CHAPTER I.

FROM HIPPARCHUS TO LAPLACE.

In the year 134 B.C., a temporary star blazed out in the constellation Scorpio. It was observed by a man of extraordinary genius, and furnished the incentive to one of his most memorable works. This was the construction, on essentially modern principles, of a catalogue of 1,080 stars. Hipparchus thus, with deliberation and singular prescience, furnished a standard by which future changes in the heavens might be detected. He was a native of Rhodes, but belonged to the school of Alexandria; and at Alexandria, after three centuries, he found an able and ambitious successor.

Claudius Ptolemæus was one of the many “inheritors of unfulfilled renown.” He combined, completed, and preserved what his predecessors, eminent or obscure, had done. Gathering materials from all quarters, and adding much of his own, he reared an astronomical edifice so imposing, coherent, and substantial, that the lapse of fourteen centuries left it virtually unassailed, and, to a superficial judgment, unassailable. Fitly, then, this monument of industry and ingenuity kept the title bestowed upon it by the Arabs of “Almagest,” signifying “the Greatest.” It bears, nevertheless, perennial witness to the possibility of satisfying the human mind with the truth of appearances, apart from the truth of things. For although the Almagest embodies a large amount of real knowledge, that knowledge is throughout falsely interpreted. The Ptolemaic system was constructed on the principle of “saving the phenomena”—that is, of providing expedients geometrically valid, even if physically inadmissible, by which to represent the apparent movements of the heavenly bodies. That they might, to a great extent, be apparent only, was obvious to the cultivated Greek mind. The rotation of the earth on an axis was a familiar Pythagorean doctrine; it was adopted by Plato, and Aristarchus of Samos went to the length of ranking our green world as a planet revolving yearly round the sun. The idea, however, was too recondite for vulgar apprehension; it was tainted with a suspicion of impiety, and its development would, besides, have proved extremely embarrassing to the nascent science of that age. So Hipparchus chose the prudent alternative of treating astronomy from the purely mathematical standpoint; he submitted to the restrictions imposed by the hypothesis of equable circular motion; and, with wonderful skill, fitted the Apollonian eccentrics and epicycles to expound celestial wanderings. Ptolemy inevitably followed suit. He set some five dozen spheres in motion, while leaving the earth at rest; and at rest it remained until, in long meditations by the foggy shores of the Baltic, a grave-browed ecclesiastic elaborated certain cogent arguments in favour of its motion.

During the interval between Ptolemy and Copernicus, astronomy kept in the Alexandrian groove. Early in the eighth century, the seat of learning having been transferred to Baghdad, the charge of its crystalline machinery devolved upon Arabs and Jews, men of fine technical acquirements, but small originative power, men of the kind described in the “Vicar of Wakefield,” who, “had they been bred cobblers, would all their lives have only mended shoes, but never made them.” Not but that they executed the necessary repairs with uncommon ingenuity, modifying the cumbrous structure given into their keeping to suit the fresh inequalities brought to light by their patient watchfulness. But their improvements consisted in adding to already intolerable complications—in piling orb on orb, in devising “trepidations” and oscillations, of which nature took small heed; so that the better they observed, the worse their system became.

The science was diligently cultivated. Al-Mamûm, son and successor of “good Harûn-al-Raschid,” founded at Baghdad a school of astronomy, of which Albategnius, called “the Ptolemy of the Arabs,” was the brightest ornament. He discovered, early in the tenth century, the movement of the “sun’s apogee”—that slow revolution of the longer axis of the earth’s orbit, regarded by astronomical glacialists as a factor in the production of recurring Ice Ages. The Persian grandee, Al-Sûfi (903–986) belonged to the same group. His “Description of the Stars” was a revised edition, not a simple reprint, of the Alexandrian list, and has the value derived from personal consultation with the skies. Thus, Algol, now purely white, is recorded in it as a decidedly red star. About a century later, Aboul Wefa detected the moon’s “variation,” independently noted, after five centuries, by Tycho Brahé. Then the Tartars had their turn. Nasir Eddin (1201–1274) was a native of Khorassan; but his love of learning drew him to the city of the Khalifs, where he assembled a band of experts for the construction of new planetary tables, the old ones having lapsed into hopeless disaccord with the heavens. Last came Ulugh Beigh, grandson of the furious Tamerlane. He founded at Samarcand a kind of astronomical Solomon’s House, built a grand observatory, and worked in it assiduously. His vigorous and ennobling reign of forty years was terminated by one of those domestic catastrophes which ordinarily fix the chronology of Eastern dynasties. He was murdered by his son in 1447, and the sands of the desert thereupon closed, so to speak, over his civilising efforts. His star catalogue, edited by Francis Baily in 1843, is the outcome of fresh observations made in the old way. A Tartar prince, he ranks as an Arab astronomer.

