h. Higli temperatures. For high temperatures {T^^O) we tind : 



Cr,— — {\ I (21) 



Hence the deviation in the specitic heat is of a smaller order of 

 magnitude than that in the pressure. The temperature at which Co 

 deviates 1 "/oo fi'o™ the constant equipartition value, is determined 

 by X ^ 0,85. For helium at normal density this temperature is 

 found to be T=0,9; hence except at a considerably larger density 

 a deviation of the specitic heat from the equipartition value could 

 not be observed experimentally. 



c. Low temperatures. For the theory of free electrons in metals 

 it is of interest to develop the formula for the specific heat at low 

 temperatures. From (17j we find immediately (Tw^o)- 

 12jr^ /Ty Sji* /TV 



'^"= — ^H^o)=-r-^'-UJ • • ■ • (^^) 



Cyoo , the value to which Q, approaches at high T, being one 

 half of the corresponding value for a solid the multiplicand of 



I — I is equal to that for a solid : cf. Debue, I.e. p. 800. 



From (20) in connection with (22) it follows on account of the 

 well known thermodynamic relation between Cj> and Co that their 

 ratio X approaches to the value 1 as 7^ approaches to q. 



Physics. — "On the theory of free electrons In metals". By Dr.W. H. 

 Keesom. Supplement N". 30i^ to the Communications from the 

 Physical Laboratory at Leiden. (Communicated by Prof. H. 

 Kamerlingh Onnesj. 



{Communicated in the meeting of May 31, 1913), 



§ 1. Introduction. Summary. It seems natural to transfer to the 

 theory of free electrons^) in metals the considerations of the former 

 paper regarding the application of the quantum-theory to the equation 

 of state of an ideal monatomic gas. The frequencies in an electron 



1) Planck, Berlin Sitz.-Ber. April 3, 1913, has recently treated the equilibrium 

 between oscillators, free electrons and radiation on very special suppositions, which 

 for the free electrons lead to the equipartition laws. The mode of treatment 

 followed in this paper may in some measure be considered as the reverse of that 

 by LoRENTz, These Proceedings April 1903, where from the motions of the free 

 electrons (in the case of equipartition) he deduced the law of radiation (which 

 holds in that case). 



