34 GENERAL PRELIMINARY RESULTS. 



Hence 



We have before supposed 



and as 8 - = 0, we immediately obtain 



Again, since we have at the surface itself 



r being the distance between p and the element do-, we hence 

 deduce 



this substituted in the general value of 8Z7, before given, there 

 arises 8Z7, = 0, and consequently = 8?7. The result just ob- 

 tained being general, and applicable to any point p" within the 

 surface, gives immediately 



w 



and we have by substituting in the equation determining 8F, 



= 8F. 



In a preceding part of this article, we have obtained the 

 equation 



which combined with = 8 (-7- J , gives 



and therefore the density (p) induced on any element <7<r, which 

 is evidently a function of the co-ordinates a?, y, z, of ^>, is also 



