ELECTROMAGNETIC THEORY 15 



equations (11) and (12) immediately apply but, at least at high 

 frequencies, the approximations introduced above to derive the tele- 

 graph equation are not legitimate. This is due to the geometry of 

 the conductor, and also to the fact that the impressed field is not 

 approximately concentrated but is distributed over the entire length 

 of the coil. It is intended to apply these equations to a detailed 

 study of this problem. In the meantime, however, it may be noted 

 that the current depends not only on the line integral of the impressed 

 electric intensity hut also on its mode of distribution along the length of 

 the coil. This fact may possibly have practical significance in the 

 design of coil antenna and their calibration at very short wave lengths. 



Appendix 



In the beginning of this paper, it was stated that the analysis applied 

 only to the case of conductors of unit permeability and specific induc- 

 tive capacity which obey Ohm's Law. The reason for this restriction 

 and the formal extension of the analysis to the more general case will 

 now be briefly discussed.^ 



Suppose that the conductor, instead of having the restricted proper- 

 ties noted above, obeys Ohm's Law but has a permeability n and 

 specific inductive capacity k which may differ from unity. 



The equation (1), 



E = E° - grad $ - iwA, (1) 



still holds, as do also the potential formulas (2) and (3) and the 

 formulas for the electric and magnetic intensities (4) and (5). The 

 relation 



— iwp = div u 



is also valid. 



The equation u — gE must, however, be modified in the following 

 manner. If we write 



47r 



4:TIJ. 



then the foregoing equations are correct, provided we substitute for 

 the equation u = gE the more general expression 



u = gE -\- iwP + curl M. 



'For a previous discussion, see "A Generalization of the Reciprocal Theorem," 

 B. S. T. J., July, 1924. 



