402 Dr. Oliver Lodge on Opacity. 



red, is all stopped by a thickness less than half a wave-length. 

 The green light may conceivably be due to atoms vibrating 

 fairly in concordance, and not calling out the conducting 

 opacity of the metal. If the calculated opacity, notwith- 

 standing this, is still too great, it is no use assuming a higher 

 conductivity at higher frequency, for that would act the 

 wrong way. What must be assumed is either some special 

 molecular dispersion theory, or else greater specific resistance 

 for oscillations of the frequency which get through ; nor 

 must the imaginative suggestion made immediately below 

 equation (13) be altogether lost sight of. 



There is, however, the possibility mentioned above that the 

 relative specific inductive capacity of gold, K/K , if a 

 meaning can be attached to it, may be very large, perhaps 

 (though very improbably, see Drude, Wied. Ann. vol. xxxix. 

 p. 481) comparable with 1800. Suppose for a moment that 

 it is equal to 1800 ; then the value of the critical quantity (7) 

 is 1 and the value of a is 



= 19xl0 5 , 



which reduces the calculated opacity considerably, though 

 still not enough. 



In general, calling K/K = r, and writing the critical 



number — — as h/c. we have 

 ape 



% a 2 _ I a 2 //3 2 = XV/27T 2 = ^ (7j2 _j_ c 2) _ c . 



so that aX/'Iir ranges from s/ ^1l when h/c is big, to \h/^ c 

 when h/c is small. 



Writing the critical number h/c as tan e, the general value 

 of a is given by 



aX=7r \/2c(sece — 1) (14) 



This is the ratio of the wave-length in air to the damping 

 distance in the material in general ; meaning by " the damp- 

 ing distance " the thickness which reduces the amplitude in 

 the ratio e : 1. (14) represents expression (5) ; compare 

 with (120- 



Theory of a Film. 



So far nothing has been said about the limitation of the 

 medium in space, or the effect of a boundary, but quite 

 recently Mr. Heaviside has called my attention to a special 



