Dawes’ limit with the 9.4 inch instrument. With none
of the others did he reach it and in fact fell short of it by 15 to
60%. All observations being by the same notably skilled observer
and representing discoveries of doubles, so that no aid could have
been gained by familiarity, the issue becomes exceedingly plain
that size with all its advantages in resolving power brings serious
countervailing limitations due to atmosphere.

But a large aperture has besides its possible separating power one
advantage that can not be discounted in “light grasp,” the power of
discerning faint objects. This is the thing in which a small telescope
necessarily fails. The “light grasp” of the telescope obviously depends
chiefly on the area of the objective, and visually only in very minor
degree on the absorption of the thicker glass in the case of a large
lens.

According to the conventional scale of star magnitudes as now in
universal use, stars are classified in magnitudes which differ from
each other by a light ratio of 2.512. a number the logarithm of which
is 0.4, a relation suggested by Pogson some forty years ago. A second
magnitude star therefore gives only about 40% of the light of a first
magnitude star, while a third magnitude star gives again a little less
than 40% of the light of a second magnitude star and so on.

But doubling the aperture of a telescope increases the available area
of the objective four times and so on, the “light grasp” being in
proportion to the square of the aperture. Thus a 10 inch objective will
take in and deliver nearly 100 times as much light as would a 1 inch
aperture. If one follows Pogson’s scale down the line he will find that
this corresponds exactly to 5 stellar magnitudes, so that if a 1 inch
aperture discloses, as it readily does, a 9th magnitude star, a 10 inch
aperture should disclose a 14th magnitude star.

Such is substantially in fact the case, and one can therefore readily
tabulate the minimum visible for an aperture just as he can tabulate
the approximate resolving power by reference to Dawes’ limit. Fig. 186
shows in graphic form both these relations for ready reference, the
variation of resolving power with aperture, and that of “light grasp,”
reckoned in stellar magnitudes.

It is hardly necessary to state that considerable individual and
observational differences will be found in each of these cases, in the
latter amounting to not less than 0.5 to 1.0 magnitude either way.
The scale is based on the 9th magnitude star just being visible with
1 inch aperture, whereas in fact under varying conditions and with
various observers the range may be from the 8th to 10th magnitude. All
these things, however convenient, must be taken merely at their true
value as good working approximations.

Even the diffraction theory can be taken only as an approximation since
no optical surface is absolutely perfect and in the ordinary refracting
telescope there is a necessary residual chromatic aberration beside
whatever may remain of spherical errors.

[Illustration: FIG. 186.—Light-grasp and Resolving Power.]

It is a fact therefore, as has been shown by Conrady (M.N. =79=
575) following up a distinguished investigation by Lord Rayleigh
(Sci. Papers =1= 415), that a certain small amount of aberration can
be tolerated without material effect on the definition, which is
very fortunate considering that the secondary spectrum represents
aberrations of about 1/2,000 of the focal length, as we have already
seen.

The chief effect of this, as of very slight spherical aberration,
is merely to reduce the maximum intensity of the central disc of
the diffraction pattern and to produce a faint haze about it which
slightly illuminates the diffraction minima. The visible diameter
of the disc and the relative distribution of intensity in it is not
however materially changed so that the main effect is a little loss and
scattering of light.

With larger aberrations these effects are more serious but where the
change in length of optical path between the ray proceeding through the
center of the objective and that from the margin does not exceed ¼λ
the injury to the definition is substantially negligible and virtually
disappears when the image is focussed for the best definition, the loss
of maximum intensity in the star disc amounting to less than 20%.

Even twice this error is not a very serious matter and can be for
the most part compensated by a minute change of focus as is very
beautifully shown in a paper by Buxton(M. N. =81=, 547), which should
be consulted for detail of the variations to be effected.

Conrady finds a given change _dp_ in the difference in lengths of the
optical paths, related to the equivalent linear change of focus, _df_,
as follows:—

  _df_ = 8_dp_(_f_/_A_)²

A being the aperture and f the focal length, which indicates for
telescopes of ordinary focal ratio a tolerance of the order of ±0.01
inch before getting outside the limit λ for variation of path.

For instruments of greater relative aperture the precision of focus
and in general the requirements for lessened aberration are far more
severe, proportional in fact to the square of this aperture. Hence
the severe demands on a reflector for exact figure. An instrument
working at F/5 or F/6 is extremely sensitive to focus and demands great
precision of figure to fall within permissible values, say ¼λ to ½λ,
for _dp_.

Further, with a given value of _dp_ and the relation established by
the chromatic aberration, _i.e._, about _f_/2000, a relation is also
determined between _f_ and _A_, required to bring the aberration within
limits. The equation thus found is

  _f_ = 2.8_A_²

This practically amounts to the common F/15 ratio for an aperture of
approximately 5 inches. For smaller apertures a greater ratio can be
well used, for larger, a relatively longer focus is indicated, the
penalty being light spread into a halo over the diffraction image and
reducing faint contrasts somewhat seriously.

