368 VIII. NEWTONIAN POTENTIAL FUNCTION. 



In the case of the disc, we had 



When h = we have 



89 ) =." " 



The attraction of a disc upon a particle in contact with it at its 

 center is independent of the radius of the disc, and is equal to 2# 

 times the surface density. 



If the force on a particle in contact on the 

 right he called JF 2 , positive if to the right, 



- * we have 



90) F 2 = + 



By symmetry, the force on a particle at 

 Fig. 132. the left in contact with the disc is 



91) F 2 -F,= 



Now if x denote the direction of the normal to the right, 



Jbc, = y 



f 



and we see that on passing through the surface there is a discon- 

 tinuity in the value of ^ of the magnitude 4#(7. 



Consider a thin spherical shell. We have for an external point 



92 ) v = w W - W - (^ - ^) W + ^ A + 



and making B% E = e, lim R^ = lim 



dV _ _ 4:1t6 



dh ~ ~ ^ 



and on the outside for h = R, 



dV 



Within we have everywhere 



V=cmst., 5 



