Encyclopædia Britannica, Ninth Edition/Telescope

by David Gill

TELESCOPE

The telescope is an optical instrument employed to view or discover distant objects.^[1] The fundamental optical principles involved in its construction have already been dealt with in the articles Light and Optics, and these should be first perused by the reader.

History.

The credit of the discovery of the telescope has been a fruitful subject of discussion. Thus, because Democritus announced that the milky way is composed of vast multitudes of stars, it has been maintained that he could only have been led to form such an opinion from actual examination of the heavens with a telescope. Other passages from the Greek and Latin authors have similarly been cited to prove that the telescope was known to the ancients. But, as has been remarked by Dr Robert Grant (History of Physical Astronomy, p. 515), we are no more warranted in drawing so important a conclusion from casual remarks, however sagacious, than we should be justified in stating that Seneca was in possession of the discoveries of Newton because he predicted that comets would one day be found to revolve in periodic orbits. Molyneux, in his Dioptrica Nova, p. 256, declares hisRoger Bacon opinion that Roger Bacon (who died c. 1294) "did perfectly well understand all kinds of optic glasses, and knew likewise the method of combining them so as to compose some such instrument as our telescope." He cites a passage from Bacon's Opus Majus, p. 377 of Jebb's edition, 1733, translated as follows:

"Greater things than these may be performed by refracted vision. For it is easy to understand by the canons above mentioned that the greatest objects may appear exceedingly small, and the contrary, also that the most remote objects may appear just at hand, and the converse; for we can give such figures to transparent bodies, and dispose them in such order with respect to the eye and the objects, that the rays shall be refracted and bent towards any place we please, so that we shall see the object near at hand or at any distance under any angle we please. And thus from an incredible distance we may read the smallest letters, and may number the smallest particles of dust and sand, by reason of the greatness of the angle under which we see them. . . . Thus also the sun, moon, and stars may be made to descend hither in appearance, and to be visible over the heads of our enemies, and many things of the like sort, which persons unacquainted with such things would refuse to believe."

Molyneux also cites from Bacon's Epistola ad Parisiensem, "Of the Secrets of Art and Nature," chap. 5: —

"Glasses or diaphanous bodies may be so formed that the most remote objects may appear just at hand, and the contrary, so that we may read the smallest letters at an incredible distance, and may number things, though never so small, and may make the stars also appear as near as we please."

These passages certainly prove that Bacon had very nearly, if not perfectly, arrived at theoretical proof of the possibility of constructing a telescope and a microscope; but his writings give no account of the trial of an actual telescope, nor any detailed results of the application of a telescope to an examination of the heavens. It has been pointed out by Dr Smith, in his Complete System of Optics, that Bacon imagines some effects of telescopes which cannot be performed by them, and his conclusion is that Bacon never actually looked through a telescope.

Della PortaGiambattista della Porta, in his Magia Naturalis, printed in 1558, makes the following remarkable statement:—

"If you do but know how to join the two (viz., the concave and the convex glasses) rightly together, you will see both remote and near objects larger than they otherwise appear, and withal very distinct."

Wolfius infers from this passage that its author was the first actual constructor of a telescope, and it appears not improbable that by happy accident Porta really did make some primitive form of telescope which excited the wonder of his friends. Here, however, his interest in the matter appears to have ceased, and he was unable either to appreciate the importance of his discovery or to describe the means by which the object was attained. Kepler, who examined Porta's account of his concave and convex lenses by desire of his patron the emperor Rudolph, declared that it was perfectly unintelligible. Poggendorff (Gesch. der Physik, p. 134) throws considerable doubt on the originality of Porta's statement.

Leonard Digges.Thomas Digges, in his Stratioticus, p. 359, published in 1579, states that his father, Leonard Digges,

"among other curious practices had a method of discovering by perspective glasses set at due angles all objects pretty far distant that the sun shone upon, which lay in the country round about,"

and that this was by the help of a manuscript book of Roger Bacon of Oxford, who he conceived was the only man besides his father who knew it. There is also the following passage in the Pantometria(bk. i. chap. 21) of Leonard Digges^[2] (originally published by his son Thomas in 1571, and again in 1591):—

"Marvellous are the conclusions that may be performed by glasses concave and convex, of circular and parabolic forms, using for multiplication of beams sometime the aid of glasses transparent, which, by fraction, should unite or dissipate the images or figures presented by the reflection of other."

He then describes the effects of magnification from a combination of lenses or mirrors, adding:—

"But of these conclusions I minde not here to intreate, having at large in, a volume^[3] by itselfe opened the miraculous effects of perspective glasses."

It is impossible to discredit the significance of these quotations, for the works in which they occur were published more than twenty years before the original date claimed for the discovery of the telescope in Holland.

That Roger Bacon had tolerably clear ideas as to the practical possibility of constructing telescopes, and that Leonard Digges had access to some unpublished MSS. of Bacon, and by their aid constructed some form of telescope, seem to be obvious inferences from the preceding evidence. But it is quite certain that previous to 1600 the telescope was unknown, except possibly to individuals who failed to see its practical importance, and who confined its use to "curious practices " or to demonstrations ofThe Dutch telescope of 1608. "natural magic." The practical discovery of the instrument was certainly made in Holland about 1608, but the credit of the original invention has been claimed on behalf of three individuals, Hans Lippershey and Zacharias Jansen, spectacle-makers in Middelburg, and James Metius of Alkmaar (brother of Adrian Metius the mathematician).

Descartes, in his treatise on Dioptrics (1637), attributes the discovery to Metius "about thirty years ago," whilst Schyrælus de Rheita, a Capuchin friar, in his Oculus Enoch et Eliæ (Antwerp, 1645), gives the credit to Lippershey about 1609. Peter Borel, physician to the king of France, published at The Hague, in 1655, a work De Vero Telescopii Inventore. He was assisted in its preparation by William Borel, Dutch envoy at the court of France, and the latter declares, as the result of patient investigation, that

Jansen. Jansen and his father were the real inventors of the telescope in 1610, and that Lippershey only made a telescope after hints accidentally communicated to him of the details of Jansen's invention. But the most trustworthy information on the subject is to be got from the researches of Van Swinden. ^[4] Briefly summarized, this evidence is as follows. In the library of the university of Leyden, amongst the MSS. of Huygens there is an original copy of a document (dated 17th October 1608) addressed to the states-general by Jacob Andrianzoon (the same individual who is called JamesMetius. Metius by Descartes), petitioning for the exclusive right of selling an instrument of his invention by which distant objects appear larger and more distinct. He states that he had discovered the instrument by accident when engaged in making experiments, and had so far perfected it that distant objects were made as visible and distinct by his instrument as could be done with the one which had been lately offered to the states by a citizen and spectacle-maker of Middelburg. Among the Acts of the states-general preserved in the Government archives at The Hague, Van Swinden found that on 2d October 1608 the assembly of the states took into consideration the Lippershey. petition of Hans Lippershey, spectacle-maker, a native of Wesel and an inhabitant of Middelburg, inventor of an instrument for seeing at a distance. On 4th October a committee was appointed to test the instrument, and on the 6th of the same month the assembly agreed to give Lippershey 900 florins for his instrument. Further, on the 15th December of the same year they examined an instrument invented by Lippershey at their request to see with both eyes, and gave him orders to execute two similar instruments at 900 florins each ; but, as many other persons had knowledge of this new invention to see at a distance, they did not deem it expedient to grant him an exclusive privilege to sell such instruments. The dates of these documents dispose effectually of Borel's statement that Lippershey borrowed the ideas of Jansen in 1610. They also prove that, whilst Metius was in possession of a telescope, with which he may have experimented, about the time when Lippershey presented his application for patent rights, yet he makes no pretension that Lippershey borrowed the invention from him. The conclusion is that Lippershey was the first person who independently invented the telescope, and at the same time made the instrument known to the world. The common story is that Lippershey, happening one day, whilst holding a spectacle-lens in either hand, to direct them towards the steeple of a neighbouring church, was astonished, on looking through the nearer lens, to find that the weathercock appeared nearer and more distinct. He fitted the lenses in a tube, in order to adjust and preserve their relative distances, and thus constructed his first telescope. But doubt may be thrown on this traditional account owing to the further statement that the image of the weathercock so viewed was seen turned upside down. All the original Dutch telescopes were composed of a convex and a concave lens, and telescopes so constructed do not invert. The inverting telescope, composed of two convex lenses, was a later invention ; still it is not impossible that the original experiment was made with two convex lenses.

Telescopes seem to have been made in Holland in considerable numbers soon after the date of their invention, and rapidly found their way over Europe. Sirturus, in his De Telescopio (1618), states that "a Frenchman proceeded to Milan in the month of May 1609 and offered a telescope for sale to Count di Fuentes"; and Lorenzi Pigorna writes, ^[5] under date 31st August 1609, that "Galileo had been appointed lecturer at Padua for life on account of a perspective like the one which was sent from Flanders to Cardinal Borghese." Simon Marius, the German astronomer, appears to have made astronomical observations in 1609 with a telescope which he procured from Holland, and Professor Rigaud of Oxford found from the MSS. of Harriot, the mathematician, that he had been making astronomical observations with a Dutch telescope as Galileo.early as July 1609. Galileo, in his Nuncius Sidereus, states that, happening to be in Venice about the month of May 1609, he heard that a Belgian had invented a perspective instrument by means of which distant objects appeared nearer and larger, and that he discovered its construction by considering the effects of refraction. In his Saggiatore Galileo states that he solved the problem of the construction of a telescope the first night after his return to Padua from Venice, and made his first telescope next day by fitting a convex lens in one extremity of a leaden tube and a concave lens in the other one. A few days afterwards, having succeeded in making a better telescope than the first, he took it to Venice, where he communicated the details of his invention to the public, and presented the instrument itself to the doge Leonardo Donato, sitting in full council. The senate, in return, settled him for life in his lectureship at Padua and doubled his salary, which was previously 500 florins, and which then became treble that which any of his predecessors had enjoyed. Galileo may thus claim to have invented the telescope independently, but not till he had heard that others had done so. In fact the time was ripe; and, as often happens in similar circumstances, only a hint was necessary to complete the latent chain of thought. Galileo devoted all his time to improving and perfecting the telescope. Knowing the theory of his instrument, and possessed of much practical skill, coupled with unwearied patience, he conquered the difficulties of grinding and polishing the lenses, and soon succeeded in producing telescopes of greatly increased power. His first telescope magnified three diameters, but he soon made instruments which magnified eight diameters, and finally one that magnified thirty-three diameters.^[6] With this last instrument he discovered in 1610 the satellites of Jupiter, and soon afterwards the spots on the sun, the phases of Venus, and the hills and valleys on the moon. He demonstrated the rotation of the satellites of Jupiter round the planet, and gave rough predictions of their configurations, proved the rotation of the sun on its axis, established the general truth of the Copernican system as compared with that of Ptolemy, and fairly routed the fanciful dogmas of the philosophers. These brilliant achievements, together with the immense improvement of the instrument under the hands of Galileo, overshadowed in a great degree the credit due to the original discoverer, and led to the universal adoption of the name of the Galilean telescope for the form of the instrument invented by Lippershey.

Kepler.Kepler first explained the theory and some of the practical advantages of a telescope constructed of two convex lenses in his Catoptrics (1611). The first person who actually constructed a telescope of this form was Father Scheiner, who gives a description of it in his Rosa Ursina Gascoigne.(1630). William Gascoigne was the first who practically appreciated the chief advantages of the form of telescope suggested by Kepler, viz., the visibility of the image of a distant object simultaneously with that of a small material object placed in the common focus of the two lenses. This led to his invention of the micrometer and his application of telescopic sights to astronomical instruments of precision (see Micrometer, vol. xvi. p. 242). But it was not till about the middle of the 17th century that Kepler's telescope came into general use, and then, not so much because of the advantages pointed out by Gascoigne, but because its field of view was much larger than in the Galilean telescope. The first powerful telescopes of this Huygens.construction were made by Huygens, after much labour, in which he was assisted by his brother. With one of these, of 12-feet focal length, he discovered the brightest of Saturn's satellites (Titan) in 1655, and in 1659 he published his Systema Saturnium, in which was given for the first time a true explanation of Saturn's ring, founded on observations made with the same instrument. The sharpness of image in Kepler's telescope is very inferior to that of the Galilean instrument, so that when a high magnifying power is required Cassini.it becomes essential to increase the focal length. Cassini discovered Saturn's fifth satellite (Rhea) in 1672 with a telescope of 35 feet, and the third and fourth satellites in 1684 with telescopes made by Campani of 100 and 136 feet focal length. Huygens states that he and his brother made object-glasses of 170 and 210 feet focal length, and he presented one of 123 feet to the Royal Society of London. Auzout and others are said to have made telescopes of from 300 to 600 feet focus, but it does not appear that they were ever able to use them in practical observations. Bradley, on 27th December 1722, actually measured the diameter of Venus with a telescope whose object-glass had a focal length of 2121/4 feet. In these very long telescopes no tube was employed, and they were consequently Aerial telescopes.termed aerial telescopes, Huygens contrived some ingenious arrangements for directing such telescopes towards any object visible in the heavens,—the focal adjustment and centring of the eye-piece being preserved by a braced rod connecting the object-glass and eye-piece. Other contrivances for the same purpose are described by La Hire (Mém. de l'Acad., 1715) and by Hartsoeker {Miscel. Berol., vol. i. p. 261). Telescopes of such great length were naturally difficult to use, and must have taxed to the utmost the skill and patience of the observers. One cannot but pay a passing tribute of admiration to the men who, with such troublesome tools, achieved such results.

Reflecting telescopes.Until Newton's discovery of the different refrangibility of light of different colours, it was generally supposed that object-glasses of telescopes were subject to no other errors than those which arose from the spherical figure of their surfaces, and the efforts of opticians were chiefly directed to the construction of lenses of other forms of curvature. Gregory.James Gregory, in his Optica Promota (1663), discusses the forms of images of objects produced by lenses and mirrors, and shows that when the surfaces of the lenses or mirrors are portions of spheres the images are curves concave towards the objective, but if the curves of the surfaces are conic sections the spherical aberration is corrected. He was well aware of the failures of all attempts to perfect telescopes by employing lenses of various forms of curvature, and accordingly proposed the form of reflecting telescope which bears his name. But Gregory, according to his own confession, had no practical skill; he could find no optician capable of realizing his ideas, and after some fruitless attempts was obliged to abandon all hope of Newton.bringing his telescope into practical use. Newton was the first to construct a reflecting telescope. When in 1666 he made his discovery of the different refrangibility of light of different colours, he soon perceived that the faults of the refracting telescope were due much more to this cause than to the spherical figure of the lenses. He over-hastily concluded from some rough experiments (Optics, bk. i. pt. ii. prop. 3) "that all refracting substances diverged the prismatic colours in a constant proportion to their mean refraction and he drew the natural conclusion "that refraction could not be produced without colour," and therefore "that no improvement could be expected from the refracting telescope" (Treatise on Optics, p. 112). But, having ascertained by experiment that for all colours of light the angle of incidence is equal to the angle of reflexion, he turned his attention to the construction of reflecting telescopes. After much experiment he selected an alloy of tin and copper as the most suitable material for his specula, and he devised means for grinding and polishing them. He did not attempt the formation of a parabolic figure on account of the probable mechanical difficulties, and he had besides satisfied himself that the chromatic and not the spherical aberration formed the chief faults of previous telescopes. Newton's first telescope so far realized his expectations that he could see with its aid the satellites of Jupiter and the horns of Venus, Encouraged by this success, he made a second telescope of 6 1/3-inches focal length, with a magnifying power of 38 diameters, which he presented to the Cassegrain.Royal Society of London in December 1671. A third form of reflecting telescope was devised in 1672 by Cassegrain (Journal des Sçavans, 1672). No further practical advance appears to have been made in the design or construction of Hadley.the instrument till the year 1723, when John Hadley (best known as the inventor of the sextant) presented to the Royal Society a reflecting telescope of the Newtonian construction, with a metallic speculum of 6-inches aperture and 62 5/8-inches focal length, having eye-pieces magnifying up to 230 diameters. The instrument was examined by Pound and Bradley, the former of whom reported upon it in Phil. Trans., 1723, No. 378, p. 382. After remarking that Newton's telescope "had lain neglected these fifty years," they stated that Hadley had sufficiently shown "that this noble invention does not consist in bare theory." They compared its performance with that of the object-glass of 123 -feet focal length presented to the Royal Society by Huygens, and found that Hadley's reflector

"will bear such a charge as to make it magnify the object as many times as the latter with its due charge, and that it represents objects as distinct, though not altogether so clear and bright. . . Notwithstanding this difference in the brightness of the objects, we were able with this reflecting telescope to see whatever we have hitherto discovered with the Hugenian, particularly the transits of Jupiter's satellites and their shadows over his disk, the black list in Saturn's ring, and the edge of his shadow cast on his ring. We have also seen with it several times the five satellites of Saturn, in viewing of which this telescope had the advantage of the Hugenian at the time when we compared them ; for, being in summer, and the Hugenian telescope being managed without a tube, the twilight prevented us from seeing in this some of these small objects which at the same time we could discern with the reflecting telescope."

