NEWTON. 199 



by the effects of its rotation. That the centrifugal force due to rota- 

 tion would act most upon the part of the earth near the equator, and 

 not at all upon the regions about the poles, is probably sufficiently 

 obvious. Newton calculated the amount of this centrifugal force, and 

 he found that at the equator it is the two hundred and eighty-ninth part 

 of the force of gravitation ; that is, if on a spring balance were hung 

 at the equator a weight which marked two hundred and eighty-eight 

 ounces on the scale, the same would, if the earth ceased to rotate, bring 

 down the index of the scale to two hundred and eighty-nine ounces. 

 Newton illustrated the effect of this centrifugal force on the figure of 

 the earth by supposing that a canal extended from the pole to the 

 centre, and from the centre another canal extended to the equator. 

 If these canals were filled with water, the two columns of water must 

 balance each other \ that is, the whole weight or total effect of gravity 

 must be the same in both. Taking account of the centrifugal force, 

 Newton calculated what must be the relative lengths of these columns, 

 and he found that the length of the equatorial must be to that of the 

 axial column as two hundred and thirty to two hundred and twenty- 

 nine. This amounts to a determination of the proportion the earth's 

 equatorial radius must bear to its polar radius. At the time these de- 

 terminations were made, there existed no measurements from which 

 the earth's deviation from the perfectly spherical form could be in- 

 ferred, although Newton's investigation of this question had probably 

 been suggested by Cassini's discovery of the spheroidal form of the 

 planet Jupiter, to which we shall presently direct the reader's attention. 

 The spheroidal figure would add its effect to that of the centrifugal 

 force in diminishing the force with which bodies at the surface of the 

 earth are attracted as we pass from the polar to the equatorial regions. 

 We have already alluded to a fact which the observations of astrono- 

 mers had long before disclosed, namely, that the equinoctial points, 

 in which the apparent annual path of the sun in the heavens intersects 

 the equator, were affected by a slow but constant retrograde motion 

 by which they shift their position about 50" of arc annually, so that 

 they make a complete circuit of the heavens in something less than 

 26,000 years. No astronomer had as yet been able to assign a cause 

 for this motion. Now, Newton not only showed that the precession 

 of the equinoxes must necessarily result from the spheroidal form of 

 the earth, but he calculated the rate of movement which the effect of 

 gravity on the protuberant matter about the earth's equator must pro- 

 duce, and the result was in perfect agreement with observation. 



The concordance of the general results deduced from the principle 

 of gravitation with the observed facts stated in Kepler's law, has been 

 mentioned as justifying the adoption of the principle as one of the 

 fundamental laws of nature. Yet if Kepler's laws were strictly true, 

 universal gravitation cannot also be the true law of the universe, for 

 Kepler's laws take account only of the actions between each planet and 



