B. Galitzine on Radiant Energy. 119 



rfT T ~ T' 



thus leading us back to equation (7) again. 



Equation (10a) enables us to find a relation between T and 

 h for adiubatic processes. As e, and therefore P, are functions 

 of T alone, it follows from (10a) that 



7 oT e + F , 



or from (7). 



rfT 



dP 



h^ = -T~ (13) 



dh de v ' 



aT 



We can also obtain these formulae by a comparison of the 

 two integrals in equation (11). These give 



d$h{ T l^dT\=0< 



{"0» 



dh 



or h dT e+F 



dh de 



In order to evaluate the expressions in equations (5) and 

 (13), we should require to know the relation between radiating 

 power and absolute temperature. But if a direct relation 

 between P and e could be found by any means, it would enable 

 us to obtain directly the unknown law of radiation by inte- 

 grating equation (7). As I have said before, 1 do not consider 

 Bartoli's argument to be tenable. I have not succeeded in dis- 

 covering a relation between P and e from purely mechanical 

 considerations. Maxwell also, according to his own confession, 

 was equally unsuccessful*. But the relation sought for may 

 be deduced from the principles of the electromagnetic theory 

 of light, and indeed by a simple application of Maxwell's 

 fundamental conceptions to our case, as Boltzmannf was the 

 first to show. I should like to give a slightly different proof 

 of Boltzmann's relation, however. 



* Maxwell, 'Electricity and Magnetism,' vol. i. p. 154 (2nd edit,), 

 t Wied. Ann. xxii. p. 291 (1884). 



