790 Dr. L. Silberstein on Radiation from 



sufficiently accurate in the case of line spectra, when K is 

 of the order 10 7 . Thus the relative emissivity e» is inversely 

 proportional to the fifth power, and 8;w to the square of the 

 intrinsic refractive index (K?) of the source. 



To have a numerical example, take the first line of the 

 diffuse hydrogen series, H a , as treated in Table III., for 

 instance (First Note). Then & = 47r 2 a 2 K = 8*527 and, by (30), 



K = 2-591.10 7 ; K 5 / 2 = 3*418 . 10 18 , 

 477V 5 cos 2 u 6 = 4-882. 10 3 ; G x = 6-76J, 

 and the relative emissivity for H a * becomes, by (33), 



ei = 2-113.10- 16 (37) 



Again, i^cot i£ 1 = 4'494 ; therefore, by (36), 



5 1 w=l-734,10- 7 , (38) 



i. e. the wave-length difference between maximum- and zero- 

 intensity,, 



S 1 \=\ 1 -v 1 = 27r ^8 1 u = 2'50S . 10" 8 micron, (38 a) 



so that the detection of this difference would require an 

 instrument of resolving power \ 1 j8 l \ = 26,000,000. This 

 extraordinary sharpness of the theoretical lines has already 

 been hinted at. (It is needless to remark that the experi- 

 mental H a is a very complex line.) Of equal interest is the 

 extreme smallness of the.. relative emissivity as exemplified 

 by (37). From (37) we see that this energy emitted per 

 period is only the 5 . 10 16 -th part of the mean energy contained 

 within the sphere a in electromagnetic form. The latter 

 energy (U, belonging to the internal field E, M) will not be 

 confounded with the source's store of generally non-electro- 

 magnetic energy, say W, which makes good the (almost 

 evanescent) losses due to emission. If the amplitude e of 

 the " impressed force " is, as hitherto supposed, to be 

 rigorously or at least practically constant, we have to 

 imagine an enormous store W. But, in general, if e and 

 hence also U, and the corresponding external energy XT', are 

 slowly varying with time, we cannot assert about W any- 

 thing more than 



where W is the average of W taken over a period of oscil- 

 lation. Here it is assumed, of course, that all energy 



* More exactly, for the place of maximum radiation-intensity in the 

 narrow region of spectrum thus denominated. 



