790 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



A" 



For example, consider a coil whose mean radius is 27 cms. wound 

 with wire of diameter .06 cms. There is a maximum possible change 

 of 3.5 per cent for very high frequency in the self-inductance of a single 



turn, while in a coil of 716 turns 

 the total possible change is nearly 

 0.3 per cent. This is not a neg- 

 ligible amount, so that in standard 

 coils and work of precision it is 

 necessary to know what the cor- 

 rections are for any frequency. 



Derivation of the Formula. 



Consider an infinite circular 

 current sheet of thickness d, of 

 inside radius r x and outside r 2 . 



Let the symbols S ( ) and 

 V ( ) denote the scalar and vector 

 products respectively. V is the 

 Hamiltonian operator. W ( ) is 

 the same as curl ( ) or rot ( ), 

 while *SV ( ) is the same as 

 div ( ). 



By symmetry, the field inside 

 the coil is axial, and a function 

 of r alone, at any given time, 

 and on account of the coil being 

 infinite in length, the field is all 

 inside of it. 



In the dielectric, Maxwell's 

 equations are, if we neglect the 

 displacement current, 



FV#=0and SVH=0. (1) 



d 



Figure 1. 



From the second relation we find 

 that H is independent of z, and 



from the first relation, that it is independent of x andy; hence it is 



constant inside the coil, and for 



r < r x assume H = H e l 



(2) 



