126, 127] 



DISC, CYLINDER, CONE. 



367 



Let E be the radius of base, a the altitude, h the height of P 

 above the vertex. 



A disc at distance x below vertex and radius r causes potential 

 at P, 



and 



E 



E 



85) 



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 

 determination was carried out by 

 Mendenhall, on Fujiyama, Japan, in 

 1880, giving 5.77 for the earth's 

 density. m * 1S1 - 



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

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



s 2 = a 2 -f (b r cos <p) 2 -f r 2 sin 2 <p, 



# 

 86) F = 







an elliptic integral. 



srdrdcp 



i* -f (& r cos qp) 2 -f f 2 sin 8 93 



127. Surface Distributions. In the case of the circular disc 

 of thickness a, SQ 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 s be considered infinite- 

 simal Q increases so that the product eg remains finite. The product 

 SQ = 6 is called the surface density, and the distribution is called a 

 surface distribution. 



We have 



87) 



dm = <5dS, V 



C CedS 

 ~JJ r 



