“Through Newton theory had made a great advance and was ahead of observation; the latter now made efforts to come once more level with theory.”—Bessel.
196. Newton virtually created a new department of astronomy, gravitational astronomy, as it is often called, and bequeathed to his successors the problem of deducing more fully than he had succeeded in doing the motions of the celestial bodies from their mutual gravitation.
To the solution of this problem Newton’s own countrymen contributed next to nothing throughout the 18th century, and his true successors were a group of Continental mathematicians whose work began soon after his death, though not till nearly half a century after the publication of the Principia.
This failure of the British mathematicians to develop Newton’s discoveries may be explained as due in part to the absence or scarcity of men of real ability, but in part also to the peculiarity of the mathematical form in which Newton presented his discoveries. The Principia is written almost entirely in the language of geometry, modified in a special way to meet the requirements of the case; nearly all subsequent progress in gravitational astronomy has been made by mathematical methods known as analysis. Although the distinction between the two methods cannot be fully appreciated except by those who have used them both, it may perhaps convey some impression of the differences between them to say that in the geometrical treatment of an astronomical problem each step of the reasoning is expressed in such a way as to be capable of being interpreted in terms of the original problem, whereas in the analytical treatment the problem is first expressed by means of algebraical symbols; these symbols are manipulated according to certain purely formal rules, no regard being paid to the interpretation of the intermediate steps, and the final algebraical result, if it can be obtained, yields on interpretation the solution of the original problem. The geometrical solution of a problem, if it can be obtained, is frequently shorter, clearer, and more elegant; but, on the other hand, each special problem has to be considered separately, whereas the analytical solution can be conducted to a great extent according to fixed rules applicable in a larger number of cases. In Newton’s time modern analysis was only just coming into being, some of the most important parts of it being in fact the creation of Leibniz and himself, and although he sometimes used analysis to solve an astronomical problem, it was his practice to translate the result into geometrical language before publication; in doing so he was probably influenced to a large extent by a personal preference for the elegance of geometrical proofs, partly also by an unwillingness to increase the numerous difficulties contained in the Principia, by using mathematical methods which were comparatively unfamiliar. But though in the hands of a master like Newton geometrical methods were capable of producing astonishing results, the lesser men who followed him were scarcely ever capable of using his methods to obtain results beyond those which he himself had reached. Excessive reverence for Newton and all his ways, combined with the estrangement which long subsisted between British and foreign mathematicians, as the result of the fluxional controversy (chapter IX., § 191), prevented the former from using the analytical methods which were being rapidly perfected by Leibniz’s pupils and other Continental mathematicians. Our mathematicians remained, therefore, almost isolated during the whole of the 18th century, and with the exception of some admirable work by Colin Maclaurin (1698-1746), which carried Newton’s theory of the figure of the earth a stage further, nothing of importance was done in our country for nearly a century after Newton’s death to develop the theory of gravitation beyond the point at which it was left in the Principia.
In other departments of astronomy, however, important progress was made both during and after Newton’s lifetime, and by a curious inversion, while Newton’s ideas were developed chiefly by French mathematicians, the Observatory of Paris, at which Picard and others had done such admirable work (chapter VIII., §§ 160-2), produced little of real importance for nearly a century afterwards, and a large part of the best observing work of the 18th century was done by Newton’s countrymen. It will be convenient to separate these two departments of astronomical work, and to deal in the next chapter with the development of the theory of gravitation.
197. The first of the great English observers was Newton’s contemporary John Flamsteed, who was born near Derby in 1646 and died at Greenwich in 1720.111 Unfortunately the character of his work was such that, marked as it was by no brilliant discoveries, it is difficult to present it in an attractive form or to give any adequate idea of its real extent and importance. He was one of those laborious and careful investigators, the results of whose work are invaluable as material for subsequent research, but are not striking in themselves.
