228 THE OCEAN. [Booe. X. 



PROPOSITION III. 



Theorem. — The ratio which the revolving force of the 

 gravitation of a sphere bears to its direct force is 

 inversely as the distance from the sphere. 



Because the revolvmg force depends on the 

 amount by which the force of the gravitation of the 

 nearer exceeds that of the remoter half of the 

 sphere. Therefore, the diiFerence in those forces 

 depends on the ratio which the distance from the 

 sphere bears to its diameter ; increasing as the ratio 

 which the diameter of the sphere bears to the distance 

 from the sphere increases. And, as the ratio which 

 the diameter bears to the distance is inversely as the 

 distance, therefore the ratio which the revolving force 

 of the gravitation of a sphere bears to its direct 

 force is inversely as the distance from the sphere. 



Definition. — The point from which the relative 

 distances must be measured is neither the nearest 

 point of the sphere nor its centre, but an interme- 

 diate point. The table on page 82, however, shows 

 that for our present purposes the above ratio is 

 sufficiently accurate if the relative distances be 

 measured from the centre of the sphere, and the 

 subject need not, therefore, be involved with that 



