“Coelorum perrupit claustra.”

Herschel’s Epitaph.251. Frederick William Herschel was born at Hanover on November 15th, 1738, two years after Lagrange and nine years before Laplace. His father was a musician in the Hanoverian army, and the son, who shewed a remarkable aptitude for music as well as a decided taste for knowledge of various sorts, entered his father’s profession as a boy (1753). On the breaking out of the Seven Years’ War he served during part of a campaign, but his health being delicate his parents “determined to remove him from the service—a step attended by no small difficulties,” and he was accordingly sent to England (1757), to seek his fortune as a musician.

After some years spent in various parts of the country, he moved (1766) to Bath, then one of the great centres of fashion in England. At first oboist in Linley’s orchestra, then organist of the Octagon Chapel, he rapidly rose to a position of great popularity and distinction, both as a musician and as a music-teacher. He played, conducted, and composed, and his private pupils increased so rapidly that the number of lessons which he gave was at one time 35 a week. But this activity by no means exhausted his extraordinary energy; he had never lost his taste for study, and, according to a contemporary biographer, “after a fatiguing day of 14 or 16 hours spent in his vocation, he would retire at night with the greatest avidity to unbend the mind, if it may be so called, with a few propositions in Maclaurin’s Fluxions, or other books of that sort.” His musical studies had long ago given him an interest in mathematics, and it seems likely that the study of Robert Smith’s Harmonics led him to the Compleat System of Optics of the same author, and so to an interest in the construction and use of telescopes. The astronomy that he read soon gave him a desire to see for himself what the books described; first he hired a small reflecting telescope, then thought of buying a larger instrument, but found that the price was prohibitive. Thus he was gradually led to attempt the construction of his own telescopes (1773). His brother Alexander, for whom he had found musical work at Bath, and who seems to have had considerable mechanical talent but none of William’s perseverance, helped him in this undertaking, while his devoted sister Caroline (1750-1848), who had been brought over to England by William in 1772, not only kept house, but rendered a multitude of minor services. The operation of grinding and polishing the mirror for a telescope was one of the greatest delicacy, and at a certain stage required continuous labour for several hours. On one occasion Herschel’s hand never left the polishing tool for 16 hours, so that “by way of keeping him alive” Caroline was “obliged to feed him by putting the victuals by bits into his mouth,” and in less extreme cases she helped to make the operation less tedious by reading aloud: it is with some feeling of relief that we hear that on these occasions the books read were not on mathematics, optics, or astronomy, but were such as Don Quixote, the Arabian Nights, and the novels of Sterne and Fielding.252. After an immense number of failures Herschel succeeded in constructing a tolerable reflecting telescope—soon to be followed by others of greater size and perfection—and with this he made his first recorded observation, of the Orion nebula, in March 1774.

This observation, made when he was in his 36th year, may be conveniently regarded as the beginning of his astronomical career, though for several years more music remained his profession, and astronomy could only be cultivated in such leisure time as he could find or make for himself; his biographers give vivid pictures of his extraordinary activity during this period, and of his zeal in using odd fragments of time, such as intervals between the acts at a theatre, for his beloved telescopes.

A letter written by him in 1783 gives a good account of the spirit in which he was at this time carrying out his astronomical work:—

“I determined to accept nothing on faith, but to see with my own eyes what others had seen before me.... I finally succeeded in completing a so-called Newtonian instrument, 7 feet in length. From this I advanced to one of 10 feet, and at last to one of 20, for I had fully made up my mind to carry on the improvement of my telescopes as far as it could possibly be done. When I had carefully and thoroughly perfected the great instrument in all its parts, I made systematic use of it in my observations of the heavens, first forming a determination never to pass by any, the smallest, portion of them without due investigation.”

In accordance with this last resolution he executed on four separate occasions, beginning in 1775, each time with an instrument of greater power than on the preceding, a review of the whole heavens, in which everything that appeared in any way remarkable was noticed and if necessary more carefully studied. He was thus applying to astronomy methods comparable with those of the naturalist who aims at drawing up a complete list of the flora or fauna of a country hitherto little known253. In the course of the second of these reviews, made with a telescope of the Newtonian type, 7 feet in length, he made the discovery (March 13th, 1781) which gave him a European reputation and enabled him to abandon music as a profession and to devote the whole of his energies to science.

“In examining the small stars in the neighbourhood of ? Geminorum I perceived one that appeared visibly larger than the rest; being struck with its uncommon appearance I compared it to ? Geminorum and the small star in the quartile between Auriga and Gemini and finding it so much larger than either of them, I suspected it to be a comet.”

If Herschel’s suspicion had been correct the discovery would have been of far less interest than it actually was, for when the new body was further observed and attempts were made to calculate its path, it was found that no ordinary cometary orbit would in any way fit its motion, and within three or four months of its discovery it was recognised—first by Anders Johann Lexell (1740-1784)—as being no comet but a new planet, revolving round the sun in a nearly circular path, at a distance about 19 times that of the earth and nearly double that of Saturn.

No new planet had been discovered in historic times, and Herschel’s achievement was therefore absolutely unique; even the discovery of satellites inaugurated by Galilei (chapter VI., §121) had come to a stop nearly a century before (1684), when Cassini had detected his second pair of satellites of Saturn (chapter VIII., §160). Herschel wished to exercise the discoverer’s right of christening by calling the new planet after his royal patron Georgium Sidus, but though the name was used for some time in England, Continental astronomers never accepted it, and after an unsuccessful attempt to call the new body Herschel, it was generally agreed to give a name similar to those of the other planets, and Uranus was proposed and accepted.

Although by this time Herschel had published two or three scientific papers and was probably known to a slight extent in English scientific circles, the complete obscurity among Continental astronomers of the author of this memorable discovery is curiously illustrated by a discussion in the leading astronomical journal (Bode’s Astronomisches Jahrbuch) as to the way to spell his name, Hertschel being perhaps the best and Mersthel the worst of several attempts.254. This obscurity was naturally dissipated by the discovery of Uranus. Distinguished visitors to Bath, among them the Astronomer Royal Maskelyne (chapter X., §219), sought his acquaintance; before the end of the year he was elected a Fellow of the Royal Society, in addition to receiving one of its medals, and in the following spring he was summoned to Court to exhibit himself, his telescopes, and his stars to George III. and to various members of the royal family. As the outcome of this visit he received from the King an appointment as royal astronomer, with a salary of £200 a year.

