125] 



ATTRACTION OF SPHERE. 



365 



geneous spherical shell exercises no force on a body within. (On 

 account of symmetry the force can be only radial.) 



If P is in the substance of the shell, we divide the shell into 

 two by a concentric spherical surface passing through P, find the 

 potential due to the part within P, and add it to that without, getting 



80) F = 



8A 



dV 



dh ~ 3 h* 



dh*~ 3 h s 



Tabulating these results, 





81) 



F 

 dV 



dh 



3 



3 h* 



Plotting the above results (Fig. 129) shows the continuity of V 

 and its first derivative and the discontinuity of the second derivative 

 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 



fe-o, 



dV 



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, if 



the earth were homogeneous. Experiment shows, however, that. this 

 is not the case. 



- 129 - 