This is one of the factors aside from atmosphere, interfering with
the full advantage of large apertures in refractors. While as already
noted small amounts of spherical aberration may be to a certain
extent focussed out, the sign of _df_ must change with the sign of
the residual aberration, and a quick and certain test of the presence
of spherical aberration is a variation in the appearance of the image
inside and outside focus.

To emphasize the importance of exact knowledge of existing aberrations
note Fig. 187, which shows the results of Hartmann tests on a typical
group of the world’s large objectives. All show traces of residual
zones, but differing greatly in magnitude and position as the attached
scales show. The most conspicuous aberrations are in the big Potsdam
photographic refractor, the least are in the 24 inch Lowell refractor.
The former has since been refigured by Schmidt and revised data are not
yet available; the latter received its final figure from the Lundins
after the last of the Clarks had passed on.

Now a glance at the curves shows that the bad zone of the Potsdam glass
was originally near the periphery, (I), hence both involved large area
and, from Conrady’s equation, seriously enlarged _df_ due to the large
relative aperture at the zone. An aberrant zone near the axis as in the
stage (III) of the Potsdam objective or in the Ottawa 15 inch objective
is much less harmful for corresponding reasons. Such differences have
a direct bearing on the use of stops, since these may do good in case
of peripheral aberration and harm when the faults are axial. Unless
the aberrations are known no general conclusions can be drawn as to
the effect of stops. Even in the Lowell telescope shown as a whole in
Fig. 188, the late Dr. Lowell found stops to be useful in keeping down
atmospheric troubles and reducing the illumination although they could
have had no effect in relation to figure. Fig. 188 shows at the head
of the tube a fitting for a big iris diaphragm, controlled from the
eye-end, the value of which was well demonstrated by numerous observers.

There are, too, cases in which a small instrument, despite intrinsic
lack of resolving power, may actually do better work than a big one.
Such are met in instances where extreme contrast of details is
sought, as has been well pointed out by Nutting (Ap. J. =40=, 33) and
the situation disclosed by him finds amplification in the extraordinary
work done by Barnard with a cheap lantern lens of 1½ inch diameter
and 5½ inches focus (Pop. Ast., =6=, 452).

[Illustration: FIG. 187.—Hartmann Tests of Telescopes [From Hartmann’s
Measures].]

The fact is that every task must seek its own proper instrument. And in
any case the interpretation of observed results is a matter that passes
far beyond the bounds of geometrical optics, and involves physiological
factors that are dominant in all visual problems.

With respect to the visibility of objects the general diffraction
theory again comes into play. For a bright line, for example, the
diffraction figure is no longer chiefly a cone like Fig. 183,
but a similar long wedge-shaped figure, with wave-like shoulders
corresponding to the diffraction rings. The visibility of such a line
depends not only on the distribution of intensity in the theoretical
wedge but on the sensitiveness of the eye and the nature of the
background and so forth, just as in the case of a star disc.

If the eye is from its nature or state of adaptation keen enough
on detail but not particularly sensitive to slight differences of
intensity, the line will very likely be seen as if a section were made
of the wedge near its thin edge. In other words the line will appear
thin and sharp as the diffraction rings about a star frequently do.

With an eye very sensitive to light and small differences of contrast
the appearance of absolutely the same thing may correspond to a section
through the wedge near its base, in other words to a broad strip
shading off somewhat indistinctly at the edges, influenced again by
irradiation and the character of the background.

If there be much detail simultaneously visible the diffraction patterns
may be mixed up in a most intricate fashion and one can readily see the
confusion which may exist in correlating the work of various observers
on things like planetary and lunar detail.

In the planetary case the total image is a complex of illuminated
areas of diffraction at the edges, which may be represented as the
diffraction solid of Fig. 185, in which the dotted lines show what may
correspond fairly to the real diameter of the planet, the edge shading
off in a way again complicated by irradiation.

[Illustration: FIG. 188.—The Lowell Refractor Fitted with Iris
Diaphragm.]

Fancy detail superimposed on a disc of this sort and one has a vivid
idea of the difficulty of interpreting observations.

It would be an exceedingly good thing if everyone who uses his
telescope had the advantage of at least a brief course in microscopy,
whereby he would gain very much in the practical understanding of
resolving power, seeing conditions, and the interpretation of the
image. The principles regarding these matters are in fact very much the
same with the two great instruments of research.

Aperture, linear in the case of the telescope and the so-called
numerical in the case of the microscope, bear precisely the same
relation to resolution, the minimum resolvable detail being in each
case directly proportional to aperture in the senses here employed.

Further, although the turbulence of intervening atmosphere does
not interfere with the visibility of microscopic detail, a similar
disturbing factor does enter in the form of irregular and misplaced
illumination. It is a perfectly easy matter to make beautifully
distinct detail quite vanish from a microscopic image merely by
mismanagement of the illumination, just as unsteady atmosphere will
produce substantially the same effect in the telescopic image.