Mohammedan science had already fulfilled its appointed task. A torch, still alight, had been handed on from East to West. Its extinction would have been a calamity. A total break in the cultivation of astronomy, for instance, would have cost ages to repair. The Ptolemaic system, it is true, disguised rather than revealed nature; yet it constituted a regulated body of knowledge, only looked at from a wrong point of view. An unbiassed spectator had merely to shift his position and open his eyes, in order to perceive the simplicity of the real celestial mechanism. No better illustration could be adduced of Bacon’s aphorism that “truth emerges more easily from error than from confusion.”

It was from the Moors in Spain that Christian Europe took its first lessons in antique science. The Alphonsine Tables were due to Oriental industry. They were compiled at Toledo about 1270 by an assemblage of Arab experts directed by Hassan, the Jew delegate of Alfonso X. of Castile. But they caught Western attention, and drew Western intelligence towards the abstruse art they exemplified. Thus a little treatise on the Sphere composed about 1230, by John Holywood, a Yorkshireman, known to cosmopolitan fame as Johannes de Sacrobosco, obtained astonishing popularity; at least sixty-five Latin editions of it appearing between 1472 and 1647, besides French, Italian, German, and Spanish versions, and endless commentaries. With the revival of classical learning, the Almagest, previously known in blundering Latin translations from the Arabic, came to be read in the original Greek, and thus re-emergent, roused fresh enthusiasm. Inspired by the afflatus, George Purbach (1423–1461) and his brilliant pupil, Johannes Müller of Königsberg in Franconia (Regiomontanus), successively professors of mathematics at Vienna, applied themselves to burnishing up the ancient epicyclical apparatus; while in Italy, the seductive opinions of the Pythagorean school gained ground, as evidence came to light, that there had been astronomers before Ptolemy no less than kings before Agamemnon. The orthodox doctrine naturally continued to be taught at the universities; but some of the professors held esoteric opinions of a different cast, which they freely imparted to privileged disciples. The earth’s rotation was spoken of as a matter of common knowledge by Lionardo da Vinci; it was inculcated in rhyme, before the close of the fifteenth century, by Girolamo Tagliavia, a Calabrese poet; it was debated by scholars and pedants; on all sides influences wrought to shatter the integrity of Ptolemaic convictions.

True progress, however, consists less in destruction than in re-organisation. And this demands powers of a high order. They were brought into play just at the right moment. Nicholas Copernicus was born at Thorn on the Vistula, February 19, 1473. At the age of twenty-three, having exhausted the teaching resources of the university of Cracow, he crossed the Alps in quest of instruction in Greek and mathematics. Towards the close of 1496, then, he was enrolled as a student at Bologna, and shortly afterwards became the pupil, assistant, and friend of the Ferrarese astronomer, Domenico Maria Novara. Here, beyond reasonable doubt, Copernicus adopted Copernican opinions. The question, _An terra moveatur?_ was incessantly mooted at Bologna; advanced thinkers replied in the affirmative; Novara himself most likely took his intellectual beliefs from Plato and Aristarchus, while looking to Ptolemy for his daily bread. The transalpine scholar, at any rate, brought back with him to Poland in 1505, an unalterable persuasion that the heliocentric system belonged to the reality of things. He devoted eighteen years of his abode within the cathedral precincts of Frauenburg—from 1512 to 1530—to demonstrating its detailed conformity with the phenomena of the heavens; but allowed only a sketch of his results to be published. It was only at the earnest request of the Bishop of Culm that he finally delivered up to him the manuscript of “De Revolutionibus Orbium Coelestium,” the first printed copy of which was laid on his deathbed, May 24, 1543.

