might be supposed to offer some difficulty. These were, first, that the inter- 

 ( vals between the supposed successive returns to perihelion were not precisely 

 equal ; and, secondly, that the inclination of the comet's path to the plane of the 

 earth's orbit was not exactly the same in each case. Halley, however, with a 

 degree of sagacity which, considering the state of knowledge at the time, can- 

 not fail to excite unqualified admiration, observed that it was natural to suppose 

 that the same causes which disturbed the planetary motions must likewise act 

 upon comets ; and that their influence would be so much the more sensible upon 

 these bodies because of their great distances from the sun. Thus, as the at- 

 traction of Jupiter upon Saturn was known to affect the velocity of the latter 

 planet, sometimes retarding and sometimes accelerating it, according to their 

 relative position, so as to affect its period to the extent of thirteen days, it 

 might well be supposed that the comet might suffer by a similar attraction, an 

 effect sufficiently great to account for the inequality observed in the interval 

 between its successive returns ; and also for the variation to which the direc- 

 tion of its path upon the plane of the eclipti,c was found to be subject. He 

 observed, in fine, that as in the interval between 1607 and 1682 the comet 

 passed so near Jupiter that its velocity must have been augmented, and conse- 

 quently its period shortened by the action of that planet, this period, therefore, 

 having been only seventy-five years, he inferred that the following period would 

 < probably be seventy-six years or upward ; and consequently that the comet 

 > ought not to be expected to appear until the end of 1758, or the beginning of 

 $ 1759. It is impossible to imagine any quality of mind more enviable than that 

 which, in the existing state of mathematical physics, could have led to sucli a 

 prediction. The imperfect state of mathematical science rendered it impossible 

 for Halley to offer to the world a demonstration of the event which he foretold. 

 " He therefore," says M. de Pontecoulant, " could only announce these felicitous 

 conceptions of a sagacious mind as mere intuitive perceptions, which must be 

 received as uncertain by the world, however he might have felt them himself, 

 until they cculd le verified by the process of a rigorous analysis." 



The theory of gravitation, which was in its cradle at the time of Halley's 

 investigations, had grown to comparative maturity before the period at which 

 his prediction could be fulfilled. The exigencies of that theory gave birth to 

 new and more powerful instruments of mathematical inquiry : the differential 

 and integral calculus was its first and greatest offspring. This branch of sci- 

 ence was cultivated with an ardor and success by which it was enabled to an- 

 swer all the demands of physics, and consequently mechanical science ad- 

 vanced, pari passu. Newton's discoveries having obtained reception throughout 

 the scientific world, his inquiries and his theories were followed up ; and the 

 consequences of the great principle of universal gravitation were rapidly de- 

 veloped. Among these inquiries one problem was eminently conspicuous for 

 the order of minds whose powers vrere brought to bear upon it. One of the 

 first and simplest results of the theory of gravitation was, that if a single planet 

 attended the sun (its mass being insignificant compared with that of the sun), 

 that planet must revolve in an "ellipse, the focus of which must be occupied by 

 the centre of the sun ; but, if a second planet be admitted into the system, then 

 the elliptic form of their paths round the sun can be preserved only by the sup- 

 position that the two planets have no attraction for each other, and that, no 

 physical influence is in operation, except the attraction of the solar mass for 

 each of them. But the law of universal gravitation is founded upon the prin- 

 ciple that every body in nature must attract and be attracted by every othr.r body. 

 Thus, the elliptic character of the orbit is effaced the moment a second planet 

 is introduced. But let us remember that in this case each of the two supposed 

 planets are in mass absolutely insignificant co.npared with the sun. The 



