GALILEO 35 are 11ot less remarkable for the sagacity wl1icl1 directed, than for the inspiration which prompted them. With the sure instinct of genius, he seized the characteristic features of the phenomena presented to his attention, and his inferences, except when distorted by polemical exigencies, have been strikingly confirmed by modern investigations. Of his two capital errors, regarding respectively the theory of the tides and the nature of comets, the first was insidi- ously recommended to him by his passionate desire to find a physical confirmation of the earth’s double motion ; the second was adopted for the purpose of rebutting an anti- Copernican argument founded on the planetary analogies of those erratic subjects of the sun. Within two years of their first discovery, he had constructed approximately accurate tables of the revolutions of J upiter’s satellites, a11d he proposed their frequent eclipses as a means of determin- ing longitudes, not only on land, but at sea. This method, on which he laid great stress, and for the facilitation of ' which"he invented a binocular glass, and devised some skilful mechanical contrivances, was offered by him in 1616 to the Spanish Government, and afterwards to that of Tuscany, but in each case unsuccessfully ; and the close of his life was occupied with prolonged but fruitless negotia- tions on the same subject with the states—general of Holland. The idea, though ingenious, has been found of little practical utility at sea, where the method founded on the observed distance of the moon from a known star is that usually employed. A series of careful observations made him acquainted with the principal appearances revealed by modern instru- ments in the solar spots. He pointed out that they were limited to a certain defined zone on the sun’s surface; he noted the faculce with which they are associated, the penumbra by which they are bordered, their slight proper motions, and their rapid changes of form. He inferred from the regularity of their general movements the rotation of the sun on its axis in a period of little less than amonth (the actual period is 25d. 7h. 48m.); and he grounded o11 the varying nature of the paths apparently traversed by them a plausible, though inconclusive, argument in favour of the eartl1’s annual revolution. Twice in the year, he observed, they seem to travel across the solar disk in straight lines; at other times, in curves. These appear- ances he referred with great acuteness to the slight inclina- tion of the sun’s axis of rotation to the plane of the ecliptic. Thus, when the earth finds herself in the plane of the sun’s equator, which occurs at two opposite points of her orbit, the spots, travelling in circles parallel with that plane, necessarily appear to describe right lines; but when the earth is above or below the equatorial level, the paths cf the spots open out into curves turned downwards or up- wards, according to the direction in which they are seen. The explanation, however, of this phenomenon is equally consistent with the geocentric as with the heliocentric theory of the solar system. The idea of a universal force of gravitation seems to have hovered around the borders of this great man’s mind, without ever fully entering it. He perceived the analogy between the power which holds the moon in the neighbourhood of the earth, and compels J upiter’s satellites to circulate round their primary, and the attraction exercised by the earth on bodies at its surface ;1 but he failed to conceive the combination of central force with initial velocity, and was disposed to connect the revolu- 1 The passage is sufliciently remarkable to deserve quotation in the original:—-“Le parti dclla Terra hanno tal propensione al centro di essa, che quando ella cangiasse luogo, le dette parti, benche lontane da‘. gl'obo.11e_1 tempo delle mutazioni di esso, lo seguirebbero per tutto; esempio di cu‘) sia il seguito perpetuo delle ltledicee, ancorehé separate continuamcnte da Giove. L’istesso si deve dire della Luna, obbligata 3 S‘3o'Ui1' la "1‘.c‘rra.’:fDiol0go dell xllccssimi S¢'.stemz', Giornata. terza, p. 351 of All)‘.‘l‘l s edition. tions of the planets with the axial rotation of the sun. This notion, it is plain, tended rather towards Descartes’s theory of vortices than towards N ewton’s theory of gravita- tion. More valid instances of the anticipation of modern discoveries may be found in his prevision that a small annual parallax would eventually be found for some of the fixed stars, and that extra-Saturnian planets would at some future time be ascertained to exist, and in his conviction that light travels with a measurable although, in relation to terrestrial distances, infinite velocity. The invention of the miscroscope, attributed to Galileo by his first biographer, Vincenzo Viviani, does not in truth belong to him. Such an instrument was made as early as 1590 by Zacharias Jansen of Middleburg; and although Galileo discovered, in 1610, a means of adapting his tele- scope to the examination of minute objects, he did not become acquainted with the compound microscope until 1624, when he saw one of Drebbel’s instruments in Rome, a11d, with characteristic ingenuity, immediately introduced some material improvements into its construction. The most substantial, if not the most brilliant part of his work consisted undoubtedly in his contributions towards the establishment of mechanics as a science. Some valu- able but isolated facts and theorems were previously dis- covered and proved, but it was he who first clearly grasped the idea of force as a mechanical agent, and extended to the external world the conception of the invariability of the relation between cause and effect. From the time of Archimedes there had existed a science of equilibrium, but the science of motion began to exist with Galileo. It is not too much to say that the final triumph of the Copernican system was due in larger measure to his labours in this department than to his direct arguments in its favour. The problem of the heavens is essentiallya mechanical one ; and without the mechanical conceptions of the dependence of motion upon force which Galileo familiarized to men‘s minds, that problem might have remained a sealed book even to the intelligence of Newton. The interdependence of motion and force was not indeed formulated into definite laws by Galileo, but his writings on dynamics are every- where suggestive of those laws, and his solutions of dyna- mical problems involve their recognition. The extraor- dinary advances made by him i11 this branch of knowledge were owing to his happy method of applying mathematical analysis to physical problems. As a pure mathematician he was, it is true, surpassed in profundity by more than one among his pupils and contemporaries; and in the wider imaginative grasp of abstract geometrical principles he cannot be compared with Fermat, Descartes, or Pascal. to say nothing of Newton or Leibnitz. Still, even in the region of pure mathematics, his powerful and original mind left notable traces of _its working. He studied the proper- ties of the eycloid, and attempted the problem of its quadrature earlier than Mersenne ; and in the “infinitesi- mals,” which he was one of the first to introduce into geo- metrical demonstrations, was contained the fruitful germ of the differential calculus. But the method which was peculiarly his, and which still forms the open road to dis- coveries in natural science, consisted in the combination cf experiment with calculation—in the transformation of the concrete into the abstract, and the assiduous comparison of results. The first fruits of the new system of investigation was his determination of the laws of falling bodies. Con- ceiving that the simplest principle is the most likely to be true, he assumed as a postulate that bodies falling freely towards the earth descend with a uniformly accelerated motion, and deduced thence the principal mathematical. con- sequences, as that the velocities acquired are in the direct, and the spaces traversed in the duplicate ratio of the times,
counted from the beginning of motion; finally, he proved,