Theoretical Evaluation of 7. (547 



where a is, for the present, supposed to be independent of E 

 and F. 



Suppose that F is subject to dissipation of amount eF per 

 unit time, of which a fraction equal to 6 times the whole is 

 regained by absorption of energy from the aether. Suppose, 

 further, that the pulses at collisions are sent out and absorbed 

 in such a way that F increases, from this cause, at a rate 



VE(£F + £E), 



in which the first tactor is proportional to the number of 

 -collisions, and the second to the mean intensity of pulses. 

 We may now replace equation (1) by 



/p 



^ = -*^E(F-iE)~e(l-0)F+\/E(fF + ?E) 



at 



and in the steady state 

 Writing 





6(1-0) 



*"(«-£) Ei + e(l-6>) : 



■we easily find that 



x( E )= ——> 



/t(E) = ^£(l-*)(l + i*0. 



As E increases from to x , a? decreases from unity to 

 zero, so that /'(E) starts from zero and continually increases 



to the value Q«4 $/(*— f)- The etf ' ect of the " la g " in F > 



when small, may be measured by /'(E) /^(E), and therefore by 



*(1-*)(1 + J«), 



a quantity which vanishes when E = 0. 



We therefore see that at low temperatures 7 will approx- 

 imate to the value which would be found for it on the 

 assumption that internal vibrations did not exist, namely, 



2 



7 = 1+^-7—, 

 o + n 



and as the temperature increases, the value of 7 will con- 

 tinually increase until it reaches the value which would be 



2 U 2 



