Multilayer Coils with Square and Circular Section. 991 

 Substituting (40), (39), (37), (37 a) into (31), 



Co,, -^(^^[-~ i + ' 371 + ' 858 + i(() ' 198)2] 



= 0-0412a; /. . (41) 



Now substituting (38), (41), (20) into 



it follows that 



C 9 = 0-0796*eZ + 0-0944tf Z, 



C = 10- 12 [0'886K^ + 0-1050K Z] farads 



= [0*0886 K e Z + 0-1050 K /] micromicrofarads. (42) 



Both (18') and (42) involve the constant K e . As stated 

 previously, a theoretical derivation of K c is, in general, 

 difficult. However, an experimental investigation is possible. 

 For this purpose, it is only necessary to introduce a slab of 

 the complex medium between two plates of a condenser and 

 measure the increase in capacity caused thereby, treating 

 the slab as if it were a homogeneous dielectric. Of course, 

 care must be taken to have the layers of the complex medium 

 parallel to the condenser plates. One must also remember 

 that the mean value treatment can be applied only in the 

 case of coils having a large number of turns per layer. 



In some special cases the value of K e may be obtained 

 without difficulty. Such is the case, for example, of a 

 winding such as shown in fig. 6, when adjacent turns almost 

 touch. In such a case the effective dielectric constant K e is 



pK, where K is the dielectric constant of the medium 



between turns and where h is the distance between homo- 

 logous points of two layers, while It is the shortest distance 

 between two layers. This principle may be extended also 

 to the case of wires of circular cross section if the distance 

 between layers is large and the winding of each layer is 

 close, provided each layer is replaced by an equivalent layer 

 of uniform thickness, this thickness being made equal to 

 the average double ordinate of the circle. 



A few words must be said as to the meaning of I in (18') 

 and (42). Strictly speaking, the derivation given applies 

 only to the case when the perimeter of one turn is the same 

 as that of any other. However, the considerations as to 

 the distribution of charge will apply approximately even if 

 the turns are not of equal perimeter. In this case I becomes 



