Theory of Surface Tension. 651 



found to be 



+ *!" ("I 5 + *•«? -B.D.-BJ1.1 



>• W 



Y= . , . , 



Z = . . . , 



where X, Y, Z are the components of the impressed force 

 per unit volume. 



Now, suppose that the layer of transition is not placed 

 under an external electric field, so that we may take the 

 component electric force parallel to the surface o~ = const., 

 which passes through the point under consideration, to 

 vanish. 



When the capillary layer is not horizontal, there will be a 

 component of the electric force parallel to the layer, due to 

 the effect of gravity, bat this is so small that for all practical 

 purposes it may be neglected. The electric displacement 

 outside the layer is, by the same reasoning, taken to be zero. 



Let us consider a line orthogonal to the series of surfaces 

 ct— const, and take two points P' and P" on this line, 

 P / being in the first fluid and P" in the second, both being- 

 very near to the transition layer ; and let ds be the element 

 of the line. Then it immediately follows from (4) that the 

 surface tension is 



<r,|^-EDW . . . (5) 



do's J 



-j"( 



where cr s denotes the magnitude*, of the vector (<r r , a^, ov), 

 and E and D are the electric force and electric displacement 

 respectively, and the integral is to be taken from P' to P". 

 By dint of these suppositions, the position of P' along the 

 curve does not alter the value of the right-hand side of (5) 

 so long as P' lies outside the transition layer. 



Now suppose that the axis of x is vertical, and that the 

 surfaces <r = const. are horizontal planes and that the variables 

 are independent of y and z. In this case we may write (5) 

 in the form 



T =J"('-S;- ED )* 



(6) 



