98 Mr. A. S. Eve on the Radioactive 



energy per cubic cm. of vibrations of frequencies between k 

 and k + die, is 



— 2y3« ak, 



or, in terms of the wave-length A. in free cether, the energy of 

 wave-lengths between \ and A, + d\ is 



87rRT\- 4 dA (7) 



This is one-eighth of the amount found by Lord Bayleigh 

 (' Nature/ May 16th), but agrees exactly with that given by 

 Planck (Drucle's Annalen, iv. p. 553) for large values of X. It 

 seems to me that Lord Bayleigh has introduced an un- 

 necessary factor 8 by counting negative as well as positive 

 values of his integers £, i], f. From formula (7), it follows 

 that the total energy of radiation at temperature T is 



8ttRT \- 4 ^\+ f(\,T,t)d\, ... (8) 

 Ja Jo 



in which \ is the shortest wave-length for which the 

 vibrations may be supposed to possess their full energy, and 

 the second integral represents the energy of waves of wave- 

 length less than X , the energy of radiation of these waves 

 being a function not only of T and X, but also of r, the time 

 which has elapsed since the closing in of the aether. Formula 

 (8) does not, of course, claim to express the partition of energy 

 in the radiation emitted by a hot solid : it is the radiation 

 when a mass of gas has been shut up for time t in a perfectly 

 reflecting enclosure. And the formula applies only to the 

 continuous spectrum of the gas produced by molecular motions; 

 no account is taken of the line spectrum, produced, so far as 

 we know, by atomic vibrations. 



XII. On the Radioactive Matter present in the Atmosphere. 

 By A. S. Eve, M.A., McGill University, Montreal*. 



THE presence of radium in the earth, and cf the emanation 

 of radium in the atmosphere, has been well established. 

 Exact measurements of the amount of the radioactive sub- 

 stance in the air are, however, needed. Professor Rutherford 

 was kind enough to propose to the writer some methods and 

 experiments by which to estimate the quantities present, 

 and to throw further light on their effects. 



The main objects of these investigations were : — 



1. To estimate the amount of radioactive matter present in 



* Communicated by Professor E. Rutherford, F.E.S. 



