160 THEORY OF NEWTONIAN FORCES. [PT. I. CH. IV. 



In the case of the disc, we had 



8F ^ | h_ ) 



When h = we have 



'8F\ 



The repulsion 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?r 

 times the surface density. 



Ff 



FIG. 38. 



If the force on a particle in contact on the right be called F 2 , 

 positive if to the right, we have 



^ 2 ^4- 2-7TO-. 



By symmetry, the force on a particle at the left in contact 

 with the disc is 



F! = - 27TC7, 

 F^-F Z = - 47T<7. 



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



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



continuity in the value of ^ of the magnitude 47ror. 



ox 



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

 V = i (JV - Sf) * <E(Jfe- J&) (Ef 



