304 On Absorption and Dispersion. 



So that i£ the rether resistance is 2/ei, a free motion of 

 amplitude ar/Lt/4/c, which is large compared with c, is 

 maintained, and the rate of dissipation per molecule is 

 proportional to «V//f. 



Hence the ratio of the absorption per unit length to the 

 density is proportional to a 2 , that is, to the pressure : more 

 briefly, the absorption per unit length is proportional to the 

 square of the pressure. This simple quantitative relation 

 holds good, it must be remembered, only when a is small. 



The absorption being inversely proportional to /e, which is 

 very small, may be of considerable magnitude. 



While radiation of frequency fi/^ir is almost altogether 

 reflected, that of frequency (yu+n)/27r is only slowly absorbed. 

 Bv sufficient increase of pressure a might be brought to such 

 magnitude that both radiations would be transmitted with 

 comparable absorptions. This condition would be the most 

 favourable for the spectroscopic observation of the apparent 

 group resonance. 



2. If the solution (2) is carried to a higher order of approxi- 

 mation, we find that the amplitude of that part of the forced 

 motion which has the same period and phase as the forcing- 

 disturbance is 



{(jl— n) 2 — jbu 2 ' 



Tf therefore v is the velocity of transmission and V the 

 velocity in free aether, 



Sellmever's formula for complete transmission thus under- 

 goes modification when there is moderate absorption. 



The velocity regarded as a function of the frequency 

 exhibits a very rapid variation of small magnitude at the 

 frequency (/x — n)/27r ; there is therefore a definite limit to 

 the accuracy of interpolation methods of determining the 

 wave-length when there is absorption. 



Only the frequencies which correspond to the simple 

 normal oscillations, e. g. yLt/27r, give very large values for 1/v, 

 and that only when a is small. As u increases the velocities 

 for yLt/27r and (/x — ii)\2tt tend to become comparable. 

 Evidently the true normal frequencies might be distin- 

 guished through their property of selective refraction at low 

 pressure. 



3. Since normal motions always interact and the necessary 

 consequences are exhibited in the phenomena of radiating 



