of Ether Waves in Air. 787 



d 

 second in each cubic centimetre, -j (Nmic) . Ordinarily, in 



such an expression, speed is the variable; but here w is a 

 terminal velocity, which must ultimately be attained by all 

 the fresh matter encountered, so N is the variable ; and 

 dN/dt signifies the number of ions continually produced by 

 extraneous causes in each c.c. per second. Hence our 



equation is 



dF dN 



dz at 



m 2 ' 2ttv 



'0 



•Or the wave energy-density remaining, after a journey of 

 length 2, is 



p=p <T*o. 



It must here be remembered that the relevant variation of 

 P has nothing to do with its natural decrease with distance 

 as a function of r, but represents solely its gradual diminu- 

 tion by absorption in successive layers, in geometrical pro- 

 gression. Hence the distance needed to reduce the wave 

 energy per c.c, or the momentum per second per square 

 centimetre, to l/eth of the value it would otherwise have 

 bad at any given place, is £ > where 



9, 



iTTV 711 

 '0 = AT „„*\2 > 



N/xA- 



(6) 



which is of length dimension, as it ought to be. We see 

 that it will be shorter for electrons than for any other kind 

 of ions, and that the absorption will vary with the square of 

 the wave-length. 



To get an idea of its value we can remember 



that fie 2 \m 2 is of the order 10 u c.g.s., for electrons, 



that v = 3x 10 10 centimetres per second, 



that m is of the order 10 -27 grammes, 

 and that in practice \ may be anything from 100 metres to 

 10 kilometres. 



Taking these two extreme cases as typical ; and assuming, 

 as a moderate estimate, that 10,000 electrons are liberated 

 by sunshine or other agency, per c.c. per second, all along the 

 effective path of the wave; the distance required for etherial- 

 wave-energy to fall to 1/^th of the value it would otherwise have 



6ttx10 23 

 had is z = " ^ 2 — centimetres, or 20xl0 19 /A, 2 . 