Bradley and Molyneux, having been instructed by Hadley in his methods of polishing specula, succeeded in producing some telescopes of considerable power, one of which had a focal length of 8 feet; and, Molyneux having communicated these methods to Scarlet and Hearn, two London opticians, the manufacture of telescopes as a matter of business was commenced by them (Smith's Optics, bk. iii. ch. 1), But James Short.it was reserved for James Short of Edinburgh to give practical effect to Gregory's original idea. Born at Edinburgh in 1710 and originally educated for the church, Short attracted the attention of Maclaurin, professor of mathematics at the university, who permitted him about 1732 to make use of his rooms in the college buildings for experiments in the construction of telescopes. In Short's first telescopes the specula were of glass, as suggested by Gregory, but he afterwards used metallic specula only, and succeeded in giving to them true parabolic and elliptic figures. Short then adopted telescope-making as his profession, which he practised first in Edinburgh and afterwards in London, All Short's telescopes were of the Gregorian form, and some of them retain even to the present day their original high polish and sharp definition. Short died in London in 1768, having realized a considerable fortune by the exercise of his profession.

Achromatic telescope.The historical sequence of events now brings us to the discovery of the achromatic telescope. The first person who succeeded in making achromatic refracting telescopes. Chester M. Hallseems to have been Chester Moor Hall, a gentleman of Essex. He argued that the different humours of the human eye so refract rays of light as to produce an image on the retina which is free from colour, and he reasonably argued that it might be possible to produce a like result by combining lenses composed of different refracting media.^[7] After devoting some time to the inquiry he found that by combining lenses formed of different kinds of glass the effect of the unequal refrangibility of light was corrected, and in 1733 he succeeded in constructing telescopes which exhibited objects free from colour. One of these instruments of only 20-inches focal length had an aperture of 21/2 inches. Hall was a man of independent means, and seems to have been careless of fame: at least he took no trouble to communicate his invention to the world. At a trial in Westminster Hall about the patent rights granted to Dollond (Watkin v. Dollond), ^[8] Hall was admitted to be the first inventor of the achromatic telescope; but it was ruled by Lord Mansfield that "it was not the person who locked his invention in his scrutoire that ought to profit for such invention, but be who brought Euler.it forth for the benefit of mankind."^[9] In 1747 Euler communicated to the Berlin Academy of Sciences a memoir in which be endeavoured to prove the possibility of correcting both the chromatic and the spherical aberration of an object-glass. Like Gregory and Hall, he argued that, since the various humours of the human eye were so combined as to produce a perfect image, it should be possible by suitable combinations of lenses of different refracting media to construct a perfect object-glass. Adopting a hypothetical law of the dispersion of differently coloured rays of light, be proved analytically the possibility of constructing an achromatic object-glass composed of lenses of glass and water. But all his efforts to produce an actual object-glass of this construction were fruitless,—a failure which he attributed solely to the difficulty of procuring lenses worked precisely to the requisite curves (Mem. Acad. Berlin, 1753). Dollond admitted the accuracy of Euler's analysis, but disputed his hypothesis on the grounds that it was purely a theoretical assumption, that the theory was opposed to the results of Newton's experiments on the refrangibility of light, and that it was impossible to determine a physical law from analytical reasoning alone (Phil. Trans. 1753, p. 289). In 1754 Euler communicated to the Berlin Academy a further memoir, in which, starting from the hypothesis that light consists of vibrations excited in an elastic fluid by luminous bodies, and that the difference of colour of light is due to the greater or less frequency of these vibrations in a given time, he deduced his previous results. He did not doubt the accuracy of Newton's experiments quoted by Dollond, because he asserted that the difference between the law deduced by Newton and that which he assumed would not be rendered sensible by such an experiment. ^[10] Dollond did not reply to this memoir, but soon afterwards he received an abstract of a memoir by Klingenstierna,Klingenstierna. the Swedish mathematician and astronomer, which led him to doubt the accuracy of the results deduced by Newton on the dispersion of refracted light. Klingenstierna showed from purely geometrical considerations, fully appreciated by Dollond, that the results of Newton's experiments could not be brought into harmony with other universally accepted facts of refraction. Like a practical man, Dollond Dollond.at once put his doubts to the test of experiment, confirmed the conclusions of Klingenstierna, discovered "a difference far beyond his hopes in the refractive qualities of different kinds of glass with respect to their divergency of colours," and was thus rapidly led to the construction of object-glasses in which first the chromatic and afterwards the spherical aberration were corrected (Phil. Trans., 1758, p. 733).

We have thus followed somewhat minutely the history of the gradual process by which Dollond arrived independently at his invention of the refracting telescope, because it has been asserted that he borrowed the idea from others. Montucla, in his Histoire des Mathématiques (pp. 448-449), gives the following footnote, communicated to him by Lalande:—

"Ce fut Chestermonhall" (an obvious misprint for Chester Moor Hall) "qui, vers 1750, eut I'idée des lunettes achromatiques. Il s'adressoit à Ayscough,^[11] qui faisoit travaillir Bass. Dollond ayant eu besoin de Bass pour un verre que demandoit le duc d'Yorck, Bass lui fit voir du crown-glass et du flint-glass. Hall donna une lunette à Ayscough, qui la montra à plusieurs personnes; il en donna la construction à Bird, qui n'en tint pas compte. Dollond en profita. Dans le procès qu'il y eut entre Dollond et Watkin, au banc du roi, cela fut prouvé; mais Dollond gagna, parce qu'il étoit le premier qui eût fait connoître les lunettes achromatiques."

It is clearly established that Hall was the first inventor of the achromatic telescope; but Dollond did not borrow the invention from Hall without acknowledgment in the manner suggested by Lalande. His discovery was beyond question an independent one. The whole history of his researches proves how fully he was aware of the conditions necessary for the attainment of achromatism in refracting telescopes, and he may be well excused if he so long placed implicit reliance on the accuracy of experiments made by so illustrious a philosopher as Newton. His writings sufficiently show that but for this confidence he would have arrived sooner at a discovery for which his mind was fully prepared. It is, besides, impossible to read Dollond's memoir (Phil. Trans., 1758, p. 733) without being impressed with the fact that it is a truthful account, not only of the successive steps by which he independently arrived at his discovery, but also of the logical processes by which these steps were successively suggested to his mind.

The triple object-glass, consisting of a combination of two convex lenses of crown glass with a concave flint lens between them, was introduced in 1765 by Peter, son of John Dollond, and many excellent telescopes of this kind were made by him.

The limits of this article do not permit a further detailed historical statement of the various steps by which the powers of the telescope were developed. Indeed, in its practical form the principle of the instrument has remained unchanged from the time of the Dollonds to the present day; and the history of its development may be summed up as consisting not in new optical discoveries but in utilizing new appliances for figuring and polishing, improved material for specula and lenses, more refined means of testing, and more perfect and W. Herschel.convenient methods of mounting. About the year 1774 William Herschel, then a teacher of music in Bath, began to occupy his leisure hours with the construction of specula, and finally devoted himself entirely to their construction and use. In 1778 he had selected the chef d'œuvre of some 400 specula which he made for the celebrated instrument of 7 -feet focal length with which his early brilliant astronomical discoveries were made. In 1783 he completed his reflector of 18 7/10-inches aperture and 20-feet focus, and in 1789 his great reflector of 4-feet aperture and 40-feet focal length. The fame of these instruments was rapidly spread by the brilliant discoveries which their maker's genius and perseverance accomplished by their aid. The reflecting telescope became the only available tool of the astronomer when great light grasp was requisite, as the difficulty of procuring disks of glass (especially of flint glass) of suitable purity and homogeneity limited the dimensions of the achromatic telescope. It was in vain that the French Academy of Sciences offered prizes for perfect disks of optical flint glass. Some of the best chemists and most enterprising glass-manufacturers exerted their utmost efforts without succeeding in producing perfect disks of more than 31/2 inches in diameter. All the larger disks were crossed by striæ, or were otherwise deficient in the necessary homogeneity and purity.

Guinand.Pierre Louis Guinand, a humble watchmaker living near Chaux de Fond in Neuchâtel, Switzerland, was the first who succeeded in making marked progress in the manufacture of optical flint glass. After making preliminary experiments extending over seven years (1784–90), and nothing daunted by their comparative want of success, he erected a furnace near Les Brenets, and devoted most of his slender earnings (then derived from making the bells, or rather gongs, of repeating watches) to the fulfilment of his ambition. His persistency, courage, and self-denial recall forcibly the story of Palissy. In 1805 he joined the optical establishment of Fraunhofer and Utzschneider and remained with them about nine years. During this period extensive experiments were instituted with remarkable success. It is said that the disks for the Dorpat refractor (9·6 inches aperture, with which the observations of Wilhelm Struve were made) were manufactured during this period, though the complete instrument Fraunhofer.was not delivered till 1823. Fraunhofer had, however, profited so fully by the suggestions of Guinand, and had probably also so far improved on the original methods, that he afterwards succeeded in producing still larger object-glasses. After Fraunhofer's death in 1826 his successors Merz and Mahler carried out successfully the methods handed down to them by Guinand and Fraunhofer, and produced some large and excellent telescopes, which are hereafter mentioned. Meanwhile Guinand, having returned to his native country in 1814, resumed there the manufacture of disks of optical glass, discovered a method of removing striæ by breaking and reuniting the portions by heat, when the glass was in a plastic state, and eventually produced perfect disks up to 18 inches in diameter. Most of these he disposed of to Lerebours and Secretan, opticians in Paris, by both of whom some fine object-glasses were made. ^[12] Guinand communicated his secrets to his sons before his death in 1823. About 1829 Bontemps entered into partnership with one of the sons, and another son carried on his father's manufacture in partnership with his mother. The latter firm was succeeded by Dauget of Soleure, whose exhibits of optical glass excited so much attention at the London exhibition of 1851. About 1848 Bontemps joined the firm of Chance Brothers of Birmingham, and thus carried the secret of Guinand's methods to England. It is not a little remarkable that the only firms in the world by whom large disks of optical glass have been produced trace their success to information derived more or less directly from Guinand. MM. Feil of Paris, who are direct descendants of Guinand, and Messrs Chance Brothers of Birmingham are at the present time the only makers of optical glass in disks of larger diameter than 20 inches.

Instruments, &c.

We now proceed to give an account of the methods and principles of construction of the various kinds of telescopes, and to describe in detail special typical instruments, which, owing to the work accomplished by their aid or the practical advances exemplified in their construction, appear most worthy of record or study.

Refracting Telescope.

Early forms.In its simplest form the telescope consists of a convex object-lens capable of forming an image of a distant object and of an eye-lens, concave or convex, by which the image so formed is magnified. When the axis of the eye-lens coincides with that of the object-glass, and the focal point of the eye-lens is coincident with the principal focus of the object-lens, parallel rays incident upon the object-glass will emerge from the eye-piece as parallel rays.

Fig. 1.

These, falling in turn on the lens of the human eye, are converged by it and form an image on the retina. ^[13] Fig. 1 shows the course of the rays when the eye-lens is convex (or positive), fig. 2 when the eye-lens is concave (or negative). The former represents Kepler's, the latter Lippershey's or the Galilean telescope.

Fig. 2.

The magnifying power obviously depends on the proportion of the focal length of the object-lens to that of the eye-lens, that is,

magnifying power $={\frac {\mathrm {F} }{e}}$

where F is the focal length of the object-lens and e that of the Magnifying power.eye-lens. Also the diameter of the pencil of parallel rays emerging from the eye-lens is to the diameter of the object-lens inversely as the magnifying power the telescope. Hence one of the best methods of determining the magnifying power of a telescope is to measure the diameter of the emergent pencil of rays, after the telescope has been adjusted to focus upon a star, and to divide the diameter of the object-glass by the diameter of the -emergent pencil. If we desire to utilize all the parallel rays which fall upon an object-glass it is necessary that the full pencil of emerging rays should enter the observer's eye. Assuming with Sir William Herschel that the normal pupil of the eye distends to one-fifth of an inch in diameter when viewing faint objects, we obtain the rule that the minimum magnifying power which can be efficiently employed is five times the diameter of the object-glass expressed in inches. The defects of the Galilean and Kepler telescopes are due to the chromatic and spherical aberration of the simple lenses of which they are composed (see Optics, vol. xvii. p. 802 sq.) The substitution of a positive or negative eye-piece for the simple convex or concave eye-lens, and of an achromatic object-glass for the simple object-lens, transforms these early forms into the modern achromatic telescope. The Galilean telescope with a concave eye-lens instead of an eye-piece still survives as the modern opera-glass, on account of its shorter length, but the object-glass and eye-lens are achromatic combinations.

Achromatic object-glass.The principles of an achromatic combination of prisms or lenses have been explained in Light (vol. xiv. pp. 592, 595) and further developed in Optics (vol. xvii. p. 804 sq.). As a lens may be regarded as built up of a series of thin slices of prisms, divided from each other by planes parallel to the axis of the lens, it will be seen that, if a prism perfectly achromatic for rays of two definite wave-lengths, and approximately achromatic for all rays, can be constructed by combining two prisms of different kinds of glass, all that is required to produce an object-glass with similar small chromatic errors is to combine a convex lens of crown glass and a concave one of flint glass as in fig. 3, their surfaces being of such curvatures as to form a series of imaginary prisms (such as we have supposed an object-glass to consist of) through any one of which all kinds of light falling on the object-glass parallel to its axis will be refracted very nearly to a common focus F. Accordingly any proposed object-glass can be tested as regards its optical conditions by "tracing a ray," i.e., calculating the point at which, after refraction through the two lenses, the ray so traced will cut their common axis. For the analytical solution of this problem it is necessary to assume that the adjacent surfaces of the supposed infinitely numerous prisms form together some continuous curved surface, which practically is nearly spherical.

Fig. 3.

But the actual differences between the curves which may be required in certain conditions for producing a perfect lens differ so slightly from true spherical surfaces that it is impossible by any previously designed mechanical process to predict whether the resulting figure will be that of a sphere or some other curve very nearly that of a sphere. The mathematician, therefore, who discusses the subject is compelled to adopt spherical curves as the basis of his calculation. On this assumption we may then trace a ray rigidly through any supposed object-glass as follows. Let A, B, A', B' be respectively the points where the refracted ray produced would intersect the optical axis after refraction at the first, second, third, and fourth refracting surfaces respectively; also let a be the first angle of incidence, μ and μ' the refractive indexes for the crown and flint lens respectively for a ray of the wave-length whose course is to be traced, r and s the first and second radii for the crown lens, r' and s' the first and second radii for the flint lens, α, β, α', β' a' and b' auxiliary angles, d the thickness of the crown lens, d' the thickness of the flint lens, Δ the distance between the second and third surfaces. Then for the intersect after refraction at the first surface

$\sin \alpha ={\frac {1}{\mu }}\sin a;$

$(A)=a-\alpha ;A={\frac {r\sin \alpha }{\sin(A)}}+r;$

for the intersect after refraction at the second surface

$\sin b={\frac {A+s-d}{s}}\sin(A);$

$\sin \beta =\mu .\sin b;$

$(B)=(A)+\beta -b;B={\frac {s\sin \beta }{\sin(B)}}-s;$

for the intersect after refraction at the third surface

$\sin \alpha '=-(B-r'-\Delta ){\frac {\sin(B)}{r'}};$

$\sin \alpha '={\frac {1}{\mu '}}\sin a';$

$(A')=(B)+\alpha '-a';\quad A'=r-r'.{\frac {sin\beta }{\sin(A')}};$

for the intersect after refraction at the fourth surface

$\sin b'=-(A'+s'-d')\sin {\frac {(A')}{s'}};$

$\sin \beta '=\mu '\sin b';$

$(B')=(A')+b'-\beta ';\quad B'=-s-s'.{\frac {sin\beta '}{sin(B')}};$

The computation is very much simplified when we consider the angle of incidence to be very small —i.e., the point of incidence very near the optical axis, viz.,

${\frac {r}{A}}={\frac {\mu -1}{\mu }};{\frac {s}{B}}={\frac {\mu s}{A-d}}+mu-1;$

${\frac {r'}{A'}}={\frac {r'}{\mu '(B-\Delta )}}+{\frac {\mu '-1}{\mu '}};{\frac {s'}{B'}}={\frac {\mu 's'}{A'-d'}}+mu'-1;$

