992 On the Effective Capacity of Multilayer Coils. 



indefinite. If the cross section is symmetrical about a line 

 through its centroid parallel to the axis, I may be taken 

 simply as the perimeter of the turn through the centroid 

 because the mean between the perimeters of two turns 

 symmetrically situated as to the centroid is that value of I, 

 and because the charge density on these turns is the same. 



Summary. 



A method of calculating the effective capacity of multi- 

 layer coils has been given. It has been shown that the 

 average density of volume and surface charge may be 

 obtained in terms of a constant K e which depends on the 

 spacing between the turns of the coil and the insulation 

 used. This constant is analogous to the dielectric constant 

 of a homogeneous medium. 



The method has been applied to the case of a coil having 

 a circular section, and also to the case of a coil with a square 

 section. 



The results are : 



C = (0*08453K e + 0-08230 K )Z micromicrofarads 



for the case of a coil with circular section 

 and 



C = (0-0886 K e + 0-1050 K )Z micromicrofarads 



for the case of a coil with square section. 



Here K is the dielectric constant of the medium outside 

 the coil, K e is the effective dielectric constant of the medium 

 inside the coil, I is the perimeter of a single turn passing the 

 centre of the cross section. In both cases, the diameter of 

 the coil is taken to be large in comparison with the maximum 

 dimension of the cross section, the winding is assumed to 

 be close, the number of turns large, and the coil itself 

 is taken to be insulated from all objects except the tuning- 

 condenser. 



Bureau of Standards, 



Washington, D.C., 

 June 25, 1921. 



