of Ether Waves in Air. Ill 



But for a conductivity like that of sea-water (which may 

 well be reached aud considerably exceeded in the atmosphere, 

 -even without special ionization, by mere reduction of density, 

 -at the best conducting horizontal level — at least when the 

 electric force surpasses a certain critical intensity below 

 which even rarefied air must insulate unless ionized — ), 



say cr = 3 x 10 10 /n sq. centimetres per second, 

 the critical number, 



2v\ 2X 



aj/jL "™ 1 centimetre' 

 is certainly big ; and in that case the other or diffusion solu- 

 tion applies, namely 



.and the distance for reduction of amplitude to l/<?th of its 

 value would then depend on the frequency, for it is 



ri = \/(2^)=^\/(S) = \/( XX ^ centim -)- 

 For a 4 kilometre wave this distance is 1 metre ; and the 

 absorption constant varies inversely with the square root of 

 ~the wave-length. Differently sized waves, moreover, would 

 travel at different rates ; and accordingly the trouble of dis- 

 tortion, so familiar in cables, would be introduced by high 

 atmospheric conductivity. But we have no knowledge of 

 the actual existence of such conductivity except at great 

 elevation, where, if it formed a sharply defined smooth 

 horizontal layer it would be a help, not a hindrance, and 

 would assist in overcoming the curvature of the earth — 

 either for the mirage-like reason suggested by Dr. Eccles 

 or by still more simple reflexion. 



A law of absorption dependent on the inverse root of the 

 wave-length has been suggested by observation ; and such a 

 law indicates greater effective conductivity in the general 

 atmosphere than is usually considered likely. 



Connexion between Ionization and Conductivity. 



It may be convenient here to write out the connexion 

 between ionization and conductivity for air, as ordinarily 

 treated electrolytically. 



Let n be the number of ions of one sign per c.c. supposed 



equal, e the charge on each, and u ( = u-\-v) their combined 



velocities. current _ 



Ine intensity of current, ■ = i = neu. 



J area 



The dissociation ratio «/N we may call Jc, N being the 



