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.