He made some astronomical observations while quite a boy, and wrote several papers, of a technical character, on astronomical subjects, which attracted some attention. In 1675 appointed a member of a Committee to report on a method for finding the longitude at sea which had been offered to the Government by a certain Frenchman of the name of St. Pierre. The Committee, acting largely on Flamsteed’s advice, reported unfavourably on the method in question, and memorialised Charles II. in favour of founding a national observatory, in order that better knowledge of the celestial bodies might lead to a satisfactory method of finding the longitude, a problem which the rapid increase of English shipping rendered of great practical importance. The King having agreed, Flamsteed was in the same year appointed to the new office of Astronomer Royal, with a salary of £100 a year, and the warrant for building an Observatory at Greenwich was signed on June 12th, 1675. About a year was occupied in building it, and Flamsteed took up his residence there and began work in July 1676, five years after Cassini entered upon his duties at the Observatory of Paris (chapter VIII., § 160). The Greenwich Observatory was, however, on a very different scale from the magnificent sister institution. The King had, it is true, provided Flamsteed with a building and a very small salary, but furnished him neither with instruments nor with an assistant. A few instruments he possessed already, a few more were given to him by rich friends, and he gradually made at his own expense some further instrumental additions of importance. Some years after his appointment the Government provided him with “a silly, surly labourer” to help him with some of the rough work, but he was compelled to provide more skilled assistance out of his own pocket, and this necessity in turn compelled him to devote some part of his valuable time to taking pupils.
198. Flamsteed’s great work was the construction of a more accurate and more extensive star catalogue than any that existed; he also made a number of observations of the moon, of the sun, and to a less extent of other bodies. Like Tycho, the author of the last great star catalogue (chapter V., § 107), he found problems continually presenting themselves in the course of his work which had to be solved before his main object could be accomplished, and we accordingly owe to him the invention of several improvements in practical astronomy, the best known being his method of finding the position of the first point of Aries (chapter II., § 42), one of the fundamental points with reference to which all positions on the celestial sphere are defined. He was the first astronomer to use a clock systematically for the determination of one of the two fundamental quantities (the right ascension) necessary to fix the position of a star, a method which was first suggested and to some extent used by Picard (chapter VIII., § 157), and, as soon as he could get the necessary instruments, he regularly used the telescopic sights of Gascoigne and Auzout (chapter VIII., § 155), instead of making naked-eye observations. Thus while Hevel (chapter VIII., § 153) was the last and most accurate observer of the old school, employing methods not differing essentially from those which had been in use for centuries, Flamsteed belongs to the new school, and his methods differ rather in detail than in principle from those now in vogue for similar work at Greenwich, Paris, or Washington. This adoption of new methods, together with the most scrupulous care in details, rendered Flamsteed’s observations considerably more accurate than any made in his time or earlier, the first definite advance afterwards being made by Bradley (§ 218).
Flamsteed compared favourably with many observers by not merely taking and recording observations, but by performing also the tedious process known as reduction (§ 218), whereby the results of the observation are put into a form suitable for use by other astronomers; this process is usually performed in modern observatories by assistants, but in Flamsteed’s case had to be done almost exclusively by the astronomer himself. From this and other causes he was extremely slow in publishing observations; we have already alluded (chapter IX., § 192) to the difficulty which Newton had in extracting lunar observations from him, and after a time a feeling that the object for which the Observatory had been founded was not being fulfilled became pretty general among astronomers. Flamsteed always suffered from bad health as well as from the pecuniary and other difficulties which have been referred to; moreover he was much more anxious that his observations should be kept back till they were as accurate as possible, than that they should be published in a less perfect form and used for the researches which he once called “Mr. Newton’s crotchets”; consequently he took remonstrances about the delay in the publication of his observations in bad part. Some painful quarrels occurred between Flamsteed on the one hand and Newton and Halley on the other. The last straw was the unauthorised publication in 1712, under the editorship of Halley, of a volume of Flamsteed’s observations, a proceeding to which Flamsteed not unnaturally replied by calling Halley a “malicious thief.” Three years later he succeeded in getting hold of all the unsold copies and in destroying them, but fortunately he was also stimulated to prepare for publication an authentic edition. The Historia Coelestis Britannica, as he called the book, contained an immense series of observations made both before and during his career at Greenwich, but the most important and permanently valuable part was a catalogue of the places of nearly 3,000 stars.112
Flamsteed himself only lived just long enough to finish the second of the three volumes; the third was edited by his assistants Abraham Sharp (1651-1742) and Joseph Crosthwait; and the whole was published in 1725. Four years later still appeared his valuable Star-Atlas, which long remained in common use.
