422 Mr green, -ON THE DETERMINATION OF THE 



If now we suppose moreover 



__ 1 d^ _ f f> dx dy d% 



the method before explained (No 11), will immediately give 



Z) = — , — T— a cu / T — , 



p/ w'+ 1 \ J^ abc 



and therefore if for abridgment we make 



-'^d') .,, 



the total differential of V may be written 

 rfr=i»f{2^rf^/^-^^ + 2s.rfy/^-^^ + 2.t/./^— j-^ + 2«rf./^-^^}, 



which being integrated in the usual way by first supposing h constant, 

 and then completing the integral with a function of h, to be after- 

 wards determined by making every thing in F variable, we get 



A being a quantity absolutely constant, which is equal to zero when 

 w' > 1. What has just been advanced will be quite clear if we recollect 

 that h may be regarded as a function of x, y, % and u, determined by 

 the equation 



» = ?^' + 4^ + ?4^ ^- 1 - f + -' + f' -^ ' <''^>' 



seeing that a' = a'*-\-h\ V = b'' + h\ and & = c" + h\ 



After what precedes, it seems needless to enter into an examination 

 of the values of V belonging to other values of the density p, since 

 it must be clear that the general method is equally applicable when 