By means of these formulæ we can compute B' (the point where a ray, entering the first surface of the object-glass, will intersect the optical axis) for any angle of incidence = α, when for a ray of that wave-length the indexes of refraction are known for the glass of which the lenses are composed, if the radii of curvature of the lenses are also known. The most perfect object-glass would be one in which the value of B' is the same for two rays of the two selected wave-lengths, through whatever portion of the object-glass they may pass. This, however, is a condition which cannot be mathematically satisfied with spherical surfaces. It is of course possible to find values of the four unknown quantities r, s, r' and s' such that four conditions shall be satisfied. The ordinary approximate method is to find such values of the radii that B' is the same for rays of two different wave-lengths when the incident rays are near the axis, and for mean rays which enter near the margin of the lens; but of course, this solution is indeterminate, and only becomes rigid when two radii are assumed. Thus, for any crown lens of any radii of curvature it is possible to find a flint lens to satisfy these conditions. The rigid solution becomes one of successive approximation to such four conditions as the computer may consider most desirable. Herschel advocates satisfying the terms depending on the second power of the aberration, Klügel that the refractions of the rays should be as small as possible; or we may make it a condition that the second and third surfaces shall have the same radius, so that the surfaces may he cemented together. The fourth condition is of course the desired focal length. But for all practical purposes it is sufficient to have placed the reader in a position to test the optical conditions of any combinations, that may be proposed, and to refer Practical methods of computation.him to the works mentioned in the subjoined note^[14]; for, in fact the construction of object-glasses on paper is of far higher interest as a mathematical exercise than as a practical matter. By a slight departure from the spherical figure – a departure so minute that there are no mechanical means sufficiently delicate to measure it with certainty – the optician may fail to realize true spherical surfaces, and thus on the one hand miss the fine definition which his calculation led him to expect, or on the other hand convert an object-glass which with spherical curves would have large spherical aberration into one perfectly corrected in this respect. Having, therefore, for particular kinds of glass ascertained a good general form of object-glass, it becomes only necessary for the optician to perform an approximate calculation of the curvatures requisite to produce correction of the chromatic aberration. and to trust to the process of final figuring for correction of the final spherical and chromatic aberration. It fortunately happens that in the rigid equations the terms which express the thickness and distance apart of the lenses involve only the focal distances of central rays, and have but a small influence on the ratios of the aberrations of the lenses; and, further, they affect chiefly the focal length of the lens, and have a very small influence on the chromatic aberration. Thus in the preliminary computation the optician may neglect the thickness of the lenses and employ the simple approximate formulæ given under Optics, vol. xvii. p. 804—

${\frac {\delta \mu }{\mu -1}}.{\frac {1}{f}}+{\frac {\delta \mu '}{\mu '-1}}.{\frac {1}{f'}}=0,$

${\frac {1}{\mathrm {F} }}={\frac {1}{f}}+{\frac {1}{f'}},$

where${\frac {\delta \mu }{\mu -1}}$and${\frac {\delta \mu '}{\mu '-1}}$are the dispersive powers of the two kinds of glass for the two rays which he desires to unite, f and f' the corresponding focal lengths of the two lenses, and F the focal length of the combination. The focal lengths of the two lenses which secure the conditions of achromatism having been thus computed, the radii of curvature may be computed for either lens by the usual formula (see Light, vol. xiv. p. 593)—

${\frac {1}{f}}=(\mu -1){\biggl (}{\frac {1}{r}}-{\frac {1}{s}}{\biggr )}.$

In the last expression, where r and s correspond to the radii of curvature, the optician has an infinite range of choice. He will of course select such a proportion of r to s as experience or more elaborate calculation has shown to be favourable. In the form of object-glass recommended by Sir John Herschel, as fulfilling the most favourable conditions for correction of a spherical aberration for parallel as well as nearly parallel rays, the required curvatures for the exterior surfaces of the crown and the flint lens were found to vary very slightly for a considerable range of the ratio of the dispersive powers of the crown and the flint glass. Assuming μ (the mean index of refraction) to be 1·542 for crown glass and 1·585 for flint glass. Herschel proved that, if the radii in question are taken to be 6·72 for the crown lens and 14·20 for the flint lens (supposing the focal length of the desired combination to be 10), we have only to compute the radii of the second and third surfaces by means of the above simple formula and the measured dispersive and refractive power of the glass of the lenses. (The method of determining μ &c., is given under Optics, vol. xvii. p. 800.) The form generally adopted (see fig. 4) in the best modern object-glasses is extremely simple, viz., an equi-convex crown lens and a flint lens whose first surface has the same radius of curvature as the surfaces of the crown lens – this radius depending on the focal length which it is desired to give to the object-glass.

Fig. 4.

Since in order to fulfil the conditions of achromatism the focal lengths of the two lenses have to be proportional to their dispersive powers (for the rays which it is desired to unite), and as in the two descriptions of glass in question the dispersion of flint glass for C to rays between F and G is very nearly twice that of crown glass, the posterior surface of the flint lens becomes nearly a plane. The final correction for achromatism is made, if necessary, by departing slightly from a plane in the curvature of the last surface of the flint lens, and the final correction for spherical aberration in the figuring of the surfaces. In a lecture delivered at the Royal Institution on 2d April 1886 Sir Howard Grubb, optician, of Dublin, said:

"A truly spherical curve is the exception, not the rule. When I tell you that a sensible difference in correction for spherical aberration can be made by half an hour's polishing, corresponding probably to a difference in the first place of decimals in radii of the curves, you will see that it is practically not necessary to enter upon any calculation for spherical aberration. We know about what form gives an approximate correction; we adhere nearly to that, and the rest is done by figuring of the surface. To illustrate what I mean. I would be quite willing to undertake to alter the curves of the crown or flint lens of any of my objectives by a very large quantity, increasing one and decreasing the other so as to still satisfy the conditions of achromatism, but introducing theoretically a large amount of positive or negative spherical aberration, and yet to make out of the altered lens an object-glass perfectly corrected for spherical aberration.. . . I may remark that it is sometimes possible to make a better objective by deviating from the curves which give a true correction for spherical aberration, and correcting that aberration by figuring, rather than by strictly adhering to the theoretical curves."

Colour correction.When an object-glass is designed for use as an ordinary telescope it is usual to select for the rays of different colour to be united those near C and those between F and G, since rays of lower and higher refrangibility produce a comparatively faint impression on the sense of sight. In such a telescope of any considerable aperture the image of a bright star at focus is surrounded by a halo of bluish or violet-coloured light,—a defect which is unavoidable in an object-glass composed of a crown and flint lens on account of the irrationality of their spectra (Light, vol. xiv. p. 592). There seems to be no doubt that different eyes are differently impressed by rays of different wave-length.^[15] Thus two observers will often have different opinions as to the chromatic corrections of the same object-glass: the observer whose eye is abnormally sensitive to violet light will pronounce the chromatic aberration over-corrected in an object-glass which another will consider perfect in this respect, and vice versa. Probably it is partly owing to this cause that the object-glasses of different makers show Correction for chromatic aberration.systematic differences in their colour correction. An exceedingly sensitive method of testing this correction devised by Professor Stokes is given under Optics, vol. xvii. p. 804. Another method, due to Professor Harkness and first carried out by Dr Vogel, is the following. Place behind the eye-piece a direct vision prism (cf. Optics, p. 801). The image of a star in the field will then he converted into a narrow spectrum, which, if there were no chromatic aberration, would when focused be represented by a faint coloured straight line, uniformly sharp and narrow. But in an ordinary object-glass only two points in the spectrum can he perfectly focused simultaneously; therefore all its other parts are spread out, forming a coloured band of variable breadth. If we focus on the brightest part of the spectrum, both its extreme ends become spread out into a more or less trumpet-shaped form, enabling the observer to note the range of the spectrum over which precise definition can he expected. The amount of this extension will depend in some degree on the form of the object-glass, but much more (if the achromatism is fairly well corrected) on the irrationality of the spectra of the glass of which the lenses are composed. If we then focus, for example, on the C line, we shall have the band of light contracted at C and at another point (probably between F and G), widening to a slightly trumpet-shaped form below C, and markedly so above G. This second point of greatest contraction gives the wave-length of the ray which has the same focus as C. If the telescope has a focusing scale, we can also measure directly in this way the change of focus for rays of different colours. The chromatic aberration will be best corrected for the rays of minimum focus, and this minimum focus should for an ordinary telescope correspond with the brightest part of the spectrum, viz., with rays between D and E. A comparison of the chromatic correction of object-glasses by different makers is given by Dr Vogel (Monatsber. der Berliner Akad., April 1880), obtained in the manner just described. The telescopes compared are—

Maker.	Observatory to which Instrument belongs.	Aperture of Object-Glass.	Focal Length.	No. of Apertures in Focal Length.
		m.	m.
Schröder	Potsdam	0·298	5·4	18·1
Grub	"	0·207	3·16	15·3
Fraunhofer	Berlin	0·243	4·331	17·8

Fig. 5, taken from the above-quoted paper, affords most interesting information as to the colour-correction of these three typical object-glasses. The curves of the diagram show the variation of the focal point for rays of different wave-lengths in the case of each, object-glass.

Fig. 5.

It will he seen that Fraunhofer has united the rays about C with those of wave-length 525 millionths millimetres, Grubb with those about wave-length 494, and Schröder about wave-length 403. The object-glasses of Grubb and Schröder are composed of modern glass, which is comparatively colourless, whilst Fraunhofer's glass is decidedly green in colour. The minimum focus in Fraunhofer's telescope is placed near D (rather at wave-length 585), because the absorption of the blue and violet rays of the spectrum by the flint lens renders the brightest part of the spectrum less blue than in an objective composed of modern glass by Chance or Feil, which is nearly colourless. This circumstance enabled Fraunhofer to apply a very large over-correction for colour,—that is, to unite as perfectly as possible the red and central part of the spectrum, and to leave the outstanding violet rays to be in great part absorbed by the colour of the glass. The colour-corrections in the object-glasses of Grubb and Schröder are very different in character. In Grubb's object-glass the minimum focus is for rays of wave-length about 545, that of Schröder's is about wave-length 533, which appears to prove that Grubb's eye is more sensitive to red and Schröder's to blue light. Also Grubb's object-glass unites the red rays very closely with the brightest part of the spectrum, and leaves the blue and violet rays outstanding. Schröder, on the other hand, leaves the red rays outstanding in order to unite the rays between D and F more closely. The conclusion is that to Grubb's eye the red rays would be obtrusively prominent in Schröder's telescope, and that he would pronounce the object-glass under-corrected; whilst Schröder's eye would find the outstanding violet rays too prominent in Grubb's telescope, and pronounce it over-corrected. The absolute amount of light in the secondary spectrum in viewing the same object depends, cæteris paribus, upon the square of the aperture; therefore telescopes of large aperture have to be made of greater proportional focal length than those of small aperture, in order to diminish the secondary spectrum. Figs, α, β, γ, δ in the diagram give the form of the spectrum of a star in Schröder's telescope for various adjustments of the focus; figs. α' and γ' give the corresponding forms for Fraunhofer's telescope. Fig. α represents the eye -piece focused for the brightest part of the spectrum; fig. β when the red rays and those near Hα are simultaneously focused; fig. γ when the extreme red rays are in focus, the corresponding focus being a little below Hγ; fig. δ when focused on Hγ.

Photographic object-glasses.When a telescope is to be constructed for photographic purposes the aim should be to unite, as perfectly as possible, the rays near that portion of the spectrum which act most powerfully on the photographic plate to be employed. This latter point has been determined for the various photographic processes by Captain Abney. ^[16] The results are shown graphically in fig. 6 for the processes practically employed at present in astronomical photography.

Fig. 6.

To unite the rays near G or H the angle of the flint prism must be diminished; that is, the focal length of the flint lens must be lengthened as compared with that of an object-glass of similar construction suited for eye observations; and the rays of greatest photographic action can be united more perfectly than the visible rays.

Triple object-glasses.If an object-glass is composed of three lenses of different kinds of glass it is theoretically possible to unite three instead of two points of the spectrum, besides improving the correction for spherical aberration. The most important practical applications of such a system have been—(1) the triple object-glass of John Dollond; (2) the application of a convex crown glass in front of an ordinary object-glass in order to alter its chromatic correction from that best suited for eye observations to that best suited for photographic observation. John Dollond's object-glass is generally described as a concave flint lens between two crown lenses. If the crown lenses are of similar glass, there is no gain as to the correction of the secondary spectrum; it becomes only possible to correct the spherical aberration more perfectly. Very few telescopes with triple object-glasses have been made since the days of John Dollond. But the great and detrimental obtrusiveness of the secondary spectrum in the large object-glasses of the present day can be diminished in no other way, unless very extreme focal lengths are adopted, or some new kinds of glass that can be produced in large disks are discovered, in which the irrationality of their spectra is less, and in which also there is the necessary difference in the relation between refractive index and dispersive power. The cost of a triple object-glass would of course be at least 50 per cent. greater than that of a double object-glass; but, on the other hand, the extreme focal length necessary for large object-glasses might be considerably reduced. Thus the cost saved by a less heavy mounting and a smaller observatory and dome might counterbalance to some extent, if not entirely, the additional cost of the triple object-glass. Dr Schröder has constructed for the present writer an exquisite triple object-glass (three different kinds of glass) of 31/4-inches aperture and only 18-inches focal length. Its performance with its highest eye-piece of 1/4-inch focus (power 72) is most admirable. It would probably be impossible to construct large telescopes approaching such short focal length, but there is no doubt that a large triple object-glass of 10 or 12 apertures focus would have an enormous advantage in colour correction, and probably in spherical aberration, over a double object-glass of the same aperture and much greater focal length. One peculiarity of such a triple object-glass is that three points in the spectrum can have the same focus, and therefore the point of minimum focus may for the best chromatic adjustment not quite correspond with the focal point for the brightest part of the spectrum; but, obviously, the rays of the whole visible spectrum may thus be brought to intersect the axis much more nearly at the same point. There will probably be a far wider adoption of the triple-object-glass in the future, especially as the greater intrinsic brilliancy of the image in short-focus telescopes is a matter of high importance in the spectroscopic and photographic processes of modern astronomy. On the subject of triple object-glasses the reader is referred to an admirable paper by Professor C. S. Hastings (Amer. Journal of Science and Arts for December 1879, p. 429), which exhibits the results to be got from combinations of different existing kinds of glass.

The following table exhibits the excess of the focus for any ray over the true focus, the unit being of the focal length, in— I. the actual results of Dr Vogel's observations on three existing object-glasses already quoted, but each reduced to comparison with its true or minimum focus; II. the theoretically best possible results from a double object-glass consisting of Feil's crown 1219 and Feil's flint 1237, as computed by Hastings; III. the theoretical results of four different triple object-glasses, capable of practical construction, of which details are given by Hastings.

	Double Object-Glasses.				Triple Object-Glasses.
	I.			II.	III.
	Fraunhofer.	Grubb.	Schröder.	Hastings.	Hastings 1	Hastings 2	Hastings 3	Hastings 4
A	. . .	. . .	. . .	+ 135	. . .	+ 2	. . .	- 3
B	+ 47	+ 64	+ 106	+ 66	+ 1	- 53	- 22	- 35
C	+ 36	+ 41	+ 78	0	0	+ 41	+ 91	+ 50
D	0	+ 8	+ 23	0	0	+ 28	+ 41	+ 2
E	+ 27	+ 29	0	+ 13	+ 25	- 10	- 67	- 10
F	+ 64	+ 56	+ 33	+ 73	0	- 14	- 60	- 4
G	+ 171	+ 226	+ 243	+ 287	0	+ 2	+ 21	- 3

Prof. Hastings's first condition in these computations is that the radius of curvature of none of the surfaces shall exceed one-fifteenth of the focal length. He also neglects the thickness and distance apart of the lenses, since these affect chiefly the focal length, but do not very materially affect the difference of the foci for different rays. The expression for the focal length F is then

$\phi =(\mu '-1){\biggl (}{\frac {1}{r_{1}}}+{\frac {1}{r_{2}}}{\biggr )}+(\mu ''-1){\biggl (}{\frac {1}{r_{3}}}+{\frac {1}{r_{4}}}{\biggr )}+(\mu '''-1){\biggl (}{\frac {1}{r_{5}}}+{\frac {1}{r_{6}}}{\biggr )};$

where $\phi ={\frac {1}{\mathrm {F} }},\mu ',\mu '',\mu '''$are the indexes of refraction for the three kinds of glass, and $r_{1},r_{2}...r_{6}$the radii of curvature for the six successive surfaces. Writing this in the form

$\phi =(\mu '-1)\mathrm {A} +(\mu ''-1)\mathrm {B} +(\mu '''-1)\mathrm {C} ,$

we may call A, B, and C the curvature sums of the first, second, and third lenses respectively. The problem then is to find, for existing specimens of glass, values of A, B, and C no one of which shall exceed 30 when $\phi =1$ and which shall make $\phi$independent of the wave-length of the light transmitted. The resulting values of A, B, and C for the first combination (marked "Hastings 1") are

A	B	C
3·47026	7·20827	-8·36472

the curvatures are therefore very moderate and perfectly practicable. The constants for the glass of the first and second lenses have been determined by the author with great accuracy (see Amer. Jour., vol xv. p. 273). The third glass is Fraunhofer's flint 13 (Hastings t, misprinted v in his table, in Amer. Jour., vol, xviii. p. 131), for which the constants are given in Schumacher's Astron. Abhandlung für 1823. If this glass can be reproduced in large disks, as no doubt it could be, we have the means of making an object-glass very superior to any in existence and equally available for eye and photographic observation. Such an object-glass could be made of much shorter proportional focus than is usual or possible in double object-glasses, not only because of the absence of secondary spectrum but also from the command afforded over the spherical aberration by six surfaces. After satisfying the conditions of focal length, the first power of the spherical aberration, and two conditions of achromatism, we have still two available arbitrary conditions, which may be that $r_{2}=r_{3}$ and $r_{4}=r_{5}$. If these lead to convenient forms, as seems likely in the case in point, the whole may constitute a cemented lens; thus the loss of light at the interior surfaces may be eliminated, and the final perfecting of the spherical aberration be left to the figuring of the surfaces.

