792 Dr. L. Silberstein on Radiation from 



the internal oscillations. Now, let through the agency of the ex- 

 ternal stimulus, such as sparking, the radii a of all, or of some, 

 atomic sources undergo slight variations, 8a. Then, the frequencies 

 n remaining as in the normal state, the values of u will be slightly 

 varied, and each source will begin to emit its waves, the emission 

 of each of them being more or less intense according to the magni- 

 tude 8a of the individual variation *. The maximum emission of 

 a given atom will be attained when the change of its radius 

 happens to be such that 



5 2*VK S . 



du = ca = — d { u, 



i. e., by (36), when the radius of the atomic source shrinks by the 

 amount 



8a=d { a = — o-irs /2 u ? c °t u i (-39) 



For any smaller or larger shrinkage or expansion, the emission 

 will be weaker, ranging from to J;. The observable spectrum 

 would be an average result of all such individual contributions, 

 which — cceteris paribus — would be unequally distributed among 

 the various lines (*=1, 2, 3, &c), since d^a, d 2 a, &c. have slightly 

 different values. The shrinkage may in one atom be most favour- 

 able for the emission of the waves X x , say, and in another of X 2 , 

 and so on. Details of this kind, however, need not detain us 

 here. But what seems worthy of notice is the smallness of shrink- 

 age of an atomic source, (39), required for even the most efficient 

 release of imprisoned energy, i. e. for the passage from zero to 

 maximum emission. Thus, for instance, returning to the numerical 

 example (38), we have, for the first member of the diffuse hydrogen 

 series, 



0-6563.1-734.10-7 . • • . 



V>= " 2^(2-591 -10 T ) ~ - - 3 ' 56 * 10 miCr ° n ' 



and taking « = 9-13 . 10~ 5 micron, as in (30), 



^ = _3'90.10- 8 (40) 



a J 



Thus the shrinkage would amount to four hundred-million ths of 

 the " normal" atomic radius only. 



It will be understood that the above is here offered merely as a 

 vague suggestion whose acceptance or rejection would be a matter 

 of indifference to the essential parts of the proposed theory. 



* The same result would follow on the assumption that K undergoes 

 a change. On any electronic theory the permittivity of our sphere 

 would depend on the configuration, and chiefly on the density of spacing, 

 of the subatomic entities, so that both K and the radius a would be 

 changed simultaneously. To fix the ideas, we have supposed above that 

 the latter onlv is being varied. 



