392 Dr. Oliver Lodge on Opacity. 



while 



giving the solution 



F=F ,--^cos j p(j-^-). . . (8) 



This expresses the transmission of light through imperfect 

 insulators, and is the case specially applied by Maxwell to cal- 

 culations of opacity. Its form serves likewise for telegraphic 

 signals or Hertz waves transmitted by a highly-conducting 

 aerial wire ; the damping, if any, is independent of frequency 

 and there is true undistorted wave-propagation at velocity 

 v = 1/ VLB ; the constants belonging to unit length of the wire. 

 The current (or potential) at any time and place is 



iu- — 



C = C e-2Lv cosp(t— x vLS). ... (9) 



The other extreme case, that of diffusion, represented by 

 equation (2), is analogous to the well-known transmission of 

 slow signals by Atlantic cables, that is by long cables where 

 resistance and capacity are predominant, giving the so-called 

 KR law (only that I will write it RS), 



C = C oe - 7(l?,RS)x cos{^-v(^RS) ( r}; . . (10) 



wherefore the damping distance in a cable is 



#Q 



-\/Grs) 



Thus, in comparing the cable case with the penetration of 

 waves into a conductor and with the case of thermal con- 

 duction, the following quantities correspond : 



2W 2o- ? 2k' 



cp is the heat-capacity per unit volume, S is the electric 

 capacity per unit length ; k is the thermal conductivity per 

 unit volume, 1/R is the electric conductance per unit length. 

 So these agree exactly ; but in the middle case, that of waves 

 entering a conductor, there is a notable inversion, representing 

 a real physical fact. 4z7Tfju may be called the density and may 

 be compared with p or with 1/S, that is with elasticity-hv 2 ; 

 but a is the resistance per unit volume instead of the con- 

 ductance. The reason of course is that whereas good con- 

 ductivity helps the cable-signals or the heat along, it by no 

 means helps the waves into the conductor. Conductivity aids 