With this appointment his career as a musician came to an end, and in August 1782 the brother and sister left Bath for good, and settled first in a dilapidated house at Datchet, then, after a few months (1785-6) spent at Clay Hall in Old Windsor, at Slough in a house now known as Observatory House and memorable in Arago’s words as “le lieu du monde oÙ il a ÉtÉ fait le plus de dÉcouvertes.”255. Herschel’s modest salary, though it would have sufficed for his own and his sister’s personal wants, was of course insufficient to meet the various expenses involved in making and mounting telescopes. The skill which he had now acquired in the art was, however, such that his telescopes were far superior to any others which were available, and as his methods were his own, there was a considerable demand for instruments made by him. Even while at Bath he had made and sold a number, and for years after moving to the neighbourhood of Windsor he derived a considerable income from this source, the royal family and a number of distinguished British and foreign astronomers being among his customers.

The necessity for employing his valuable time in this way fortunately came to an end in 1788, when he married a lady with a considerable fortune; Caroline lived henceforward in lodgings close to her brother, but worked for him with unabated zeal.

By the end of 1783 Herschel had finished a telescope 20 feet in length with a great mirror 18 inches in diameter, and with this instrument most of his best work was done; but he was not yet satisfied that he had reached the limit of what was possible. During the last winter at Bath he and his brother had spent a great deal of labour in an unsuccessful attempt to construct a 30-foot telescope; the discovery of Uranus and its consequences prevented the renewal of the attempt for some time, but in 1785 he began a 40-foot telescope with a mirror four feet in diameter, the expenses of which were defrayed by a special grant from the King. While it was being made Herschel tried a new form of construction of reflecting telescopes, suggested by Lemaire in 1732 but never used, by which a considerable gain of brilliancy was effected, but at the cost of some loss of distinctness. This Herschelian or front-view construction, as it is called, was first tried with the 20-foot, and led to the discovery (January 11th, 1787) of two satellites of Uranus, Oberon and Titania; it was henceforward regularly employed. After several mishaps the 40-foot telescope (fig. 82) was successfully constructed. On the first evening on which it was employed (August 28th, 1789) a sixth satellite of Saturn (Enceladus) was detected, and on September 17th a much fainter seventh satellite (Mimas). Both satellites were found to be nearer to the planet than any of the five hitherto discovered, Mimas being the nearer of the two (cf. fig. 91).

Although for the detection of extremely faint objects such as these satellites the great telescope was unequalled, for many kinds of work and for all but the very clearest evenings a smaller instrument was as good, and being less unwieldy was much more used. The mirror of the great telescope deteriorated to some extent, and after 1811, Herschel’s hand being then no longer equal to the delicate task of repolishing it, the telescope ceased to be used though it was left standing till 1839, when it was dismounted and closed up.256. From the time of his establishment at Slough till he began to lose his powers through old age the story of Herschel’s life is little but a record of the work he did. It was his practice to employ in observing the whole of every suitable night; his daylight hours were devoted to interpreting his observations and to writing the papers in which he embodied his results. His sister was nearly always present as his assistant when he was observing, and also did a good deal of cataloguing, indexing, and similar work for him. After leaving Bath she also did some observing on her own account, though only when her brother was away or for some other reason did not require her services; she specialised on comets, and succeeded from first to last in discovering no less than eight. To form any adequate idea of the discomfort and even danger attending the nights spent in observing, it is necessary to realise that the great telescopes used were erected in the open air, that for both the Newtonian and Herschelian forms of reflectors the observer has to be near the upper end of the telescope, and therefore at a considerable height above the ground. In the 40-foot, for example, ladders 50 feet in length were used to reach the platform on which the observer was stationed. Moreover from the nature of the case satisfactory observations could not be taken in the presence either of the moon or of artificial light. It is not therefore surprising that Caroline Herschel’s journals contain a good many expressions of anxiety for her brother’s welfare on these occasions, and it is perhaps rather a matter of wonder that so few serious accidents occurred.

In addition to doing his real work Herschel had to receive a large number of visitors who came to Slough out of curiosity or genuine scientific interest to see the great man and his wonderful telescopes. In 1801 he went to Paris, where he made Laplace’s acquaintance and also saw Napoleon, whose astronomical knowledge he rated much below that of George III., while “his general air was something like affecting to know more than he did know.”

In the spring of 1807 he had a serious illness; and from that time onwards his health remained delicate, and a larger proportion of his time was in consequence given to indoor work. The last of the great series of papers presented to the Royal Society appeared in 1818, when he was almost 80, though three years later he communicated a list of double stars to the newly founded Royal Astronomical Society. His last observation was taken almost at the same time, and he died rather more than a year afterwards (August 21st, 1822), when he was nearly 84.

He left one son, John, who became an astronomer only less distinguished than his father (chapter XIII., §§306-8). Caroline Herschel after her beloved brother’s death returned to Hanover, chiefly to be near other members of her family; here she executed one important piece of work by cataloguing in a convenient form her brother’s lists of nebulae, and for the remaining 26 years of her long life her chief interest seems to have been in the prosperous astronomical career of her nephew John.257. The incidental references to Herschel’s work that have been made in describing his career have shewn him chiefly as the constructor of giant telescopes far surpassing in power any that had hitherto been used, and as the diligent and careful observer of whatever could be seen with them in the skies. Sun and moon, planets and fixed stars, were all passed in review, and their peculiarities noted and described. But this merely descriptive work was in Herschel’s eyes for the most part means to an end, for, as he said in 1811, “a knowledge of the construction of the heavens has always been the ultimate object of my observations.”

