142 PROCEEDINGS OF THE AMERICAN ACADEMY. 



tion, w may be replaced by coo except in the expression (co 2 — co 2 ) 10 . 

 Performing the integration in this way, one obtains for the rate of 

 absorption by vibrations in the £ direction only, the value 



(6) f ' 7 =/^ 



v 4 m 



independent of coo or b. 



To see what amplitude is required to emit as fast as this, we may 

 use the well known equation for the rate of emission, 



e 2 



1 4 t 2 



i^co 4 |o 2 . 



For the limiting case, let us set this« equal to U and thus find the least 



permissible amplitude, £o- 



Thus 



3c 3 / 



?o" — 



4 m coo 4 

 Inserting the value coo = 2itp and 



r 3 2 7T 2 h v 3 1 



3c : 



3 hv 



kT , 



e — 1 



Evidently this amplitude will be greatest for the lowest frequencies 

 for which equation (3) can be expected to hold with any accuracy, 

 that is for frequencies situated somewhere in the visible range. It is, 

 of course, impossible to set any precise limits here, but for the purpose 

 of forming a rough idea of these magnitudes, let us calculate the ampli- 

 tude for X = 6000A at temperatures of 300, 1000, and 2000° absolute. 



For this case we have v = 5 X 10 14 sec -1 and since h = 6.415 X 10~ 27 



era: 

 erg. sec, m = 8.8 X 10~ 28 gm and k = 1.34 X 10" 16 -p we have 



hv =3.2X10" 12 eig, while k T has the values 4.02X10" 14 , 1.34X10" 13 , 

 and 2.68 X 10~ 13 erg respectively. Thus the values of £ at these 

 temperatures are 3 X 10" 17 , 2.5 X 10~ 5 and 6.5 X 10" 2 A respectively. 



10 See Lorentz "Theory of Electrons," note 62. 



