124 B. Galitzine on Radiant Energy. 



diathermanous body whose dielectric constant for swings of 

 frequency n is k n . As the temperature remains the same, 

 the range of frequencies is the same as before, namely, from 

 „=0ton OT = o,(f). 



Equation (19) shows that the energy transferred across 

 any section of the cylinder will be k n times greater than before, 

 for swings of frequency n, because the external medium takes 

 part in the vibratory movement. Also, since the velocity of 

 propagation V M of these particular waves is smaller than in 

 vacuum, the energy present in each unit of volume will be 

 increased k n Y/Y n -told ; and if eh is the total energy per unit 

 volume we have, as in § 3, 



f y 



** = const. | k n ^jr f(n ) T)cj)(?i)dn, . . . (23) 



Jo * n 



the constant having the same value as in equation (21), which 

 may be looked upon as a special case of the more general 

 equation (23). 



If we neglect the effect of dispersion of the different waves 

 we can write down the mean values k and Yh instead of kn 

 and Y n , and we thus obtain 



e k = k Tk e; 



or, having regard to equations (1) and (3), 



47T€jfc _ , V , 47T6 



from which 



e k = ke. 



This is exactly Clausius's law of radiation*, since, according 

 to the electromagnetic theory of light, provided we neglect 

 dispersion, we are perfectly justified in taking the square of 

 the mean index of refraction as equal to the dielectric constant. 

 Clausius's law of radiation appears, then, to be a necessary 

 consequence of Maxwell's fundamental conceptions. 



§ 5. Meaning of the Second Law of Thermodynamics* 



The above investigation of the radiant energy in a cylinder 

 enables us to understand more clearly the meaning of the 

 second law. In the course of the third proof of the formula 



* Clausius, ' Mechanical Theory of Heat,' p. 314, § 10 (Macmillan, 

 1879) ; Bartoli, N. dm. [3] vi. pp. 265-276 (1880) ; Beibl. iv. p. 889 

 (1880). 