The catalogue was not only three times as extensive as Tycho’s, which it virtually succeeded, but was also very much more accurate. It has been estimated113 that, whereas Tycho’s determinations of the positions of the stars were on the average about 1′ in error, the corresponding errors in Flamsteed’s case were about 10″. This quantity is the apparent diameter of a shilling seen from a distance of about 500 yards; so that if two marks were made at opposite points on the edge of the coin, and it were placed at a distance of 500 yards, the two marks might be taken to represent the true direction of an average star and its direction as given in Flamsteed’s catalogue. In some cases of course the error might be much greater and in others considerably less.
Flamsteed contributed to astronomy no ideas of first-rate importance; he had not the ingenuity of Picard and of Roemer in devising instrumental improvements, and he took little interest in the theoretical work of Newton;114 but by unflagging industry and scrupulous care he succeeded in bequeathing to his successors an immense treasure of observations, executed with all the accuracy that his instrumental means permitted.
199. Flamsteed was succeeded as Astronomer Royal by Edmund Halley, whom we have already met with (chapter IX., § 176) as Newton’s friend and helper.
Born in 1656, ten years after Flamsteed, he studied astronomy in his schooldays, and published a paper on the orbits of the planets as early as 1676. In the same year he set off for St. Helena (in latitude 16° S.) in order to make observations of stars which were too near the south pole to be visible in Europe. The climate turned out to be disappointing, and he was only able after his return to publish (1678) a catalogue of the places of 341 southern stars, which constituted, however, an important addition to precise knowledge of the stars. The catalogue was also remarkable as being the first based on telescopic observation, though the observations do not seem to have been taken with all the accuracy which his instruments rendered attainable. During his stay at St. Helena he also took a number of pendulum observations which confirmed the results obtained a few years before by Richer at Cayenne (chapter VIII., § 161), and also observed a transit of Mercury across the sun, which occurred in November 1677.
After his return to England he took an active part in current scientific questions, particularly in those connected with astronomy, and made several small contributions to the subject. In 1684, as we have seen, he first came effectively into contact with Newton, and spent a good part of the next few years in helping him with the Principia.
200. Of his numerous contributions to astronomy, which touched almost every branch of the subject, his work on comets is the best known and probably the most important. He observed the comets of 1680 and 1682; he worked out the paths both of these and of a number of other recorded comets in accordance with Newton’s principles, and contributed a good deal of the material contained in the sections of the Principia dealing with comets, particularly in the later editions. In 1705 he published a Synopsis of Cometary Astronomy in which no less than 24 cometary orbits were calculated. Struck by the resemblance between the paths described by the comets of 1531, 1607, and 1682, and by the approximate equality in the intervals between their respective appearances and that of a fourth comet seen in 1456, he was shrewd enough to conjecture that the three later comets, if not all four, were really different appearances of the same comet, which revolved round the sun in an elongated ellipse in a period of about 75 or 76 years. He explained the difference between the 76 years which separate the appearances of the comet in 1531 and 1607, and the slightly shorter period which elapsed between 1607 and 1682, as probably due to the perturbations caused by planets near which the comet had passed; and finally predicted the probable reappearance of the same comet (which now deservedly bears his name) about 76 years after its last appearance, i.e. about 1758, though he was again aware that planetary perturbation might alter the time of its appearance; and the actual appearance of the comet about the predicted time (chapter XI., § 231) marked an important era in the progress of our knowledge of these extremely troublesome and erratic bodies.
201. In 1693 Halley read before the Royal Society a paper in which he called attention to the difficulty of reconciling certain ancient eclipses with the known motion of the moon, and referred to the possibility of some slight increase in the moon’s average rate of motion round the earth.
This irregularity, now known as the secular acceleration of the moon’s mean motion, was subsequently more definitely established as a fact of observation; and the difficulties met with in explaining it as a result of gravitation have rendered it one of the most interesting of the moon’s numerous irregularities (cf. chapter XI., § 240, and chapter XIII., § 287).