In the matter of magnification the two cases run quite parallel, and
magnification pushed beyond what is justified by the resolving power
of the instrument does substantially little or no good. It neither
discloses new detail nor does it bring out more sharply detail which
can be seen at all with a lower power.

The microscopist early learns to shun high power oculars, both from
their being less comfortable to work with, and from their failing to
add to the efficiency of the instrument except in some rare cases
with objectives of very high resolving power. Furthermore in the
interpretation of detail the lessons to be learned from the two
instruments are quite the same, although one belongs to the infinitely
little and the other to the infinitely great.

Nothing is more instructive in grasping the relation between resolving
power, magnification, and the verity of detail, than the study under
the microscope of some well known objects. For example, in Fig. 189
is shown a rough sketch of a common diatom, _Navicula Lyra_. The
tiny siliceous valve appears thus under an objective of slightly
insufficient resolving power. The general form of the object is
clearly perceived, as well as the central markings, standing boldly out
in the form which suggests the specific name. No trace of any finer
detail appears and no amount of dexterity in arranging the illumination
or increase of magnifying power will show any more than here appears,
the drawing being one actually made with the camera lucida, using an
objective of numerical aperture just too small to resolve the details
of the diatoms on this particular slide.

Figure 189_a_ shows what happens when, with the same magnifying power,
an objective of slightly greater aperture is employed. Here the whole
surface of the valve is marked with fine striations, beautifully
sharp and distinct like the lines of a steel engraving. There is a
complete change of aspect wrought by an increase of about 20% in the
resolving power. Again nothing further can be made out by an increase
of magnification, the only effect being to make the outlines a little
hazier and the view therefore somewhat less satisfactory.

[Illustration: FIG. 189.—The Stages of Resolution.]

Finally in Fig. 189_b_ we have again the same valve under the same
magnifying power, but here obtained from an objective of numerical
aperture 60% above that used for the main figure. The sharp striæ now
show their true character. They had their origin in lines of very
clearly distinguished dots, which are perfectly distinct, and are due
to the resolving power at last being sufficient to show the detail
which previously merely formed a sharp linear diffraction pattern
entirely incapable of being resolved into anything else by the eye,
however much it might be magnified.

Here one has, set out in unmistakable terms, the same kind of
differences which appear in viewing celestial detail through telescopes
of various aperture. What cannot be seen at all with a low aperture
may be seen with higher ones under totally different aspects; while in
each case the apparent sharpness and clarity of the image is somewhat
extraordinary.

Further in Fig. 189_b_ in using the resolving power of the objective
of high numerical aperture, the image may be quite wrecked by a little
carelessness in focussing, or by mismanagement of light, so that one
would hardly know that the valve had markings other than those seen
with the objectives of lower aperture, and under these circumstances
added magnification would do more harm than good. In precisely the same
way mismanagement of the illumination in Fig. 189_a_ would cause the
striæ to vanish and with _Navicula Lyra_, as with many other diatoms,
the resolution into striæ is a thing which often depends entirely on
careful lighting, and the detail flashes into distinctness or vanishes
with a suddenness which is altogether surprising. For “lighting” read
“atmosphere,” and you have just the sort of conditions that exist in
telescope vision.

With respect to magnifying powers what has already been said is
sufficient to indicate that on the whole the lowest power which
discloses to the eye the detail within the reach of the resolving power
of the objective is the most satisfactory.

Every increase above this magnifies all the optical faults of the
telescope and the atmospheric difficulties as well, beside decreasing
the diameter of the emergent pencil which enters the eye, and thereby
causing serious loss of acuity. For the eye like any other optical
instrument loses resolving power with decrease of effective aperture,
and, besides, a very narrow beam entering it is subject to the
interference of entoptic defects, such as floating motes and the like,
to a serious extent.

Figure 190 shows from Cobb’s experiments (Am. Jour. of Physiol., =35=,
335) the effect of reduction of ocular aperture upon acuity. The curve
shows very plainly that for emergent pencils below a millimeter (1/25
inch) in diameter, visual acuity falls off almost in direct proportion
to the decreasing aperture. Below this figure there can be only
incidental gains, such as may be due to opening up double stars and
simultaneously so diminishing the general illumination as to render the
margins of the star discs a little less conspicuous.

An emergent pencil of this diameter is not quite sufficient for the
average eye to utilize fully the available resolving power and some
excess of magnification even though it actually diminishes visual
acuity materially, may be of some service.

[Illustration: FIG. 190.—Resolving Power of the Eye.]

Increased acuity will of course be gained for the same magnification
in using an objective of greater diameter, to say nothing of increased
resolving power, at the cost, of course, of relatively greater
atmospheric troubles.

