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XXX. On Absorption and Dispersion *. 

 By Andrew Stephenson f. 



1. "VXTHILE the ordinary theory of transmission through 

 TT a medium is applicable only to the limiting cases 

 of zero absorption and total reflexion, it has long been 

 recognized that in transmitted light the dissipation of energy 

 is not in general wholly due to scattering. It is evident 

 that such dissipation is characteristic of a medium in the 

 molecule of which the normal motions of the visible spectrum 

 are subject to the influence of other normal motions of 

 relatively small frequency. 



Even with only a few slow modifying vibrations the 

 spectrum may be of considerable complexity, since each 

 element of freedom of higher frequency may contribute a 

 large number of simple components in its free motion {. If 

 now a train of frequency corresponding to any minor com- 

 ponent is passing through the medium, it will generate a 

 free oscillation in the coordinate to which the component is 

 due, and since only a small part of the energy of the free 

 oscillation belongs to the component, there must follow a 

 dissipation of energy through emission. A steady state will 

 result when the energy emitted by the coordinate in its free 

 motion is equal to that gained from the incident train. 



If the equation of motion of the coordinate affected is 



z + {/j? + 2xfin cos (nt + e)}z=0, 



where n/fi is small, the amount of the absorption for the 

 frequency (^±n)/2ir is simply found when a. is small, not 

 greater than 0*1 say. 

 The free motion is 



2 = cos^ + J«{cos(/* — nt— e) —cos (ji + n t + e)}, 

 and the forced motion given by 



z + {fj? + 2dfjLn cos (nt + e) }z = r> 2 sin p— n t . . (1) 



is 



z= —\acfxt [cos (fit + e) + ^«{cos fi — nt — cos (fi+nt + 2e) }] 



1 fi . 



— ,r c -sin//,— nt. . : . . . (2) 



2 n r v / 



* Cf. " On Displacement in the Spectrum due to Pressure " Phil 

 Mag. October 1910, p. 788. 



t Communicated by the Author. 



% "On the Forcing of Oscillations by Disturbances of Different 

 Frequencies," § 3, Phil. Mag. July 1907, p. 115. 



