46 Mr. S. B. McLaren on the 



It follows that pApBdY A dYB is a particular value of <2N in 

 (3) and (4), and since (7) gives the general solution 



f(H A ) x/(Hb) 



is by (6) a function of JJa + JETb, the total energy. 



Hence f(H) varies as e~ hH , and we have the result (5). 



§ 3. Interaction of Matter and Radiation. 



The motion of the material system and the distribution 

 represented by (5) are disturbed by the presence of radiation. 

 At any instant the actual values a^ + Sffj, &c. of the co- 

 ordinates differ slightly from jj 1} x 2 ... a n , the coordinates in 

 what I shall call the undisturbed motion. The increments 

 Sx, &c, are due to the radiation, and are small quantities 

 (see Phil. Mag. July 1911, p. 69). Their average values 

 are calculated directly by allowing material systems distri- 

 buted according to (5) to move for a sufficient time in the 

 presence of radiation. The full effect of that radiation will 

 be reached after a period described in kinetic theory as the 

 time of a free path. Only the deviation arising within 

 this very short interval is correlated with the disturbing 

 forces at any instant. It is the source of absorption and 

 refraction. 



Let (/> be any function of x 1 x 2 ... a n , and 8(f> the increment 

 in <j> due to the increments &u l5 6> 2 , &c, in the values of 

 # l5 a 2 . . . a n * Then the average value of B<f> is 



J 



*8<l>dN (8) 



For start at time t with a distribution such that the fre- 

 quency dN of systems lying in the w'ple volume element 

 dY is given by 



d'No = Poe~ hH °dY . 



Let these systems move disturbed by radiation till time t. 

 Then the average value of Bd> at this time is 



.c 



tyrfN . 



But in the undisturbed motion 



dN =dN (9) 



(8) follows, and it is to be remembered that the integrations 



