ACTION OF A SPHERE. 35 



the point P v /> the mean density of the whole sphere, and p the 

 mean density of the external layers, we shall have 



M 

 The force at the surface is F x = , which gives 



r, ^ 



The force may at first be an increasing one on starting from the 

 surface, then attain a maximum, and then go on decreasing to the 

 centre. This, for instance, is the case with the variations of gravity 

 in the interior of the globe. For this we must have 



If the thickness h = R r is very small as compared with R, this 

 condition may be written 



(r\^ h p r h p 2 



\ <2 , or <-<o'67. 



The mean density of the Earth being about equal to 5-5, and 

 that of the surface to 2-5, we have, in fact, 



P 2 '5 



= = 0-45. 



ft) 5'5 



D 2 



