Thermodynamics of Radiation. 871 



was deduced, in the first instance, from a quasi-moleculai 

 theory of radiation, and free -use was made of the clos£ 

 analogy between full radiation and an ideal vapour, as bein^ 

 the method most likely to appeal to experimentalists familial 

 with the application of the gas analogy to other branches of 

 physics. The same result might have been deduced in a 

 variety of other ways, since it is to a great extent independent 

 of the particular analogy employed. It now seems desirable 

 to give an alternative method, which has the advantage of 

 being more direct and of throwing more light on the 

 essential points of difference between the proposed theory 

 and that commonly accepted. 



In order to explain the notation and to indicate the 

 assumptions which are taken as the basis of the present 

 method, it will be well to give a brief summary of the 

 fundamental facts, which are generally accepted, and are to 

 be found in many textbooks, such as Poynting's 'Heat/ 

 cap. xx. p. 333. 



The Energy Stream Q. — A study of the laws of emission 

 and absorption of radiation in relation to the equilibrium of 

 temperature, has led to the conclusion that the condition 

 existing inside a vacuous enclosure at a uniform temperature 

 T may be represented by an isotropic energy-stream Q per 

 second per sq. cm., which is the same in every direction and 

 in all parts of the enclosure, and is a function solely of the 

 temperature. A similar proposition must be true for each 

 separate frequency into which the radiation may be analysed. 

 We may define q as the energy-stream of a particular 

 frequency v per unit range of frequency, such that qdv 

 represents the energy-stream included between the limits of 

 frequency v and v + dv in full radiation. The partial stream 

 q is a function only of the temperature T in addition to the 

 frequency considered. Its rate of variation with temperature 

 {dq/dT) v at constant frequency is equally definite. 



The Energy Density U. — If we suppose the radiation to be 

 continually travelling in all directions with the velocity of 

 light c, the energy-density of the stream Q, or the quantity 

 existing in the medium at any moment per c. c, will be 

 4Q/c, for the full stream Q. Similarly the energy-density 

 u per unit range of frequency will be ty/c, for the partial 

 stream q. 



The Doppler Effect. — The simplest case to consider is that 

 of a perfectly reflecting sphere expanding symmetrically with 

 uniform velocity, small compared with that of light, and 

 filled with a homogeneous and isotropic mixture of different 

 frequencies. As the sphere expands, the wave-length of 



3M2 



