272 Methods for the Solution of Special Problems [CH. vm 



Example II. Send of a Lei/den Jar. 



329. The method of conjugate functions enables us to approximate to 

 the correction required in the formula for the capacity of a Leyden Jar, on 

 account of the presence of the sharp bend in the plates. 



-Is 



FIG. 92. 



As a preliminary, let us find the capacity of a two-dimensional condenser 

 formed of two conductors, each of which consists of an infinite plate, bent 

 into an L-shape, the two L's being fitted into one another as in fig. 92. 



Let us assume the five points A, B, (CD), E, F to be f= oo, a, 0, 

 + b, + oo respectively, and let us for convenience suppose the potential 

 difference which occurs on passing through the value f= to be TT. Then 

 the transformation is 



- 1 - * 



where W= log f (cf. 326). 



To integrate, we put u = (+)"" *(?&)> and obtain 



(246), 



where (7 is a constant of integration. 



To make C vanish, we must have 5 = when u 

 We shall accordingly take E as origin, so that (7=0. 



0, i.e. at the point E. 



