TO THE THEORY OF ELECTRICITY. 45 



In precisely the same way we obtain, by writing R for the 

 radius of curvature in the plane (w, w"}, 



both rays being accounted positive on the side where w, i. e. w, 

 is negative. These values substituted in = F, there results 



dw* 



for the required value of -r- *-> and thus the sum of the two 

 equations into which it enters, yields 



and the difference of the same equations gives 



-# = 29r(p-p)0; 

 therefore the required values of the densities p and p are 



which values are correct to quantities of the order 6 2 p, or, which 

 is the same thing, to quantities of the order 0; these having 

 been neglected in the latter part of the preceding analysis, as 

 unworthy of notice. 



Suppose do- is an element of the surface A, the cor- 

 responding element of B, cut off by normals to A 9 will be 



da- jl + 6 (-ft + gHj- , and therefore the quantity of fluid on this 

 last 



element will be ~pdcr l + 6 -^ + - ; substituting for p ita 



