466 THE PRINCIPLES OF SCIENCE. [CHAP. 



Newton's successful solution of the problem of the 

 planetary movements entirely depended at first upon a 

 great simplification. The law of gravity only applies 

 directly to two infinitely small particles, so that when we 

 deal with vast globes like the earth, Jupiter, and the 

 sun, we have an immense aggregate of separate attractions 

 to deal with, and the law of the aggregate need not coincide 

 with the law of the elementary particles. But Newton, 

 by a great effort of mathematical reasoning, was able to 

 show that two homogeneous spheres of matter act as if 

 the whole of their masses were concentrated at the centres ; 

 in short, that such spheres are centrobaric bodies (p. 364). 

 He was then able with comparative ease to calculate the 

 motions of the planets on the hypothesis of their being 

 spheres, and to show that the results roughly agreed with 

 observation. Newton, indeed, was one of the few men 

 who could make two great steps at once. He did not 

 rest contented with the spherical hypothesis; having 

 reason to believe that the earth was really a spheroid 

 with a protuberance around the equator, he proceeded to 

 a second approximation, and proved that the attraction of 

 the protuberant matter upon the moon accounted for the 

 precession of the equinoxes, and led to various complicated 

 effects. But, (p. 459), even the spheroidal hypothesis is 

 far from the truth. It takes no account of the irregu- 

 larities of surface, the great protuberance of land in 

 Central Asia and South America, and the deficiency in 

 the bed of the Atlantic. 



To determine the law according to which a projectile, 

 such as a cannon ball, moves through the atmosphere is 

 a problem very imperfectly solved at the present day, but 

 in which many successive advances have been made. So 

 little was known concerning the subject three or four 

 centuries ago that a cannon ball was supposed to move 

 at first in a straight line, and after a time to be deflected 

 into a curve. Tartaglia ventured to maintain that the 

 path was curved throughout, as by the principle of con- 

 tinuity it should be ; but the ingenuity of Galileo was 

 required to prove this opinion, and to show that the curve 

 was approximately a parabola. It is only, however, under 

 forced hypotheses that we can assert the path of a projec- 

 tile to be truly a parabola : the path must be through a 