Astronomy had for many centuries been concerned almost wholly with the positions of the various heavenly bodies on the celestial sphere, that is with their directions. Coppernicus and his successors had found that the apparent motions on the celestial sphere of the members of the solar system could only be satisfactorily explained by taking into account their actual motions in space, so that the solar system came to be effectively regarded as consisting of bodies at different distances from the earth and separated from one another by so many miles. But with the fixed stars the case was quite different: for, with the unimportant exception of the proper motions of a few stars (chapter X., §203), all their known apparent motions were explicable as the result of the motion of the earth; and the relative or actual distances of the stars scarcely entered into consideration. Although the belief in a real celestial sphere to which the stars were attached scarcely survived the onslaughts of Tycho Brahe and Galilei, and any astronomer of note in the latter part of the 17th or in the 18th century would, if asked, have unhesitatingly declared the stars to be at different distances from the earth, this was in effect a mere pious opinion which had no appreciable effect on astronomical work.

The geometrical conception of the stars as represented by points on a celestial sphere was in fact sufficient for ordinary astronomical purposes, and the attention of great observing astronomers such as Flamsteed, Bradley, and Lacaille was directed almost entirely towards ascertaining the positions of these points with the utmost accuracy or towards observing the motions of the solar system. Moreover the group of problems which Newton’s work suggested naturally concentrated the attention of eighteenth-century astronomers on the solar system, though even from this point of view the construction of star catalogues had considerable value as providing reference points which could be used for fixing the positions of the members of the solar system.

Almost the only exception to this general tendency consisted in the attempts—hitherto unsuccessful—to find the parallaxes and hence the distances of some of the fixed stars, a problem which, though originally suggested by the Coppernican controversy, had been recognised as possessing great intrinsic interest.

Herschel therefore struck out an entirely new path when he began to study the sidereal system per se and the mutual relations of its members. From this point of view the sun, with its attendant planets, became one of an innumerable host of stars, which happened to have received a fictitious importance from the accident that we inhabited one member of its system.258. A complete knowledge of the positions in space of the stars would of course follow from the measurement of the parallax (chapter VI., §129 and chapter X., §207) of each. The failure of such astronomers as Bradley to get the parallax of any one star was enough to shew the hopelessness of this general undertaking, and, although Herschel did make an attack on the parallax problem (§263), he saw that the question of stellar distribution in space, if to be answered at all, required some simpler if less reliable method capable of application on a large scale.

Accordingly he devised (1784) his method of star-gauging. The most superficial view of the sky shews that the stars visible to the naked eye are very unequally distributed on the celestial sphere; the same is true when the fainter stars visible in a telescope are taken into account. If two portions of the sky of the same apparent or angular magnitude are compared, it may be found that the first contains many times as many stars as the second. If we realise that the stars are not actually on a sphere but are scattered through space at different distances from us, we can explain this inequality of distribution on the sky as due to either a real inequality of distribution in space, or to a difference in the distance to which the sidereal system extends in the directions in which the two sets of stars lie. The first region on the sky may correspond to a region of space in which the stars are really clustered together, or may represent a direction in which the sidereal system extends to a greater distance, so that the accumulation of layer after layer of stars lying behind one another produces the apparent density of distribution. In the same way, if we are standing in a wood and the wood appears less thick in one direction than in another, it may be because the trees are really more thinly planted there or because in that direction the edge of the wood is nearer.

In the absence of any a priori knowledge of the actual clustering of the stars in space, Herschel chose the former of these two hypotheses; that is, he treated the apparent density of the stars on any particular part of the sky as a measure of the depth to which the sidereal systems extended in that direction, and interpreted from this point of view the results of a vast series of observations. He used a 20-foot telescope so arranged that he could see with it a circular portion of the sky 15' in diameter (one-quarter the area of the sun or full moon), turned the telescope to different parts of the sky, and counted the stars visible in each case. To avoid accidental irregularities he usually took the average of several neighbouring fields, and published in 1785 the results of gauges thus made in 683156 regions, while he subsequently added 400 others which he did not think it necessary to publish. Whereas in some parts of the sky he could see on an average only one star at a time, in others nearly 600 were visible, and he estimated that on one occasion about 116,000 stars passed through the field of view of his telescope in a quarter of an hour. The general result was, as rough naked-eye observation suggests, that stars are most plentiful in and near the Milky Way and least so in the parts of the sky most remote from it. Now the Milky Way forms on the sky an ill-defined band never deviating much from a great circle (sometimes called the galactic circle); so that on Herschel’s hypothesis the space occupied by the stars is shaped roughly like a disc or grindstone, of which according to his figures the diameter is about five times the thickness. Further, the Milky Way is during part of its length divided into two branches, the space between the two branches being comparatively free of stars. Corresponding to this subdivision there has therefore to be assumed a cleft in the “grindstone.”

This “grindstone” theory of the universe had been suggested in 1750 by Thomas Wright (1711-1786) in his Theory of the Universe, and again by Kant five years later; but neither had attempted, like Herschel, to collect numerical data and to work out consistently and in detail the consequences of the fundamental hypothesis.

That the assumption of uniform distribution of stars in space could not be true in detail was evident to Herschel from the beginning. A star cluster, for example, in which many thousands of faint stars are collected together in a very small space on the sky, would have to be interpreted as representing a long projection or spike full of stars, extending far beyond the limits of the adjoining portions of the sidereal system, and pointing directly away from the position occupied by the solar system. In the same way certain regions in the sky which are found to be bare of stars would have to be regarded as tunnels through the stellar system. That even one or two such spikes or tunnels should exist would be improbable enough, but as star clusters were known in considerable numbers before Herschel began his work, and were discovered by him in hundreds, it was impossible to explain their existence on this hypothesis, and it became necessary to assume that a star cluster occupied a region of space in which stars were really closer together than elsewhere.

Moreover further study of the arrangement of the stars, particularly of those in the Milky Way, led Herschel gradually to the belief that his original assumption was a wider departure from the truth than he had at first supposed; and in 1811, nearly 30 years after he had begun star-gauging, he admitted a definite change of opinion:—

“I must freely confess that by continuing my sweeps of the heavens my opinion of the arrangement of the stars ... has undergone a gradual change.... For instance, an equal scattering of the stars may be admitted in certain calculations; but when we examine the Milky Way, or the closely compressed clusters of stars of which my catalogues have recorded so many instances, this supposed equality of scattering must be given up.”

