80, 81] NEWTONIAN POTENTIAL FUNCTION. 157 



Plotting the above results (Fig. 35) shows the continuity of 



FIG. 35. 



V and its first derivatives and the discontinuity of the second 

 derivatives at the surfaces of the attracting mass. 



We see that the attraction of a solid sphere at a point within 

 it is proportional to the distance from the center, for if R^ 0, 



d V 4f7rph 

 dh = ~3~' 



and is independent of the radius of the sphere. Hence experi- 

 ments on the decrease of the force of gravity in mines at known 

 depths might give us the dimensions of the earth. 



81. Disc, Cylinder, Cone. Let us find the attraction of a 

 circular disc of infinitesimal thickness at a point on a line normal 



FIG. 36. 



