388 Dr. Oliver Lodge on Opacity. 



reduce the result at the 16 frequency to insignificance (each 

 55-metre-layer reducing the energy to \ of what entered it) ; 

 but if the frequency were, say, 400 per second instead of 16 

 it would be five times more damped, and the damping thick- 

 ness (the depth reducing the amplitude in the ratio e : 1) 

 would in that case be only eleven metres. 



It is clear that in a sea 10 fathoms (or say 20 metres) 

 deep the failure to inductively operate a "call " responding to 

 a frequency of 1 6 per second was not due to the screening effect 

 of sea-water *. 



Maxwell, however, is more interested in the propagation 

 of actual light, that is to say, in waves whose frequency is 

 about 5 x 10 u per second ; and for that he evidently does 

 not consider that the simple diffusion theory is suitable. It 

 certainly is not applicable to light passing through so feeble 

 a conductor as salt water. He attends mainly therefore to 

 the other and more interesting case, where electric inductive- 

 capacity predominates over the damping effect of conduc- 

 tivity, and where true waves therefore advance with an 

 approximately definite velocity 



though it is to be noted that the slight sorting out of waves 

 of different frequency, called dispersion, is an approximation 

 to the case of pure diffusion where the speed is as the square 

 root of the frequency, and is accompanied, moreover, as it 

 ought to be, by a certain amount of differential or selective 

 absorption. 



To treat the case of waves in a conductor, the same damping 

 term as before has to be added to the ordinary wave equation, 

 and so we have 



£-*£+?£ m 



Taking ¥ =e ipt again, it may be written 



g=(-^ + ^)F, .... (*) 

 the same form as equation (1 ; ) ; so the solution is again 



Y = e -Q*+ipt } 



* I learn that the ship supporting the secondary cable was of metal, 

 and that the primary or submerged cable was sheathed in uninsulated 

 metal, viz. in iron, which would no doubt be practically short-circuited 

 by the sea-water. Opacity of the medium is in that case a superfluous 

 explanation of the failure, since a closed secondary existed close to both 

 sending and receiving circuit. 