To come down to figures as to the resolving power of the eye, often
repeated experiments have shown that two points offering strong
contrast with the background can be noted as separate by the normal eye
when at an angular separation of about 3′ of arc. People, as we have
seen, differ considerably in acuity so that now and then individuals
will considerably better this figure, while others, far less keen
sighted, may require a separation of 4′ or even 5′.

The pair of double stars ε_{1}, ε_{2}, Lyræ, separated by 3′ 27″
mags. nearly 4 and 5 respectively, can be seen as separate by those
of fairly keen vision, while Mizar and Alcor, 11′ apart, seem thrown
wide to nearly every one. On the other hand the writer has never known
anybody who could separate the two components of Asterope of the
Pleiades, distant a scant 2½ but of mags. 6.5 and 7.0 only, while
Pleione and Atlas, distance about 5¼′, mags. 6.5 and 4, are very
easy.

Assuming for liberality that the separation constant is in the
neighborhood of 5′ one can readily estimate the magnification that for
any telescope will take full advantage of its resolving power. As we
have already seen this resolving power is practically 4.″56/_A_ for
equal stars moderately bright. An objective of 4.56′ inches aperture
has a resolving constant of 1″ and to develop this should take a
magnification of say 300, about 65 to the inch of aperture, requiring a
focal length of ocular about 0.20 to 0.25 inch for telescopes of normal
relative aperture, and pushing the emergent pencil down to little more
than 0.02 inch,—rather further than is physiologically desirable.
Except for these extreme stunts of separation, half to two thirds this
power is preferable and conditions under which one can advantageously
go above this limit are very rare indeed.

A thoroughly good objective or mirror will stand quite 100
magnification to the inch without, as the microscopist would say,
“breaking down the image,” but in at least nine cases out of ten the
result will be decidedly unsatisfactory.

As the relative aperture of the instrument increases, other things
being equal, one is driven to oculars of shorter and shorter focus
to obtain the same magnification and soon gets into trouble. Very
few oculars below 0.20 inch in focus are made, and such are rarely
advisable, although occasionally in use down to 0.15 inch or
thereabouts. The usual F/15 aperture is a figure quite probably as much
due to the undesirability of extremely short focus oculars as to the
easier corrections of the objective.

In the actual practice of experienced observers the indications of
theory are well borne out. Data of the habits of many observers of
double stars are of record and the accomplished veteran editor of _The
Observatory_, Mr. T. Lewis, took the trouble in one of his admirable
papers on “Double Star Astronomy” (Obs. =36=, 426) to tabulate from the
original sources the practice of a large group of experts. The general
result was to show the habitual use with telescopes of moderate size
of powers around 50 per inch of aperture, now and then on special
occasions raised to the neighborhood of 70 per inch.

But the data showed unequivocally just what has been already indicated,
that large apertures, suffering severely as they generally do from
turbulence of the air, will not ordinarily stand their due proportion
of magnification. With the refractors of 24 inches aperture and
upwards the records show that even in this double star work, where, if
anywhere, high power counts, the general practice ran in the vicinity
of 30 per inch of aperture.

Analyzing the data more completely in this respect Mr. Lewis found that
the best practise of the skilled observers studied was approximately
represented by the empirical equation

_m_ = 140 √_A_

Of course the actual figures must vary with the conditions of location
and the general quality of the seeing, as well as the work in hand. For
other than double star work the tendency will be generally toward lower
powers. The details which depend on shade perception rather than visual
acuity are usually hurt rather than helped when magnified beyond the
point at which they are fairly resolved, quite as in the case of the
microscope.

Now and then they may be made more distinct by the judicious use of
shade glasses. Quite apart from the matter of the high powers which can
advantageously be used on a telescope, one must for certain purposes
consider the lowest powers which are fairly applicable. This question
really turns on the largest utilizable emergent pencil from the eye
piece. It used to be commonly stated that ⅛ inch for the emergent
pencil was about a working maximum, leading to a magnification of 8
per inch of aperture of the objective. This in view of our present
knowledge of the eye and its properties is too low an estimate of
pupillary aperture. It is a fact which has been well known for more
than a decade that in faint light, when the eye has become adapted to
its situation, the pupil opens up to two or three times this diameter
and there is no doubt that a fifth or a fourth of an inch aperture
can be well utilized, provided the eye is properly dark-adapted. For
scrutinizing faint objects, comet sweeping and the like, one should
therefore have one ocular of very wide field and magnifying power of 4
or 5 per inch of aperture, the main point being to secure a field as
wide is practicable. One may use for such purposes either a very wide
field Huyghenian, or, if cross wires are to be used, a Kellner form.
Fifty degrees of field is perfectly practicable with either. As regards
the rest of the eyepiece equipment the observer may well suit his own
convenience and resources. Usually one ocular of about half the maximum
power provided will be found extremely convenient and perhaps oftener
used than either the high or low power. Oculars of intermediate power
and adapted for various purposes will generally find their way into any
telescopic equipment. And as a last word do not expect to improve bad
conditions by magnifying. If the seeing is bad with a low power, cap
the telescope and await a better opportunity.




