Lii/Iit by I asymmetrical Atoms and Molecules. 397 

 in all directions the average values are as follows : — 



1,2 = 4> Zy(«^ 3 + b ~ * + c - a 2 ) =/ =p 4 / Z 2 , say j 



30 



** = - Zy (3(a 2 4 6 2 + c 2 ) + 2ab + 2ac + 2bc) =p 4 gZ 2 ; 



fy = hk= jL=Q. 



The energy of the scattered liglit per unit volume at P is 

 thus equal to fc / 



1 2 



1 6" 



since / and g are positive quantities, this expression cannot 

 vanish whatever may be the values of I, ??i, n unless f~0, 

 i. e. unless a = b — c : this requires the system of electrons to 

 be quite symmetrical. 



We may write the expression for the energy in the 

 scattered light in the form 



where 3 is the angle between the direction in which the 

 scattered light is observed and the direction of the electric 

 force in the incident light. 



Since g—f is positive, the energy is a minimum when 

 = and a maximum when 6 — ir\2. 



The ratio of the minimum to the maximum energy is 

 2// (/+.</) ; this is equal to 



2 a? + }? + c ?-ab-ac-bc) m 



If a, b, c are positive the greatest value for this ratio 

 is 1/2 when ab -f ac -+- be == ; so that two out of the three 

 quantities a, b, c must vanish. When the incident light 

 has the same period as one of the free vibrations of the 

 atom, mp 2 will equal one of the three quantities A, B, C, 

 so that either a, b, c will be infinite : in this case the 

 minimum value of the intensity is one-half the maximum 

 value. For still greater frequencies the values of one 

 or more of the quantities a, b, c might be negative, and 

 in such a case the minimum intensity might be more than 

 half the maximum. 



Hitherto we have been considering polarized light. If 

 the incident light is not polarized the intensity of the light 

 scattered in any direction can be found as follows : — Let 

 01 be the direction of the incident light, OP that of the 