The method of star-gauging was intended primarily to give information as to the limits of the sidereal system—or the visible portions of it. Side by side with this method Herschel constantly made use of the brightness of a star as a probable test of nearness. If two stars give out actually the same amount of light, then that one which is nearer to us will appear the brighter; and on the assumption that no light is absorbed or stopped in its passage through space, the apparent brightness of the two stars will be inversely as the square of their respective distances. Hence, if we receive nine times as much light from one star as from another, and if it is assumed that this difference is merely due to difference of distance, then the first star is three times as far off as the second, and so on.

That the stars as a whole give out the same amount of light, so that the difference in their apparent brightness is due to distance only, is an assumption of the same general character as that of equal distribution. There must necessarily be many exceptions, but, in default of more exact knowledge, it affords a rough-and-ready method of estimating with some degree of probability relative distances of stars.

To apply this method it was necessary to have some means of comparing the amount of light received from different stars. This Herschel effected by using telescopes of different sizes. If the same star is observed with two reflecting telescopes of the same construction but of different sizes, then the light transmitted by the telescope to the eye is proportional to the area of the mirror which collects the light, and hence to the square of the diameter of the mirror. Hence the apparent brightness of a star as viewed through a telescope is proportional on the one hand to the inverse square of the distance, and on the other to the square of the diameter of the mirror of the telescope; hence the distance of the star is, as it were, exactly counterbalanced by the diameter of the mirror of the telescope. For example, if one star viewed in a telescope with an eight-inch mirror and another viewed in the great telescope with a four-foot mirror appear equally bright, then the second star is—on the fundamental assumption—six times as far off.

In the same way the size of the mirror necessary to make a star just visible was used by Herschel as a measure of the distance of the star, and it was in this sense that he constantly referred to the “space-penetrating power” of his telescope. On this assumption he estimated the faintest stars visible to the naked eye to be about twelve times as remote as one of the brightest stars, such as Arcturus, while Arcturus if removed to 900 times its present distance would just be visible in the 20-foot telescope which he commonly used, and the 40-foot would penetrate about twice as far into space.

Towards the end of his life (1817) Herschel made an attempt to compare statistically his two assumptions of uniform distribution in space and of uniform actual brightness, by counting the number of stars of each degree of apparent brightness and comparing them with the numbers that would result from uniform distribution in space if apparent brightness depended only on distance. The inquiry only extended as far as stars visible to the naked eye and to the brighter of the telescopic stars, and indicated the existence of an excess of the fainter stars of these classes, so that either these stars are more closely packed in space than the brighter ones, or they are in reality smaller or less luminous than the others; but no definite conclusions as to the arrangement of the stars were drawn.259. Intimately connected with the structure of the sidereal system was the question of the distribution and nature of nebulae (cf. figs. 100, 102, facing pp. 397, 400) and star clusters (cf. fig. 104, facing p. 405). When Herschel began his work rather more than 100 such bodies were known, which had been discovered for the most part by the French observers Lacaille (chapter X., §223) and Charles Messier (1730-1817). Messier may be said to have been a comet-hunter by profession; finding himself liable to mistake nebulae for comets, he put on record (1781) the positions of 103 of the former. Herschel’s discoveries—carried out much more systematically and with more powerful instrumental appliances—were on a far larger scale. In 1786 he presented to the Royal Society a catalogue of 1,000 new nebulae and clusters, three years later a second catalogue of the same extent, and in 1802 a third comprising 500. Each nebula was carefully observed, its general appearance as well as its position being noted and described, and to obtain a general idea of the distribution of nebulae on the sky the positions were marked on a star map. The differences in brightness and in apparent structure led to a division into eight classes; and at quite an early stage of his work (1786) he gave a graphic account of the extraordinary varieties in form which he had noted:—

“I have seen double and treble nebulae, variously arranged; large ones with small, seeming attendants; narrow but much extended, lucid nebulae or bright dashes; some of the shape of a fan, resembling an electric brush, issuing from a lucid point; others of the cometic shape, with a seeming nucleus in the center; or like cloudy stars, surrounded with a nebulous atmosphere; a different sort again contain a nebulosity of the milky kind, like that wonderful inexplicable phenomenon about ? Orionis; while others shine with a fainter mottled kind of light, which denotes their being resolvable into stars.”

260. But much the most interesting problem in classification was that of the relation between nebulae and star clusters. The Pleiades, for example, appear to ordinary eyes as a group of six stars close together, but many short-sighted people only see there a portion of the sky which is a little brighter than the adjacent region; again, the nebulous patch of light, as it appears to the ordinary eye, known as Praesepe (in the Crab), is resolved by the smallest telescope into a cluster of faint stars. In the same way there are other objects which in a small telescope appear cloudy or nebulous, but viewed in an instrument of greater power are seen to be star clusters. In particular Herschel found that many objects which to Messier were purely nebulous appeared in his own great telescopes to be undoubted clusters, though others still remained nebulous. Thus in his own words:—

“Nebulae can be selected so that an insensible gradation shall take place from a coarse cluster like the Pleiades down to a milky nebulosity like that in Orion, every intermediate step being represented.”

These facts suggested obviously the inference that the difference between nebulae and star clusters was merely a question of the power of the telescope employed, and accordingly Herschel’s next sentence is:—

“This tends to confirm the hypothesis that all are composed of stars more or less remote.”

The idea was not new, having at any rate been suggested, rather on speculative than on scientific grounds, in 1755 by Kant, who had further suggested that a single nebula or star cluster is an assemblage of stars comparable in magnitude and structure with the whole of those which constitute the Milky Way and the other separate stars which we see. From this point of view the sun is one star in a cluster, and every nebula which we see is a system of the same order. This “island universe” theory of nebulae, as it has been called, was also at first accepted by Herschel, so that he was able once to tell Miss Burney that he had discovered 1,500 new universes.