The immediate effect was small. The new system of astronomy was admired, but not adopted. It indeed contradicted the evidence of the senses, and failed to compel assent from the understanding. For its author had not completely broken with tradition. He unfortunately retained the false supposition of equable circular motion, and thus greatly marred the simplicity of his scheme of the heavens. Orbs still kept rolling upon orbs, Mercury alone demanding a combination of seven to bear him over his course. But if seven, it might have been asked, why not seven times seven? The principle of representing appearances by transcendental means remained the same as before. Ignorance of the laws of motion raised other formidable objections. A whirling earth, it was thought, should leave behind all detached objects; absolute repose was taken to be the condition _sine quâ non_ of stability. Then the seeming immobility of the stars implied for them a remoteness so extravagant, according to prevalent ideas, that even Kepler admitted it to be “a big pill to swallow.” Copernicus was fully aware that the earth’s orbital revolution must occasion stellar perspective displacements; indeed, he staked the truth of his theory upon future measurements of annual parallax. Nevertheless, four centuries passed before they were successfully executed.

Tycho Brahé was the last great mediæval observer. Like Hipparchus, he was summoned by a star—the marvellous “new star” of 1572; and, having obtained from Frederick II. of Denmark the grant of an islet in the Sound, he built upon it a mansion “royal, rich and wide,” erected magnificent instruments, and used them, not only with consummate skill, but also with a certain princely pomp, donning robes of state before admitting the bright “populace of heaven” to audience. His stormy temper, however, led to disputes with the young King Christian IV.; he forsook Uraniborg, and died at Prague in 1601. Curiously enough, the very accuracy of his observations led him astray from speculative truth. For it enabled him to perceive the incompatibility of many facts with Copernican expedients for harmonising them, and intensified the difficulty raised to Copernican views by the absence of stellar parallax. So he devised a system of his own, in which the planets revolved round the sun, but the sun round the earth. It scarcely survived its contriver.

The invention of the telescope created descriptive astronomy. Without it, the mechanism of the solar system could have been laid bare, and the law of force regulating its action discovered; and in point of fact, Kepler’s achievements owed nothing, and Newton’s very little, to the optician’s art. Inquiries, on the other hand, into the nature of the heavenly bodies were wholly inspired by it; it disclosed the amazing multitude of the stars, and opened endless vistas of research. No one could at first have divined the momentous character of the accident by which Hans Lippershey, a spectacle-maker at Middleburg in Holland, hit upon an arrangement of lenses serving virtually to abridge distance. It happened in 1608; and Galileo Galilei (1564–1642), hearing of it shortly afterwards at Venice, prepared on the hint a “glazed optic tube,” and viewed with it, early in 1610, the satellites of Jupiter, the mountains of the moon, the star streams of the Milky Way, and in 1611, the phases of Venus, the spots on the sun, and the strange appendages of Saturn. Thus, amid a tumult of applause, the telescopic revelation of the heavens began. It was brilliantly illustrative, although not demonstrative, of Copernican theory; and Galileo drove his own vivid conviction on the subject home to general apprehension by the literary skill with which he treated it in his famous “Dialogues” (1632). He most substantially promoted the new views, however, by his recognition of the laws of motion, and of force as the cause of motion. The problem of the heavens, stript thereby of metaphysical obscurities, was laid bare to the reason as one of pure mechanics; the planets came to be treated as ordinary projectiles, and distinct reasoning about the nature of their paths was rendered possible. Newton’s great task was thus prepared and defined by Galileo.