APPENDIX

WORK FOR THE TELESCOPE


To make at first hand the acquaintance of the celestial bodies is, in
and of itself, worth the while, as leading the mind to a new sense of
ultimate values. To tell the truth the modern man on the whole knows
the Heavens less intimately than did his ancestors. He glances at his
wrist-watch to learn the hour and at the almanac to identify the day.
The rising and setting of the constellations, the wandering of the
planets among the stars, the seasonal shifting of the sun’s path—all
these are a sealed book to him, and the intricate mysteries that lie in
the background are quite unsuspected.

The telescope is the lifter of the cosmic veil, and even for merely
disclosing the spectacular is a source of far-reaching enlightenment.
But for the serious student it offers opportunities for the genuine
advancement of human knowledge that are hard to underestimate. It is
true that the great modern observatories can gather information on
a scale that staggers the private investigator. But in this matter
fortune favors the pertinacious, and the observer who settles to a line
of deliberate investigation and patiently follows it is likely to find
his reward. There is so much within the reach of powerful instruments
only, that these are in the main turned to their own particular spheres
of usefulness.

For modest equipment there is still plenty of work to do. The study
of variable stars offers a vast field for exploration, most fruitful
perhaps with respect to the irregular and long-period changes of which
our own Sun offers an example. Even in solar study there are transient
phenomena of sudden eruptions and of swift changes that escape the eye
of the spectro-heliograph, and admirable work can be done, and has been
done, with small telescopes in studying the spectra of sun spots

Temporary stars visible to the naked eye or to the smallest instruments
turn up every few years and their discovery has usually fallen to the
lot of the somewhat rare astronomer, professional or amateur, who knows
the field of stars as he knows the alphabet. The last three important
novæ fell to the amateurs—two to the same man. Comets are to be had
for the seeking by the persistent observer with an instrument of fair
light-grasp and field; one distinguished amateur found a pair within a
few days, acting on the theory that small comets are really common and
should be looked for—most easily by one who knows his nebulæ, it should
be added.

And within our small planetary system lies labor sufficient for
generations. We know little even about the superficial characters of
the planets, still less about their real physical condition. We are not
even sure about the rotation periods of Venus and Neptune. The clue to
many of the mysteries requires eternal vigilance rather than powerful
equipment, for the appearance of temporary changes may tell the whole
story. The old generation of astronomers who believed in the complete
inviolability of celestial order has been for the most part gathered to
its fathers, and we now realize that change is the law of the universe.
Within the solar system there are planetary surfaces to be watched,
asteroids to be scanned for variability or change of it, meteor swarms
to be correlated with their sources, occultations to be minutely
examined, and when one runs short of these, our nearest neighbor the
Moon offers a wild and physically unknown country for exploration. It
is suspected with good reason of dynamic changes, to say nothing of the
possible last remnants of organic life.

Much of this work is well within the useful range of instruments of
three to six inches aperture. The strategy of successful investigation
is in turning attention upon those things which are within the scope of
one’s equipment, and selecting those which give promise of yielding to
a well directed attack. And to this end efforts correlated with those
of others are earnestly to be advised. It is hard to say too much of
the usefulness of directed energies like those of the Variable Star
Association and similar bodies. They not only organize activities to
an important common end, but strengthen the morale of the individual
observer.




INDEX


  A

  Abbé, roof prism, 162

  Aberration, compensated by minute change of focus, 266
    illuminates the diffraction minima, 265
    relation determines of focus and aperture, 266

  Achromatic long relief ocular, 146
    objective, 77

  Achromatism, condition for, 78
    determination of, 78
    imperfection of, 87

  Adjustment where Polaris invisible, 235

  Air waves, length of, 255

  Alt-azimuth mount for reflector, 102
    mounts, with slow motions, 102
    setting up an, 228

  Anastigmats, 84

  Annealing, pattern of strain, 68

  Astigmatism, 84, 209
    of figure, 210

  Astronomy, dawn of popular, 19


  B

  Bacon, Roger, alleged description of telescopes, 6

  Barlow lens, 152

  “Bent,” objective, 86

  Binocular, 2
    advantage of, exaggerated, 151
    for strictly astronomical use, 152
    telescopes for astronomical use, 163


  C

  Camouflage, in optical patents, 97

  Cassegrain, design for reflecting telescope, 22

  Cassegrain, sculptor and founder of statues, 22

  Cell, taking off from a telescope, 202

  Chromatic aberration, 11, 76
    investigation of, 210
    correction, differences in, 91
    error of the eye, 90

  Clairault’s condition, 81
    two cemented forms for, 81

  Clarks, portable equatorial mounting, 109
    terrestrial prismatic eyepiece, 158