Herschel, however, was one of those investigators who hold theories lightly, and as early as 1791 further observation had convinced him that these views were untenable, and that some nebulae at least were essentially distinct from star clusters. The particular object which he quotes in support of his change of view was a certain nebulous star—that is, a body resembling an ordinary star but surrounded by a circular halo gradually diminishing in brightness.

“Cast your eye,” he says, “on this cloudy star, and the result will be no less decisive.... Your judgement, I may venture to say, will be, that the nebulosity about the star is not of a starry nature.”

If the nebulosity were due to an aggregate of stars so far off as to be separately indistinguishable, then the central body would have to be a star of almost incomparably greater dimensions than an ordinary star; if, on the other hand, the central body were of dimensions comparable with those of an ordinary star, the nebulosity must be due to something other than a star cluster. In either case the object presented features markedly different from those of a star cluster of the recognised kind; and of the two alternative explanations Herschel chose the latter, considering the nebulosity to be “a shining fluid, of a nature totally unknown to us.” One exception to his earlier views being thus admitted, others naturally followed by analogy, and henceforward he recognised nebulae of the “shining fluid” class as essentially different from star clusters, though it might be impossible in many cases to say to which class a particular body belonged.

The evidence accumulated by Herschel as to the distribution of nebulae also shewed that, whatever their nature, they could not be independent of the general sidereal system, as on the “island universe” theory. In the first place observation soon shewed him that an individual nebula or cluster was usually surrounded by a region of the sky comparatively free from stars; this was so commonly the case that it became his habit while sweeping for nebulae, after such a bare region had passed through the field of his telescope, to warn his sister to be ready to take down observations of nebulae. Moreover, as the position of a large number of nebulae came to be known and charted, it was seen that, whereas clusters were common near the Milky Way, nebulae which appeared incapable of resolution into clusters were scarce there, and shewed on the contrary a decided tendency to be crowded together in the regions of the sky most remote from the Milky Way—that is, round the poles of the galactic circle (§258). If nebulae were external systems, there would of course be no reason why their distribution on the sky should shew any connection either with the scarcity of stars generally or with the position of the Milky Way.

It is, however, rather remarkable that Herschel did not in this respect fully appreciate the consequences of his own observations, and up to the end of his life seems to have considered that some nebulae and clusters were external “universes,” though many were part of our own system.261. As early as 1789 Herschel had thrown out the idea that the different kinds of nebulae and clusters were objects of the same kind at different stages of development, some “clustering power” being at work converting a diffused nebula into a brighter and more condensed body; so that condensation could be regarded as a sign of “age.” And he goes on:—

“This method of viewing the heavens seems to throw them into a new kind of light. They are now seen to resemble a luxuriant garden, which contains the greatest variety of productions, in different flourishing beds; and one advantage we may at least reap from it is, that we can, as it were, extend the range of our experience to an immense duration. For, to continue the simile I have borrowed from the vegetable kingdom, is it not almost the same thing, whether we live successively to witness the germination, blooming, foliage, fecundity, fading, withering and corruption of a plant, or whether a vast number of specimens, selected from every stage through which the plant passes in the course of its existence, be brought at once to our view?”

His change of opinion in 1791 as to the nature of nebulae led to a corresponding modification of his views of this process of condensation. Of the star already referred to (§260) he remarked that its nebulous envelope “was more fit to produce a star by its condensation than to depend upon the star for its existence.” In 1811 and 1814 he published a complete theory of a possible process whereby the shining fluid constituting a diffused nebula might gradually condense—the denser portions of it being centres of attraction—first into a denser nebula or compressed star cluster, then into one or more nebulous stars, lastly into a single star or group of stars. Every supposed stage in this process was abundantly illustrated from the records of actual nebulae and clusters which he had observed.

In the latter paper he also for the first time recognised that the clusters in and near the Milky Way really belonged to it, and were not independent systems that happened to lie in the same direction as seen by us.262. On another allied point Herschel also changed his mind towards the end of his life. When he first used his great 20-foot telescope to explore the Milky Way, he thought that he had succeeded in completely resolving its faint cloudy light into component stars, and had thus penetrated to the end of the Milky Way; but afterwards he was convinced that this was not the case, but that there remained cloudy portions which—whether on account of their remoteness or for other reasons—his telescopes were unable to resolve into stars (cf. fig. 104, facing p. 405).

In both these respects therefore the structure of the Milky Way appeared to him finally less simple than at first.263. One of the most notable of Herschel’s discoveries was a bye-product of an inquiry of an entirely different character. Just as Bradley in trying to find the parallax of a star discovered aberration and nutation (chapter X., §207), so also the same problem in Herschel’s hands led to the discovery of double stars. He proposed to employ Galilei’s differential or double-star method (chapter VI., §129), in which the minute shift of a star’s position, due to the earth’s motion round the sun, is to be detected not by measuring its angular distance from standard points on the celestial sphere such as the pole or the zenith, but by observing the variations in its distance from some star close to it, which from its faintness or for some other reason might be supposed much further off and therefore less affected by the earth’s motion.

With this object in view Herschel set to work to find pairs of stars close enough together to be suitable for his purpose, and, with his usual eagerness to see and to record all that could be seen, gathered in an extensive harvest of such objects. The limit of distance between the two members of a pair beyond which he did not think it worth while to go was 2', an interval imperceptible to the naked eye except in cases of quite abnormally acute sight. In other words, the two stars—even if bright enough to be visible—would always appear as one to the ordinary eye. A first catalogue of such pairs, each forming what may be called a double star, was published early in 1782 and contained 269, of which 227 were new discoveries; a second catalogue of 434 was presented to the Royal Society at the end of 1784; and his last paper, sent to the Royal Astronomical Society in 1821 and published in the first volume of its memoirs, contained a list of 145 more. In addition to the position of each double star the angular distance between the two members, the direction of the line joining them, and the brightness of each were noted. In some cases also curious contrasts in the colour of the two components were observed. There were also not a few cases in which not merely two, but three, four, or more stars were found close enough to one another to be reckoned as forming a multiple star.