Kepler’s (1573–1630) three generalisations formed a still more indispensable prelude to its accomplishment. Their immediate effect was to sweep away the Copernican remnants of Ptolemaic lumber, and to disclose the harmonious plan upon which our system is ordered. But it was a geometrical plan only. Kepler indeed divined the influence of a central power, which he surmised to be of a magnetic nature; and he aspired towards the establishment of a truly physical astronomy. Yet he was far from perceiving the full implications of the laws he had himself, after half a lifetime of trial and failure, at last triumphantly discovered. These laws are:

(I.) The planets travel in ellipses of which the sun occupies one focus.

(II.) They travel at rates varying in such a manner that the “radius vector”—or imaginary line joining each to the sun—describes equal areas in equal times.

(III.) The cubes of their mean distances from the sun are proportional to the squares of their periods of revolution.

Now these are precisely the conditions under which planetary circulation should proceed if governed by a force emanating from the sun, and decreasing as the square of the distance from him increased. Moreover, Hooke, Halley, and Wren separately got so far as to perceive that it could be explained on this principle. But Isaac Newton alone could demonstrate what they divined, and even his supreme faculties were dangerously strained by the laborious process. This was not all. He showed that the earth exerts on the moon just the same kind of pull that the sun exerts on the planets; a pull identical with the familiar “attraction of gravitation,” by which the globe we inhabit holds integrally together, retains its oceans in their beds, and bears with it through space its “cloud of all-sustaining air.” Its domestic affairs are thus guided by the same unchanging rule that dominates its foreign relations.

The publication in 1687 of Newton’s “Principia” marked an unprecedented advance in knowledge. The advance consisted in unification. A science of celestial physics, capable of indefinite future expansion, was founded on the sure basis of terrestrial experience. Canons of interpretation, derived from immediate perception, were proved applicable to the phenomena of the heavens. The line drawn in antique philosophy between the “corruptible” things under our feet and the “incorruptible” over our heads was forever rubbed out. Sublunary and empyreal regions were thrown together into one vast domain.

Although Newton’s law is, in itself, of extreme simplicity, its actual workings are highly intricate. Because dependent upon a universal and unintermittent influence, they are self-modifying, so that each consequence becomes a cause, and to each cause is attached an endless train of effects. They can be dealt with only with the aid of the infinitesimal calculus, and then, not directly, but by successive and tedious approximations, or by arts and devices of almost superhuman ingenuity. Hence Newton’s laurels would have remained comparatively barren had he not found successors in a group of men of extraordinary ability. What he had begun, Clairaut, D’Alembert, Euler, Lagrange, and Laplace carried on by showing the adequacy of a single law to account for every traceable deviation from undisturbed elliptical motion. In the course of a long and arduous campaign, they carried every position that they attacked. Over and over again, the principle of gravitation seemed to be compromised; over and over again, it was vindicated by these intrepid champions.

This process of gradual verification began in 1747, when Clairaut and D’Alembert sent to the Paris Academy of Sciences, on the same day, the first satisfactory solutions of the “Problem of three Bodies.” The motions of the moon, nevertheless, did not at once fall in with the general theory; they were rendered amenable only after years of anxious toil. Barely the initial difficulties had been overcome when Euler, in 1753, published his “Theory of the Moon,” from which Tobias Mayer of Göttingen constructed lunar tables. Now tables are the test of theories. Every row of figures they contain is a prediction, by the fulfilment, or non-fulfilment of which the underlying scheme must stand or fall. Through such comparisons, mathematical astronomers find out the shortcomings of their methods, or the insufficiency of their hypotheses, and are incited to refine the first, and correct the second. Demands for the application of the nicer criteria thus afforded suggest observational improvements, which seldom fail to bring to light minor discrepancies with theory, impelling to fresh efforts for their abolition. Such alternations of advance along the abstract and the practical lines result in a continual diminution in the _scale_ of error, although not in its annihilation; absolute exactitude being, as it were, an asymptote, continually approached, but touched only at infinity—that is, never, under subsisting conditions. Even now the length of the moons tether is four or five miles. To that extent, she may go astray from her computed path, not without occasioning disquietude to the responsible authorities.

