776 Sir Oliver Lodge on the Transmission 



constitute a better reflector than if it were gradual ; and if it 

 were not sudden enough, either greater power or longer- 

 wave-length would help to overcome the difficulty. If, 

 however, under the influence of rising sunlight or heat the 

 reflecting layer should become puckered, so as to offer some- 

 thing nearer normal incidence to approaching waves, — 

 thereby letting them escape into space, — no increase of 

 power alone will do very much towards remedying the evil ;. 

 and increased wave-length may become a necessity. 



To examine this whole question further : — 



An absorbed plane wave equation is 



d 2 F _ x cPF 47r/*dF 



dr* ~ * dt 2 + a dt ; 

 and for a solution there are two extreme cases according to- 

 whether a critical number 



4tt 4ir«yr 2v\ 



or ^ — or 



<rpK 27ra- ajfju 



is small or large. (See for instance Lodge " On Opacity " in 

 Phil. Mag. for April, 1899.) 



Now the ionization of sun-lighted air under some con- 

 ditions has been estimated as 10 ~ 12 of the total number of 

 molecules present : if so it will have a specific resistivity 



<r=2 x 10 20 fju sq. centimetres per second. 



In that case the critical number will be small, being of the 

 order 10 ~ 5 for a wave comparable with a kilometre in length. 

 The form of solution applicable in that case is 



2irnv 



~F = F e °" co$(inr— pt). 



So the distance required to reduce the amplitude of these 

 true waves to l/<?th would then be independent of the 

 frequency, i. e. would be the same for waves of any length, 

 and its value is 



ar 



r t = 



27T/JLV ' 



Inserting the above estimate of <r for ionized air, this 



comes out 



1*8 x 10 20 

 ^i= t^ — tt^7\ =10 9 centimetres 

 lb x 10 1U 



= 10,000 kilometres. 



The ionization and conductivity of air encountered by the 

 waves must therefore manifestly be greater than that — 

 i. e. the resistivity must be smaller than 10 20 c.g.s. — if the 

 atmosphere is to stop waves by sheer opacity. 



