Dr. Oliver Lodge on Opacity. 413 



An opaque slab transmits Sh 2 e~ 2al of the incident light 

 energy ; its first boundary transmits only 2nh 2 . The second 

 or emergent boundary doubles the amplitude. Taken in 

 connexion with the facts of selective absorption and the 

 timing of molecules to vibrations of certain frequency, I 

 think that this fact can hardly be without influence on the 

 green transparency of gold-leaf. 



Appendix I. 



Mr. Heaviside's Note on Electrical Waves in Sea- Water. 



[Contributed to a discussion at the Physical Society in June 1897 : 

 see Mr. Whitehead's paper, Phil. Mag. August 1897.] 



" To find the attenuation suffered by electrical waves through 

 the conductance of sea-water, the first thing is to ascertain 

 whether, at the frequency proposed, the conductance is paramount, 

 or the permittance, or whether both must be counted. 



"It is not necessary to investigate the problem for any particular 

 form of circuit from which the waves proceed. The attenuating 

 factor for plane waves, due to Maxwell, is sufficient. If its validity 

 be questioned for circuits in general, then it is enough to take the 

 case of a simply-periodic point source in a conducting dielectric 

 (' Electrical Papers,' vol. ii. p. 422, § 29). The attenuating constant 

 is the same, viz. (equation (199) loc cit.) : — 



where n/2-ir is the frequency, Tc the conductivity, c the permittivity, 

 and v=(fxc)~i, fi being the inductivity. 



" The attenuator is then e~ n \ r at distance r from the source, as 

 in plane waves, disregarding variations due to natural spreading. 

 It is thus proved for any circuit of moderate size compared with 

 the wave-length, from which simply periodic waves spread. 



" The formula must be used in general, with the best values of h 

 and c procurable. But with long waves it is pretty certain that the 

 conductance is sufficient to make 47rl-/cn large. Say with common- 

 salt-solution ^ = (30 11 )~ 1 , then 



4ttI: _ 2kjxv 2 

 en ~~ f 

 if /is the frequency. This is large unless /is large, whether we 

 assume the specific c/c to have the very large value 80 or the 

 smaller value effectively concerned with light waves. We then 

 reduce n x to 



n 1 =(2n t xJc7rf=:2r(fx7cff, 



as in a pure conductor. 



" This is practically true perhaps even with Hertzian waves, of 

 which the attenuation has been measured in common- salt-solution 

 by P. Zeeman. If then I— ] =30 n [and if the frequency is 300 per 

 second] we get n x = about -^nnr 



Phil. Mag. S. 5. Vol. 47. No. 287. April 1899. 2 F 



