xxvm 



THE PROGRESS OF 



nuking together 10A feet, which agrees pretty 

 well with what is observed in the open sea at a 

 distance from hud. 



From the force which the moon exerts on the 

 waters of the ocean, Newton concluded that the 

 quantity of matter in the moon is to that in the 

 earth as 1 to 39*78, or, in round numbers, as 1 

 to 40. He found also the density of the moon to 

 the density of the earth as 1 1 to 9. 



Much lia- been done upon the tides by 

 .Mad. mi-ill, Bernoulli, Kuler, and Laplace ; but 

 the original deduction of Newton, of which an 

 idea has just been given, will be for ever memor- 

 able. 



The motion of comets still remained to be dis- 

 cussed. They had only lately been placed be- 

 yond the range of the earth's atmosphere ; but 

 with respect to their motion, astronomers were 

 not agreed. Kepler thought that they moved in 

 straight lines, Cassini that they moved in the 

 planes of great circles, but with little curvature. 

 Hevelius had shown the curvature of their path 

 to be different in different parts, and to be 

 greatest when nearest the sun. A parabola 

 having its vertex in that point, seemed to him to 

 be the line in which the comets moved. Newton, 

 satisfied of the universality of gravitation, had 

 no doubt that the orbits of the planets were conic 

 sections, having the sun in one of the foci. The 

 curve might be an ellipse, a parabola, or an hyper- 

 bola, according to the relation between the force 

 of projection and the force tending to the centre. 

 As the eccentricity of the orbit is very great, the 

 portion of it that fell within our view could not 

 differ much from a parabola. This rendered the 

 calculation of the comet's place, when the position 

 of the orbit was once ascertained, more easy than 

 in the case of the planets. From three observa- 

 tions of the comet, the position of the orbit could 

 be determined, though the geometrical problem 

 was one of great difficulty. Newton gave a 

 solution of it, and it was by this that his theory 

 was to be brought to the test of experiment. If 

 the orbit thus calculated was not the true one 

 die places of the comet calculated on the sup- 

 position that it was, and that it described equal 

 areas in equal times about the sun, could not 

 agree with the places actually observed. Newton 

 showed, by the example of the remarkable comet 

 then (1680) visible, that this agreement was as 

 great as could reasonably be expected. Thus 

 another proof was given in support of the prin- 

 ciple of universal gravitation. 



We have been thus particular in tracing the 

 discoveries of Newton, because they constitute 

 the most memorable, the most successful, the 

 most difficult, and the most sublime set of in- 

 vestigations which had hitherto been attempted. 

 The more the doctrine of universal gravitation 



has been investigated, the more firmly has its 

 truth been established. Evt-ry improvement in 

 the infinitesimal calculus has given mathema- 

 ticians (if the expression may be permitted) a 

 firmer grnsp of the universe. New effects of the 

 mutual action of the planets on each other have 

 been detected ; but all according most harmo- 

 niously, or rather resulting as a necessary con- 

 sequence of the law of universal gravitation, as 

 laid down and investigated by Newton. No 

 other department of science can be compared to 

 this; no other branch of human knowledge r;m 

 be specified, which is built on a foundation so 

 firm that every succeeding investigation has 

 served only to render it more secure. No other 

 theory can be exhibited so perfect, that every 

 minute fact might be deduced a priori as a con- 

 sequence of it; and which does not contain a 

 single phenomenon within the whole range of 

 the science that is not merely not inconsistent 

 with it, but which does not directly flow from 

 it 



The Principia appeared in 1687 ; and the 

 doctrines which they contained were immediately 

 embraced by the small number of British 

 mathematicians who were able to read and un- 

 derstand that immortal work. But on the con- 

 tinent it was treated at first with neglect, and an 

 indifference bordering on contempt. The only 

 mathematical competitor that Newton had on the 

 continent was Leibnitz, with his disciples and 

 staunch adherents, the two Bern6ullis. The 

 question respecting the original dicoverer of the 

 fluctionary calculus was not yet agitated. Yet 

 the German mathematicians do not seem to have 

 given themselves the trouble of making them- 

 selves masters of the Principia. The cautious 

 mode of investigation which Newton had adopted 

 did not quite accord with the genius of Leibnitz, 

 who was fond of metaphysics, and in the habit of 

 introducing them into most of his investigations. 

 France, which has since that period produced 

 so many eminent mathematicians, owing to the 

 fostering care of her government, could not at 

 that time boast of any of very great eminence. 

 The philosophy of Descartes was every where 

 prevalent; and his vortices, which it was the ob- 

 ject of the Principia to overturn and subvert, 

 were too dear to the French to enable them to 

 judge of the doctrines of Newton with the re- 

 quisite impartiality. Accordingly, the first 

 mathematician who ventured publicly to defend 

 the doctrines of Newton was Maupertuis. In the 

 year 1732 he published a work, in which he 

 drew a comparison between the systems of Des- 

 cartes and Newton, and showed the superiority 

 of the latter. Fontenelle, however, in his Eloge 

 of Newton, inserted in the Memoire* of the 

 Academy for 1727, admits the infinite merit of 