Change of chromatic correction by separating lenses.In some recent large double object-glasses, especially those of Alvan Clark, it has been usual to leave a space between the crown and the flint lens sufficient to afford access, through apertures in the cell, for cleaning the inner crown and flint surfaces, without risk of disturbing the lenses and their centring. ^[17] If in fig. 3 imagine the lenses to be considerably separated and through both lenses trace a ray entering the crown lens parallel to and at some distance from the axis, we shall find that the effect of the separation is to diminish the power of the flint lens, and, therefore to change the character of the chromatic aberration. Thus an object-glass over-corrected for colour can be improved in this respect by increasing the distance between the lenses. It has been suggested that a telescope can be made suitable for both eye observation and photographic purposes if means are provided for increasing the distance between the lenses without risk of deranging the centring when the telescope is to be employed for photography. But the great change that would be necessary in such a case cannot be brought about consistently with preservation of the perfection of the corrections for spherical aberration. ^[18]

Vernon Harcourt's phosphatic glasses.Any account of the achromatic object-glass would be incomplete without reference to the labours of the Rev. W. Vernon Harcourt and Prof. Stokes. Experiments in the production of optical glass were instituted by the former in 1834; and specimens, exhibited at the meeting of the British Association at Cambridge in 1862, were placed in the hands of Prof. Stokes, who determined the optical constants of the numerous specimens of glass which Harcourt produced, and indicated from these results the direction in which fresh experiments should be undertaken. It was discovered that titanic acid extends the blue end of the spectrum more than corresponds to the dispersive power of the glass, whilst boracic acid has the opposite effect (Report Brit. Assoc., 1871, p. 38). At a meeting of the British Association at Belfast in 1874 a telescope was exhibited whose object-glass was constructed from Harcourt's glass by Sir Howard Grubb of Dublin. The following is Prof. Stokes's complete and concise account of it.

The original intention was to construct the objective of a phosphatic glass containing a suitable percentage of titanic acid, achromatized by a glass of terborate of lead. (The percentage of titanic acid was so chosen that there should be no irrationality of dispersion between the titanic glass and the terborate.) As the curvature of the convex lens would be rather severe if the whole convex power were thrown into a single lens, it was intended to use two lenses of this glass, one in front and one behind, with the concave terborate of lead placed between them. It was found that, provided not more than about one-third of the convex power were thrown behind, the adjacent surfaces might be made to fit, consistently with the condition of destroying the spherical as well as the chromatic aberration. This would render it possible to cement the glasses, and thereby protect the terborate, which was rather liable to tarnish. At the time of Mr Harcourt's death two disks of the titanic glass had been prepared which it was hoped would be good enough for employment, as also two disks of terborate. These were placed in Mr Grubb's hands. On polishing, one of the titanic disks was found to be too badly striated to be employed; the other was pretty fair. As it would have required a rather severe curvature of the first surface and an unusual convexity of the last to throw the whole convex power into the first lens, using a mere shell of glass to protect the terborate, Professor Stokes thought it more prudent to throw about one-sixth of the whole convex power into the third or crown glass lens, though at the sacrifice of an absolute destruction of secondary dispersion, which by this change from the original design might be expected to be just barely perceptible. Of the terborate disks, the less striated happened to be slightly muddy, from some accident in the preparation; but, as this signified less than the striæ, Mr Grubb deemed it better to employ this disk. The telescope exhibited to the meeting was of about 21/2-inches aperture and 28-inches focal length, and was provided with an object-glass of the ordinary kind, by which the other could be replaced, for contrasting the performance. When the telescope was turned on to a chimney seen against the sky or other suitable object, and half the object-glass covered by a screen with its edge parallel to the edges of the object, in the case of the ordinary objective vivid green and purple were seen about the two edges, whereas with the Harcourt objective there was barely any perceptible colour. It was not of course to be expected that the performance of the telescope should be good, on account of the difficulty of preparing glass free from striæ, but it was quite sufficient to show the possibility of destroying the secondary colour."

An experiment to determine whether the substitution of titanic acid for a portion of the silica in ordinary crown glass would have an effect similar to that which had been observed in the phosphatic series of glasses (viz., whilst somewhat raising the dispersive power, to produce a separation of the colours at the blue as compared with the red end of the spectrum, to an extent ordinarily belonging only to glass of much higher dispersive power) was carried out by Mr Hopkinson at the glass works of Messrs Chance of Birmingham; but it proved unfortunately in this combination that, whilst the dispersive power was increased, as in the phosphatic glasses, the blue end of the spectrum, as compared with the red end, was not spread out more than in ordinary glass of like dispersive power (Report Brit. Assoc., 1875, p. 26). It is to be hoped, however, that makers of optical glass will not relax their efforts till astronomers shall be able to obtain refracting telescopes in which the secondary spectrum is nearly if not quite eliminated. Abbe's new optical glass^[19] leads one to believe that this hope will soon be realized.

A third or photographic lens.The addition of a convex crown lens in front of the ordinary object-glass, to diminish the colour-correction and change the minimum focus from that for rays between D and E to that for rays near G, was first made by Rutherford of New York. In this way he altered his telescope from one suited for eye observations to one in the best chromatic adjustment for photographic work. The chromatic effect is the same as increasing the convexity of the crown lens, and by proper proportioning of the two radii of curvature it becomes possible also to conserve, and even to further perfect, the destruction of spherical aberration. The great object-glass of 36-inches aperture, now (1887) under construction for the Lick observatory by Messrs Clarke of Boston (Mass.), is to be provided with an additional crown lens for this purpose. ^[20]

Blair's achromatic fluid object-glasses.The problem of making a perfectly achromatic object-glass has been solved by Dr Blair (Edin. Trans., vol. iii. p. 53) by employing fluid media, and he actually constructed an object-glass consisting of a plano-convex lens and a meniscus lens, both of crown glass with their convexities turned towards each other, the space between the lenses being filled with hydrochloric acid. Unfortunately such combinations are practically useless, not only on account of unavoidable leakage, but also because currents are set up in fluid lenses by changes of temperature, which correspond in effect with want of homogeneity in the flint lens in an ordinary object-glass.

Eye-Pieces.

Eye-pieces.The first substitute for the single lens of the Galilean and Kepler telescopes was the compound eye-piece invented by Rheita. Behind the convex eye-lens of the Kepler telescope he applied a second short telescope, consisting of two convex lenses, their distance being the sum of their focal lengths. The principal effect was to erect the inverted image, and thus to constitute the simplest form of the day eye-piece, or common terrestrial telescope. The next improvement was the Huygenian eye-piece, which consists of two convex lenses (see fig. 7),—the "field-lens," that next the object-glass, having its focal length to that of the "eye-lens" as 3 to 1 ; the distance between them is twice the focal length of the latter, the combination being so placed as to form the visible image half-way between the two. This eye-piece is achromatic in the sense in which an eye-piece is said to be so: a colourless image seen through it does not appear bordered with coloured fringes, as is the case with a single lens or Rheita's eye-piece. This is not because, as in the achromatic object-glass, all the central coloured rays are collected in one focus, which in the case of an eye-piece is a matter of comparatively small consequence, but because it possesses the same magnifying power for rays of all colours on an object of sensible angular diameter, so as not to form overlapping coloured pictures of it on the retina. This condition it is which furnishes the " equation of achromaticity" of an eye-piece. An expression for the magnifying power of a telescope provided with a certain eye-piece is formed in general terms which involve the focal length of its lenses, their distances from each other, and their refractive indexes; and, this being made to vary by the variation of the last-mentioned elements only, the variation is equated to zero. The algebraic working, which even for a two-glass eye-piece is a little complex, is given in H. Lloyd's Treatise on Light and Vision (London, 1831), and in an elaborate paper by Littrow in the fourth volume of the Trans. Roy. Astron. Soc. (p. 599). From the former we extract the following proposition: An eye-glass of two lenses of the same medium is achromatic when the interval between the lenses is an arithmetical mean between their focal length,— Huygenian eye-piece.a condition which the Huygenian construction evidently satisfies. The rationale of this is obvious, independently of algebraic analysis, by inspection of the course of the rays in fig. 7, where AC, BD are the lenses, PQ the image which would be formed by the object-glass alone, pq that really formed by the action of the field-glass. The object-glass being supposed achromatic, a ray of white light, as OC, going to form the image of a point Q, will be refracted by the field-glass at C towards the corresponding point q of the new image, but not as a single white ray; it will be separated into coloured rays, following different courses. The red ray Cr being less refracted will fall on a point r of the eye-glass more remote from its centre B than the violet ray Cν, and (the prismaticity of the lens increasing from the centre outwards) will in proportion by the second transmission be more bent aside than the violet, and thus a compensation is effected, and the two rays finally emerge parallel, their exact parallelism being secured by the proportion of their focal lengths.

Fig. 7.—Huygenian eye-piece.

The Huygenian eye-piece possesses also other important advantages. The total deflexion of the light, to produce the magnifying power, is equally divided between the two glasses,—the most favourable condition for diminishing that distortion which is always perceived in looking obliquely through a lens; and the field of view is greatly enlarged in proportion to the size of the eye-lens, being such as would require, to produce the same magnifying power, a single lens of the much greater semi-diameter bd, found by drawing Qb parallel to qB and erecting bd. The inconvenience of this eye-piece (whence it is improperly termed a negative eye-piece) is that the image, being formed between its lenses, undergoes a certain amount of distortion by the field-glass, owing to which equal linear portions of it do not correspond precisely to equal angular measures of the distant object. Equal parts of a micrometer applied at the place of the image, so as to be seen at the same time through the eye-lens, will not correspond to precisely equal angular intervals. Common or positive eye piece.The common astronomical or positive eye -piece, described by Ramsden (Phil. Trans., 1783), consists of two plano-convex lenses of equal lengths, having their convexities turned towards each other and separated by two-thirds of the focal length of either, as in fig. 8. This combination is placed behind the image PQ

Fig. 8.—Common or positive eye-piece.

formed by the object-glass, at a distance AP equal to one-fourth of the focal length of A. The first or field-glass, therefore, forms an enlarged image pq, at a distance one-third of that focal length which places it in the focus of the eye-glass. This eye-piece is not properly achromatic, but its spherical aberration is much less than in any of the other constructions, and it has the advantage of giving a flat field of view, requiring no change of focus to see the

Fig. 9.—Erecting or terrestrial eye-piece.

Erecting or terrestrial eye-piece.centre and borders of the field with equal distinctness. The erecting or terrestrial eye-piece was invented by Dollond. The principle of its construction will be understood from fig. 9. It is convenient for telescopes of ordinary use, because it presents a non-inverted image to the eye, although at some sacrifice of light and definition.

Airy on eye-pieces.For an account of the theory of the chromatic and spherical aberration of eye-pieces by Sir George B. Airy, see Trans. Phil. Soc, Camb., vol. ii. p. 243 and vol. iii. p. 61. The author's conclusions are the following. (1) To secure the greatest distinctness with an eye-piece of the Huygenian type, the field-lens should be a meniscus of focal length 3, the radii of its surfaces 11 : 4, and its convexity towards the object-glass; the eye-lens should be a double convex of focal length 1, the radii of its surfaces 1 : 6, and its more convex side towards the field-lens. The distance of the lenses should be 2. There should be a perforated diaphragm at distance 1 from the eye-lens. If a bright object appears yellow or a dark one blue at the edge farthest from the centre of the field, the lenses must be brought a little nearer together. (2) For an eye-piece of Ramsden's type the two lenses should be plano-convex, of focal length 3, placed at distance 2, their convex surfaces being turned towards each other. (3) For an erecting eye-piece of four lenses the first and fourth (reckoned from the object-glass towards the eye) should be crossed lenses of focal length 3, the radii of their surfaces 1 : 6, with their convex surfaces towards each other. The second lens should be a meniscus of focal length 4, the radii of its surfaces 25 : 11, and its convexity towards the eye. The third lens should be plano-convex, of focal length 4, its piano side towards the eye. The distance of the centre of the second lens from that of the first = 4; that of the third from the second = 6; and that of the fourth from the third = 5·13. If a bright object appears yellow or a dark one blue at the edge farthest from the centre of the field, the third and fourth lenses must be together pushed inwards towards the second lens.

In many telescopes constructed specially for star observation only the object-glass is over-corrected for colour and under-corrected for spherical aberration; both these errors may sometimes be nearly eliminated by a properly constructed Huygenian eye-piece (see Microscope, vol. xvi. pp. 266 267). But, when a telescope is to be used over a considerable range of field for micrometric measurements, it is obvious that the spherical aberration should be corrected by the object-glass alone. It is possible, however, to improve the appearance of objects somewhat in a telescope in which the chromatic aberration is over - corrected by employing an eye -piece somewhat under-corrected for colour, and vice versa; but the only satisfactory plan is to have both object-glass and eye-piece as free as possible from both chromatic and spherical aberration. In order to secure this, or a very large field of view, many forms of eye-piece have been devised. Achromatic combinations have been substituted in some cases for the field-lens, in others for the eye-lens, in others for both simple lenses of the Ramsden eye-piece. The best of these combinations which the present writer has tested and which practically fulfil all requirements of the astronomer are due to Dr Hugo Schröder, to whom he is indebted for information as to their construction. Fig. 10 represents Schröder's high power H. Schröder's high power eye-piece.

Fig. 10.–Schröder's high power eye-piece.

eye-piece, which is admirably suited for micrometer work, not only because there are only two reflecting surfaces in the triple lens of which it is composed, but also because there is a comparatively large distance between the lens and the micrometer web when the latter is in focus. This condition is essential when it is desired to get the best bright illumination of the wires in a dark field (see Microscope, vol. xvi. p. 248). The triple lens is composed of a dense fluid plano-convex lens between two lenses of soft crown glass. The radii of curvature are—

	r1=80.026 convex	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$Soft crown glass
surfaces cemented$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,}$	R2=36.536 convex
	R3=36.536 concave	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$Dense flint glass
surfaces cemented$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,}$	R4=∞ plane
	R5=∞ plane	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$Soft crown glass
	R6=80.026 convex

The corresponding foci for zones of different distance from the axis are—axis = 100·00; zones 12·5 from axis, 99·81; 25 from axis, 99·32; 40 from axis, 93·35; 45 from axis, 100·15; 50 from axis, 101·85. Thus the aperture of the lens may be half its focal length without any sensible defect. Fig, 11 represents O. Schröder's aplanatic eye -piece.Dr O. Schröder's aplanatic eye-piece. The glass employed is Dauget's crown $(\mathrm {C} b_{1})$ and flint $(\mathrm {F} b_{1})$. The refractive power of crown is 1·5126 for D, that of flint 1·6405 ; the dispersive power of both kinds of glass is 0·588

Fig. 11.—Schröder's aplanatic eye-piece.

The radii of curvature for a lens of 1 inch (27·07 mm.) focal length are—

mm.	mm.
$r_{1}=20.12$	$r_{5}=13.30$
$r_{2}=r_{3}=10.94$ cemented	$r_{6}=r_{7}=7.00$ cemented
$r_{4}=\infty$	$r_{8}=\infty$

$\mathrm {F} _{1}$ = focal point of combination= - 9·05 mm. from vertex of $r_{1}$,

$\mathrm {F} _{2}$ = position of observer's eye= - 14·49 mm. from vertex of $r_{2}$.

The thicknesses and distances apart of the surfaces are—

1st vertex to 2d	=	0·70	mm.	flint glass,
3d""4th	=	-3·50	"	crown glass,
4th""5th	=	19·51	"	air,
5th""6th	=	0·61	"	flint glass,
7th""8th	=	2·45	"	crown glass.

The distance between the plane surfaces is 22·57 mm. This form of eye-piece has been employed by Schönfeld in his southern "Durchmusterung," and Dr Schröder has made one for the present writer which gives a perfect field 41/4 in diameter on the telescope of 18 inches focal length and SJ inches aperture already referred to.

Reflecting Telescope.

Gregorian telescope.The following are the various forms of reflecting telescopes. The Gregorian telescope is represented in fig. 12. AA and BB are

Fig. 12.-Gregorian telescope.

concave mirrors having a common axis and their concavities facing each other. The focus of A for parallel rays is at F, that of B for parallel rays at $f$—between B and F. Parallel rays falling on AA converge at F, where an image is formed; the rays are then reflected from B and converge at P, where a second and more enlarged image is formed. Gregory himself showed that, if the large mirror were a segment of a paraboloid of revolution whose focus is F, and the small mirror an ellipsoid of revolution whose foci are F and P respectively, the resulting image will be plane and undistorted. The image formed at P is viewed through the eye-piece at E, which maybe of the Huygenian or Ramsden type. The focal adjustment is accomplished by the screw S, which acts on a slide carrying an arm to which the mirror B is attached. The practical difficulty of constructing Gregorian telescopes of good defining quality is very considerable, because if spherical mirrors are employed their aberrations tend to increase each other, and it is extremely difficult to give a true elliptic figure to the necessarily deep concavity of the small speculum. Short appears to have systematically conquered this difficulty, and his Gregorian telescopes attained great celebrity. The use of the Gregorian form is, however, practically abandoned in the present day. The magnifying power of the telescope is= ${\frac {\mathrm {F} +f}{e+x}}$ where $\mathrm {F}$ and $f$ are respectively the focal lengths of the large and the small mirror, $e$ the focal length of the eye-piece, and $x$ the distance between the principal foci of the two mirrors (=$\mathrm {F} f$ in the diagram) when the instrument is in adjustment for viewing distant objects. The images are erect.

