ASTRONOMY OF THE MIDDLE AGES Arab astronomy, transported by the Moors to Spain, flourished temporarily at Cordova and Toledo. From the latter city the Toletan Tables, drawn up by Arzachel in 1080, took their name; and there also the Alfonsine Tables, published in 1252, were pre pared under the authority of Alphonso X. of Castile. Their ap pearance signalized the dawn of European science, and was nearly coincident with that of the Sphaera Mundi, a text-book of spheri cal astronomy, written by a Yorkshireman, John Holywood, known as Sacro Bosco (d. 1256). It had an immense vogue, perpetuated by the printing-press in fifty-nine editions. In Ger many, during the 15th century, a brilliant attempt was made to patch up the flaws in Ptolemaic doctrine. George Purbach (1423 1461) introduced into Europe the method of determining time by altitudes employed by Ibn Junis. He lectured with applause at Vienna from 145o; was joined there in 1452 by Regiomontanus (q.v.); and was on the point of starting for Rome to inspect a manuscript of the Almagest when he died suddenly at the age of thirty-eight. His teachings bore fruit in the work of Regiomon tanus, and of Bernhard Walther of Nuremberg (1430-1504), who fitted up an observatory with clocks driven by weights, and de veloped many improvements in practical astronomy.
The Tabulae Prutenicae, calculated on Copernican principles by Erasmus Reinhold (1511-1553), appeared in 1551. Although they represented celestial movements far better than the Alf on sine Tables, large discrepancies were still apparent, and the de sirability of testing the novel hypothesis upon which they were based by more refined observations prompted a reform of meth, ods, undertaken almost simultaneously by the landgrave William IV. of Hesse-Cassel (1532-1592), and by Tycho Brahe The landgrave built at Cassel in 1561 the first observatory with a revolving dome, and worked for some years at a star-catalogue finally left incomplete. Christoph Rothmann and Joost Biirgi (1552-1632) became his assistants in 1577 and 1579 respectively; and through the skill of Burgi, time-determinations were made available for measuring right ascensions. At Cassel, too, the alti tude and azimuth instrument is believed to have made its first appearance in Europe.
No more congruous arrangement could have been devised than the inheritance by Johann Kepler of the wealth of materials amassed by Tycho Brahe. The younger man's genius supplied what was wanting to his predecessor. Tycho's endowments were of the practical order ; yet he had never designed his observations to be an end in themselves. He thought of them as means towards the end of ascertaining the true form of the universe. His range of ideas was, however, restricted; and the attempt embodied in his ground-plan of the solar system to revive the ephemeral theory of Heraclides failed to influence the development of thought. Kepler, on the contrary, was endowed with unlimited powers of speculation, but had no mechanical faculty. He found in Tycho's ample legacy of first-class data precisely what enabled him to try, by the touchstone of fact, the successive hypotheses that he imagined; and his untiring patience in comparing and calcu lating the observations at his disposal was rewarded by a series of unique discoveries. He long adhered to the traditional belief that all celestial revolutions must be performed equably in circles; but a laborious computation of seven recorded oppositions of Mars at last persuaded him that the planet travelled in an ellipse, one focus of which was occupied by the sun. Pursuing the in quiry, he found that its velocity was uniform with respect to no single point within the orbit, but that the areas described, in equal times, by a line drawn from the sun to the planet were strictly equal. These two principles he extended, by direct proof, to the motion of the earth; and, by analogy, to that of the other planets. They were published in 1609 in De .lIotibus Stellae Martis. The announcement of the third of "Kepler's Laws" was made ten years later, in De Harmonice Mundi. It states that the squares of the periods of circulation round the sun of the several planets are in the same ratio as the cubes of their mean distances. This numerical proportion, as being a necessary consequence of the law of gravitation, must prevail in every system under its sway. It does in fact prevail among the satellite-families of our acquaintance, and presumably in stellar combinations as well. Kepler's ineradicable belief in the existence of some such con gruity was derived from the Pythagorean idea of an underlying harmony in nature ; but his arduous efforts for its realization took a devious and fantastic course which seemed to give little promise of their surprising ultimate success. The outcome of his discover ies was, not only to perfect the geometrical plan of the solar sys tem, but to enhance very materially the predicting power of astronomy. The Rudolphine Tables (Ulm, 1627), computed by him from elliptic elements, retained authority for a century, and have in principle never been superseded. He was deterred from research into the orbital relations of comets by his conviction of their perishable nature. He supposed their tails to result from the action of solar rays, which, in traversing their mass, bore off with them some of their subtler particles to form trains di rected away from the sun. And through the process of waste thus set on foot, they finally dissolved into the aether, and expired "like spinning insects." (De Cometis; Opera, ed. Frisch, t. vii. p. no.) This remarkable anticipation of the modern theory of light-pressure was suggested to him by his observations of the great comets of 1618.