Herschel had begun with the idea that a double star was due to a merely accidental coincidence in the direction of two stars which had no connection with one another and one of which might be many times as remote as the other. It had, however, been pointed out by Michell (chapter X., §219), as early as 1767, that even the few double stars then known afforded examples of coincidences which were very improbable as the result of mere random distribution of stars. A special case may be taken to make the argument clearer, though Michell’s actual reasoning was not put into a numerical form. The bright star Castor (in the Twins) had for some time been known to consist of two stars, a and , rather less than 5 apart. Altogether there are about 50 stars of the same order of brightness as a, and 400 like . Neither set of stars shews any particular tendency to be distributed in any special way over the celestial sphere. So that the question of probabilities becomes: if there are 50 stars of one sort and 400 of another distributed at random over the whole celestial sphere, the two distributions having no connection with one another, what is the chance that one of the first set of stars should be within 5 of one of the second set? The chance is about the same as that, if 50 grains of wheat and 400 of barley are scattered at random in a field of 100 acres, one grain of wheat should be found within half an inch of a grain of barley. The odds against such a possibility are clearly very great and can be shewn to be more than 300,000 to one. These are the odds against the existence—without some real connection between the members—of a single double star like Castor; but when Herschel began to discover double stars by the hundred the improbability was enormously increased. In his first paper Herschel gave as his opinion that “it is much too soon to form any theories of small stars revolving round large ones,” a remark shewing that the idea had been considered; and in 1784 Michell returned to the subject, and expressed the opinion that the odds in favour of a physical relation between the members of Herschel’s newly discovered double stars were “beyond arithmetic.”264. Twenty years after the publication of his first catalogue Herschel was of Michell’s opinion, but was now able to support it by evidence of an entirely novel and much more direct character. A series of observations of Castor, presented in two papers published in the Philosophical Transactions in 1803 and 1804, which were fortunately supplemented by an observation of Bradley’s in 1759, had shewn a progressive alteration in the direction of the line joining its two components, of such a character as to leave no doubt that the two stars were revolving round one another; and there were five other cases in which a similar motion was observed. In these six cases it was thus shewn that the double star was really formed by a connected pair of stars near enough to influence one another’s motion. A double star of this kind is called a binary star or a physical double star, as distinguished from a merely optical double star, the two members of which have no connection with one another. In three cases, including Castor, the observations were enough to enable the period of a complete revolution of one star round another, assumed to go on at a uniform rate, to be at any rate roughly estimated, the results given by Herschel being 342 years for Castor,157 375 and 1,200 years for the other two. It was an obvious inference that the motion of revolution observed in a binary star was due to the mutual gravitation of its members, though Herschel’s data were not enough to determine with any precision the law of the motion, and it was not till five years after his death that the first attempt was made to shew that the orbit of a binary star was such as would follow from, or at any rate would be consistent with, the mutual gravitation of its members (chapter XIII., §309: cf. also fig. 101). This may be regarded as the first direct evidence of the extension of the law of gravitation to regions outside the solar system.

Although only a few double stars were thus definitely shewn to be binary, there was no reason why many others should not be so also, their motion not having been rapid enough to be clearly noticeable during the quarter of a century or so over which Herschel’s observations extended; and this probability entirely destroyed the utility of double stars for the particular purpose for which Herschel had originally sought them. For if a double star is binary, then the two members are approximately at the same distance from the earth and therefore equally affected by the earth’s motion, whereas for the purpose of finding the parallax it is essential that one should be much more remote than the other. But the discovery which he had made appeared to him far more interesting than that which he had attempted but failed to make; in his own picturesque language, he had, like Saul, gone out to seek his father’s asses and had found a kingdom.265. It had been known since Halley’s time (chapter X., §203) that certain stars had proper motions on the celestial sphere, relative to the general body of stars. The conviction, that had been gradually strengthening among astronomers, that the sun is only one of the fixed stars, suggested the possibility that the sun, like other stars, might have a motion in space. Thomas Wright, Lambert, and others had speculated on the subject, and Tobias Mayer (chapter X., §§225-6) had shewn how to look for such a motion.

If a single star appears to move, then by the principle of relative motion (chapter IV., §77) this may be explained equally well by a motion of the star or by a motion of the observer, or by a combination of the two; and since in this problem the internal motions of the solar system may be ignored, this motion of the observer may be identified with that of the sun. When the proper motions of several stars are observed, a motion of the sun only is in general inadequate to explain them, but they may be regarded as due either solely to the motions in space of the stars or to combinations of these with some motion of the sun. If now the stars be regarded as motionless and the sun be moving towards a particular point on the celestial sphere, then by an obvious effect of perspective the stars near that point will appear to recede from it and one another on the celestial sphere, while those in the opposite region will approach one another, the magnitude of these changes depending on the rapidity of the sun’s motion and on the nearness of the stars in question. The effect is exactly of the same nature as that produced when, on looking along a street at night, two lamps on opposite sides of the street at some distance from us appear close together, but as we walk down the street towards them they appear to become more and more separated from one another. In the figure, for example, L and L' as seen from B appear farther apart than when seen from A.

If the observed proper motions of stars examined are not of this character, they cannot be explained as due merely to the motion of the sun; but if they shew some tendency to move in this way, then the observations can be most simply explained by regarding the sun as in motion, and by assuming that the discrepancies between the effects resulting from the assumed motion of the sun and the observed proper motions are due to the motions in space of the several stars.

From the few proper motions which Mayer had at his command he was, however, unable to derive any indication of a motion of the sun.