Cassegrain telescope.The Cassegrain telescope differs from the Gregorian only in the substitution of a convex hyperbolic mirror for a concave elliptical mirror as the small speculum. This form has two distinct advantages: (1) if spherical mirrors are employed their aberrations have a tendency to correct each other; (2) the instrument is shorter than the Gregorian, cæteris paribus, by twice the focal length of the small mirror. Fewer telescopes have been made of this than perhaps of any other form of reflector ; but in comparatively recent years the Cassegrain has acquired importance from the fact of its adoption for the great Melbourne telescope. The magnifying power is computed by the same formula as in the case of the Gregorian telescope.

Newtonian telescope.The Newtonian telescope is represented in fig. 13. AA is a concave mirror whose axis is aa. Parallel rays falling on AA converge on the plane mirror BB, and are thence reflected at right angles to the axis, forming an image in the focus of the eye-piece E.

Fig. 13.—Newtonian telescope.

The surface of the large mirror should be a paraboloid of revolution, that of the small mirror a true optical plane. The magnifying power is ${\frac {F}{e}}$. This form is employed in the construction of most modern reflecting telescopes. A glass prism of total reflexion is sometimes substituted for the plane mirror.

Herschelian. telescope.The Herschelian or front view reflector is represented in fig. 14. AA is a concave parabolic mirror, whose axis ac is inclined to the axis of the tube ab so that the image of an object in the focus of the mirror may be viewed by an eye-piece at E, the angle bac being equal to the angle caE. This form w-as adopted by the elder

Fig. 14—Herschelian reflector.

Herschel to avoid the loss of light from reflexion in the small mirror of the Newtonian telescope. It has several disadvantages. (1) The upper part of the observer's head must necessarily obstruct some of the rays which would otherwise fall on the large mirror; but when a telescope of very large aperture is employed the loss of light thus occasioned is comparatively insignificant. Moreover, disturbance of the air in front of the telescope is created by heat from the observer's head and body, and this is fatal to the best definition. To avoid the latter drawback Sir John Herschel (Ency. Brit., 8th ed., art. "Telescope," vol. xxi. p. 128) suggested the employment of a small right-angled prism of total reflexion placed close to the eye-lens of the eye-piece, to permit the observer to view the image by looking in a direction at right angles to the eye-piece, and therefore at right angles to the tube. (2) In consequence of the tilting of the mirror aberration is created, and this increases rapidly with increased tilting. The construction is thus limited to telescopes in which the proportion of aperture to focal length is not too great. In Herschel's 40-feet telescope the proportion was 1 to 10, and the construction would hardly be applicable to modern telescopes, in which the proportion often rises to 1 to 5 or 6. Yet, when exceedingly faint objects have to be observed, this form of telescope has great advantages. Herschel found that some objects which he discovered with such an instrument could not even be seen when the same telescope was used in the Newtonian form. The front view telescope, however, has hardly been at all employed except by the Herschels. But at the same time none but the Herschels have swept the whole sky for the discovery of faint nebulæ; and probably no other astronomers have worked for so many hours on end for so many nights as they did, and they emphasize the easy position of the observer in using this form of instrument.

Construction of Object-Glasses.

Testing object-glasses. The first point is the selection of glass disks of suitable quality. The requisites are (1) general transparency and freedom from mechanical defects, such as specks, air-bubbles, &c.; (2) homogeneity; (3) freedom from internal strain. The disk being roughly polished on the sides, faults of the first class are easily detected by inspection. In order to secure the maximum of light grasp for aperture it is desirable that the glass should be as colourless as possible; if the roughly polished disk is laid upon white paper the amount of discoloration can be readily estimated by comparing the colour of the sheet as seen directly with that seen through the glass. Fraunhofer's glass was far from colourless, Dollond's more coloured still; and we have shown that, for purposes when extreme light grasp is not an object, the less transparency of such glass to the blue rays of the spectrum affords advantages for a better correction of the chromatic aberration of rays in the brighter part of the spectrum. The amount of light excluded by specks, air-bubbles, or even scratches is quite insignificant; but these blemishes create diffraction phenomena and scattered light in the field, which are very injurious to the performance of the instrument, especially when faint objects are searched for in the neighbourhood of brighter ones. It is essential for a telescope lens that the glass should be perfectly homogeneous; that is, the refractive index must be identical for every part of the disk. This can be tested with extreme delicacy by grinding the disk into the form of a lens and testing it by Töppler's method, ^[21] described under Optics (vol. xvii. p. 805). If the disk is intended for a concave lens and is already so thin that it becomes undesirable to make it thinner at the edges by converting it, in the first place, into a convex lens, it may be tested by placing one of its surfaces in contact with and at right angles to the axis of a crown lens of known perfection, and testing the combination by Töppler's method. If a glass disk is not properlyAnnealing. annealed—that is, if it has been too quickly cooled, so that the outer shell has hardened before the inner portion —the finally solidified mass must be in a state of tension, like that of "Rupert's drops." Unless cooled very gradually an optical disk would fly to pieces, but a very much smaller defect in the annealing process would be fatal for refined optical purposes. Changes of temperature would produce changes of curvature, and the lens would also change its form when successive portions of the strained outer shell were removed in the process of grinding and polishing. Fortunately defects in annealing are very easily detected by means of the polariscope. The polished disk is placed in light reflected from a polarizing surface, such as a sheet of glass blackened at the back, and examined with a Nicol's prism as an analyser. If the bright rings and black cross (see Light, vol. xiv. p. 613) are visible the disk is unfit for use; but, since few disks are so perfectly annealed as not to show a trace of the black cross, such as show it in no marked degree may be safely employed. Perfect annealing has now become the most difficult portion of the art of making optical glass, and large disks (more particularly of crown glass) are rejected by the optician more frequently for defects in annealing than for any other cause.

The disks having been selected, their refractive and dispersive powers determined, and the radii of curvature computed, it remains to convert the disks into lenses with surfaces of the required curvature, and to complete the object-glass. The work consists of five distinct operations—(1) rough grinding by a revolving tool supplied with sand and water; (2) fine grinding with emery; (3) polishing with oxide of iron, rouge, or putty powder, the grinder being faced with fine cloth, satin, paper, or—best of all—pitch; (4) centring; (5) figuring and testing. These processes are essentially of a technical character, and can only be familiar to those who practise the art. The details would be out of place here, but are well described in a lecture delivered by Sir Howard Grubb at the Royal Institution, 6th April 1886, and printed in Nature, 27th May 1886.

Construction of Specula.

Construction of Specula.The composition of metallic specula in the present day differs very little from that used by Sir Isaac Newton. Many different alloys have been suggested, some including silver, nickel, zinc, or arsenic; but that which has practically been found best is an alloy of four equivalents of copper to one of tin, or the following proportions by weight:—copper 252, tin 117·8. Such speculum metal is exceedingly hard and brittle, takes a fine white polish, and when protected from damp has little liability to tarnish. The process of casting and annealing, in the case of the specula of the great Melbourne telescope, was admirably described by Dr Robinson in Phil. Trans., 1869, vol. clix. p. 135. Shaping, polishing, and figuring of specula are accomplished by methods and tools precisely similar to those employed in the construction of lenses. The reflecting surface is first ground to a spherical form, the parabolic figure being given in the final process by regulating the size of the pitch squares and the stroke of the polishing machine. The process of testing is identical with that of an object-glass.

Soon after Liebig's discovery of a process for depositing a film of pure metallic silver upon glass from a salt of silver in solution, Steinheil (Gaz. Univ. d'Augsburg, 24th March 1856), and later, independently, Foucault (Comptes Rendus, vol. xliv., February 1857), proposed to employ glass for the specula of telescopes, the reflecting surface of the glass speculum to be covered with silver by Liebig's process. These silver-on-glass specula are now the rivals of the achromatic telescope, and it is not probable that many telescopes with metal specula will be made in the future. The best speculum metal and the greatest care are no guarantee of freedom from tarnish, and, if such a mirror is much exposed, as it must be in the hands of an active observer, frequent repolishing will be necessary. This involves refiguring, which is the most delicate and costly process of all. Every time, therefore, that a speculum is repolished, the future quality of the instrument is at stake; its focal length will probably be altered, and thus the value of the constants of the micrometer also have to be redetermined. Partly for these reasons the reflecting telescope with metallic mirror has never been a favourite with the professional astronomer, and has found little employment out of England. In England, in the hands of the Herschels, Rosse, Lassell, and De la Rue it has done splendid service, but in all these cases the astronomer and the instrument-maker were one. The silver-on-glass mirror has the enormous advantage that it can be resilvered with little trouble, at small expense, and without danger of changing the figure. Its chief work has been done in the hands of Draper and Common, who were the engineers, if not the actual constructors, of their own instruments. Glass is lighter, stiffer, less costly, and easier to work than speculum metal. The silvered mirrors have also some advantage in light grasp over those of speculum metal, though, aperture for aperture, the former are inferior to the modern object-glass. Comparisons of light grasp derived from small, fresh, carefully silvered surfaces are sometimes given which lead to illusory results, and from such experiments Foucault claimed superiority for the silvered speculum over the object-glass. But the present writer has found from experience and careful comparison that a silvered mirror of 12-inches aperture mounted as a Newtonian telescope (with a slivered plane for the small mirror), when the surfaces are in fair average condition, is equal in light grasp to a first-rate refractor of 10-inches aperture, or area for area as 2 : 3. This ratio will become more equal for larger sizes on account of the additional thickness of larger object-glasses and the consequent additional absorption of light in transmission.

Mounting of Telescopes.

Mounting of Telescopes.The proper mounting of a telescope is hardly of less importance than its optical perfection. Freedom from tremor, ease and delicacy of movement, facility of directing the instrument to any desired point in the heavens, are the primary qualifications. Our scopes forbid an historical account of the earlier endeavours to fulfil these ends by means of motions in altitude and azimuth, nor can we do more than refer to mountings such as those employed by the Herschels, or those designed by Lord Rosse to overcome the engineering difficulties of mounting his huge telescope of 6 feet aperture. Both are abundantly illustrated in most popular works on astronomy, and it seems sufficient to refer the reader to the original descriptions. ^[22]

EquatorialWe pass, therefore, directly to the equatorial telescope, the instrument par excellence of the modern extra-meridian astronomer, and relegate to the article Transit Circle (q. v.) a description of those mountings in which the telescope is simply a refined substitute for the sights or pinules of the old astronomers. The equatorial in its simplest form consists of an axis parallel to the earth's axis, called the "polar axis"; a second axis, at right angles to this, called the "declination axis" ; and a telescope fixed at right angles to the latter. In fig. 15 AA is the polar axis; the telescope is attached to the end of the declination axis; the latter rotates in bearings attached to the polar axis, and concealed by the telescope itself.

Fig.15.—Equatorial telescope.

The telescope is counterpoised by a weight attached to the opposite end of the declination axis. The lower pivot of the polar axis rests on a cup bearing at C, the upper pivot upon a strong metal casting MM, attached to a stone pier S. A vertical plane passing through AA is therefore in the meridian, and, when the declination axis is horizontal, the telescope moves in the plane of the meridian by rotation on the declination axis only. Thus, if a graduated circle BB is attached to the declination axis, together with the necessary microscopes or verniers V, V for reading it (see Transit Circle), so arranged that when the telescope is turned on the declination axis till it is parallel to AA the vernier reads 0° or 90°, and when at right angles to AA 90° or 0°, then we can employ the readings of this circle to measure the polar distance or declination of any star seen in the telescope, and these readings will also be true (apart from the effects of atmospheric refraction) if we rotate the instrument through any angle on the axis AA. Thus one important attribute of an equatorially mounted telescope is that, if it is directed to any fixed star, it will follow the diurnal motion of that star from rising to setting by rotation of the polar axis only. If we further attach to the polar axis a graduated circle DD, called the "hour circle," of which the microscope or vernier R reads 0° when the declination axis is horizontal, we can obviously read off the hour angle from the meridian of any star to which the telescope may be directed at the instant of observation. If the local sidereal time of the observation is known, the right ascension of the star becomes known by adding the observed hour angle to the sidereal time if the star is west of the meridian, or subtracting it if east of the meridian. Since the equatorial is unsuitable for such observations when great accuracy is required (see Transit Circle), the declination and hour circles of an equatorial are employed not for determination of the right ascensions and declinations of celestial objects, but for directing the telescope , with ease and certainty to any object situated in a known position, and which may or may not be visible to the unaided eye, or to define approximately the position of an unknown object. Further, by causing the hour circle, and with it the polar axis, to rotate by clockwork or some other mechanical contrivance at the same angular velocity as the earth on its axis, but in the opposite direction, the telescope will automatically follow a star from rising to setting.

Types of equatorials.Equatorial mountings may be divided into five types. (A) The pivots or bearings of the polar axis are placed at its extremities. The declination axis rests on bearings attached to opposite sides of the polar axis. The telescope is attached to one end of the declination and counterpoised by a weight at the other end, as in fig. 15, (B) The polar axis is supported as in type A; the telescope is placed between the bearings of the declination axis and is mounted symmetrically with respect to the polar axis; no counterpoise is therefore requisite. (C) The declination axis is mounted on the prolongation of the upper pivot of the polar axis; the telescope is placed at one end of the declination axis and counterpoised by a weight at the other end. (D) The declination axis is mounted on a forked piece or other similar contrivance attached to a prolongation of the upper pivot of the polar axis; the telescope is mounted between the pivots of the declination axis. (E) The eye-piece of the telescope is placed in the upper pivot of the polar axis; a portion or the whole of the axis of the telescope tube coincides with the polar axis. Mountings of types A and B—that is, with a long polar axis supported at both ends—are often called the "English mounting," and types C and D, in which the declination axis is placed on the extension of the upper pivot of the polar axis, are called the "German mounting," from the first employment of type C by Fraunhofer. A description of some of the best examples of each type will illustrate their relative advantages or peculiarities.

Type A.Fig. 15 may be taken as a practical example of the earlier equatorials as made by Troughton in England and afterwards by Gambey for various Continental observatories. In the Phil. Trans. for 1824 (part 3, pp. 1-412) will be found a description by Sir John Herschel and Sir James South of the equatorial telescope which they employed in their measurements of double stars. The polar axis was similar in shape to that of fig. 15 and was composed of sheets of tinned iron. In Smyth's celebrated Bedford telescope the polar axis was of mahogany. Probably the best example of this type of mounting applied to a refractor is that made by the elder Cooke of York for Mr Fletcher of Tarnbank; the polar axis is of cast iron and the mounting very satisfactory and convenient, but unfortunately no detailed description has been published. In recent years no noteworthy refractors have been mounted on this plan; but type A has been Great Melbourne telescope.chosen by Grubb for the great Melbourne reflector, with marked ingenuity of adaptation to the peculiar requirements of the case. Fig. 16 shows the whole instrument on a small scale, and fig. 17 represents part of it on a larger scale, the upper part of the tube and polar axis being omitted. The figures show the telescope directed to the pole, the hour circle being set 6h from the meridian. The polar axis consists of a hollow cone C {fig. 17) of cast iron

Fig. 16.—Melbourne reflector.

bolted to a hollow cast-iron cube H, to the lower side of which is attached a short steel axis carrying the driving sector EF and the hour circle R, and terminating in the lower pivot of the polar axis. This pivot a is terminated by a piece of chilled cast iron polished flat on its lower face, which face revolves in contact with a piece of bell metal, flat on its upper and partly spherical on its lower side, bearing in a correspondingly shaped annulus, formed to receive it in the cast-iron block which is attached to the pier. This arrangement enables the bell-metal cushion to take its own position when the direction of the polar axis is slightly changed in process of adjustment. The pressure of the pivot on its bearings, in the direction at right angles to the polar axis, is relieved by the sector A, which is forced up by the screw d acting through laminæ of steel springs. The end pressure of a upon its bearings is relieved by a weight.

Fig. 17.—Section of Melbourne reflector.

The friction of the upper pivot is relieved by a sector pressed up against it by the action of two weights. In this way, although the moving part of the telescope weighs 18,170 lb, it can be turned with a pressure of 121/2 Ib, acting at a radius of 20 feet. The driving sector EF is 5 feet in radius; its circular rim is accurately toothed to fit a square threaded endless screw E, which is turned by the driving clock. A toothed wheel attached to H and acted on by a pinion connected with a hand-wheel affords an easy means of setting the instrument in hour angle, or moving the telescope quickly in right ascension. The telescope is clamped by iron bands to the strong cast-iron cradle, which is cast with and forms one extremity of the declination axis. The counterpoise U is attached to the other extremity. There is an elegant arrangement for diminishing the friction of the declination axis, which our limits do not permit us to describe, and the means for clamping and giving slow motion in decimation do not require special notice. The reader is referred for a fuller description to Phil. Trans., 1869, pp. 127-161. The telescope is of the Cassegrain form, the mirror having a 4-feet aperture and 301/2-feet focal length.