The formal astronomy of the ancients left Kepler unsatisfied. He aimed at finding out the cause as well as the mode of the planetary revolutions ; and his demonstration that the planes in which they are described all pass through the sun was an im portant preliminary to a physical explanation of them. But his efforts to supply such an explanation were rendered futile by his imperfect apprehension of what motion is in itself. He had, it is true, a distinct conception of a force analogous to that of gravity, by which cognate bodies tended towards union. Misled, however, into identifying it with magnetism, he imagined circulation in the solar system to be maintained through the material compulsion of fibrous emanations from the sun, carried round by his axial rotation. Ignorance regarding the inertia of matter drove him to this expedient. The persistence of movement seemed to him to imply the persistence of a moving power. He did not recognize that motion and rest are equally natural, in the sense of requiring force for their alteration. Yet his rationale of the tides in De Motibus Stellae is not only memorable as an astonishing forecast of the principle of reciprocal attraction in the proportion of mass, but for its bold extension to the earth of the lunar sphere of in fluence.
Galileo.—Galileo Galilei, Kepler's most eminent contemporary, took a foremost part in dissipating the obscurity that still hung over the very foundations of mechanical science. He had, indeed, precursors and co-operators. Michel Varo of Geneva wrote cor rectly in 1584 on the composition of forces; Simon Stevinus of Bruges (1548-162o) independently demonstrated the principle; and G. B. Benedetti expounded in his 'Speculationum Liber (Turin, 1585) perfectly clear ideas as to the nature of acceler ated motion, some years in advance of Galileo's dramatic experi ments at Pisa. Yet they were never assimilated by Kepler ; while, on the other hand, the laws of planetary circulation he had enounced were strangely ignored by Galileo. The two lines of inquiry remained for some time apart. Had they at once been made to coalesce, the true nature of the force controlling celestial movements should have been quickly recognized. As it was, the importance of Kepler's generalizations was not fully appreciated until Sir Isaac Newton made them the corner-stone of his new cosmic edifice.
Galileo's contributions. to astronomy were of a different quality from Kepler's. They were easily intelligible to the general pub lic ; in a sense, they were obvious, since they could be verified by every possessor of one of the Dutch perspective-instruments, just then in course of wide and rapid distribution. And similar results to his were in fact independently obtained in various parts of Europe by Christopher Scheiner at Ingolstadt, by Johann Fabricius at Osteel in Friesland, and by Thomas Harriot at Syon House, Isleworth. Galileo was nevertheless by far the ablest and most versatile of these early telescopic observers. His gifts of exposition were on a par with his gifts of discernment. What he saw, he rendered conspicuous to the world. His sagacity was indeed sometimes at fault. He maintained with full conviction to the end of his life a grossly erroneous hypothesis of the tides, early adopted from Andrea Caesalpino ; the "triplicate" appear ance of Saturn always remained an enigma to him ; and in regard ing comets as atmospheric emanations he lagged far behind Tycho Brahe. Yet he unquestionably ranks as the true founder of descriptive astronomy; while his splendid presentment of the laws of projectiles in his dialogue of the "New Sciences" (Leyden, 1638) lent potent aid to the solid establishment of celestial mechanics.