202. Halley also rendered good service to astronomy by calling attention to the importance of the expected transits of Venus across the sun in 1761 and 1769 as a means of ascertaining the distance of the sun. The method had been suggested rather vaguely by Kepler, and more definitely by James Gregory in his Optics published in 1663. The idea was first suggested to Halley by his observation of the transit of Mercury in 1677. In three papers published by the Royal Society he spoke warmly of the advantages of the method, and discussed in some detail the places and means most suitable for observing the transit of 1761. He pointed out that the desired result could be deduced from a comparison of the durations of the transit of Venus, as seen from different stations on the earth, i.e. of the intervals between the first appearance of Venus on the sun’s disc and the final disappearance, as seen at two or more different stations. He estimated, moreover, that this interval of time, which would be several hours in length, could be measured with an error of only about two seconds, and that in consequence the method might be relied upon to give the distance of the sun to within about 1∕500 part of its true value. As the current estimates of the sun’s distance differed among one another by 20 or 30 per cent., the new method, expounded with Halley’s customary lucidity and enthusiasm, not unnaturally stimulated astronomers to take great trouble to carry out Halley’s recommendations. The results, as we shall see (§ 227), were, however, by no means equal to Halley’s expectations.
203. In 1718 Halley called attention to the fact that three well-known stars, Sirius, Procyon, and Arcturus, had changed their angular distances from the ecliptic since Greek times, and that Sirius had even changed its position perceptibly since the time of Tycho Brahe. Moreover comparison of the places of other stars shewed that the changes could not satisfactorily be attributed to any motion of the ecliptic, and although he was well aware that the possible errors of observation were such as to introduce a considerable uncertainty into the amounts involved, he felt sure that such errors could not wholly account for the discrepancies noticed, but that the stars in question must have really shifted their positions in relation to the rest; and he naturally inferred that it would be possible to detect similar proper motions (as they are now called) in other so-called “fixed” stars.
204. He also devoted a good deal of time to the standing astronomical problem of improving the tables of the moon and planets, particularly the former. He made observations of the moon as early as 1683, and by means of them effected some improvement in the tables. In 1676 he had already noted defects in the existing tables of Jupiter and Saturn, and ultimately satisfied himself of the existence of certain irregularities in the motion of these two planets, suspected long ago by Horrocks (chapter VIII., § 156); these irregularities he attributed correctly to the perturbations of the two planets by one another, though he was not mathematician enough to work out the theory; from observation, however, he was able to estimate the irregularities in question with fair accuracy and to improve the planetary tables by making allowance for them. But neither the lunar nor the planetary tables were ever completed in a form which Halley thought satisfactory. By 1719 they were printed, but kept back from publication, in hopes that subsequent improvements might be effected. After his appointment as Astronomer Royal in succession to Flamsteed (1720) he devoted special attention to getting fresh observations for this purpose, but he found the Observatory almost bare of instruments, those used by Flamsteed having been his private property, and having been removed as such by his heirs or creditors. Although Halley procured some instruments, and made with them a number of observations, chiefly of the moon, the age (63) at which he entered upon his office prevented him from initiating much, or from carrying out his duties with great energy, and the observations taken were in consequence only of secondary importance, while the tables for the improvement of which they were specially designed were only finally published in 1752, ten years after the death of their author. Although they thus appeared many years after the time at which they were virtually prepared and owed little to the progress of science during the interval, they at once became and for some time remained the standard tables for both the lunar and planetary motions (cf. § 226, and chapter XI., § 247).
205. Halley’s remarkable versatility in scientific work is further illustrated by the labour which he expended in editing the writings of the great Greek geometer Apollonius (chapter II., § 38) and the star catalogue of Ptolemy (chapter II., § 50). He was also one of the first of modern astronomers to pay careful attention to the effects to be observed during a total eclipse of the sun, and in the vivid description which he wrote of the eclipse of 1715, besides referring to the mysterious corona, which Kepler and others had noticed before (chapter VII., § 145), he called attention also to “a very narrow streak of a dusky but strong Red Light,” which was evidently a portion of that remarkable envelope of the sun which has been so extensively studied in modern times (chapter XIII., § 301) under the name of the chromosphere.
It is worth while to notice, as an illustration of Halley’s unselfish enthusiasm for science and of his power of looking to the future, that two of his most important pieces of work, by which certainly he is now best known, necessarily appeared during his lifetime as of little value, and only bore their fruit after his death (1742), for his comet only returned in 1759, when he had been dead 17 years, and the first of the pair of transits of Venus, from which he had shewn how to deduce the distance of the sun, took place two years later still (§ 227).
206. The third Astronomer Royal, James Bradley, is popularly known as the author of two memorable discoveries, viz. the aberration of light and the nutation of the earth’s axis. Remarkable as these are both in themselves and on account of the ingenious and subtle reasoning and minutely accurate observations by means of which they were made, they were in fact incidents in a long and active astronomical career, which resulted in the execution of a vast mass of work of great value.