Type B.The best existing examples of type B are Airy's equatorial at Greenwich, the equatorial at Liverpool (also designed by Airy), and the photographic equatorial recently erected at the Paris observatory. Greenwich equatorial.The polar axis of the Greenwich equatorial consists of six iron tubes arranged so as to form two triangular braced beams connected by very strong elliptical wheels of cast iron, which carry the upper and lower pivots of the polar axis. These tubes are shown in section at the points T, fig. 18, which represents a section through the declination axis in the plane of the equator when the telescope is directed to a star at the equator (for the general arrangement of the mounting, see fig. 19). The driving circle is 6 feet in diameter, and turns freely on the lower pivot of the polar axis, under the action of the driving clock. The hour circle is graduated on the driving circle, and may be set to show sidereal time during

Fig. 18.—Greenwich equatorial.

the whole of a night's work; thus the observer, in order to direct the instrument on a particular object, has only to set an index connected with the polar axis to the star's right ascension upon the hour circle, without the trouble of computing the hour angle at the instant of observation. This convenient arrangement was first introduced by Airy. The whole mounting is very massive, but very inconvenient to use when a great many different objects have to be examined on the same night; but on account of its freedom from tremor and the excellence of its driving clock it should be very suitable for prolonged study of a single object or for long photographic exposures. ^[23]New Greenwich telescope. Quite recently Sir Howard Grubb has signed a contract to make a telescope of 28-inches aperture and 28-feet focal length, ^[24] which is to be substituted for the present telescope by Merz & Son of 123/4-inches aperture and 18-feet focus. Fig.19 is engraved from a photograph of the model of the original polar axis.

The model was prepared to illustrate the manner in which the new telescope is to be mounted, and we are indebted for the picture to the kindness of Mr Christie, astronomer royal. The object-glass will be actually outside the dome when the telescope is pointed near the zenith or near the horizon. The dew-cap, not shown in the model, will be always outside the dome, and it is not impossible

Fig. 19.—Grubb's telescope for Greenwich.

that this arrangement may be favourable to good definition, except in case of high wind. When the telescope is not in use the dew-cap slides backwards on four rails parallel to the axis of the telescope, and the whole is housed in the position shown in fig.19. The spectroscope is used at right angles to the telescope tube, a right-angled prism of total reflexion being interposed in the converging cone of rays near the focus. This prism can be turned 180° and an eye-piece inserted on the opposite side from the spectroscope for observations near the zenith or horizon, otherwise the eye end would be too near the floor or northern pier. ^[25]

Paris photographic telescope.A figure of the new photographic telescope erected at the Paris observatory may be seen in Nature, 18th May 1886. The object-glass is by MM. Paul and Prosper Henry, the mounting by M. Gautier. Here Airy's braced tubes are replaced by hollow metal beams of triangular shape (as for the Liverpool equatorial). The hour circle has two toothed circles cut upon it, one acted upon by a screw attached to the pier and driven by the clock, the other by a second screw attached to the polar axis, which can be turned very slowly by a handle in the observer's hand. Thus a very slow movement can be given to the telescope in right ascension, independently of the clock. Slow motion in declination can be communicated by a screw acting on a long arm, which can be clamped at pleasure to the polar axis by a convenient handle. An oblong metallic box, fitted with pivots, whose bearings are attached to the triangular beams, forms the tube for two parallel telescopes ; these are separated throughout their length by a metallic diaphragm. The chromatic aberration of the object-glass of one of these telescopes is corrected for photographic rays, and the image formed by it is received on a highly sensitive photographic plate. The other telescope is corrected for visual rays and its image is formed on the plane of the spider lines of a filar micrometer. The peculiar form of the tube is eminently suited for rigid preservation of the relative parallelism of the axes of the two telescopes, so that, if a certain, selected star is retained in bisection by two intersecting wires in the micrometer, by means of the driving clock, aided by small corrections given by the observer in right ascension and declination (required on account of irregularity in the clock movement, error in astronomical adjustment of the polar axis, or changes in the star's apparent place produced by refraction), the image of a star will continue on the same spot of the photographic plate during the whole time of exposure. Exquisite photographs of star clusters, double stars, the moon, and planets have been obtained by MM. Henry, and they are the most eloquent testimony to the optical perfection of the object-glass and the efficiency of the mounting. They show also that we are entering upon a new era in practical astronomy, in which photography is destined to play a leading part. The Henry photographic object-glass is of 13·4-inches aperture and only 10 apertures in focal length. The "guiding telescope" is of 91/2-inches aperture and nearly 12-feet focus. The photographic object-glass, notwithstanding its small proportional focal length covers a field of 21/2° in diameter with perfect precision.

Type C.Many more telescopes have been made of type C than of any other, and it is now almost exclusively employed for the mounting of modern refractors. Its essential features are (1) a comparatively short polar axis and (2) a cross-head attached to the extension of the upper pivot of the polar axis, to carry the bearings of the declination axis. Dorpat refractor.Fig. 20 shows the Dorpat refractor, the chef d'oeuvre of Fraunhofer, and the first equatorial of any importance that was provided with clockwork. AA is the polar axis, B the hour circle graduated on the face and read by the vernier V. C' is the driving clock, which turns an endless screw S, that gears in the toothed edge of the circle B. D is the cross head supporting at its extremities the bearings of the declination axis. The wooden telescope tube rests in a strong cradle FF of cast brass, which is screwed to a flange on one end of the declination axis; the declination circle EE, which is attached to its opposite end, serves to clamp the instrument in declination to the arm G. H is a weight acting on a lever which presses the wheels k (one only seen in the figure) against the upper pivot of the polar axis in order to relieve the friction of that pivot on its bearing.

Fig. 20—Dorpat reflector.

The counterpoise W balances the tube about the polar axis. M, M are counterpoise weights which act on levers m,m, whose fulcra are universal joints at n attached to the cradle. These weights serve to counterpoise the longer end of the tube and to check its flexure. QQ is the finder, a small telescope whose axis is parallel to the great telescope; having a low magnifying power and a large field of view, it serves to direct the large telescope to any object seen in the sky, which otherwise would be difficult to find in the comparatively limited field of the large telescope. The stand TTT is of oak. The instrument is described in detail by Struve (Beschreibung des auf der Sternwarte zu Dorpat befindlichen grossen Refractors von Fraunhofer, Dorpat, 1825, fol.). The instrument was an enormous advance upon all previous telescopes for micrometric research. In the hands of Struve results were obtained by it which in combined quality and quantity had never before been reached in micrometric research. Its success was such that the type of Fraunhofer's telescope became stereotyped for many years not only by his successors but throughout Germany. When twelve years afterwards Struve ordered the 15-inch refractor for the new observatory at Pulkowa, the only important change made by Fraunhofer's successors was, at Struve's suggestion, the substitution of a stone pier for the wooden stand in the original instrument.

Both the Dorpat and the Pulkowa refractor are defective in rigidity, especially in right ascension. The declination circle is most inconvenient of access, and slow motion in declination can only be effected when the instrument is clamped by a long and inconvenient handle, so that practically clamping in declination was not employed. The slow motion in right ascension is defective, being accomplished in the Dorpat refractor by changing the rate of the clock, and in the Pulkowa refractor by a handle which when used affects very injuriously the rate of the clock for the time being. Struve's skill as an observer was such that he used to complete the bisection on the fixed wire of the micrometer by a pressure of the finger on the side of the tube,—a method of proved efficiency in such hands, but plainly indicative of the want of rigidity in the instrument and of the deficiency of the slow motions (see Micrometer, vol. xvi. p. 245). The driving circle is also much too small, so that a very slight mechanical freedom of the screw in the teeth involves a large angular freedom of the telescope in right ascension, whilst its position at the lower end of a too weak polar axis tends to create instability in right ascension from torsion of that axis. Strange to say, the wooden tube has till very recently retained its place in German mountings.

Oxford heliometer.About 1840 a great advance was made in the right direction by the Repsolds of Hamburg in the equatorial mounting of the Oxford heliometer. The driving circle was greatly increased in diameter, and placed at the upper end of the polar axis, and both the polar axis and the declination axis were made much stronger in proportion to the mass of the instrument they were destined to carry. (A figure of this instrument is given in the Oxford Observations for 1850.) Cooke's equatorial.About 1850 Thomas Cooke of York began his career as a maker of equatorial telescopes, and gave a new character to the German mounting. Fig. 21 represents a typical equatorial of his design.

Fig. 21—Cooke's equatorial.

A strong cast-iron pillar is substituted for Fraunhofer's stand. On the semi-cylindrical top of the pillar rests the cast-iron box AA, which contains at its upper and lower extremities the bearings of the polar axis. Its mode of connexion with the pillar permits the inclination of the box to be changed for adjustment of the inclination of the polar axis. The strong cross-head C, supporting the bearings of the declination axis, is of cast iron, bolted to a flange on the upper pivot of polar axis. Fraunhofer's cradle and wooden tube are abolished, and in their place is a cast-iron cylindrical tube D, flanged at both ends and also at the point where it is bolted to a corresponding flange on the end of the decimation axis, all three flanges being cast in one piece with the central tube ; the rest of the tube consists of two slightly tapered brass cylinders bolted by strong flanges to the central tube D. The handle F clamps the arm H to the cross-head C at pleasure, and slow motion in declination is communicated by the handles at E and G. Two circles at K and M are attached to the upper part of the polar axis. To one of these motion is communicated by the tangent screw at M (turned by the clock N) acting on teeth cut at the edge of the circle. The other is a graduated hour circle read by two opposite microscopes, one of which is seen at P. The endless cord hanging down and holding a sliding ring at Q is employed to give slow motion in right ascension, in some instruments by moving the frame of the driving screw in the direction of the axis of the screw, in others by moving differential wheels which accelerate or retard the velocity of rotation of the driving screw without affecting the rate of the clock. The decimation circle RR, is attached to the farther end of the declination axis and is inconvenient of access. Cooke's stand is admirable for its symmetry and simplicity of design, its just apportioning of strength, and a general rigidity with suitability of means to ends.

It is not a little curious that the obvious improvement of transferring the declination circle as well as the declination clamp to the telescope end of the declination axis was so long delayed; we can ascribe the delay only to a desire to retain the decimation circle as part of the counterpoise. We believe that the first important equatorials in which the declination axis was read from the eye end were the 15-inch by Grubb and the 6-inch by Cooke, made for the observatory of Lord Crawford (then Lord Lindsay) at Dun Echt (Aberdeenshire) about 1873. The plan is now almost universally adopted. Telescopes of such dimensions can be conveniently directed to any object by the circles without the observer being under the necessity to climb a special ladder. But when much larger instruments are required the hour circle becomes inaccessible from the floor, and means have to be devised for reading both circles from the eye end. This was first accomplished by Grubb in the great refractor of 27-inches aperture which he constructed for the Vienna observatory, represented in section in fig. 22.

Fig. 22.—Grubb's 27-inch refractor (Vienna).

Great Vienna telescope.The observer's eye is applied to the small telescope E, which (by means of prisms numbered 1, 2, 3, 4) views the vernier attached to the cross-head simultaneously with the hour circle attached to the upper end of the polar axis. Light to illuminate the vernier and circle is thrown from the lamp L upon prism 4 by the prisms 6 and 5. Prism 1 is in the axis of the decimation circle always reflects rays along that axis, whatever the position of the telescope may be, whilst the prisms 2, 3, 4, 5, and 6 are attached to the cross-head and therefore preserve their relative positions to each other. Through the eye-piece of the bent^[26] telescope E' another hour circle attached to the lower end of the polar axis can be seen; thus an assistant is able to direct the telescope by a handle at H to any desired hour angle. A slight rotatory motion of the telescope E on its axis enables the vernier of the declination circle to be read through prism 1. The leading features of this fine instrument represent those of all Grubb's large telescopes.

Fig. 23.—Dr Engelmann's 8-inch refractor.

The mode of relieving the friction of the declination axis is similar to that employed in the Melbourne telescope and in the account of the Vienna telescope published by Grubb. The end friction of the polar axis is relieved by a ring of conical rollers shown in section beside the principal figure.

From this point we must condense further description into critical remarks on a few typical modern instruments.

(1) Telescopes of Moderate Size for Micrometric Research only.—

Fig. 23 shows the mounting of the 8-inch refractor, of 9-feet focal length, at the private observatory of Dr Engelmann, Leipsic. The object-glass is by Messrs Clark of Cambridge, Mass., the mounting by the Repsolds of Hamburg. Repsolds' small equatorial.The declination circle reads from the eye end, and four handles for clamping and slow motion in right ascension and declination are situated near the observer's hands.

Fig. 24.—Dr Engelmann's 8-inch refractor.

The tube is of sheet steel, light, stiff, and free from tremor. The eye end carries the micrometer with an illuminating apparatus similar to that previously described under Micrometer, vol. xvi. p. 246 sq., figs. 16, 17, 20, and 21. The lamp near the eye end illuminates the field or the wires at pleasure, as well as the position circle of the micrometer and the declination circle; a separate lamp illuminates the hour circle. An excellent feature (see fig. 24) is the short distance between the eye-piece and the declination axis, so that the observer has to follow the eye end in a comparatively small circle; another good point is the flattening of the cast-iron centre-piece of the tube so that the flange of the declination axis is attached as near to the axis of the telescope tube as is consistent with free passage of the cone of rays from the object-glass. For purposes of micrometric research with the ordinary micrometer this instrument is the most elegant, satisfactory, and useful that we know, as was shown by the exceedingly accurate observations of the minor planets Victoria and Sappho for solar parallax, by Galle's method (see Parallax, vol. xviii. p. 249), made by Dr Engelmann in 1882. The substitution of small incandescent electric lamps for the oil lamps would be an improvement.

Grubb's small equatorial.(2) Telescopes of Moderate Size for General Purposes.—The modern small equatorial should for general purposes be capable of carrying spectroscopes of considerable weight, so that the strength of the axis and the rigidity of the instrument generally have to be considerably increased. Grubb has realized our ideas of what such an instrument should be in an equatorial of 6-inches aperture which he has recently made for the royal observatory at the Cape of Good Hope. The principal features are its great strength and rigidity, with special precautions to ensure preservation of the instrumental declination. The observations of Victoria and Sappho in 1882 revealed the great deficiency of most modern equatorials in this respect. That is to say, if a star near the meridian is first made to run along the measuring web of the micrometer, the clockwork then set in action, and the star brought back to the centre of the field by the slow-motion handle in right ascension, it will be found that the perfection of the bisection is no longer preserved. Thus at most observatories the measures of difference of declination when the clockwork was employed were far inferior to those made with the telescope at rest. The reason seems to be that in most equatorials the lower pivot is cylindrical, and enters an ordinary cylindrical bearing which cannot be a perfect fit. Also the cross-head, telescope, counterpoise, &c., generally together overbalance the polar axis about the upper bearing, so that the lower pivot presses upwards in its bearing, and its rotation, under the action of the clock or slow motion coupled with the friction of the surfaces, gives rise to a small rolling freedom which creates the errors in question. In this telescope the lower pivot is of steel, made slightly conical, and carefully ground to fit a long conical bearing, in which it would work very tightly, or even jam, but for spring pressure brought to bear on its lower hardened flat end, which relieves the greater part of the thrust; and the polar axis is accurately balanced about its upper bearing by a weight at the lower end of the polar axis, so that the thrust is exactly in the axis of the cone. The upper pivot (4 inches in diameter) is also of steel, finished with the same care as that of a transit circle, so that the telescope rotates with the precision of a meridian instrument. Unusual rigidity has also been given to the declination clamping arms, and the new slow motion in declination is by far the best yet contrived; it is a recent invention of Grubb's, and is described below in his own words. The eye end, suitable for heavy spectroscopes, &c., is fitted to the butt end of the telescope by bayonet joints and tightening screws, so that it can be exchanged for a micrometric eye end with almost as little trouble as the exchanging of an eye-piece. The illumination of the circles and the micrometer is by electric incandescent lamps. The instrument may be adjusted to any latitude and is probably the most practical and serviceable equatorial made. The subjoined description of the new slow motion in declination is taken from Proc. R. Dubl. Soc., 1886, p. 107.

"The slow motion arrangements usually used in equatorials are of either of two forms, viz., (a) an endless screw working into a sector or portion of a toothed circle of long radius, or (b) a screw applying or pushing directly against an arm, that arm being kept in contact with the screw by a spiral or some other form of spring having a considerable range of motion, The first (a) possesses the disadvantage that, however carefully made, it is impossible it is quite free from 'loss' or 'back lash'; and consequently the position of the telescope is not perfectly determinate in declination, which fault is inconvenient when delicate measures are required. The second (b) has practically no 'back lash,' as spring keeps the arm in perfect contact with screw, but it has the disadvantage that, whatever range of motion is required, the spring must be capable of working through the same range; consequently the spring will be much stronger in action at one end of the range than the other, unless it be made very long indeed, in which case its action is uncertain and unpleasant. To remedy these defects the author [Grubb] has devised the following, which possesses the advantages of both:—ABCD (fig. 25) is a portion of the arms attached to telescope, or cradle, on which is planted the block (b), forming the bearing of the screw.

Fig. 25.

