Dr. Oliver Lodge on Opacity. 389 



with Q 2 equal to the coefficient of F in (3') . Maxwell, however, 

 does not happen to extract the square root of this quantity, 

 but, assuming the answer to be of the form (for a simply 

 harmonic disturbance) [modifying his letters, vol. ii. § 798] 



e~™ cos (pt — qx), 



he differentiates and equates coefficients, thus getting 



q 2 — r 2 = fJbKp 2 , 2rq= — , 



as the conditions enabling it to satisfy the differential equa- 

 tion. This of course gives for the logarithmic decrement, 

 or coefficient of absorption, 



2jrji .p 



? * 

 p/q being precisely the velocity of propagation of the train of 



waves. Though not exactly equal- to 1/ V/llK, the true velo- 

 city of wave propagation, except as a first approximation, in 

 an absorbing medium, yet practically this velocity p/q or X/T 

 is independent of the frequency except in strongly absorbent 

 substances where there are dispersional complications ; and 

 so the damping is_, in simple cases, practically independent 

 of the frequency too. 



With this simple velocity in mind Maxwell proceeds to 

 apply his theory numerically to gold-leaf, calculating its 

 theoretical transparency, and finding, as every one knows, 

 that it comes out discordant with experiment, being out of 

 all comparison * smaller than what experiment gives. 



But then it is somewhat surprising to find gold treated as 

 a substance in which conductivity does not predominate over 

 specific inductive capacity. 



The differential equation is quite general and applies to 

 any substance, and since the solution given is a true solu- 

 tion, it too must apply to any substance when properly 

 interpreted ; but writing it in the form just given does not 

 suggest the full and complete solution. It seems to apply 

 only to slightly damped waves, and indeed, Maxwell seems to 

 consider it desirable to rewrite the original equation with omis- 

 sion of K, for the purpose of dealing with good conductors. 



By a slip, however, he treats gold for the moment as if it 

 belonged to the category of poor conductors, and as if ab- 

 sorption in a thickness such as gold-leaf could be treated as 

 a moderate damping of otherwise progressive waves. 



* The fraction representing the calculated transmission by a film half 

 a wave thick has two thousand digits in its denominator : see below. 



