THEORY OF APPROXIMATION. 85 



Xe \vton, 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 approxima- 

 tion, and proved that t 1 _ attraction of the protuberant 

 matter upon the moon accounted for the precession of the 

 equinoxes, and led to various complicated effects. But, 

 as I have already mentioned (vol. ii. p. 76), even the 

 spheroidal hypothesis is far from the truth. It takes no 

 account of the irregularities of surface, the great protu- 

 berance of land, for instance, 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 resisting atmo- 

 sphere 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 only after a time to 

 be deflected into a curve. Tartaglia ventured to maintain 

 that the path was curved throughout, as by the principle 

 of continuity it should be ; but the ingenuity of Galileo was 

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

 wa> approximately a parabola. It is only, however, under 

 several forced hypotheses that we can assert the path of a 

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

 a perfect vacuum, where there is no resisting medium of 

 any kind ; the force of gravity must be equal and act in 

 parallel lines ; and the moving body must be either a 

 mere point, or a perfect centrobaric body, that is a body 

 possessing a definite centre of gravity. None of these 

 conditions can be really Fulfilled in practice. The next 

 great step in the problem was made by Newton and 

 Huyghens, the latter of whom asserted that the atmo- 