The nut (n) is in the form of a ball working in a socket on the extremity of the clamp-arm EFG. A short stiff spring (S) is attached to this clamp-arm, bearing, not directly against any part of other arm, but against end of a second screw of same pitch as the main screw, the nut of which (oo) is toothed on edge, and works into a wheel of equal size (pp) on main screw. The point of this second screw, therefore, advances as much in one direction as the frame ABCD is carried in other, according as the milled head is turned; and consequently the point of the screw does not sensibly vary in its position with respect to the clamp-arm EFG. A short stiff spring can therefore be used, and the disadvantage above mentioned disappears."

This form of slow motion could be applied with advantage to the right ascension also, and probably to the separation of the segments of heliometers.

Large equatorials (3) Of large equatorials we name first the great refractor at Large Washington of 26-inches aperture and 321/2-feet focal length. ^[27] Washington telescope. The mounting appears to be unworthy of the well-known excellence of the object-glass. To illuminate the micrometer an assistant is required to hold a lamp in his hand. No convenient means are provided for illuminating the declination axis; and in order to point the telescope in declination the following elaborate process has to be performed:—

"The instrument is brought into the meridian and set by the observer within a degree by means of coarse divisions painted on the edge of the declination circle. These divisions are rendered visible by lighting one or two of the gas burners of the dome, and viewed by the astronomer with an opera-glass. Then an assistant mounts by a ladder to a high platform and holds a gas lamp near the vernier, and the fine setting is accomplished by the observer seated in the observing chair, the declination clamp and slow-motion screw being convenient to his hand" (Washington Observations, 1874, Appendix I., p. 33).

The polar and declination axes are of steel, only 7 inches in diameter at the thickest point, and the driving arc, which is far too small, is placed at the lower end of this slender axis. There must thus be considerable liability to tremor in right ascension. However well the instrument may act in specially practised hands with an excellent Clark's micrometer (art. Micrometer, vol. xvi. p. 245), the instrument must be considered wanting in the rigidity and convenience which a modern equatorial should possess. In his official report on the instruments of European observatories Newcomb defends the want of solidity and convenience of this instrument as compared with the Vienna telescope, because its smaller axes (notwithstanding Grubb's anti-friction arrangements) permit it to turn more easily and the mounting to be of far simpler design. But at the time of Newcomb's visit the Vienna telescope had not been brought into work, and cannot have been in proper working order if the motion in declination was so stiff as he describes it, at least when the present writer tested the instrument in Dublin that motion was surprisingly easy.

Pulkowa refractor.The great Pulkowa refractor (fig. 26) erected in 1885 is of 30-inches aperture and 45-feet focal length. The object-glass is by Clark, the mounting by the Repsolds. The tube is cylindrical, of riveted steel plate, graduated in thickness from the centre to its extremities, and bolted by very powerful flanges to a strong short cast-iron central tube, in which, as in Dr Engelmann's telescope (fig. 23), the attachment to the flange of the declination axis is placed as close as it can be to the axis of the tube without with rays converging from the object-glass to any point in the field of view. A new feature in this instrument is the platform at the lower end of the polar axis, where an assistant can view the hour circle by one eye-piece and the declination circle by another (looking up the perforated polar axis), and where he can also set the telescope to any hour angle by one wheel, or to any declination by a second, with the greatest ease. The observer at the eye end can also read off the hour and declination circles and communicate quick or slow motions to the telescope both in right ascension and declination by conveniently placed handles.

Fig. 26.—Pulkowa refractor.

The eye end presents an appearance too complicated to be figured here; it has a micrometer and its illumination for the position circle, a micrometer head, and a bright or dark field,^[28] clamps in right ascension and declination and quick and slow motion in the same, a finder, microscopes for reading the hour and declination circles, an illuminated dial showing sidereal time and driven by a galvanic current from the sidereal clock, and counter weights which can be removed when a spectroscope or other heavy appliance is added. All these, although making up an apparently complicated apparatus, are conveniently arranged, and are all necessary for the quick and easy working of so large an instrument. We have the authority of Otto Struve for stating that in practice they are all that can be desired. There is in this instrument a remarkably elegant method of relieving the friction of the polar axis. Let AA (fig. 27) be a section of the polar axis; it is then easy to adjust the weight P of the circles, &c., attached to its lower end so that the centre of gravity X of the whole moving parts of the instrument shall be in the vertical (VV) of a line passing through the apex of the hollowed flange pq at q, which flange forms part of the polar axis.

Fig. 27.

If now a wheel W is forced up against q with a pressure equal to the weight of the moving part of the instrument, the whole weight of the moving part would rest upon W in unstable equilibrium; or if a pressure R, less than W, is employed, we have the end friction on the lower bearing removed to an extent $=\mathrm {R} \sin \phi ,$ and the friction on the bearings of the upper pivot removed to the extent of $\mathrm {F} \cos \phi ,$—where $\phi$ is the latitude of the place. The wheel W is therefore mounted on a guided rod, which is forced upwards by suitable levers and weights, and this relief of pressure is precisely proportional to the pressure on the respective bearings. The Repsolds find it unnecessary to relieve the friction of the declination axis.

Grubb's design for 36-inch refractor.Fig. 28 shows the equatorial mounting which Grubb designed for the great object-glass of 36-inches aperture that Messrs Clark have completed for the Lick trustees, and which may be supposed to express Grubb's latest ideas as to the mounting for a very large telescope. The Repsolds have a large driving circle at the upper end of the polar axis, thus avoiding torsion of the polar axis at the expense of greatly increased length of the cross-head. Grubb by employing a driving arc gets the telescope much closer to the polar axis with an increased radius for driving, and he makes the polar axis a very large hollow steel or cast-iron cylinder in which torsion is insensible. Both Grubb and the Repsolds seem to think that for the tube of the telescope all necessary rigidity can be attained with cylindrical tubes of riveted steel, the thickness of the successive sheets of which diminish from the centre-piece outwards without making the extremities cone-shaped.

Fig. 28.—Grubb's mounting for the Lick object-glass.

In these very large telescopes the arrangements for giving access to the eye end and for following its diurnal motion have hitherto proved a source of difficulty. The travelling stages of the new Pulkowa telescope are the most manageable and practical that have yet been contrived, but even they leave much to be desired. For energetic work the standing position is best, provided that the eye-piece is situated at the precise height above the stage which is most convenient for the observer, and that the altitude of the observed object is not greater than 60°, For altitudes above 60° a small chair with a back, the top of which is stuffed for the head to rest upon, is the best seat, provided that the observer's eye can be kept at the height of the eye-piece. Accordingly Grubb has suggested the following plan for the observatory at Mount Hamilton, California, which is to cover the Lick telescope. The whole floor, 70 feet in diameter, is to be raised or lowered by water-power under control of the observer by means of electric keys, which act on a secondary piece of mechanism, that in turn works the valves and reversing gear of the water-engines. Other water-engines, similarly connected with keys at the observer's hands, rotate the dome and perform the quick motions in right ascension and declination. ^[29] By this arrangement a large instrument can be worked with perfect facility and comfort. There is only one other plan, that of suspending the observer's chair to the eye end, so that his eye is near the centre of motion of the chair. This is quite practicable for a 36-inch telescope, and one observer, with the necessary guiding keys at hand, could easily work a telescope and dome of the largest dimensions as quickly and with more ease than he could one of 10 or 12 inches aperture. Probably a nervous astronomer would prefer a solid floor to work upon, as in Grubb's proposal; in the latter case the quickest working can only be accomplished by two persons, one seated on the platform at the foot of the polar axis and doing the rough setting in right ascension and declination, the other meanwhile adjusting the height of the floor and the azimuth of the dome opening.

Proposed facilities for using large telescopes.In very large equatorials there must be in existing methods considerable inconvenience from the extended width of the apparatus at the eye end. Were we called upon to design a great refractor we should abolish all such apparatus and provide the observer with a few conveniently placed small handles or keys for electrical connexions, and we should perform all motions of the telescope whatsoever by electromotors. There is no form of energy so convenient for the astronomer. It provides by incandescent lamps the most suitable light for his purpose, perfectly constant, giving off little heat, and unaffected by wind; and such a light can be placed where required without the aid of reflectors or any complicated apparatus, and its intensity can be regulated with ease and precision by changing the resistance of the conductors. Moreover the electromotors can be as powerful or as delicate as we please, and can be placed in the most convenient or suitable positions. The energy of a 5-horse-power steam-engine working for ten hours can be stored in accumulators of no inconvenient dimensions ready for use as required during a whole week or even a month, and can be brought into action in force equivalent to several horse-power to raise or lower the floor or turn the dome, or to perform slow motions requiring no greater energy than that exercised by the finger and thumb, or to illuminate a lamp of 1/2or 1/4 candle-power. There would be no limit to the rigidity which could be given to such a telescope, as great ease of motion would not have to be considered, and we should abolish all complicated anti-friction apparatus for the declination axis, retaining it only for the polar axis to save wear in the teeth of the driving arc. Finally, instead of making the finder a short telescope attached to the eye end of the instrument, we should give it a focal length equal to that of the great object-glass, attaching the cell of its object-glass rigidly to the cell of the large object-glass and its eye end to the butt end of the main telescope, in order to secure the utmost rigidity in the relations of the axes of the two telescopes. Such a finder would correspond in efficiency to that of the Henry photographic telescope, and would be available as a guiding telescope in photographic work, or for keeping a star exactly on the slit of a spectroscope.

Type D.The first important instruments of type D were Mr Lassell's reflectors, the largest which, and the last, is represented in fig. 29. Lassell's mounting.The polar axis is sufficiently rigid, but the long and comparatively slender forks which carry the pivots of the central cradle are elements of instability, especially when the instrument is directed to an object of considerable hour angle. There is practical confession of this instability in the cross-bracing which connects the two forks, and which must be removed if the telescope is pointed to an object between the zenith and the elevated pole.

Fig. 29—Lassell's reflector.

Common's mounting.The best example of type D is the reflecting telescope of 36-inches aperture designed by Mr. A. A. Common, with which his exquisite photographs of nebulae, &c., were made. The principal preliminary conditions which he laid down as necessary were the following ^[30]: —(1) no tube properly so called, to avoid air-currents in the tube; (2) no mass of metal either below or at the side of the line joining the large and small mirrors, to avoid currents from possible difference of temperature between the mass of metal and the surrounding air; (3) an equatorial mounting capable of direction to any part of the visible heavens and of continued observation past the meridian without reversal; (4) an efficient means of supporting the mirror without flexure; (5) driving clock; circles to find or identify an object, and motions taken to eye end; (6) a mounting which will give the greatest amount of steadiness with the least amount of friction. Fig. 30 is a section of the instrument in the plane of the meridian. $\mathrm {D} \mathrm {D} _{1}$ is a cast-iron hollow cylinder, accurately bored out, attached to a strong base block. $\mathrm {D} _{2}$ is a cover bolted on the bottom of this cylinder, in the centre of which is a tapering steel pin $\mathrm {D} _{3}$, which enters a corresponding hole in the bottom of the polar axis E, and serves as the lower pivot of the polar axis. The cylindrical pare of the polar axis is accurately turned to a diameter one-eighth of an inch less than the outer cylinder, and the otherwise severe friction on the pin $\mathrm {D} _{3}$ is relieved by filling in the space between D and E with mercury, so far as sufficient nearly to float the whole moving part of the telescope.

Fig. 30.—Common's reflecting telescope.

The upper elbow-shaped part of the polar axis $\mathrm {E} _{2}$ is flanged and bolted to the lower part. In the section at right angles to that exhibited in fig. 30 this elbow-shaped part is T-shaped, and the cross of the T is bored to receive the declination axis; and, as the elbow puts the polar axis considerably out of balance, the T-shaped head is carried forward of the axial line about 11/4 inches, so that the whole weight of the telescope above just restores the balance. Two heavy weights X, X counterpoise the eye end F with the four braced tubes T, T which support it. B is the declination circle. It is impossible to describe this fine instrument adequately within our limits; we mention as specially worthy of study the method of supporting the mirror and the eminently ingenious and practical form of the observatory, and refer the reader to Common's illustrated account of the instrument in Mem. R.A.S., vol. xlvi. pp. 173-182.

Rosse's 3-foot mounting.There is also an admirable mounting of type D designed by Lord Rosse for his 3-foot reflector at Birr Castle, described by him in Phil. Trans., vol. clxxi. p. 153. The instrument is planned on the broad lines of Lassell's telescope (fig. 29), but the badly planned and weak fork of the latter is replaced by a thoroughly rigid bent fork made of boiler plate a quarter of an inch thick, firmly riveted to angle iron of 21/4 x 21/4 x 5/16inch scantling along each angle, the whole, as we have proved by trial, being exceedingly rigid. It would be an improvement to adopt Mr Common's plan of putting the declination axis a little out of the line of prolongation of the polar axis, and thus dispense with the counter-weight; and we should prefer hollow steel tubes with push and pull bracing rather than the angle iron rods and bracing which form the tube.

Type E.In the Proceedings of the Royal Dublin Society (vol. ii. p. 362) Grubb describes a "siderostatic telescope," which forms a good elementary example of type E. Grubb's siderostatic telescope.In fig. 31 TT is the tube of a telescope of 4-inches aperture, which is mounted to rotate about its axis, the latter forming the polar axis. MM is a plane mirror reflecting rays from a star S to the object-glass, so that its image can be viewed from the eye-piece at E. The star is retained in the field by the clock C. Stars of different declination can be viewed by rotating the mirror on its axis G, and in different hour angles by rotating the tube upon its axis.

Fig. 31.—Grubb's siderostatic telescope.

The instrument in European latitudes cannot command a view of the heavens between the elevated pole and the zenith unless the distance OG is made exceedingly great; even then only a limited range beyond the zenith is possible. The instrument is primarily intended for solar spectroscopy, and thus these drawbacks do not apply. The resulting advantage is that the observer may be in complete darkness and his observations are not interrupted by change of position.

Loewy's equatorial coudé.In Comptes Rendus for the year 1883, vol. xcvi. pp. 735-741, M. Loewy gives an account of an instrument which he calls an "equatorial coudé," designed (1) to attain greater stability and so to measure larger angles than is generally possible with the ordinary equatorial; (2) to enable a single astronomer to point the telescope and make observations in any part of the sky without changing his position; (3) to abolish the usual expensive dome, and to substitute a covered shed on wheels (which can be run back at pleasure), leaving the telescope in the open air, the observer alone being sheltered. These conditions are fulfilled in the manner shown in fig. 32. EP is the polar axis, rotating on bearings at E and P. The object-glass is at O, the eye-piece at E. There is a plane mirror at M, which reflects rays converging from the object-glass to the eye-piece at E. A second mirror N, placed at 45° to the optical axis of the object-glass, reflects rays from a star at the pole; but by rotating the box which contains this mirror on the axis of its supporting tube T a star of any declination can be observed, and by combining this motion with rotation of the polar axis the astronomer seated at E is able to view any object whatever in the visible heavens, except those situated between 10^h and 12^h hour hour angle. An hour circle attached to EP and a declination circle attached to the box containing the mirror N, both of which can be read or set from E, complete the essentials of the instrument. Its mechanical details present no great difficulty, and are most conveniently arranged. But we entertain grave doubts as to the practical value of the instrument, not on mechanical, but on optical grounds. There must be a certain loss of light from two additional reflexions; but that could be tolerated for the sake of other advantages, provided that mirrors could be made sufficiently perfect optical planes.

Fig. 32.—Loewy's coudé equatorial.

A few years ago it was very difficult to obtain an optically perfect plane 6 inches in diameter, and having obtained it there remained the further difficulty of mounting it so that in all positions it should he free from flexure. By making the mirrors of silvered glass, one-fourth of their diameter in thickness, MM. Henry have not only succeeded in mounting them with all necessary rigidity free from flexure but have given them optically true plane surfaces, notwithstanding their large diameters, viz., 11 and 15·7 inches. The present writer tested the equatorial coudé on double stars at the Paris observatory in 1884, and his last doubts as to the practical value of the instrument were dispelled. He has never seen more perfect optical definition in any of the many telescopes he has employed, and certainly never measured a celestial object in such favourable conditions of physical comfort. The easy position of the observer, the convenient position of the handles for quick and slow motion, and the absolute rigidity of the mounting leave little to be desired. In future instruments the object-glass will be placed outside the mirror N, so that both the silvered mirrors will be protected from exposure to the outer air, and probably will retain the brilliancy of their surfaces for a long period.

Adjustment of the Equatorial.

