36 by observing the times of descent of bodies falling down long inclined planes, that the postulated law was the true law. Even here, he was obliged to take for granted that the velocities acquired in descending from the same height along planes of every inclination are equal ; and it was not until shortly before his death that he found the mathe- nmtical demonstration of this not very obvious principle. The first law of motion——that which expresses the prin- ciple of i11ertia—is virtually contained in the idea of uni- formly accelerated velocity. The recognition of the second—that of the independence of diflcrent motions— must be added to form the true theory of projectiles. This was done by Galileo. Up to his time it was universally held in the schools that the motion of a body must cease with the impulse communicated to it, but for the “ reaction of the medium ” which helps it forward. Galileo showed, on the contrary, that the nature of motion once impressed is to continue indefinitely in a uniform direction, and that the effect of the medium is a retarding, not an impelling one. .' other commonly received axiom was that no body could be affected by more than one movement at one time, and it vas thus supposed that a cannon ball, or other projectile, moves forward in a right line until its first impulse is ex- hausted, when it falls vertically to the ground. In the fourth of Galileo’s dialogues on mechanics, he demonstrated that the path described by a projectile, being the result of the combination of a uniform transverse motion with a uniformly accelerated vertical motion, must, apart from the resistance of the air, be a parabola. The establishment of the principle of the composition of motions formed a con- clusive answer to the most formidable of the arguments used against the rotation of the earth, and we find it accordingly triumphantly brought forward by Galileo in the -second of his dialogues on the systems of the world. It was urged by anti-Copernicans that a body flung upwards or east downwards would, if the earth were in motion, be left behind by the rapid translation of the point from which it started; Galileo, however, proved that the reception of a fresh impulse in no way interfered with the movement already impressed, and that the rotation of the earth was insensible, because shared equally by all bodies at its sur- face. His theory of the inclined plane, combined with his satisfactory definition of “ momentum,” led him towards the third law of motion. We find Newton’s theorem, that “action and reaction are equal and opposite,” stated with approximate precision in his treatise Della Scienza ilfeccanica, which contains the substance of lectures de- livered during his professorship at Padua; and the same principle is involved in the axiom enunciated in the third of his mechanical dialogues, that “the propensity to fail of a body is equal to the least resistance which suflices to support it.” The problems of percussion, however, did not receive a definitive solution until after his death. His services were no less conspicuous in the statical than in the kinetical division of mechanics. He gave the first direct and entirely satisfactory demonstration of equilibrium on an inclined plane, reducing it to the lever by a sound and ingenious train of reasoning; while, by establishing the theory of “ virtual velocities,” he laid down the fundamental principle which, in the opinion of Lagrange, contains the general expression of the laws of equilibrium. He studi_ed with attention the still obscure subject of molecular co- hesion, and little has been added to what he ascertained on the question of transverse strains and the strength of beams, brought by him for the first time within the scope of mechanical theory. In his Discorso intorno alle cose cite stmmo su l’acqua, published in 1612, he used the principle of virtual velocities to demonstrate the more important theorems of hydrostatics, deducing from it the equilibrium of fluid in a siphon, and proved against the Aristotelians GALILEO that the floating of solid bodies in a liquid depends not upon their form, but upon their specific gravities, relative to such liquid. In order to form an adequate estimate of the stride made by Galileo in natural philosophy, it would be necessary to enumerate the confused and erroneous opinions prevailing on all such subjects in his time. His best eulogium, it has been truly said, consists in the fallacies which he exposed. The scholastic distinctions between corruptible and incor- ruptible substances, between absolute gravity a11d absolute lcvity, between natural and violent motions, if they did not wholly disappear from scientific phraseology, ceased thence- forward to hold the place of honour in the controversies of the learned. Discarding these obscure and misleading notions, Galileo taught that gravity and levity are relative terms, and that all bodies are heavy, even those which, like the air, are invisible; that motion is the result of f0l‘('L-, instantaneous or continuous; that weight is a C0illLll1UOll force, attracting towards the centre of the earth; that, in a vacuum, all bodies would fall with equal velocities; that the “inertia of matter” implies the continuance of motion, as well as the permanence of rest; and that the substance of the heavenly bodies is equally “corruptible” with that of the earth. These simple elementary ideas were emin- ently capable of development and investigation, and were not only true, but the prelude to further truth ; while those they superseded defied inquiry by their vagueness, and bafiled it with their obscurity. Galileo was a man born in due time. He was superior to his contemporaries, but not isolated amongst them. He represented and intensified a growing tendency of the age in which he lived. It was beginning to be suspected that from Aristotle an appeal lay to nature, and some were found who no longer treated the ipse cliacit of the Stagirite as the final authority in matters of science. A vigorous but ineffectual warfare had alre-any been waged against the blind traditions of the schools by Ramus and Telesius, by Patricius and Campanella, and the revolution which Galileo completed had been prepared by his predecessors. Nevertheless, the task which he so effectually accomplisherl demanded the highest and rarest quality of genius. He struck out for himself the happy middle path between the a priori and the empirical systems, and exemplified with brilliant success the method by which experimental science has wrested from nature so many of her secrets. His mind was an eminently practical one. He corcerned himself above all with what fell within the range of exact inquiry, and left to others the larger but less fruitful speculations which can never be brought to the direct test of experiment. Thus, while far—reaching but hasty generalizations have had their day and been forgotten, his work has proved permanent, because he made sure of its foundations. His keen intuition of truth, his vigour anll yet sobriety of argument, his fertility of illustration and acuteness of sarcasm, made him irresistible to his antag- onists ; and the evanescent triumphs of successful contu- versy have been___succeeded by the lasting applause of “osterit . B The fiiist complete edition of Galileo’s writings was published at Florence (1842-1856), in 15 8vo vols., by the Soeieta Editrice Fier- entina, under the able supervision of Signor Eugenio Albcri. Besidc , the works already enumerated, it contains the hitherto illfldltl I Sermoncs dc Zllotu Gravizmz, composed at Pisa between 1589 and 1591; his letters to his friends, with many of their replies, as well as several of the essays of his scientific opponents; his private com- ments on the Orlando Fm-ioso, of which he was an entlnisi-asti: admirer, and on the Gcrusalcmme Libc-ram, of which he was an equally persistent depreciator; some stanzas and sonnets of no great merit, together with the sketch of a comedy; finally, a reprint of Viviani’s Life, with valuable notes and corrections. The original documents from the archives of the Inquisition, relating to the events of 1616 and 1633, recovered from Paris i11 1846 by the efi'ort.; of Count Rossi, and now in the Vatican Library, were to a limited
extent made public by Monsignor lllarino-Marini in 1850, and