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



(6) li 



Therefore the first derivatives of V, and hence the parameter, 

 vanish at infinity to the second order. 



In like manner for the second derivatives 



Every element in all the integrals discussed is finite, unless 

 r = 0, hence all the integrals are finite. We might proceed in this 

 manner, and should thus find that : 



At points not in the attracting masses, T^and all its derivatives 

 are finite and (since their derivatives are finite) continuous, as well 

 as uniform. 



Also since 





(z - cf - 



we have by addition 



.,, 



that is, V satisfies Laplace's equation. 



This is also proved by applying Gauss's theorem ( 39 (4)) to 



each element . 

 r 



76. Points in the Attracting Mass. Let us now examine 

 the potential and its derivatives at points in the substance of 

 the attracting mass. 