Adjustment of equatorial.Let us take the usual case, that of an equatorial of type C. (1) By means of an azimuth compass, or, better, by the shadow of a plumb line at apparent noon, lay down a meridian line on the upper surface of the stone pier, or other foundation, previously built for the instrument. (2) Employ this meridian line to set up the instrument and with it the polar axis approximately in the azimuth of the meridian, which can be tested by stretching a wire through the centres of the bearings of the polar axis, and dropping a plumb line from the extremities of the wire upon the meridian line. If this is carefully done when the azimuth adjustment is near the middle of its range all desirable accuracy in this preliminary desideratum will be secured. (3) Place the polar axis approximately at the altitude of the pole. This is very easily done for an instrument in which the polar axis is cylindrical or is encased in a box with an upper side parallel to that axis (as in Grubb's or Cooke's equatorials). Prepare a right-angled triangle of wood of which the acute angles represent the latitude and co-latitude of the place. Lay the hypothenuse of this triangle upon the line of the instrument parallel to the polar axis (or the wire of operation 2) with the angle equal to the co-latitude next to the elevated pole, and change the inclination of the polar axis till a mason's level placed on the side of the triangle opposite to the angle of the latitude shows the side in question to be horizontal. (4) Adjust the movable micrometer web to coincidence with the axis of the position circle by bisecting the image of a distant object and reading the number of revolutions or fractions of a revolution at two different readings of the position circle 180° apart. The mean of these two readings is the reading for coincidence with the axis of the position circle. Set the micrometer to this mean. (5) Adjust the polar axis more exactly to the required altitude as follows. Point the telescope to a well-known star not far from the equator and near the meridian, and turn the position circle so that the image of the star by the diurnal motion runs along the web. Read the declination circle. Now reverse the telescope to the other side of the polar axis and bisect the same star again, and again read the declination circle. The mean of the two readings is the star's instrumental apparent declination; the difference of the two readings is twice the index error. To eliminate this latter it is only necessary to shift the vernier of the declination circle by the screws provided for the purpose, without unclamping in declination, till the circle reads the star's instrumental apparent declination. This being done, select another star near the meridian and compute its apparent declination (allowing for refraction). Set the telescope to this computed reading and clamp in declination ; then cause an assistant to change the altitude of the polar axis (by the screw for the purpose) till the star is bisected by the micrometer wire. (6) Select any convenient known star about six hours from the meridian; compute its apparent declination (allowing for refraction); and set the telescope to this reading in declination. Cause the assistant to turn the slow motion in azimuth till the image of the star is bisected by the micrometer web. (7) Repeat operation 5 and make final corrections if necessary (8) Repeat operation 6 with stars both east and west of the meridian, and readjust azimuth if necessary. (9) Turn the position circle of the micrometer 90°; place the declination axis nearly horizontal; clamp the telescope in right ascension; and observe the time of transit of a known star across the web of the micrometer. Compute the true hour angle of the star from the known error of the micrometer and the star's right ascension, and set the vernier so that the hour circle shall read the computed hour angle. By these means, with a previously prepared programme, the writer has frequently completely adjusted an equatorial in less than an hour, so far as operations 4 to 9 were concerned.

There still remain two instrumental errors of the stand. (1) The line joining the optical centre of the lens with the axis of rotation of the position circle may not be at right angles to the declination axis. (2) The declination axis may not be at right angles to the polar axis. In modern equatorials it is usual to leave these adjustments to the maker, as to leave them to the astronomer would be incompatible with the greatest stability of the instrument. In a good instrument these errors will certainly be extremely small and have no influence on its efficiency for practical purposes. The methods for determining their amount are given in most works on practical astronomy. ^[31]

There remain two important optical adjustments which must be very carefully attended to, viz., the centring of the lenses of the object-glass relative to each other and the centring of the axis of the object-glass relative to that of the eye-piece. The former consists in placing the lenses of the object-glass so that the centres of curvature of their surfaces shall lie in one straight line, which line is the axis of the object-glass.

Fig. 33.Fig. 34.

This operation is so delicate and requires such special experience and skill that it should be left to the maker of the object-glass. An elegant method of testing this adjustment was given by Wollaston in Phil. Trans., 1822, p. 32. If the object-glass itself is perfectly centred, the test of the centring of its axis with that of the eye-piece is very easy: are the diffraction rings which surround the image of a bright star shown as in fig. 33, or is there flare, that is, are the rings extended on one side as in fig. 34?

Figs. 35, 36.—Apparatus for adjustment of centring in a small telescope.

If the latter is the case, that side of the object-glass towards which the flare is directed is too far from the eye-piece, and should be brought towards it by the appropriate screws or other means provided by the maker. In a good object-glass perfectly centred, on a night of steady definition, a bright star in focus should appear as in fig. 33.

A useful apparatus for the adjustment of centring is a small telescope (fig. 35) whose axis is in the centre of and at right angles to a flat piece of brass in the shape of an equilateral triangle fitted with screws at the three angles. To use this instrument, place the points of the screws on the object-glass as in fig. 36, so that two angles of the triangle are in contact with the inner edge of the cell of the object-glass, and adjust the screw a so that the cross-wires in the common focus of the object-glass and eye-piece of the small telescope coincide with the image of the cross-wires of the micrometer of the telescope which mark the axis of rotation of the position circle. Now, keeping the same angles of the brass triangle in contact with the cell, move the small centring telescope round the circumference of the object-glass and note where there is the greatest departure from coincidence. Correct this departure half by the screw a of the small centring telescope and half by the centring screws of the object-glass. The adjustment is perfect when the centring telescope can be moved round the whole periphery of the object-glass in the above manner whilst its cross- wires continue to bisect the cross-wires of the micrometer of the telescope. If after this adjustment has been perfected the diffraction rings are still not circular round the images of stars, the fault is in the centring of the lenses of the object-glass with respect to each other, and the object-glass should be sent to the maker for rectification.

Driving Clock.

Driving clock. The means employed to cause an equatorial telescope to follow the diurnal motion of a star obviously must not resemble the intermittent motion of an ordinary clock. Numerous devices have been contrived for producing uniform motion. But the limits of this article will only allow us to refer briefly to a few of those most commonly in use. Fig. 37 represents Fraunhofer's governor. On its axis C is a pinion driven by a train of wheels. The axis carries an arm BB, at the extremities of which, attached by springs f,f ′ are the weights D, D′.

Fig. 37.—Fraunhofer's governor.

When these weights acquire a certain velocity of rotation the centrifugal force is sufficient to cause the weights to fly out and rub against the inside of the cylinder AA, and their velocity is checked. Instead of a cylinder, the balls may rub against the inside of a hollow cone, and by raising or lowering the axis C the contact of the weights with the cone may be made to take place when the balls have slightly greater or less velocity, and thus the rate of the clock is regulated. A much better arrangement is a modification of Watt's governor, employed by Grubb and Cooke. The governor balls g, g (fig. 38) repose on the points h, h of the arm KK till they reach their normal velocity, when they fly outwards and bring the point S (tipped with leather) into contact with the friction plate p.

Fig. 38.—Modification of Watt's governor.

Fig. 39.—Hilger's modification of Foucault's air-fan. These clocks are simple in construction and act very well. Newcomb in the Washington equatorial has employed a long suspended conical pendulum; when this pendulum in the least exceeds its normal velocity (that is, its normal departure from the vertical) it establishes an electrical contact which brings friction to bear, and thus reduces the power applied to the pendulum. There is occasional tendency to elliptical motion, and the clock is otherwise troublesome. In the Repsolds' driving clock of the 30 -inch Pulkowa refractor the conical pendulum is reversed, being a heavy weight at the top of a vertical steel rod, kept in conical rotation by a pin at its upper end, which enters a slot in a revolving arm. The rod is in fact a spring of such a form as to cause the revolutions to be nearly or perfectly isochronous whatever the angle of the cone of motion; the clock is therefore, within limits, independent of the power applied to it or the force to be overcome.

Many forms of air-fans have been suggested; probably the best is the modification of Foucault's proposed by Hilger (see Monthly Notices R.A.S., vol. xlvi. p. 155), which is shown in fig. 39. E is the axis of rotation; C and D are fans that are pulled towards the spindle E by chronometer springs in the boxes A and B. The fans fly out symmetrically when the velocity exceeds 25 or 30 revolutions per second; the increased resistance of the air thus produced checks the velocity of rotation. By means of the small weights W, W attached to arms on the fans Hilger states that it is possible to adjust this governor so that it shall even lose by an increase of the driving weight.

For the most refined work none of these governors can be said to be perfect; none would be even tolerable as a clock for astronomical time-keeping purposes. It is possible that the elaborate Greenwich driving clock may give better results, but its construction is too complicated to be frequently repeated (see, for a description of it, the Greenwich Observations for 1868). The only way in which nearly perfect uniform motion can be realized is to control it in some way from a swinging pendulum. This is done in Bond's spring governor ^[32] and by Grubb, the latter employing the arm of a remontoir train connected with a dead-beat escapement to bring friction to bear on a revolving plate connected with the axis of his governor (see fig. 38). The best existing driving clock is probably that at Lord Crawford's observatory at Dun Echt. ^[33] An account of its performance is given by Dr Copeland in Vierteljahrsschr. astron. Gesellsch., 16 Jahrg., p. 305. In this clock gain of a hundredth of a second, or even less, introduces increased friction on the revolving disk during the next second, or until the gain has been corrected. A still more perfect clock could probably be made on a similar plan by abolishing the clock weight and making the origin of power an electromotor, the current being cut off in a way similar to that in the Dun Echt clock if the clock of continuous motion gets in advance of the ordinary clock.

For information on clockwork of equatorials and telescope mountings generally, see Konkoly's Practische Anleitung zur Anstellung astron. Beobachtungen. (D. GI.)

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1. In recent years the term "photographic telescope" has been applied to instruments employed to record the appearance of celestial objects by photography.
2. He died about 1570. His son alludes to his untimely death in the preface to the Pantometria.
3. There is no further trace of this volume.
4. See Dr Moll of Utrecht, in Journ. Roy. Inst., vol, i., 1831.
5. Lettre d'Uomini Illustri, p. 112, Venice, 1744.
6. This last power could not be exceeded with advantage in this form of telescope till after the invention of the achromatic object-glass.
7. The same argument was employed by Gregory more than fifty years previously, but had been followed by no practical result. The lens of the human eye is not achromatic (see Light, vol. xiv. p. 601).
8. At a meeting of the Royal Astronomical Society held on 9th May 1886 a legal document, signed by Chester Moor Hall, was presented by Mr R. B. Prosser of the Patent Office to the society. On the same occasion Mr Lanyard made the following interesting statement respecting Hall:—
   "Some years ago very little was known about Moor Hall. It was known that, about seven years after the patent for making achromatic object-glasses was granted to Dollond, his claim to the invention was disputed by other instrument-makers, amongst them by a Mr Champness, an instrument-maker of Cornhill, who began to infringe the patent, alleging that John Dollond was not the real inventor, and that such telescopes had been made twenty-five years before the granting of his patent by Mr Moor Hall. John Dollond, to whom the Copley medal of the Royal Society had been given for his invention, was then dead, and his son brought an action for infringing the patent against Champness. There is no report of the case, but the facts are referred to in the reports of subsequent cases. It appears that workmen who had been employed by Mr Moor Hall were examined, and proved that they had made achromatic object-glasses as early as 1733. Dollond's patent was not set aside, though the evidence with regard to the prior manufacture was accepted by Lord Mansfield, who tried the case, as having been satisfactorily proved. . . Mr Hall was a bencher of the Inner Temple, and was alive at the time of the action. He was a man of some property, and is spoken of on his tombstone as an excellent lawyer and mathematician. He was not a fellow of the Royal Society, but must certainly have known of the gift of the Copley medal to Dollond. It is very curious the conflicting evidence we have to reconcile, but I think the balance of evidence is in favour of there having been a prior invention of achromatic object-glasses before the date of Dollond's patent" (Astron. Register, May 1886; see also the Observatory for same date).
9. Gentleman's Magazine, 1790, part ii. p. 890.
10. For a good account of this controversy, see Dr. H. Servus, Geschichte des Fernrohrs, p. 77 sq., Berlin, 1886.
11. Ayscough was an optician in Ludgate Hill, London.
12. See Wolf, Biographien, vol. ii. p. 301, and Clerke, History of Astronomy, pp. 146-147.
13. In the case of short-sighted persons the image for very distant objects (that is, for parallel rays) is formed in front of the retina; therefore, to enable such persons to see distinctly, the rays emerging from the eye-piece must be slightly divergent; that is, they must enter the eye as if they proceeded from a comparatively near object. For normal eyes the natural adaptation is not to focus for quite parallel rays, but on objects at a moderate distance, and practically, therefore, most persons do adjust the focus of a telescope, for most distinct and easy vision, so that the rays emerge from the eye-piece very slightly divergent. Abnormally short-sighted persons require to push in the eye-lens nearer to the object-glass, and long-sighted persons to withdraw it from the adjustment employed by those of normal sight. It is usual, however, in computations of the magnifying power of telescopes, for the rays emerging from the eye-piece when adjusted for distinct vision to be parallel.
14. Euler, Dioptrica, St Petersburg, 1767-71; Clairaut, Mém. de l'Acad. Scien., 1757; D'Alembert, Opusc., vol. iii.; Lagrange, Miscel. Taurin., iii. 2, p. 152, and Mem. Acad. Berl., 1778; Schmidt, Lekrbuch der analytischen Optik; Santiui, Teorica degli Strumenti Ottici; Klügel, in Gilbert's Ann. d. Physik, xxxiv., 1810, pp. 265-275 and 276-291; Herschel, Phil. Trans. Roy. Soc., 1821, p. 222-267; Littrow, Mem. R.A.S. (London), vol. iii. pp. 235-255; Robinson, Mechanical Philosophy, art. "Telescope," vol. iii. pp. 403-514; Gauss, "Ueber die achromatischen Doppel-Objective," in Lindenau's Zeitschr., iv., 1817, pp. 345-351, and Gilbert's Ann. d. Physik, lix. pp. 188-195; Gauss, in Louville's Journal, 1856, i. pp. 9-43; Steinheil Astron. Nach., xlviii., 1851, col. 225-228, liii., 1860, col. 305-306, and 1861, col. 269-270; A. Steinheil, Ueber Berechnung optischer Constructionen; Carl Steinheil, Repertorium, iii., 1867, pp. 430-440, and München Akad. Sitz., 1867, ii. pp. 284-297; Steinheil (Carl A. and H. A.), Göttingsche Nachrichten, 1865, pp. 131-143, 211-214.
15. See Abney and Festing, Bakerian Lecture. Phil. Trans., 1886; also Photographic News, May 1886, p. 332.
16. Proc. Roy. Soc., vol. xxxiii. pp. 164–186.
17. This arrangement also helps to equalize the temperatures of the lenses with each other and with the outer air.
18. Quite recently Prof. Stokes has suggested that to adapt a telescope to either photographic or telescopic purposes at pleasure the crown lens should be reversible as well as changeable as to distance -with respect to the flint. In this way doubtless the chromatic and spherical aberration could be preserved for the two kinds of work.
19. See Nature, vol. xxxiv. p. 622, 26th October 1886.
20. For recent literature on the secondary spectrum in double and triple object-glasses, &c., see W. Schmidt, Die Brechung des Lichtes in Gläsern, insbesondere d. achromat. und aplanat. Objectivlinse, Leipsic, 1874; W. Harkness, "On the Colour Correction of Achromatic Telescopes," in Amer. Jour. of Science and Arts, September 1879, pp. 189–196; C. S. Hastings, "Triple Objectives with Complete Colour Correction," ib., December 1879, pp. 429–435; Perty, Ueber die Grenzen der sichtbaren Schöpfung nach den jetzigen Leistungen der Mikroskope und Fernröhre, Berlin, 1874; H. C. Vogel, Ueber eine einfache Methode zur Bestimmung der Brennpunkte und der Abweichungskreise eines Fernrohr-Objectivs für Strahlen von verschiedener Brechbarkeit; C. A. Young, "The Colour-Correction of Certain Achromatic Object-Glasses," in Amer. Jour. Sci., June 1880, pp. 454–456; also a review of these papers by A. Safarik, Vierteljahrdhrschrift der astronomischen Gesellschaft, 1882, pp. 13-39.
21. Pogg. Annal., cxxxi., 1867.
22. Herschel, Phil. Trans., 1795, vol. lxxxv. P. 347; Rosse, Phil. Trans., 1840. p. 503, and 1861, p.681.
23. See the detailed account in Greenwich Observations, 1868.
24. This object-glass will have the shortest proportional focal length of any yet constructed of aperture exceeding 16 inches. The following table gives the focal length in apertures of the largest existing refractors:—

    Vienna telescope (Grubb)	27	inches aperture	focal length	15·5	apertures
    Washington"(Clark)	26	"	"	15·0	"
    Pulkowa"(Clark)	30	"	"	18·0	"

25. These inconvenient conditions are imposed by the dimensions of the existing dome and may lead to accidents in practice.
26. In the bent telescope refracting prisms are employed at the comers to change the direction of the rays.
27. Described and figured in the Washington Observations. 1874, App. 1.
28. There is also an elegant arrangement for printing on a ribbon of paper, by pressure of the finger, the readings of the number of revolutions and fractions of a revolution of the head at each observation, the ribbon being automatically moved forward for another record after each observation.
29. A woodcut showing these arrangements appeared in the Engineer, 9th July 1886.
30. Monthly Notices R.A.S., vol. xxxix. p. 384.
31. Chauvenet, Practical and Spherical Astronomy, vol. ii. pp, 379-390; Brunnow, Spherical Astronomy, p. 445 and Loomis, Practical Astronomy, pp. 28-32.
32. Konkoly, Practische Anleitung zur Anstellung astron. Beobachtungen, Brunswick, 1883.
33. Monthly Notices R.A.S., November 1873.