  Clock, the cosmic, 233

  Clock drive, 110, 174

  Clock mechanism, regulating rate of motor, 179

  Coddington lens, 137

  Cœlostat constructions, 126
    tower telescopes, 127

  Color correction, commonly used, 211
    examined by spectroscope, 211
    of the great makers, 90

  Coma-free, condition combined with Clairault’s, 83

  Comet seeker, Caroline Herschel’s 118
    seekers with triple objective, 119

  Crowns distinguished from flints, 64

  Curves, struggle for non-spherical, 18


  D

  Davon micro-telescope, 148

  Dawes’ Limit, 261
    in physiological factors, 263

  Declination circle, 108
    adjustment of, 239

  Declination circle, adjustment by, 237
    facilitates setting up instrument, 110

  Definition condition for excellence of, 254
    good in situations widely different, 254

  DeRheita, 12
    constructed binoculars, 13
    terrestrial ocular, 13

  Descartes’ dioptrics, publication of, 11
    lens with elliptical curvature, 12

  Dew cap, 219

  Diaphragms, importance of, 43

  Diffraction figure for bright line, 269
    pattern, 256
    solid, apparent diameter of, 262
    solid of planet, 269
    solid for a star, 260
    spectra, 190
    system, scale of, 260
    varies inversely with aperture, 260
    through objective, 258

  Digges, account suggests camera obscura, 7

  Dimensions, customary, telescope of, 24

  Discs, inspection of glass, 66
    roughing to form, 69

  Distortion, 86

  Dolland, John, 28
      published his discovery of achromatism, 29
    Peter, early triple objective, 29

  Dome wholly of galvanized iron, 250

  Domes, 246

  Driving clock, a simple, 174
    pendulum controlled, 177
    clocks spring operated, 175


  E

  English equatorial, 110
    mounts, mechanical stability of, 113

  Equatorial, adjustments of, 230

  Equatorial, coudé, 124
    mount, different situations in using, 229
    mount, first by Short, 104
    mount, pier overhung, 115
    mount in section, 107
    two motions necessary in, 106

  Equilibrating levers, devised by T. Grubb, 39

  Evershed, direct vision solar spectroscope, 189

  Eye lens, simple, preferred by Sir W. Herschel, 136

  Eyepiece, compensating, 142
    Huygenian, 139
    Huygenian, achromatism of, 140
    Huygenian, with cross wires, 140
    Huygenian, field of, 141
    Huygenian focal length of, 143
    measuring focus of, 136
    microscope form, 147, 148
    monocentric, 139
    a simple microscope, 134
    Tolles solid, 141


  F

  Field, curvature of, 85
    glass, arrangement of parts, 151
      Galilean, 150
      lens diameter possible, 150

  Field lens, 139

  Figuring locally, 73
    process of, 73

  Filar micrometer, 172

  Finder, 108, 132
    adjustment of, 230

  Fine grinding, 69

  Fixed eyepiece mounts, 118

  Flints, highly refractive due to Guinand, 36

  Foucault, 39
    development of silver on glass reflector, 41
    knife edge test, 212

  Foucault, methods of working and testing, 41

  Fraunhofer, 36
    applied condition of absence of coma, 82
    form of objectives, 37
    long list of notable achievements, 38

  “Front view” telescope, 32
    mechanical difficulty of, 33

  Furnaces, glass, classes of, 59


  G

  Galilean telescope, small field of, 9

  Galileo, exhibited telescope to senators of Venice, 8
    grasps the general principles, 7
    produces instrument magnifying 32 times, 8

  Gascoigne, William, first using genuine micrometer, 12

  Gauss, Objective, 82

  Gerrish, application of drive, 181
    motor drive, 179

  Ghosts, 137

  Glass, dark, as sunshade, 166
    forming and annealing, 62
    inspection of raw, 61
    losses by volatilization, 58
    materials of, 59
    origin of, 57
    persistent bubbles in, 58
    a solid solution, 57

  Grating spectroscopes, 190

  Gratings, spectroscope, 189

  Gregory, James, described construction which bears his name, 19
    failed of material success, 20

  Grubb, Sir Howard, objectives, 74

  Guinand, Pierre Louis, improvements in optical glass, 36


  H

  Hadley, disclosed test for true figure, 27
    John, real inventor of reflector, 25

  Hadley’s reflector, tested with satisfactory results, 26

  Hall, Chester Moor, designed first achromatic telescope, 27
    had telescopes made as early as 1733, 27

  Hand telescope, magnifying power, 150
    monocular, 151

  Hartmann test, 213
    on large objectives, 267
    principle of, 214

  Hartness, turret telescope, 130, 131

  Heliometer, principle of, 171

  Hensoldt, prism form, 163

  Herschel’s discovery of Uranus, 32
    forty foot telescope, 34
    Sir John, 35
    Sir John, proposed defining condition, 81
    Sir William, 31