Herschel used the proper motions, published by Maskelyne and Lalande, of 14 stars (13 if the double star Castor be counted as only one), and with extraordinary insight detected in them a certain uniformity of motion of the kind already described, such as would result from a motion of the sun. The point on the celestial sphere towards which the sun was assumed to be moving, the apex as he called it, was taken to be the point marked by the star ? in the constellation Hercules. A motion of the sun in this direction would, he found, produce in the 14 stars apparent motions which were in the majority of cases in general agreement with those observed.158 This result was published in 1783, and a few months later Pierre PrÉvost (1751-1839) deduced a very similar result from Tobias Mayer’s collection of proper motions. More than 20 years later (1805) Herschel took up the question again, using six of the brightest stars in a collection of the proper motions of 36 published by Maskelyne in 1790, which were much more reliable than any earlier ones, and employing more elaborate processes of calculation; again the apex was placed in the constellation Hercules, though at a distance of nearly 30° from the position given in 1783. Herschel’s results were avowedly to a large extent speculative, and were received by contemporary astronomers with a large measure of distrust; but a number of far more elaborate modern investigations of the same subject have confirmed the general correctness of his work, the earlier of his two estimates appearing, however, to be the more accurate. He also made some attempts in the same papers and in a third (published in 1806) to estimate the speed as well as the direction of the sun’s motion; but the work necessarily involved so many assumptions as to the probable distances of the stars—which were quite unknown—that it is not worth while to quote results more definite than the statement made in the paper of 1783, that “We may in a general way estimate that the solar motion can certainly not be less than that which the earth has in her annual orbit.”266. The question of the comparative brightness of stars was, as we have seen (§258), of importance in connection with Herschel’s attempts to estimate their relative distances from the earth and their arrangement in space; it also presented itself in connection with inquiries into the variability of the light of stars. Two remarkable cases of variability had been for some time known. A star in the Whale (? Ceti or Mira) had been found to be at times invisible to the naked eye and at other times to be conspicuous; a Dutch astronomer, Phocylides Holwarda (1618-1651), first clearly recognised its variable character (1639), and Ismael Boulliau or Bullialdus (1605-1694) in 1667 fixed its period at about eleven months, though it was found that its fluctuations were irregular both in amount and in period. Its variations formed the subject of the first paper published by Herschel in the Philosophical Transactions (1780). An equally remarkable variable star is that known as Algol (or Persei), the fluctuations of which were found to be performed with almost absolute regularity. Its variability had been noted by Geminiano Montanari (1632-1687) in 1669, but the regularity of its changes was first detected in 1783 by John Goodricke (1764-1786), who was soon able to fix its period at very nearly 2 days 20 hours 49 minutes. Algol, when faintest, gives about one-quarter as much light as when brightest, the change from the first state to the second being effected in about ten hours; whereas Mira varies its light several hundredfold, but accomplishes its changes much more slowly.

At the beginning of Herschel’s career these and three or four others of less interest were the only stars definitely recognised as variable, though a few others were added soon afterwards. Several records also existed of so-called “new” stars, which had suddenly been noticed in places where no star had previously been observed, and which for the most part rapidly became inconspicuous again (cf. chapter II., §42; chapter V., §100; chapter VII., §138); such stars might evidently be regarded as variable stars, the times of greatest brightness occurring quite irregularly or at long intervals. Moreover various records of the brightness of stars by earlier astronomers left little doubt that a good many must have varied sensibly in brightness. For example, a small star in the Great Bear (close to the middle star of the “tail”) was among the Arabs a noted test of keen sight, but is perfectly visible even in our duller climate to persons with ordinary eyesight; and Castor, which appeared the brighter of the two Twins to Bayer when he published his Atlas (1603), was in the 18th century (as now) less bright than Pollux.

Herschel made a good many definite measurements of the amounts of light emitted by stars of various magnitudes, but was not able to carry out any extensive or systematic measurements on this plan. With a view to the future detection of such changes of brightness as have just been mentioned, he devised and carried out on a large scale the extremely simple method of sequences. If a group of stars are observed and their order of brightness noted at two different times, then any alteration in the order will shew that the brightness of one or more has changed. So that if a number of stars are observed in sets in such a way that each star is recorded as being less bright than certain stars near it and brighter than certain other stars, materials are thereby provided for detecting at any future time any marked amount of variation of brightness. Herschel prepared on this plan, at various times between 1796 and 1799, four catalogues of comparative brightness based on naked-eye observations and comprising altogether about 3,000 stars. In the course of the work a good many cases of slight variability were noticed; but the most interesting discovery of this kind was that of the variability of the well-known star a Herculis, announced in 1796. The period was estimated at 60 days, and the star thus seemed to form a connecting link between the known variables which like Algol had periods of a very few days and those (of which Mira was the best known) with periods of some hundreds of days. As usual, Herschel was not content with a mere record of observations, but attempted to explain the observed facts by the supposition that a variable star had a rotation and that its surface was of unequal brightness.267. The novelty of Herschel’s work on the fixed stars, and the very general character of the results obtained, have caused this part of his researches to overshadow in some respects his other contributions to astronomy.

Though it was no part of his plan to contribute to that precise knowledge of the motions of the bodies of the solar system which absorbed the best energies of most of the astronomers of the 18th century—whether they were observers or mathematicians—he was a careful and successful observer of the bodies themselves.

His discoveries of Uranus, of two of its satellites, and of two new satellites of Saturn have been already mentioned in connection with his life (§§253, 255). He believed himself to have seen also (1798) four other satellites of Uranus, but their existence was never satisfactorily verified; and the second pair of satellites now known to belong to Uranus, which were discovered by Lassell in 1847 (chapter XIII., §295), do not agree in position and motion with any of Herschel’s four. It is therefore highly probable that they were mere optical illusions due to defects of his mirror, though it is not impossible that he may have caught glimpses of one or other of Lassell’s satellites and misinterpreted the observations.

Saturn was a favourite object of study with Herschel from the very beginning of his astronomical career, and seven papers on the subject were published by him between 1790 and 1806. He noticed and measured the deviation of the planet’s form from a sphere (1790); he observed various markings on the surface of the planet itself, and seems to have seen the inner ring, now known from its appearance as the crape ring (chapter XIII., §295), though he did not recognise its nature. By observations of some markings at some distance from the equator he discovered (1790) that Saturn rotated on an axis, and fixed the period of rotation at about 10 h. 16 m. (a period differing only by about 2 minutes from modern estimates), and by similar observations of the ring (1790) concluded that it rotated in about 10-1/2 hours, the axis of rotation being in each case perpendicular to the plane of the ring. The satellite Japetus, discovered by Cassini in 1671 (chapter VIII., §160), had long been recognised as variable in brightness, the light emitted being several times as much at one time as at another. Herschel found that these variations were not only perfectly regular, but recurred at an interval equal to that of the satellite’s period of rotation round its primary (1792), a conclusion which Cassini had thought of but rejected as inconsistent with his observations. This peculiarity was obviously capable of being explained by supposing that different portions of Japetus had unequal power of reflecting light, and that like our moon it turned on its axis once in every revolution, in such a way as always to present the same face towards its primary, and in consequence each face in turn to an observer on the earth. It was natural to conjecture that such an arrangement was general among satellites, and Herschel obtained (1797) some evidence of variability in the satellites of Jupiter, which appeared to him to support this hypothesis.

