ON ELECTKIC ENDOSMOSE AND OTHER ALLIED PHENOMENA. 509 



(x, y) near the origin. The vakies of X,, /xj, I'l for this case have been 

 given in (47), whilst we may write 



X2 : fJLo : y.2 = dx : dy : (Ax + By^dx + (Bx + Cy)dy+ . . . 



SubstitutlDg in (53) and equating coefficients of dx, dy, we find 



1 / A I -D I \ 7 r \ d't, , du , du \ 



u + {Ax + By+ . . . .)iv = l-{ Xi— + Ati-^+ »'i-^ 



L dx ay dz 



+ (Ax + By + 



v + (Bv+Cj + 



+ (Bx + Cy + 



dy ' ' dz 

 , /" .. dw dw dw\ 1 

 A^^d^+'-'Ty + '^d^j! 



dy ' \lz 

 dv 



. ^w = I < Xi^j-\- fi 



dy dz 

 -. f . dw , dw , dw\ T 

 \^^dx^''-dy+''^dzj\ I 



(54) 



In these equations u, v, w, &c., denote the values of these quantities at 

 the point (a;, ?/), and must be expanded in terms of a-, y. Performing the 

 expansions and equating coefficients of x, y, we get the following four 

 relations : — 



dit 



dx \ dx] dy ' dxdz ' dz J 



du / -n^^ p '^^^* ^^^ -R '^^\ 



dy \ dx dy dydz dz ) 



^ = l(-A *^-B ^^+ ^ + B M 

 dx \ dx dy dxdz dz ) 



lio J / . du -r, du , d-u , A dw\ \ 



dy _ / dy dv d^v dw\ 



dy ~ \ dx~ dy dydz dz J 



(55) 



If we neglect lA, IB, ZC as before, these equations combined with the 

 equation of continuity 



