Capacity of Electrolytes. 351 



accounted for by the water present in this. Pure ether has 

 a much smaller value than that given above. 



This method is capable of giving tolerably accurate results, 

 although it cannot be used with heavy oils ; for the force to 

 be measured is small and the volume of the cylinders is con- 

 siderable; hence the latter move very slowly through a quite 

 viscous liquid. The method given in the paper already 

 referred to is applicable to such liquids, and is perhaps more 

 convenient for all. 



Mathematical Theory. 



IV. An exact solution of this problem would be difficult to 

 obtain. An approximate solution may be found as follows. 

 Maxwell (vol. i. ch. v.) gives an expression for the mechanical 

 action between two electrical systems in terms of a surface 

 integral taken over one of them. The value of the Y-com- 

 ponent of the force is 



B = S ( l P*y + m Pyy + n P*J ds > 

 where ds is an element of the closed surface of one system and 

 Z, ra, n are direction-cosines of the normal to ds. Writing V 

 instead of y{r for the potential, the values of the ^>'s are 



= 1 ^L d JL 



P *y 47T " dy * da' 



P yy~~%Tr\\dy) \dz) \da) S 



= ±dV dV 

 Vz y 4tt dy ' da' 

 In the present case, if the axis of Z be taken parallel to the 



dV 

 axis of the cylinder, — = 0, and we have 



since ds = ~Lpdd, L being the length of the cylinder and p 

 its radius. K" is the specific inductive capacity of the medium, 

 assumed above to be unity. Using r and instead of a and 

 y, this expression becomes 



^ LK" Ci ,(dV\ 2 cos0 /dY\ 2 o sin0 dV dV \ , a fT> , 



(Fig. 3.) 



Since two parallel lines oppositely charged have equipoten- 

 tial surfaces which are circular cylinders more and more 

 excentric as they become larger (see figure 1), we can replace 

 our two parallel circular cylinders by two lines M, N, which 



