the Radiation from Electron Orbits. 647 



G = to Gr = co . The result is of the form 



3,1—5 ( n+i i *\ 



F p = (hm)~'n-if -J p {hm)~**=* (n — l/2/A) «-i J- , (19) 



in which /is a new function of form unknown. 



Since p is proportional to X -1 and h to T -1 it is clear that 

 the emitted radiation would satisfy a u displacement-law " of 

 the form 



xT (n+l)/(2»-2) _ cons (20) 



For natural radiation we must have (n+ l)/(2n— 2) = 1, 

 or n = 3, confirming the result previously obtained. 



5. The existence of the displacement-law (20) is, in a sense, 

 inconsistent with the displacement-law XT = cons., predicted 

 by the second law cf Thermodynamics. The law XT = cons., 

 however, refers only to a steady state, while the law (20) 

 has been derived for the natural state, which (at least in the 

 view of the present writer) is not a steady state, as the sether 

 has not the amount of vibratory energy required for the 

 steady-state condition of equi-partition of energy. 



Law of inverse square : fir~ 2 . 



6. The electrons must attract and repel according to the 

 law of the inverse square, when at sufficient distance apart. 

 There must therefore be some radiation emitted under 

 this law. 



In formula (19) put n = 2, and we obtain 



F„ = (hm)- 1 f{2p,p(hm)i}, . . . (21) 



so that p enters, not through the factor p/T but through the 

 factor p/Tl. This radiation accordingly does not obey Stefan 

 and Wien's law. 



If we replace fi by e 2 /m, and h by 1/2RT, equation (21) 

 becomes 



^ = ~f{2e 2 pm-K2m)-i\, 



showing that the emitted radiation is of frequency comparable 

 with i(2RT) 3 / 2 ™/* 2 . At 300° abs. the value of this expression 

 is about 2 x 10 12 ; at 600° it is 5 x 10 12 . Thus radiation 

 under the law of the inverse square may exist, but is neces- 

 sarily so far in the infra-red as to elude observation. 



This might in itself suggest that we must look for the 

 source of natural radiation in collisions of a sharper nature 

 than those which occur under the law fir' 2 . It is not, 

 therefore, surprising that our previous analysis has shown 

 that the law must be fjur~ d . 