So far as could be ascertained in the eighteenth century, her subjection to known law was completed by the dispersal of the mystery surrounding a slight, continuous acceleration of her orbital velocity detected by Halley in 1693. It had been in progress since the earliest recorded eclipse in 721 B.C., if not longer; there was no sign of its cessation or reversal, and the grave question arose, Was the principle of universal attraction, elsewhere unreservedly obeyed, here fatally complicated by the action of a resisting medium involving the eventual collapse of the earth-moon system? Laplace gave the answer, November 19, 1787, by proving the observed quickening of pace to be a necessary and simple consequence of a secular diminution in the ellipticity of the earths orbit. This, however, will not go on for ever in the same direction; after many ages the tide of change will turn, and a complete restoration to the _status quo ante_ will ensue.

Another master-stroke of Laplace’s genius was his explanation, also in 1787, of the “long inequality” of Jupiter and Saturn. He demonstrated its strictly gravitational origin in the mutual disturbance of the two giant planets, rendered up to a certain point cumulative by the approximate commensurability of their periods. While Jupiter performs five circuits Saturn accomplishes nearly two, and the perturbation set up at their conjunction is hence both intensified and balked of compensation for 918 years.

The epoch of trial and confirmation immediately following the publication of the “Principia” lasted then a full century. During its course, difficulties had arisen only to be overcome; suggested qualifications of the single and simple law of gravity had proved unnecessary; at its close, recalcitrance had everywhere been overcome, and there was victory all along the line. And not only were the workings of the planetary system exhibited as depending upon an elementary principle, but they were further shown to be perfectly equilibrated. It contained within itself, so far as could be ascertained, no seeds of decay; its destruction could only come from without. This remarkable conclusion was established in a series of splendid treatises by Lagrange and Laplace. The special adaptation to permanence of the solar mechanism was demonstrated in them. Ruinous disturbances were shown to be excluded by the overwhelming disparity of mass between the central body and its attendants, no less than by the regularity and harmony of their movements and distribution. Thus only slight oscillatory changes can occur. Millions of years will elapse without producing any fundamental alteration. The machine is so beautifully adjusted as to right itself automatically through the mutual action of its various parts. And it is the force which perturbs that eventually restores.

The astronomical acquisitions of the century were embodied in Laplace’s “Mécanique Céleste,” published 1799–1805. This “Almagest of the eighteenth century,” as it has been termed, is in a rare degree comprehensive and complete. It leaves nothing enigmatical. Every question propounded in it receives an answer, if not definitive, at least highly authoritative; and the range of these questions is very wide. All the phenomena which the Greeks and Arabs had rightly observed, but wrongly interpreted, are not merely “saved” by geometrical artifices, but derived as a connected whole from one physical cause, absolutely prescribing that they should be thus, and no otherwise. The work is a record of unmixed triumphs. It seems as if the author, for want of more worlds to conquer, had laid down the sword of the calculus to take up the pen of the chronicler. With grave exultation, he proceeds from point to point, recounting the events of the campaign, commemorating the battles won by the brilliant staff of mathematical heroes to which he himself belonged, and expatiating in the broad subjugated plain. He scarcely looked beyond. There was indeed at that time no “beyond” where his methods of investigation were applicable. The “Mécanique Céleste” hints at no unsatisfied ambitions; it is a book of the _teres atque rotundus_ sort—a world in itself well arranged and compact, to which outlying perplexities are allowed no access. Nor should this be counted a defect. As a monument to one of the greatest periods in the history of science, its fitting character was that of an ordered collection of acquired certainties.

