of Ether Waves in Air. 781 



mobility on which conducting power, or any influence which 

 they could exert, must depend. Thus whether ions act 

 by ordinary conductivity, or in some other way such as is 

 considered below, we can at least say that opacity and con- 

 ductivity are similarly affected, both being reduced by the 

 presence of mist. 



Going back to the opacity equation, pp. 776, 7, and its two 

 cases there considered, there is one intermediate possibility ; 

 namely that the resistivity of the medium might sometimes 

 have a value such as would make the critical number neither 

 large nor small, but say unity. We may consider what will 

 happen then. 



If krrjcrpK. is to be 1, it follows that <r = 2fjLv\ ; or, for a 

 kilometre wave, that a is of the order 



6 X 10 15 /jl sq. centimetres per second. 



This appears a very possible value for rarefied air ; — indeed 

 Dr. Schuster has estimated that, at a height of 100 kilometres, 

 atmospheric conductivity is of the order 10 -13 c.g.s., equi- 

 valent to 10,000 ohms per c.c, in order to satisfy the require- 

 ments of his theory of magnetic variations ; — and in that case 

 we must use the general solution 



F = F e~ ar cos(pt — fir) 

 Or calling the critical constant c, 



■-^{V(i+^-»}* 



while / e = ^| 2v /(l + c 2 ) + 2| i . 



These are general values ; so,' taking c unity, as the special 

 -case we are now considering, we get 



,8=^(2^2 + 2)^2-1^. 



Hence, with the intermediate value for <r, the distance for 

 reduction of amplitude to 1/eth is comparable with the wave- 

 length ; being, in the special case just written, about V3. 

 The absorption constant begins in this case to be inversely as 

 the root of the wave-length, and there is incipient departure 

 from true wave propagation. 



Any local approach to such atmospheric conductivity as 

 belongs to the intermediate case, — for instance by the stirring 



