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 PHYSICS

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PHYSICS

programme made three demands: first, that general mechanics and celestial mechanics advance in the way indicated by Newton; secondly, that electric and magnetic phenomena be explained by a theory analogous to that of universal gravitation; thirdly, that molecular attraction furnish the detailed expla- nations of the various changes investigated by physics and chemistry.

Many followed in the path outlined by Newton, and tried to extend the domain of general and celestial mechanics, but there were three who seem to have surpassed all the others: Alexis-Claude Clairaut (1713-65), Jean-Baptiste le Rond d'Alembert (1717- 83), and Leonhard Euler (1707-83). The progress which, thanks to these three able men, was made in general mechanics, may be summed up as follows: In 1743, by his principle of the equilibrium of chan- nels, which was easily connected with the principle of virtual displacements, Clairaut obtained the gen- eral equations of the equilibrium of liquids. In the same year d'Alembert formulated a rule whereby all problems of motion were reduced to problems of equilibrium and, in 1744, applied this rule to the equation of hydrostatics given by Clairaut and arrived at the equations of hydrodynamics. Euler trans- formed these equations and, in his studies on the motion of liquids, was enabled to obtain results no less important than those which he had obtained by analysing the motion of solids. Clairaut extended the consequences of universal attraction in all directions, and, in 1743, the equations of hydrostatics that he had established enabled him to perfect the theory of the figure of the earth. In 17.52 he published his theory of lunar inequalities, which he had at first despaired of accounting for by Newton's principles. The methods that he devised for the study of the perturbations which the planets produce on the path of a star permitted him, in 1758, to announce with accuracy the time of the return of Halley's Comet. The confirmation of this prediction in which Clairaut had received assistance from Lalande (17.32-1807) and Mme. Lepaute, both able mathematicians, placed beyond doubt the applicability of Newton's hypotheses to comets.

Great as were Clairaut's achievements in perfecting the system of universal attraction, they were not as important as those of d'Alembert. Newton could not deduce from his suppositions a satisfactory theory of the precession of the equinoxes, and this failure marred the harmony of the doctrine of uni- versal gravitation. In 1749 d'Alembert deduced from the hypothesis of gravitation the explanation of the precession of the equinoxes and of the nutation of the earth's axis; and soon afterwards Euler, tlrawing upon the admirable resources of his mathe- matical genius, made still further improvements on d'Alembert's discoverj'. Clairaut, d'Alembert, and Euler were the most brilliant stars in an entire con- stellation of mechanical theorists and astronomers, and to this group there succeeded another, in which shone two men of surpassing intellectuality, Joseph- Louis Lagrange (1736-1813) and Pierre-Simon Laplace (1749-1827). Laplace was said to have been born to complete celestial mechanics, if, indeed, it were in the nature of a science to admit of com- pletion; and quite as much could be said of Lagrange with regard to general mechanics. In 1787 Lagrange published the first edition of his "Mecanique analy- tique"; the second, which was greatly enlarged, was published after the author's death. Laplace's "Me- canique celeste" was published from 1799 to 1805, and both of these works give an account of the greater part of the mechanical conquests made in the course of the eighteenth centurj', with the assistance of the principles that Newion had assigned to general mechanics and the laws that he had impo.sed upon universal gravitation. However exhaustive and

effective these two treatises are, they do not by any means include all the discoveries in general and celestial mechanics for which we are indebted to their authors. To do Lagrange even meagre justice his able researches should be placed on a par with his "Mecanique analytique"; and our idea of Laplace's work would be verj' incomplete were we to omit the grand cosmogonic hypothesis with which, in 1796, he crowned his "Exposition du systeme du monde". In developing this hypothesis the illustrious geometri- cian was unaware that in 1755 Kant had expressed similar suppositions which were marred by serious errors in dynamic theories.

XXVI. EST.\BLISHMENT OF THE ThEORY OP ELEC- TRICITY .\ND Magxeti.sm. — For a long time the study of electric action was merely superficial and, in the beginning of the eighteenth centurj', it was still in the condition in which Thales of Miletus had left it, remaining far from the point to which the study of magnetic attraction and repulsion had been carried in the time of Pierre of Maricourt. When, in 1733 and 1734, Charles-Frangois de Cisternaj- du Fay distin- guished two kinds of electricity, resinous and vitreous, and when he proved that bodies charged with the same kind of electricity repel one another, whereas those charged with different kinds attract one another, electrical science was brought up to the level that magnetic science had long before attained, and thenceforth these two sciences, united by the closest analogy, progressed side by side. They advanced rapidly as, in the eighteenth centurj% the study of electrical phenomena became a popular craze. Physi- cists were not the only ones devoted to it ; men of the world crowded the salons where popularizers of the science, such as the Abbe Nollet (1700-70), enfisted as votaries dandified marquesses and sprightly marchionesses. Numberless experimentalists applied themselves to multiplying observations on electricity and magnetism, but we shall restrict ourselves to mentioning Benjamin Franklin (1706-90) who, by his logically-conducted researches, contributed more than any other man to the formation of the theories of electricity and magnetism. The researches of Henrj' Cavendish (1731-1810) deserve to be placed in the same rank as Franklin's, though they were but little known before his death.

Bv means of Franklin's experiments and his own, .Epinus (Franz ITlrich Theodor Hoch, 1724-1802) was the first to attempt to solve the problem suggested by Newton and, by the hypothesis of attractive and repellent forces, to ex-plain the distribution of elec- tricity and magnetism over the bodies which they affect. His researches could not be pushed very far, as it was still unknown that these forces depend upon the distance at which they are exerted. Moreover, ^pinus succeeded in drawing still closer the connexion already established between the sciences of electricity and magnetism, by showing the polarization of each of the elements of the insulating plate which separates the two collecting plates of the condenser. The experiment he made in this fine in 1759 was destined to suggest to Coulomb the experiment of the broken magnets and the theory of magnetic polarization, which is the foundation of the study of magnets; and was also to be the starting-point of an entire branch of electrical science, namely the study of dielectric bodies, which study was developed in the nineteenth century by Michael Faraday and James Clerk-Maxwell.

Their analogy to the fertile law of universal gravi- tation undoubtedly led physicists to suppose that electrical and magnetic forces vary inversely as the square of the distance that separates the acting ele- ments; but, so far, this opinion had not been con- firmed by experiment. However, in 1780 it received this confirmation from Charles-Augustin de Coulomb with the aid of the torsion balance. By the use of