The countrymen of Newton took no part in the striking series of operations by which the intricate consequences of the law of gravity were deduced and shown to correspond with reality. During the whole of the eighteenth century, they stood aside from the race towards verification. Their effacement was due to no lack of ability, but to a mistaken choice of means. Newton’s synthetic method was a veritable Bow of Ulysses. It was too tough to be bent by other hands than his own. Thus, no sequel could be given to the “Principia.” There was no possibility of following up the line of demonstration pursued in it. Newton himself would have vainly attempted to carry it much further. In order to advance, it was necessary, as Dr. Whewell remarked, to begin afresh. This, British mathematicians were unwilling to do. The easy and flexible analytical method brought to perfection on the continent remained strange to them. With inadequate strength, they persisted in wielding the cumbrous weapon of a giant—in using main force, so to speak, where skill and agility were required. Our insularity in this respect lasted until about 1816, when, by the joint efforts of the younger Herschel, Charles Babbage, and George Peacock (afterwards Dean of Ely), mathematical studies were revolutionised at the University of Cambridge.

The neglect in England of theoretical research was, however, partly compensated by the steady progress of practical astronomy. For a century and a half after its foundation in 1675, the Royal Observatory at Greenwich continued to be the main—almost the only source of information regarding the places of the heavenly bodies. Thence were obtained the data necessary for the correction of theory, since there alone the visible positions of the sun, moon, and planets were systematically determined. _Actual_, compared with _predicted_, movements gave so-called “tabular errors”; and tabular errors indicated theoretical shortcomings, the rectification of which led gradually, but surely, towards a higher plane of knowledge.

John Flamsteed (1646–1719), the first astronomer-royal, was, in Professor De Morgan’s phrase, “Tycho Brahé with a telescope.” By his diligence and insight he set on foot modern astronomy of precision. The “British Catalogue” of nearly 3,000 stars, was, in its day, an unique and most valuable work. His lunar observations were indispensable to Newton’s calculations, which, indeed, through the insufficient supply of them, now and again came to a halt; he constructed new solar tables, and kept watch over the careers of planets and comets. His completion, in 1689, of a seven-foot mural quadrant, constituted a marked advance in the art of instrument-making. It was firmly fixed in the meridian, so that the distances from the zenith of the heavenly bodies at the moment of culmination could be read off on the limb, the time being simultaneously noted by a clock. Their positions in the sky relative to a set of forty otherwise known stars were thus completely determined, and they were determined essentially after the manner still in use.

On Flamsteed’s death in 1719, Edmund Halley (1656–1742) succeeded to his place. An expedition to St. Helena in 1677, for the purpose of observing stars invisible in these latitudes, got him the name of the “southern Tycho.” They were the very first so situated to be located on the sphere (except those few that came within Ptolemy’s range), and a list of them, to the number of 341, was appended to the “British Catalogue.” The purpose to which Halley devoted most sustained attention was, unluckily, that in which he was least successful. Early in life he formed the design of observing the moon through an entire revolution of its nodes, so as to bring lunar tables to the perfection required for solving the prize-problem of longitudes. But the _contumax sidus_—his opprobrious term for our satellite—proved more than a match for him. The eighteen years’ watch was kept, notwithstanding that the watcher had reached the age of sixty-five before he was able to set about it; but in vain; nothing came of it. Halley’s varied performances were, nevertheless, so considerable as to warrant Lalande in describing him as “the greatest of English astronomers”; and he ranked next to Newton among contemporary English men of science.

His cometary labours alone sufficed to perpetuate his name. He initiated the computation, on Newtonian principles, of the orbits traversed by such bodies—then a most toilsome process; and, among twenty-four, found three so much alike as to suggest the identity of the great comets of 1531, 1607, and 1682. A renewed apparition might then be expected in 1758, and he appealed to “candid posterity to acknowledge that this was first discovered by an Englishman.” The prediction roused widespread interest, and as the epoch for its fulfilment drew near, Clairaut undertook the formidable task of determining to what extent it might be postponed by the retarding influence of Jupiter and Saturn. Many times he despaired of its execution, even with the efficient aid of Lalande and Madame Lepaute, the wife of a Paris clock-maker; and at last, after months of wearisome calculation, having succeeded in forming the differential equations representing the comet’s disturbed motion, he threw down the paper on which they were written, with the exclamation, “Now, integrate them who can!” Eventually this, too, was done; and the comet, caught sight of on Christmas Day, 1758, by Palitzsch, a rustic star-gazer in Saxony, passed the sun within the month’s “law” permitted to it by the French geometer. This signal triumph laid the sure foundation of cometary astronomy.