The external events of Bradley’s life may be dealt with very briefly. Born in 1693, he proceeded in due course to Oxford (B.A. 1714, M.A. 1717), but acquired his first knowledge of astronomy and his marked taste for the subject from his uncle James Pound, for many years rector of Wansted in Essex, who was one of the best observers of the time. Bradley lived with his uncle for some years after leaving Oxford, and carried out a number of observations in concert with him. The first recorded observation of Bradley’s is dated 1715, and by 1718 he was sufficiently well thought of in the scientific world to receive the honour of election as a Fellow of the Royal Society. But, as his biographer115 remarks, “it could not be foreseen that his astronomical labours would lead to any establishment in life, and it became necessary for him to embrace a profession.” He accordingly took orders, and was fortunate enough to be presented almost at once to two livings, the duties attached to which do not seem to have interfered appreciably with the prosecution of his astronomical studies at Wansted.
In 1721 he was appointed Savilian Professor of Astronomy at Oxford, and resigned his livings. The work of the professorship appears to have been very light, and for more than ten years he continued to reside chiefly at Wansted, even after his uncle’s death in 1724. In 1732 he took a house in Oxford and set up there most of his instruments, leaving, however, at Wansted the most important of all, the “zenith-sector,” with which his two famous discoveries were made. Ten years afterwards Halley’s death rendered the post of Astronomer Royal vacant, and Bradley received the appointment.
The work of the Observatory had been a good deal neglected by Halley during the last few years of his life, and Bradley’s first care was to effect necessary repairs in the instruments. Although the equipment of the Observatory with instruments worthy of its position and of the state of science at the time was a work of years, Bradley had some of the most important instruments in good working order within a few months of his appointment, and observations were henceforward made systematically. Although the 20 remaining years of his life (1742-1762) were chiefly spent at Greenwich in the discharge of the duties of his office and in researches connected with them, he retained his professorship at Oxford, and continued to make observations at Wansted at least up till 1747.
207. The discovery of aberration resulted from an attempt to detect the parallactic displacement of stars which should result from the annual motion of the earth. Ever since the Coppernican controversy had called attention to the importance of the problem (cf. chapter IV., § 92 and chapter VI., § 129), it had naturally exerted a fascination on the minds of observing astronomers, many of whom had tried to detect the motion in question, and some of whom (including the “universal claimant” Hooke) professed to have succeeded. Actually, however, all previous attempts had been failures, and Bradley was no more successful than his predecessors in this particular undertaking, but was able to deduce from his observations two results of great interest and of an entirely unexpected character.
The problem which Bradley set himself was to examine whether any star could be seen to have in the course of the year a slight motion relative to others or relative to fixed points on the celestial sphere such as the pole. It was known that such a motion, if it existed, must be very small, and it was therefore evident that extreme delicacy in instrumental adjustments and the greatest care in observation would have to be employed. Bradley worked at first in conjunction with his friend Samuel Molyneux (1689-1728), who had erected a telescope at Kew. In accordance with the method adopted in a similar investigation by Hooke, whose results it was desired to test, the telescope was fixed in a nearly vertical position, so chosen that a particular star in the Dragon (γ Draconis) would be visible through it when it crossed the meridian, and the telescope was mounted with great care so as to maintain an invariable position throughout the year. If then the star in question were to undergo any motion which altered its distance from the pole, there would be a corresponding alteration in the position in which it would be seen in the field of view of the telescope. The first observations were taken on December 14th, 1725 (N.S.), and by December 28th Bradley believed that he had already noticed a slight displacement of the star towards the south. This motion was clearly verified on January 1st, and was then observed to continue; in the following March the star reached its extreme southern position, and then began to move northwards again. In September it once more altered its direction of motion, and by the end of the year had completed the cycle of its changes and returned to its original position, the greatest change in position amounting to nearly 40′.
