Multilayer Coils loitli Square and Circular Section. 985 

 from M(y), which is readily seen to be 



because the e.m.f. induced between two layers is pro- 

 portional to the area enclosed by the layers, so that 

 remembering (26 a) 



M W= M(,)J = ^[cos(, + -) 



-2p s cos{(4s-l>-|}]. . (30) 



Care must now be exercised to differentiate between the 

 four sides of the square. In formula (30) it was assumed 

 that each layer of the coil is considered once. For this 

 reason the expression ot(v) given in (29) must be modified 

 because u(v) refers separately to all values of v, and, 

 therefore, does not combine the charges on the side for 



which —<v<0 with the equal and similarly situated 

 charges on the side for which — < v < it. Thus it is 

 necessary to double «(V) as given by (29), and to discuss 



37T 



only the range of values of v between + -«- and +27T. 



In addition, of course, the charges on the face (see fig. 11) 



(v = 0, v = -~\ as we ll as those on lv~ir,v = -x-) must be 



computed. These charges are collected on the outside 

 layer, and have simply the effect of a capacity across the 

 whole coil. Thus the effect of the charges on the surface 

 divides itself into two. The first of these is that of the 

 charges on the faces y=+a. The second is that on the 

 faces a?= +a. The contribution of the first to C is denoted 

 by C " and that of the second by C "'. The computation 

 of Co' 7 ' will be effected first, and then C " will also be 

 obtained. 



For C '" the formula 



J 3ir L 1 Sir L- I 



holds, where, as has been shown in the preceding paragraph, 



