176 Dr. L. Silberstein on Radiation 



Large K, and molecular dimensions of source. 



For any value of K, equations (6) give for the mean rate 

 of emission, per unit time and per unit volume of source, 



4n* uY(u) 



cVl-r^ 2 A (20) 



This, intermediate, form is easily obtained by remembering 

 that the productivity of the source is (by the very definition 

 of Heaviside's concept of impressed force) given by the 

 scalar product KeE. Substituting A 2 from the first of (12), 

 and developing the second of (12) for tan rj, we have, 

 ultimately, 



T ce 2 l + io 2 2 -j 



a w 



!>. ■ (25) 



iv tan 77 + I 1 Tsin u K — 1~1 

 w 2 + l = u \-g(u) + vT J J 



In the same way A 2 can be introduced into the expression 

 (8) for the mean energy U of the source. But, having 

 already J, it will be more convenient to write down the 

 expression for the more characteristic ratio, the relative emis- 

 sivity e, as defined in the last section. For this sake use the 

 intermediate form (25'), multiply it by the volume of the 

 source and by the period of oscillation, and divide by (8). 

 Then, remembering that u = ~K. 1J2 w, the result will be, for any 

 K and any frequency, 



£=4w « .$& ( 26 ) 



1+W 2 (x(w) 



The reader can verify at once that (14) and (24) are particular 

 cases of (25) and of (26), respectively, viz. for K = l. The 

 relative emissivity of the source is again independent of 

 anything but the ratios of the wave-lengths X, X s , outside 

 and inside the source, to its radius *. The factor w/(l + w 2 ) 

 is as in (24), and in the other factor of (26) u has simply 

 taken the part of w. And since u is for the source precisely 

 the same thing as w for the surrounding vacuum, we can 

 say that the structure of e is the same in the particular and 

 the general case. This makes the intrinsic character of e 

 even more pronounced. 



Our present interest lies in large values of K and even of 

 c/t' = K 1/2 . The reason for contemplating values of c/v such 



* w=27ra/A,«=2n-«/X s ; X,=X/R1'2. 