In 1679, Halley drew attention to the importance of transits of Venus for measuring the sun’s distance; and developed later a method extensively used in observing the eighteenth century pair of transits in 1761 and 1769. But the accuracy actually attained in determining the instants of contact between the limbs of the sun and planet fell far short of what he had anticipated as attainable. The “black drop” interposed its pernicious effects, and occasioned wide discrepancies. The margin of uncertainty regarding the value of the great unit was, none the less, diminished, although it still remained uncomfortably wide; while the public interest excited by such rare events, the adventurous character of the expeditions sent to the uttermost parts of the earth for their utilisation, and the combined efforts of various nations towards the same end, served to popularise astronomy, and to give it something of that cosmopolitan stamp now borne by it.

Besides the discovery of the secular acceleration of the moon’s motion, that of the long inequality of Jupiter and Saturn was due to Halley; he ascertained, in 1718, the proper movements of Sirius, Aldebaran, and Arcturus, thereby virtually demonstrating the non-existence of “fixed” stars; he associated auroræ with terrestrial magnetism; noted the globular star clusters in Hercules and Centaur; and divined nebulæ to be composed of “a lucid medium shining with its own proper lustre,” and filling “spaces immensely great.” Yet, in spite of the comprehensiveness of his genius, his administration at Greenwich was a failure. He was a better astronomer than astronomer-royal.

James Bradley (1693–1762), who came after him, gave a narrower scope to his abilities, yet was of unsurpassed sagacity in connecting effects with their causes. Robert Hooke (1635–1703) had observed, in 1669, annual displacements of γ Draconis, a star nearly crossing the zenith of London, which he took for results of parallax; and Flamsteed, in 1694, had similarly interpreted a similar affection of the pole-star. They had both been misled by an “aberration,” due to the progressive transmission of light combined with the advance of the earth in its orbit. Bradley determined to sift the matter thoroughly, and observed Hooke’s star continuously from 1725 until 1728, first at Kew with Molyneux, then at Wanstead in Essex. It evidently described a small ellipse in the sky with a period of one year; yet its place in the ellipse was not what it should have been on the parallactic hypothesis; so he remained for some time in the dark about it. During a water-party on the Thames, however, in September 1728, he noticed that the slant of the pennant varied with changes in the boat’s course, the wind remaining steady throughout. This gave him the clue he wanted; and his discovery of the “aberration of light” was communicated to the Royal Society in the month of January following. That of the nutation of the earth’s axis followed in 1748. Both, setting aside their importance in themselves, were indispensable as preliminaries to accuracy in fixing the places of the heavenly bodies. For they are vital elements in the process of “reduction,” by which the ore of truth contained in observations is extricated from the dross of casual circumstances. The raw material, collected by timing transits and reading circles, must be so refined and purified that the facts contained in it become mutually comparable. Before Bradley’s time allowance was indeed roughly made for refraction in our atmosphere, and for the precession of the equinoxes; and, in the case of the moon, for parallax; but the effects of aberration and nutation had remained mixed up with a mass of disguising errors. Their elimination constituted an inestimable improvement.

In the immediate art of observation Bradley was a master. He did not live to possess an achromatic telescope; neither astronomical circles nor equatorial mountings were at his disposal. His leading instrument was an eight-foot quadrant, by John Bird, certainly of admirable workmanship; although of a type long since, and for good reasons, superseded. He amassed with it, nevertheless, a treasure of high-class observations. The bulk of them remained in manuscript until 1798, so that it was reserved for this century to turn them to account; but their value has only developed with the efflux of years. Those relating to the moon and planets, reduced by Sir George Airy, lent efficient aid towards perfecting the theories of those bodies. Those of 3,222 stars formed into a catalogue by Bessel were published in 1818 with the proud, but not unmerited title of “Fundamenta Astronomiæ.” The same original data, again in 1886 reduced with the utmost nicety of care by Dr. Auwers of Berlin, afforded a splendid accession to knowledge of stellar proper motions. Acquaintance with Bradley’s stars now extends over 144 years; and the amount and direction of their progress across the sphere during that long interval have, for the most part, become defined with tolerable certainty.

