B. Gralitzine on Radiant Energy. 121 



We see, then, that P is proportional to e. If we substitute 

 for P in formula (7), and then for e in equations (1) and (3), 

 we find 



de __ 4e 

 or 5T~"T ; 



e=AT 4 (15) 



This is exactly Stefan's* law of radiation, which is thus 

 deduced directly from the principles of thermodynamics and 

 the electromagnetic theory of light, as Boltzmann has already 

 indicated. 



We have also 



P = CT 4 , (16) 



a formula of which further use will be made in the following 

 sections. 



Equation (14) makes it possible for us to establish a more 

 simple relation between h and T. From (13) 



dT_ _ T 

 or dh~ 3 ' 



T=c ^ < 17 > 



Ci is determined by the initial conditions of the experiment. 



It will be observed, then, that in adiabatic and reversible 

 processes, such as we have just considered, the temperature 

 varies inversely as the cube root of the volume. 



§ 3. The Meaning of Absolute Temperature. 



The energy contained in unit volume of our radiation- 

 cylinder depends directly on the sum of all the electrical 

 vibrations emitted at temperature T from the perfectly black 

 surface, these being specified not by their wave-length, which 

 is variable according to the nature of the external medium 

 but by their period or the number of vibrations per second, n. 

 If T = we must have alson = 0. But if T begins to increase 

 new swings are constantly being added, and to every tem- 

 perature there corresponds a certain maximum rate of vibration 

 w max , which the black body is capable of emitting at that 

 temperature. Plainly ?i max is a function of T. 



n m = co(T) (18) 



Let us suppose we are dealing with only one ray (the 

 whole energy in unit volume will be obtained by integration 



* Wien. Ber. lxxix. p. 423 (1879). 



