and Electromagnetic Theory, 315 



It is proposed to obtain a relation between mean values of 

 p 4 and //* independent of the angle of incidence by inte- 

 grating the two sides of (3) with regard to n and nf respec- 

 tively, while leaving the mean values p* and p'* outside the 

 sign of integration. We may dispense with a separate 

 notation, and describe the resulting relation between p and// 

 as a collective relation : this is regarded as appropriate to 

 two streams of radiation incident and reflected, the former 

 evenly distributed as regards direction. The proper limits 

 for n are r and 1. for n' they are — r and 1; it is evident 

 that a wave for which n < r fails to reach the surface, and 

 n = r corresponds to n'=—r by (I). The result of the 

 integration is 



1 ,Xi-,f(i + l)= P >xi+ry(i-l). ... (6) 



Both in (3) and in (6) p A and p /JL may be replaced by 

 rfdp and p>' z dp', and for (5) may be written pdpdn^p'dp'dn' . 

 Since the wave-length \ = 6 27r\/p, A, -1 and X /_1 may take the 

 places of p and p' 3 or d\/\ 5 and dX'/X 1 ' those of p d dp and 

 p'hip'. 



§ 2. Analytically the process is that of transformation of a 

 double integral with subsequent integration with regard to 

 one variable on each side. A continuous range of values for 

 pnnd p' is assumed, and if the range is limited the relation is 

 not applicable within a certain margin near the limit. 



The form of (3) points to its interpretation as an equation 

 for the transfer of energy by reflexion, with an allowance for 

 the work done by pressure and for the filling of the new 

 space opened out by the motion, with energy-content. In 

 Wien's theory energy-content is proportional to d\/\ h mul- 

 tiplied by a function of \0, or to p 3 dp multiplied by a function 

 of p/d, when p is variable. If in the two streams p/0 =p'/6' 

 the energies are as p z dp : p' z dp' or as p 4 : p a ; and the above 

 equation (6) connects the energy-content in a stream of 

 incident radiation with that in the reflected stream. The 

 possibility of writing p/d=p'/d' depends on the invariable 

 collective relation between p and p' . On the other hand, the 

 notion of temperature as a general energy parameter which 

 i- implied in Wien's function, is not admissible for the in- 

 dividual wave, and its application seems to demand a pre- 

 liminary treatment of a collective character. 



If x i s use d f° r t ne energy-content belonging to radiation 

 proceeding in one sense (directions covering a hemisphere), 

 and is evenly distributed, the section between the cones n 

 and n + dn is %c/?i. We take it that % and x' may replace 



