780 Prof. J. H. Jeans on the 



This equation neglects resonance, and that this neglect is 

 not justifiable is clear from the circumstance that in many 

 of Rubens and Hagen's experiments the value of C A /C X is less 

 than unity. We shall avoid this difficulty, in so far as it 

 can be avoided, by a method due to Schuster *. If we 

 allow for resonance, equation (15) must be replaced by 



©- 



1 + "NV'~ b ' 



where S is a term required by resonance, which, from the 

 principle of conservation of energy, can be shown to be 

 necessarily positive. It follows that the true value of N is 

 necessarily less than the value calculated from equation (15). 

 12. No metal seems to be sufficiently regular in its optical 

 behaviour in the infra-red to justify us in neglecting S 

 altogether. One of the most regular is platinum. For this 

 Hagen and Rubens find f 



(rA 2 —2 0, 1-17 at X = 4yL6, Sfi respectively. 



The corresponding upper limits for N are 2*3 X 10 23 

 and 2*7 xlO 23 respectively. To raise the temperature of 

 2*3 XlO 23 electrons by 1° C. requires *75 calorie, while to 

 raise the temperature of 1 c.c. of platinum by 1° C. requires 

 only *69 calorie. Thus the greatest value for N permitted 

 by the known specific heat of thft substance is 2*1 x 10 23 . 



For gold, which is less regular in its optical behaviour, 

 the upper limit given for N by equation (13) is 6 X 10 23 , while 

 the greatest value consistent with the known specific heat of 

 gold is 1-9 x 10 23 . 



The substance for which our equations give the smallest 

 upper limit for N is steel. From the reflecting power at 

 \—8fi, the upper limit for N is *96 x 10 23 , while the specific 

 heat of steel admits a value as great as 3 x 10 23 . But our 

 theory has taken no account of the magnetic properties of 

 the metals concerned, so that probably the upper limit ob- 

 tained for N on the supposition that fi = l for steel is 

 untrustworthy. 



Except for steel, there seems to be no substance for which 

 the upper limit for N is not greater than the upper limit 

 already set by the specific heat of the substance. In so far 

 as our calculations assign a value for N at all, these values 

 are in general agreement with the law derived by Schuster J 



* Phil. Mag. vii. p. 154 (1904), 



t I have used the numerical values given in Table II. p. 165, of the 

 paper of Hagen and Rubens. 

 t Phil. Mag. vii. p. 151 (1904). 