  Herschel’s time, instruments of, 35

  Hevelius, construction for objective of 150 feet, 17
    directions for designing Galilean and Keplerian telescopes, 14
    invention of first periscope, 15
    Johannes, 13
    mention of advantage of plano convex lens, 14
    mentions telescope due to DeRheita, 14

  Housing reflector of 36 inch aperture, 243
    rolling on track, 242
    simplest instrument for fixed, 241

  Huygens, Christian, devised methods of grinding & polishing, 16

  Huygens’ eyepiece, introduction of, 24

  Huygens, sketch of Mars, 16


  I

  Image, correct extra focal, 208
    critical examination of, 204

  Image, curvature of, 87
    seen without eyepiece, 134
    showing unsymmetrical coloring, 208

  Interference rings, eccentric, 205

  Irradiation, 262


  J

  Jansen, Zacharius, 4


  K

  Kellner, ocular, 145

  Kepler, astronomical telescope, 10
    differences of from Galilean form, 10

  Knife edge test of parabolic mirror, 212


  L

  Lacquer, endurance of coating, 223

  Latitude scale, 232

  Lenses, determinate forms for, 80

  Lens, magnifying power of, 134
    “crossed,” 24
    polishing the fine ground, 70
    power of, 78
    triple cemented, a useful ocular, 138
    simple achromatic, 137
    single, has small field, 137
    spotted, cleaning of, 217

  Light grasp and resolving power, 265
    small telescope fails in, 264

  Light ratio of star magnitudes, 264

  Light transmitted by glass, 53

  Lippershey, Jan, 2
    discovery, when made, 5
    retainer to, 3

  Lunette à Napoleon Troisiéme, 154, 155, 162


  M

  Magnifying power, directly as ratio of increase in tangent, 135
    powers, increase of, 273

  Marius, Simon, 5
    used with glasses from spectacles, 5

  Marius, picked up satellites of Jupiter, 5

  Meridian photometer, 194

  Metius, James, 4

  Metius, tale of, 4

  Micrometer, double image, 171
    square bar, 171

  Micrometers, 168

  Micrometry, foundations of, 12

  Mirror’s, aberrations of, 92
    adjustment of, 206
    concave spherical, 92
    final burnishing of, 226
    hyperboloidal, 96
    lacquer coating for surface, 221
    mounting, by Browning, 49
    parabolic oblique, shows aberration, 95
    surface, prevention of injury to, 220

  Mittenzwey ocular, 141

  Mountain stations, good or very bad, 254

  Mounts, alt-azimuth and equatorial, 98

  Myopia, glasses for, came slowly, 2


  N

  Navicula Lyra, stages of resolution of, 271

  Newton, abandoned parabolic mirror, 21
    blunder in experiment, 20
    gave little information about material for mirrors, 23
    Isaac, attempt at a reflector, 20

  Normal spectra, 190


  O

  Objective, adjustable mount for, 44
    adjusting screws of, 44
    Clark’s form, 83
    cleansing, 203
    examination of, 202

  Objective, four-part, 85
    Fraunhofer flint-ahead, 83
    how to clean, 216
    spacers, to take out, 217
    typical striæ in, 203

  Objective prism, photographing with, 185, 187

  Objectives, crown glass equiconvex, 80
    over-achromatized, 90
    rated on focal length for green 24

  Observatories, cost of Romsey, 252

  Observatory at small expense, 249
    Romsey, description of, 249
    with simple sliding roof, 245

  Observing box, 229

  Oblique fork alt-azimuth, 100

  Ocular, apparent angular field of, 146
    terrestrial, 147
    Tolles terrestrial, 147
    typical form, 45

  Oculars, radius of curvature of image in, 146
    undesirability of short focus, 275

  Open fork mount, 115
    well suited to big reflectors, 117

  Optical axis, to adjust declination of, 238

  Optical glass, classes of, 63
    data and analysis of, 64
    industry, due to single man, 36
    production of, 60

  Orthoscopic ocular, 145


  P

  Parallactic mount, 104

  Petition for annulment of Dolland’s patent, 29

  Photometer, artificial star Zöllner, 194
    extinction, 198
    photoelectric cell, 199
    precision of astronomical, 199
    selenium cell, 199
    Zöllner, 197

  Photometers, three classes in stellar, 193

  “Photo-visual, objective,” 89

  Pillar-and-claw stand, 98

  Pillar mount, 240

  Pitch, optician’s, 71

  Placement for tripod legs, 236

  Polar and coudé forms of reflector, 125
    axis, adjustment of by level, 232
    axis, alignment to meridian, 232
    axis, setting with finder altitude of, 234
    telescope, 119, 122

