81, 82] 



and 



NEWTONIAN POTENTIAL FUNCTION. 



159 



R 



- 

 a 



R 



r = 

 a 



If we have a conical mountain of uniform density on the earth, 

 and determine the force of gravity at its summit and at the sea 

 level, this gives us the ratio of the attraction of the sphere and 

 cone to that of the sphere alone, and from this we get the ratio of 

 the mass of the earth to the mass of the mountain. Such a deter- 

 mination was carried out by Mendenhall, on Fujiyama, Japan, in 

 1880, giving 5'77 for the earth's density. 



FIG. 37. 



Circular disc on point not on axis. Let the coordinates of P 

 with respect to the center be a, 6, 0. Then 



=/T 



J J Q 



erdrd(t> 



o Va 2 + (6 r cos $) 2 + r 2 sin 2 < ' 



an elliptic integral. The development in an infinite series will be 

 given in 102. 



82. Surface Distributions. In the case of the circular 

 disc of thickness e, ep is the amount of matter per unit of surface 

 of the disc. It is often convenient to consider distributions of 

 matter over surfaces, in such a manner that though e be considered 

 infinitesimal p increases so that the product ep remains finite. 

 The product ep o- is called the surface density, and the distribu- 

 tion is called a surface distribution. 



We have 



dS 



