966 Dr. G. Brei't on the Effective Capacity of 



This fact is truo independently of the shape of the contour, 

 ABCD. i s 



In discussing the effective capacity (loc. cit.) of a singler 

 layer coil it was only necessary to find a solution of Laplace's 

 equation which became equal to the potential of the coil at, 

 the coil and which vanished at infinity. The same is true in, 

 the case of multilayer coils. 



However, it is not feasible to look for a solution of 

 Laplace's equations in the space between the wires. This 

 solution depends on the total number of wires, on the 

 spacing, insulation, etc. A rigorous solution of the problem 

 offers considerable mathematical difficulties. For this reason 

 a different course is followed in this paper. Instead of 

 studying the small and insignificant variations of potential 

 between the layers, a mean-value treatment of the changes 

 in the field is given. This is, to be sure, approximate. 

 However, if the assumptions (1), (2), (3), (4) are realized, 

 the approximation is justified. 



A few words must now be said as to the treatment, 

 by a method of mean values, of the medium in the cross 

 section of the coil. 



As stated above, the potential of one layer such as Ei E 2 

 (fig. 3) can be considered as constant. The potential 

 between two consecutive layers does not vary considerably. 

 It is legitimate, therefore, to speak of the average potential 

 at some point in the cross section, meaning thereby the 

 potential of the layer passing through the point or nearest 

 to it. As shown above, this average potential is simply the 

 potential of (1) plus the e.m.f. induced in the area E 1 E 2 (1) 

 (fig. 3), which is proportional to the area E x E 2 (1). 



From a knowledge of the average potential, the total 

 amount of charge within a given region in the cross section 

 can be obtained by the use of Gauss's Theorem. The same 

 theorem will be used to discuss the charge collecting near 

 the edges of the layers. 



Let the rectangle ABCD (fig. 4) be the region in question. 

 Make all the sides lie entirely outside the wires and between 

 the layers as well as the wires of each layer. Now Gauss's 

 theorem will be applied to the volume enclosed by a rect- 

 angular prism having unit height and having ABCD for its 

 cross section. The layers of the coil are here taken as 

 parallel to AB. Therefore, by symmetry, there is no flux 

 of the electric intensity across AD and BC. Neither is 

 there any flux across the base— i. e., the rectangle ABCD. 

 Hence the only flux is across the faces whose traces are 

 here shown as AB and CD. 