  Polaris, hour angle of, 233
    a variable star, 199

  Polarizing photometer, 193

  Pole, position, 234

  Polishing machine, 70
    surface of tool, 72
    tool, 71

  Porro’s second form, 157
    work, original description of, 156

  Porta, description unintelligible, 7

  Portable equatorial, adjustment of, 230
    telescopes, mounting of, 228

  Porter polar reflector, 130

  Position angle micrometer of Lowell Observatory, 173

  Powers, lowest practicable, 276

  Prismatic inversion, Porro’s first form, 155

  Prismatic inverting system, the first, 154

  Prisms, Dove’s, 154

  Prism field glasses, stereoscopic effect of, 159

  Prism glass, 152
    loss of light in, 160
    objectives of, 161
    weak points of, 160


  R

  Resolving constant, magnification to develop, 275
    power and verity of detail, 2
    power of the eye, 274

  Reticulated micrometer, 169

  Reversion prism, 153

  Right ascension circle, 108

  Ring micrometer, 169
    computation of results of, 170

  Ring system faults due to strain, 205

  “Romsey” observatory type, 248

  Rack motion in altitude, 100

  Ramsden, ocular, 144

  Reflection, coefficient of, from silvered surface, 54

  Reflector costs, 55
    cover for, 242
    development in England, 41
    for astrophysical work, 56
    light-grasp of, 53
    relative aperture of, 50
    section of Newtonian, 45
    skeleton construction, 49
    suffers from scattered light, 56
    working field of, 55

  Refractive index, 63

  Refractors and reflectors, relative advantages of, 52
    few made after advent of reflector, 27
    in section, 43
    light transmission of, 53

  Refractors, relative equivalent apertures of, 54
    tubes of, 42


  S

  Scheiner, Christopher, use of Kepler’s telescope, 11
    devised parallactic mount, 11

  Secondary spectrum, 87
    new glasses reducing, 88

  Seeing, 257
    conditions, for difference of aperture, 257
    conditions generally bad, 253
    standard scale of, 256
    true inwardness of bad, 253

  Separating power, to compute, 261

  Short, James, mastered art of figuring paraboloid, 27
    took up Gregorian construction with success, 27

  Shortened telescope, 152

  Sights, on portable mount, 229

  Silver films, condition of, 54

  Silvering, Ludin’s process, 225
    processes, 222
    process, Dr. Brashear’s, 222

  Sine condition, Abbé’s, 82

  Slit, spectroscope, Abbé type, 184

  Snow cœlostat telescope, 127

  Solar diagonal, 166
    eye piece diaphragms in, 168
    early spectroscopes, 188
    polarizing eyepiece, 167
    spectroscope, 187

  Spacers, 44, 218

  Spectacle lenses, combination of, 2

  Spectacles for presbyopia, 2
    invention of, 1

  Spectra, visibility of stellar, 183

  Spectro-heliograph, principle of, 191
    simple type of Hale’s, 191

  Spectroscope, 182
    construction of astronomical, 182
    of Lowell refractor, 185
    ocular, McClean form, 183

  Specula, small, methods of support, 49

  Speculum metal composition of, 24

  Sphenoid prisms, 158, 163

  Spherical aberration, 11
    amount of, 80
    annulling in both directions, 84
    examination for, 207
    quick test of, 267
    remedy for, 79
    concave mirror, errors of, 22

  Star, appearance of, 204
    artificial, 66, 203
    diagonal, 165
    disc, apparent diameter of, 259
    image of reflector, 206

  Steinheil, achromatic ocular, 144
    Karl August, silvering specula, 39

  Striæ, location of, 67

  Surface, treatment of deterioration of, 218


  T

  Taylor, triplets with reduced secondary spectrum, 89

  Telescopes, choice and purchase of, 201
    Early in 1610 made in England, 6
    first, 3
    the first astronomical, 9
    improvement of early, 11
    lineage of, 1
    name devised, 9

  Telescopes, portable and fixed, 108
    1609, for sale in Paris, 5
    size and mounting of early, 14

  Telescopic vision, discovery of, 2

  Templets, designed curves of, 69

  Tests for striæ and annealing, 68

  Transparency, lack of in atmosphere, 255

  Triplet, cemented, 85

  Turret housing of reflector, 244


  V

  Variable stars, 192


  W

  Wedge calibrated by observation, 197
    photographic, 197
    photometer, 197

  Wind, shelter from, 240


  Z

  Zeiss, binocular of extreme stereoscopic effect, 161

  Zöllner, photometer modification of, 198

  Zonal aberration, 209


       *       *       *       *       *


Transcriber's Notes

Obvious typographical errors have been silently corrected. Variations
in hyphenation and accents have been standardised but all other
spelling and punctuation remains unchanged.

Italics are represented thus _italic_, bold thus =bold=, subscript thus
_{s} and underline thus underline=.

In caption of Fig. 49.—Spherical Aberration of Concave Lens. Concave
has been changed to Convex

In “An objective of 4.56′ inches aperture has a resolving constant of
1″ and to develop this should take a magnification of say 300,” 1″ has
been hand altered in the original and may be 1′.

The table “Characteristics of Optical Glasses″ has been divided to fit
within the width restriction.