402 Mr. 0. Heaviside on Electromagnetic Waves, and the 



The realization is a little troublesome on account of this p*- 

 The result is that the uniform alternating field of impressed force 

 of intensity , > N 



J (/i) COS 71*, 



gives rise to the internal solution 



(in) H=(^)*^^{(A + B)cosn*+(A-B)sin«*}, (191) 



where A and B are the functions of r expressed by 



B =^'-°{(^-2T a + 2^) COS -( 1 - 2 i + ^) sin ]^-' \ 



^_ fi -x(r+a 



Equation (191) showing the iuternal H, the external is got 

 by exchanging a and r in the functions A and B. 



Now xa is easily made large, in a good conductor ; then, 

 anywhere near the boundary, (r = a), we have 



^ =e -x(a-r) cog gcQz—r), \ 



-B = 6-*°-^ sin x(a-r), J ; ' * * * (194) 

 and (191) becomes 



(in) H=g) 4 if^Le-^.oo S {nt-,(a-r)--l}. { m } 



The wave-length X is 



x -(£t d*o 



Thus, in copper, a frequency of 1600 to 1700 makes X= 

 1 centim. Both X and the attenuation-rate depend inversely 

 on the square roots of the inductivity, conductivity, and 

 frequency, whereas the amplitude varies directly as the 

 square root of the conductivity, and inversely as the square 

 roots of the others. 



• To verify that very great frequency ultimately limits the 

 disturbance to the vortex line of e when there is but one, we 

 may use the last solution to construct that due to a sheet of 

 impressed force 



cosn«2^mQm 



