Forced Vibrations of Electromagnetic Systems. 151 

 from which we see that when 



and 



Zi 



(R+Lp)l {R+Lp)l 



are functions of ml, equation (89) finds the value of m* imme- 

 diately, i. e. not indirectly as functions of p. In all such 

 cases, therefore, we may advantageously have the general 

 solutions (80), (81) put into the realized form. They are 



v _ v 2e ^ (sin mz + tan cos mg)wte~g*(cos + q\~ ' sin) Ai . 



I * / d V ' ' ^ 



sec 2 0(m 2 + EK) ( 1 —cos 2 ml .. ,. tan ml ) 

 \ d(ml) J 



p_ p _ 2£o ^ (cos ms— tan sin mz)e -9, *K -jcos — (2s 2 X) -1 (X, 2 + g^) sin \\t 

 I * . same denominator 



where q, \, s , s 2 are as in (64), (65). The differentiation 

 shown in the denominator is to be performed upon the function 

 of ml to which tan ml is equated in (89) after reduction to the 

 form of such a function in the way explained ; and depends 

 upon Z thus, 



2 }, • • • (92) 



tan0=-m~ 1 (K + Sp)Z o , 

 sec 2 0=l+m- 2 Z o 2 (K + Sp; 



which are also functions of ml. It should be remarked that 

 the terms depending upon solitary roots, occurring in the 

 case m 2 = 0, are not represented in (90), (91). They must be 

 carefully attended to when they occur. 



Note A. 



An electromagnetic theory of light becomes a necessity, the 

 moment one realizes that ifc is the same medium that transmits 

 electromagnetic disturbances and those concerned in common 

 radiation. Hence the electromagnetic theory of Maxwell, the 

 essential part of which is that the vibrations of light are really 

 electromagnetic vibrations (whatever they may be), and which is 

 an undulatory theory, seems to possess far greater intrinsic pro- 

 bability than the undulatory theory, because that is not an electro- 

 magnetic theory. Adopting, then, Maxwell's notion, we see that 

 the only difference between the waves in telephony (apart from 

 the distortion and dissipation due to resistance) and light-waves is 

 in the wave-length ; and the fact that the speed, as calculated by 

 electromagnetic data, is the same as that of light, furnishes a 

 powerful argument in favour of the extreme relative simplicity of 