The star was thus observed to go through some annual motion. It was, however, at once evident to Bradley that this motion was not the parallactic motion of which he was in search, for the position of the star was such that parallax would have made it appear farthest south in December and farthest north in June, or in each case three months earlier than was the case in the actual observations. Another explanation which suggested itself was that the earth’s axis might have a to-and-fro oscillatory motion or nutation which would alter the position of the celestial pole and hence produce a corresponding alteration in the position of the star. Such a motion of the celestial pole would evidently produce opposite effects on two stars situated on opposite sides of it, as any motion which brought the pole nearer to one star of such a pair would necessarily move it away from the other. Within a fortnight of the decisive observation made on January 1st a star116 had already been selected for the application of this test, with the result which can best be given in Bradley’s own words:—
“A nutation of the earth’s axis was one of the first things that offered itself upon this occasion, but it was soon found to be insufficient; for though it might have accounted for the change of declination in γ Draconis, yet it would not at the same time agree with the phaenomena in other stars; particularly in a small one almost opposite in right ascension to γ Draconis, at about the same distance from the north pole of the equator: for though this star seemed to move the same way as a nutation of the earth’s axis would have made it, yet, it changing its declination but about half as much as γ Draconis in the same time, (as appeared upon comparing the observations of both made upon the same days, at different seasons of the year,) this plainly proved that the apparent motion of the stars was not occasioned by a real nutation, since, if that had been the cause, the alteration in both stars would have been near equal.”
One or two other explanations were tested and found insufficient, and as the result of a series of observations extending over about two years, the phenomenon in question, although amply established, still remained quite unexplained.
By this time Bradley had mounted an instrument of his own at Wansted, so arranged that it was possible to observe through it the motions of stars other than γ Draconis.
Several stars were watched carefully throughout a year, and the observations thus obtained gave Bradley a fairly complete knowledge of the geometrical laws according to which the motions varied both from star to star and in the course of the year.
208. The true explanation of aberration, as the phenomenon in question was afterwards called, appears to have occurred to him about September, 1728, and was published to the Royal Society, after some further verification, early in the following year. According to a well-known story,117 he noticed, while sailing on the Thames, that a vane on the masthead appeared to change its direction every time that the boat altered its course, and was informed by the sailors that this change was not due to any alteration in the wind’s direction, but to that of the boat’s course. In fact the apparent direction of the wind, as shewn by the vane, was not the true direction of the wind, but resulted from a combination of the motions of the wind and of the boat, being more precisely that of the motion of the wind relative to the boat. Replacing in imagination the wind by light coming from a star, and the boat shifting its course by the earth moving round the sun and continually changing its direction of motion, Bradley arrived at an explanation which, when worked out in detail, was found to account most satisfactorily for the apparent changes in the direction of a star which he had been studying. His own account of the matter is as follows:—
“At last I conjectured that all the phaenomena hitherto mentioned proceeded from the progressive motion of light and the earth’s annual motion in its orbit. For I perceived that, if light was propagated in time, the apparent place of a fixed object would not be the same when the eye is at rest, as when it is moving in any other direction than that of the line passing through the eye and object; and that when the eye is moving
in different directions, the apparent place of the object would be different.
“I considered this matter in the following manner. I imagined C A to be a ray of light, falling perpendicularly upon the line B D; then if the eye is at rest at A, the object must appear in the direction A C, whether light be propagated in time or in an instant. But if the eye is moving from B towards A, and light is propagated in time, with a velocity that is to the velocity of the eye, as C A to B A; then light moving from C to A, whilst the eye moves from B to A, that particle of it by which the object will be discerned when the eye in its motion comes to A, is at C when the eye is at B. Joining the points B, C, I supposed the line C B to be a tube (inclined to the line B D in the angle D B C) of such a diameter as to admit of but one particle of light; then it was easy to conceive that the particle of light at C (by which the object must be seen when the eye, as it moves along, arrives at A) would pass through the tube B C, if it is inclined to B D in the angle D B C, and accompanies the eye in its motion from B to A; and that it could not come to the eye, placed behind such a tube, if it had any other inclination to the line B D....
“Although therefore the true or real place of an object is perpendicular to the line in which the eye is moving, yet the visible place will not be so, since that, no doubt, must be in the direction of the tube; but the difference between the true and apparent place will be (caeteris paribus) greater or less, according to the different proportion between the velocity of light and that of the eye. So that if we could suppose that light was propagated in an instant, then there would be no difference between the real and visible place of an object, although the eye were in motion; for in that case, A C being infinite with respect to A B, the angle A C B (the difference between the true and visible place) vanishes. But if light be propagated in time, (which I presume will readily be allowed by most of the philosophers of this age,) then it is evident from the foregoing considerations, that there will be always a difference between the real and visible place of an object, unless the eye is moving either directly towards or from the object.”
