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.

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]

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.

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.

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.

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[Pg 40]
[Pg 41] the pendulum experiment, his measurement of the velocity of light, and the discovery of the electrical eddy currents that bear his name.

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.

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.

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.

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 s₁, s₁₁ 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 s₁₁ 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.

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.

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 posi[Pg 47]
[Pg 48]tion for observation. One or more handles, N, are provided for this purpose.

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 ? to ¼ that diameter.

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.

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.

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.

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 mⁿ per cent. Thus if one half inch passes .98, two inches will transmit .98⁴, 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 mⁿ. 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.

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.