Nathaniel Bliss (1700–1764), the fourth astronomer-royal, filled the post only two years. Yet the observations made under his care form a sequel to Bradley’s well worth having. The reign of his successor, Nevil Maskelyne (1732–1811), extended over forty-six years. His determinations of the sun, moon, and planets, were in great demand abroad for the correction of tables, and as criteria of theories; while, of the stars, he paid attention only to thirty-six, catalogued as reference-points in 1790. Their proper motions served Herschel for his second investigation, in 1805, of the sun’s translation through space. By the close of the century, Maskelyne’s instruments had lapsed into decrepitude; and only the stimulus supplied by Pond’s strictures roused him to order one of Troughton’s improved circles. But he died before it was mounted, and its employment fell to the share of his critic, John Pond (1767–1836), the sixth astronomer-royal. Maskelyne’s most enduring title to fame is his foundation, in 1767, of the “Nautical Almanac.”

English observers were ably seconded by English artists. Graham, Sisson, Cary, Bird, Ramsden, had, from the beginning to the end of the eighteenth century, no foreign competitors of note. Their quadrants and sectors were distinguished both for stability and for refinement of execution. The mechanical skill displayed in their construction was no less necessary for the promotion of practical astronomy than the subtlety of eye and hand needed to employ them to the best advantage. Bradley’s work was conditioned by the performances of Graham and Bird. Without Graham’s sector he could not have discovered the aberration of light; without Bird’s quadrant the perennial worth of his Greenwich observations would have been impaired, if not destroyed. Observatories all over the continent were furnished in the latter half of the eighteenth century with instruments of English make; the art of accurately dividing circular limbs was invented in England, and nowhere else successfully practised. The innovation of substituting entire circles for quadrants was effectively introduced by Ramsden; and Piazzi came from Palermo in 1788 for the purpose of securing from him a five-foot altazimuth, at that date the finest sky-measuring machine in the world. Edward Troughton (1753–1835) ably carried on the tradition of his predecessors, and brought the altazimuth, transit circle, and equatorial up to the modern standard of efficiency. But they were no longer in exclusive demand. The foundation, in 1804, of Reichenbach’s Institute at Munich finally abolished the British monopoly in supplying astronomers with their exquisite and ingenious tools.

The improvement of refracting telescopes ran a somewhat similar course. The essential step of combining flint and crown glass, so as to bring differently-coloured rays to one focus, was taken in 1733 by Chester More Hall, a gentleman of fortune in Essex; but he published nothing, and the re-invention of the “achromatic” lens was left to John Dollond (1706–1761) a Spitalfields weaver. “I obtained,” he wrote in 1758, “a perfect theory for making object-glasses, to the apertures of which I could scarcely conceive any limits.” The excise duty on glass, however, which was repealed only in 1845, drew these limits very narrowly in this country; and it was through the extraordinary perseverance of a Swiss artisan named Guinand, in overcoming the difficulties connected with glass-making, and the genius of Joseph Fraunhofer (1787–1826) in moulding the material thus placed at his disposal, that refractors began at Munich to rise towards their present power and perfection.

The history of the reflecting telescope is British throughout. It was invented by Newton, made practically effective by John Hadley (1682–1744), and brought very near to theoretical perfection by James Short of Edinburgh (1710–1768); yet it is remarkable that not a single observation of lasting interest was made with any of his instruments, a few of which have survived, and are regarded with admiration to this day. The career of reflectors as engines of discovery began, but did not end, with William Herschel.