96# Dr. G. Breit on the Effective Capacity of 



Hence the charge is distributed as if 



9 " 4tt dy 2 

 were its average density. 



The above treatment applies to the inside of the coil. 

 The contour of the cross section needs special consideration. 

 Let A B (fig. 5) be a small part of this contour. Draw the 



Fig. 5 — Structure of multilayer coil near edge. 



O O O ( 



O O 



o o 



OOOOOOOQOO 



o~"o b o — d~6~~o~ o ~i o~ o' o 



parallelogram EFGH with sides EF, GH parallel to AB, and 

 with GF, HE parallel to the layers of the winding. Make 

 GA sufficiently large to obtain a field along GH which is 

 the same as that at similarly situated points G 2 , H l5 inside 

 the c©il. Make EA sufficiently large to obliterate the irre- 

 gularities in the field caused by the individual wires. Finally 



FTTT 

 make -t-ti large. Suppose in the space outside the coil 



a solution of Laplace's equation has been found which at the 

 contour AB becomes equal to the average potential. Then 

 it is clear that at EF this solution gives the actual value of 

 the potential to within the small irregularities which are 

 caused by the individual wires. If V is this potential and 

 K the dielectric constant of the medium outside the cross 

 section of the coil, then letting 



K = 8-989 xlO 11 /^, 

 the quantity 



4-7T ~dn 

 is the component of the electric displacement perpendicular 

 to FE in the direction of DM. The symbol ^— denotes 

 here the directional derivative along DM. Hence, if a 