Bradley’s explanation shews that the apparent position of a star is determined by the motion of the star’s light relative to the earth, so that the star appears slightly nearer to the point on the celestial sphere towards which the earth is moving than would otherwise be the case. A familiar illustration of a precisely analogous effect may perhaps be of service. Any one walking on a rainy but windless day protects himself most effectually by holding his umbrella, not immediately over his head, but a little in front, exactly as he would do if he were at rest and there were a slight wind blowing in his face. In fact, if he were to ignore his own motion and pay attention only to the direction in which he found it advisable to point his umbrella, he would believe that there was a slight head-wind blowing the rain towards him.
209. The passage quoted from Bradley’s paper deals only with the simple case in which the star is at right angles to the direction of the earth’s motion. He shews elsewhere that if the star is in any other direction the effect is of the same kind but less in amount. In Bradley’s figure (fig. 74) the amount of the star’s displacement from its true position is represented by the angle B C A, which depends on the proportion between the lines A C and A B; but if (as in fig. 75) the earth is moving (without change of speed) in the direction A B′ instead of A B, so that the direction of the star is oblique to it, it is evident from the figure that the star’s displacement, represented by the angle A C B′, is less than before; and the amount varies according to a simple mathematical law118 with the angle between the two directions. It follows therefore that the displacement in question is different for different stars, as Bradley’s observations had already shewn, and is, moreover, different for the same star in the course of the year, so that a star appears to describe a curve which is very nearly an ellipse (fig. 76), the centre (S) corresponding to the position which the star would occupy if aberration did not exist. It is not difficult to see that, wherever a star is situated, the earth’s motion is twice a year, at intervals of six months, at right angles to the direction of the star, and that at these times the star receives the greatest possible displacement from its mean position, and is consequently at the ends of the greatest axis of the ellipse which it describes, as at A and A′, whereas at intermediate times it undergoes its least displacement, as at B and B′. The greatest displacement S A, or half of A A′, which is the same for all stars, is known as the constant of aberration, and was fixed by Bradley at between 20″ and 20-1∕2″, the value at present accepted being 20″·47. The least displacement, on the other hand, S B, or half of B B′, was shewn to depend in a simple way upon the star’s distance from the ecliptic, being greatest for stars farthest from the ecliptic.
210. The constant of aberration, which is represented by the angle A C B in fig. 74, depends only on the ratio between A C and A B, which are in turn proportional to the velocities of light and of the earth. Observations of aberration give then the ratio of these two velocities. From Bradley’s value of the constant of aberration it follows by an easy calculation that the velocity of light is about 10,000 times that of the earth; Bradley also put this result into the form that light travels from the sun to the earth in 8 minutes 13 seconds. From observations of the eclipses of Jupiter’s moons, Roemer and others had estimated the same interval at from 8 to 11 minutes (chapter VIII., § 162); and Bradley was thus able to get a satisfactory confirmation of the truth of his discovery. Aberration being once established, the same calculation could be used to give the most accurate measure of the velocity of light in terms of the dimensions of the earth’s orbit, the determination of aberration being susceptible of considerably greater accuracy than the corresponding measurements required for Roemer’s method.
211. One difficulty in the theory of aberration deserves mention. Bradley’s own explanation, quoted above, refers to light as a material substance shot out from the star or other luminous body. This was in accordance with the corpuscular theory of light, which was supported by the great weight of Newton’s authority and was commonly accepted in the 18th century. Modern physicists, however, have entirely abandoned the corpuscular theory, and regard light as a particular form of wave-motion transmitted through ether. From this point of view Bradley’s explanation and the physical illustrations given are far less convincing; the question becomes in fact one of considerable difficulty, and the most careful and elaborate of modern investigations cannot be said to be altogether satisfactory. The curious inference may be drawn that, if the more correct modern notions of the nature of light had prevailed in Bradley’s time, it must have been very much more difficult, if not impracticable, for him to have thought of his explanation of the stellar motions which he was studying; and thus an erroneous theory led to a most important discovery.
