66 POPULAR LECTURES AND ADDRESSES. 



surface of a nearly spherical homogeneous solid 

 ellipsoid is approximately an ellipsoid with axes 

 differing from one another by three-fifths of the 

 amounts of the differences of the corresponding 

 axes of the ellipsoidal boundary. Now it is 

 known 1 that a homogeneous prolate spheroid of 

 revolution attracts points outside it approximately 

 as if its mass were collected in a uniform bar 

 having its ends in the foci of the equipotcntial 

 spheroid. If, for example, a globe of water of 

 21,000,000 feet radius (this being nearly enough 

 the earth's radius) be altered into a prolate spheroid 

 with longest radii exceeding the shortest radii by 

 two feet, the equipotcntial spheroid will have 

 longest and shortest radii differing by !| of a foot. 

 The foci of this latter will be at 7,100 feet on 

 each side of the centre ; and therefore the resultant 

 of gravitation between the supposed spheroid of 

 water and external bodies will be the same as if 

 its whole mass were collected in a uniform bar of 

 14,200 feet length. But by a well-known proposi- 

 tion, 2 a uniform line FF' (a diagram is unneces- 

 sary), attracts a point M in the line M K bisect- 

 ing the angle F M F'. Let C Q be a perpendicular 

 from C, the middle point of F'F, to this bisecting 

 line M K. If C M be 60 x 21 x 10 (the moon's 

 distance), and if the angle F C M be 45 we find, 

 by elementary geometry, CO -02 of a foot (about 



1 Thomson and Tail's Natural riiilosopliy, 501 and 480 (c). 

 - Ibid., 48o(/<) and (a). 