Herschel’s observations of other planets were less numerous and important. He rightly rejected the supposed observations by Schroeter (§271) of vast mountains on Venus, and was only able to detect some indistinct markings from which the planet’s rotation on an axis could be somewhat doubtfully inferred. He frequently observed the familiar bright bands on Jupiter commonly called belts, which he was the first to interpret (1793) as bands of cloud. On Mars he noted the periodic diminution of the white caps on the two poles, and observed how in these and other respects Mars was of all planets the one most like the earth.268. Herschel made also a number of careful observations on the sun, and based on them a famous theory of its structure. He confirmed the existence of various features of the solar surface which had been noted by the earlier telescopists such as Galilei, Scheiner, and Hevel, and added to them in some points of detail. Since Galilei’s time a good many suggestions as to the nature of spots had been thrown out by various observers, such as that they were clouds, mountain-tops, volcanic products, etc., but none of these had been supported by any serious evidence. Herschel’s observations of the appearances of spots suggested to him that they were depressions in the surface of the sun, a view which derived support from occasional observations of a spot when passing over the edge of the sun as a distinct depression or notch there. Upon this somewhat slender basis of fact he constructed (1795) an elaborate theory of the nature of the sun, which attracted very general notice by its ingenuity and picturesqueness and commanded general assent in the astronomical world for more than half a century. The interior of the sun was supposed to be a cold dark solid body, surrounded by two cloud-layers, of which the outer was the photosphere or ordinary surface of the sun, intensely hot and luminous, and the inner served as a fire-screen to protect the interior. The umbra (chapter VI., §124) of a spot was the dark interior seen through an opening in the clouds, and the penumbra corresponded to the inner cloud-layer rendered luminous by light from above.

“The sun viewed in this light appears to be nothing else than a very eminent, large, and lucid planet, evidently the first or, in strictness of speaking, the only primary one of our system; ... it is most probably also inhabited, like the rest of the planets, by beings whose organs are adapted to the peculiar circumstances of that vast globe.”

That spots were depressions had been suggested more than twenty years before (1774) by Alexander Wilson of Glasgow (1714-1786), and supported by evidence different from any adduced by Herschel and in some ways more conclusive. Wilson noticed, first in the case of a large spot seen in 1769, and afterwards in other cases, that as the sun’s rotation carries a spot across its disc from one edge to another, its appearance changes exactly as it would do in accordance with ordinary laws of perspective if the spot were a saucer-shaped depression, of which the bottom formed the umbra and the sloping sides the penumbra, since the penumbra appears narrowest on the side nearest the centre of the sun and widest on the side nearest the edge. Hence Wilson inferred, like Herschel, but with less confidence, that the body of the sun is dark. In the paper referred to Herschel shews no signs of being acquainted with Wilson’s work, but in a second paper (1801), which contained also a valuable series of observations of the detailed markings on the solar surface, he refers to Wilson’s “geometrical proof” of the depression of the umbra of a spot.

Although it is easy to see now that Herschel’s theory was a rash generalisation from slight data, it nevertheless explained—with fair success—most of the observations made up to that time.

Modern knowledge of heat, which was not accessible to Herschel, shews us the fundamental impossibility of the continued existence cf a body with a cold interior and merely a shallow ring of hot and luminous material round it; and the theory in this form is therefore purely of historic interest (cf. also chapter XIII., §§298, 303).269. Another suggestive idea of Herschel’s was the analogy between the sun and a variable star, the known variation in the number of spots and possibly of other markings on the sun suggesting to him the probability of a certain variability in the total amount of solar light and heat emitted. The terrestrial influence of this he tried to measure—in the absence of precise meteorological data—with characteristic ingenuity by the price of wheat, and some evidence was adduced to shew that at times when sun-spots had been noted to be scarce—corresponding according to Herschel’s view to periods of diminished solar activity—wheat had been dear and the weather presumably colder. In reality, however, the data were insufficient to establish any definite conclusions.270. In addition to carrying out the astronomical researches already sketched, and a few others of less importance, Herschel spent some time, chiefly towards the end of his life, in working at light and heat; but the results obtained, though of considerable value, belong rather to physics than to astronomy, and need not be dealt with here.271. It is natural to associate Herschel’s wonderful series of discoveries with his possession of telescopes of unusual power and with his formulation of a new programme of astronomical inquiry; and these were certainly essential elements. It is, however, significant, as shewing how important other considerations were, that though a great number of his telescopes were supplied to other astronomers, and though his astronomical programme when once suggested was open to all the world to adopt, hardly any of his contemporaries executed any considerable amount of work comparable in scope to his own.

Almost the only astronomer of the period whose work deserves mention beside Herschel’s, though very inferior to it both in extent and in originality, was Johann Hieronymus Schroeter (1745-1816).

Holding an official position at Lilienthal, near Bremen, he devoted his leisure during some thirty years to a scrutiny of the planets and of the moon, and to a lesser extent of other bodies.

As has been seen in the case of Venus (§267), his results were not always reliable, but notwithstanding some errors he added considerably to our knowledge of the appearances presented by the various planets, and in particular studied the visible features of the moon with a minuteness and accuracy far exceeding that of any of his predecessors, and made some attempt to deduce from his observations data as to its physical condition. His two volumes on the moon (Selenotopographische Fragmente, 1791 and 1802), and other minor writings, are a storehouse of valuable detail, to which later workers have been largely indebted.