212. Bradley had of course not forgotten the original object of his investigation. He satisfied himself, however, that the agreement between the observed positions of γ Draconis and those which resulted from aberration was so close that any displacement of a star due to parallax which might exist must certainly be less than 2″, and probably not more than 1∕2″, so that the large parallax amounting to nearly 30″, which Hooke claimed to have detected, must certainly be rejected as erroneous.
From the point of view of the Coppernican controversy, however, Bradley’s discovery was almost as good as the discovery of a parallax; since if the earth were at rest no explanation of the least plausibility could be given of aberration.
213. The close agreement thus obtained between theory and observation would have satisfied an astronomer less accurate and careful than Bradley. But in his paper on aberration (1729) we find him writing:—
“I have likewise met with some small varieties in the declination of other stars in different years which do not seem to proceed from the same cause.... But whether these small alterations proceed from a regular cause, or are occasioned by any change in the materials, etc., of my instrument, I am not yet able fully to determine.”
The slender clue thus obtained was carefully followed up and led to a second striking discovery, which affords one of the most beautiful illustrations of the important results which can be deduced from the study of “residual phenomena.” Aberration causes a star to go through a cyclical series of changes in the course of a year; if therefore at the end of a year a star is found not to have returned to its original place, some other explanation of the motion has to be sought. Precession was one known cause of such an alteration; but Bradley found, at the end of his first year’s set of observations at Wansted, that the alterations in the positions of various stars differed by a minute amount (not exceeding 2″) from those which would have resulted from the usual estimate of precession; and that, although an alteration in the value of precession would account for the observed motions of some of these stars, it would have increased the discrepancy in the case of others. A nutation or nodding of the earth’s axis had, as we have seen (§ 207), already presented itself to him as a possibility; and although it had been shewn to be incapable of accounting for the main phenomenon—due to aberration—it might prove to be a satisfactory explanation of the much smaller residual motions. It soon occurred to Bradley that such a nutation might be due to the action of the moon, as both observation and the Newtonian explanation of precession indicated:—
“I suspected that the moon’s action upon the equatorial parts of the earth might produce these effects: for if the precession of the equinox be, according to Sir Isaac Newton’s principles, caused by the actions of the sun and moon upon those parts, the plane of the moon’s orbit being at one time above ten degrees more inclined to the plane of the equator than at another, it was reasonable to conclude, that the part of the whole annual precession, which arises from her action, would in different years be varied in its quantity; whereas the plane of the ecliptic, wherein the sun appears, keeping always nearly the same inclination to the equator, that part of the precession which is owing to the sun’s action may be the same every year; and from hence it would follow, that although the mean annual precession, proceeding from the joint actions of the sun and moon, were 50″, yet the apparent annual precession might sometimes exceed and sometimes fall short of that mean quantity, according to the various situations of the nodes of the moon’s orbit.”
Newton in his discussion of precession (chapter IX., § 188; Principia, Book III., proposition 21) had pointed out the existence of a small irregularity with a period of six months. But it is evident, on looking at this discussion of the effect of the solar and lunar attractions on the protuberant parts of the earth, that the various alterations in the positions of the sun and moon relative to the earth might be expected to produce irregularities, and that the uniform precessional motion known from observation and deduced from gravitation by Newton was, as it were, only a smoothing out of a motion of a much more complicated character. Except for the allusion referred to, Newton made no attempt to discuss these irregularities, and none of them had as yet been detected by observation.
Of the numerous irregularities of this class which are now known, and which may be referred to generally as nutation, that indicated by Bradley in the passage just quoted is by far the most important. As soon as the idea of an irregularity depending on the position of the moon’s nodes occurred to him, he saw that it would be desirable to watch the motions of several stars during the whole period (about 19 years) occupied by the moon’s nodes in performing the circuit of the ecliptic and returning to the same position. This inquiry was successfully carried out between 1727 and 1747 with the telescope mounted at Wansted. When the moon’s nodes had performed half their revolution, i.e. after about nine years, the correspondence between the displacements of the stars and the changes in the moon’s orbit was so close that Bradley was satisfied with the general correctness of his theory, and in 1737 he communicated the result privately to Maupertuis (§ 221), with whom he had had some scientific correspondence. Maupertuis appears to have told others, but Bradley himself waited patiently for the completion of the period which he regarded as necessary for the satisfactory verification of his theory, and only published his results definitely at the beginning of 1748.