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



If we take L = in this problem, we make r = oo, and 

 bring the whole of the waves into operation immediately. 

 (70) becomes 



c '=^(^) Vl, " 7 " ; • • • • <75) 



and similarly for C 2 , C 3 , &c. In this simplified form the 

 identity is that obtained by Sir W. Thomson* in connexion 

 with his theory of the submarine cable ; also discussed by 

 A. Cayley* and J. W. L. Glaisherf. 



In order to similarly represent the history of the establish- 

 ment of V , we require to use the series (53) or some equi- 

 valent. In other respects there is no difference. 



Whilst it is impossible not to admire the capacity possessed 

 by solutions in Fourier series to compactly sum up the effect 

 of an infinite series of successive solutions, it is greatly to be 

 regretted that the Fourier solutions themselves should be of 

 such difficult interpretation. Perhaps there will be discovered 

 some practical way of analyzing them into easily interpretable 

 forms. 



Some special cases of (66), (67) are worthy of notice. 

 Thus Y is established in the same way when K = as when 

 K = 0, provided the value of K/S in the first case be the same 

 as that of Pt/L in the second. Calling this value 2q, we have 

 in both cases 



But the current is established in quite different manners. 

 When it is K that is zero, (71) is the solution ; but if R vanish 

 instead, then (67) gives 



V and C express the first approximation to a complete theory. Thus the 

 wires are assumed to be instantaneously penetrated by the magnetic in- 

 duction as a wave passes over their surfaces, as if the conductors were 

 infinitely thin sheets of the same resistance. It is only a very partial 

 remedy to divide a wire into several thinner wires, unless we at the same 

 time widely separate them. If kept quite close it would, with copper, be 

 no remedy at all. 



* Math, and Physical Papers, vol. ii. Art. lxxii. ; with Note by A. 

 Cayley. 



f Phil. Mag. June 1874. 



