360 



Prof. Gr. W. Todd on the Variation of the 



These figures give the continuous line in fig. 1, and 

 Eucken's experimental values are shown as small circles. 



Fis\ 1 



o > 



100 120 140 160 180 200 220 



The agreement is good. Of course, if further degrees of 

 freedom develop at higher critical molecular velocities, the 

 expression for K„ will be modified, and the theoretical curve, 

 instead of running asymptotically to the value representing 

 five degrees of freedom for every molecule, would go on rising. 

 The development of further degrees of freedom would 

 explain Bjenum's * values for hydrogen at very high 

 temperatures. 



The Ratio of the Specific Heats. 



Whatever we assume about the number of degrees of 

 freedom of the gas molecules, the ratio of the increase in 

 translational energy to the increase in total energy of the 

 gas molecules is 



A (IV) 3. n 



A(To) = 2 (fy -^ 



where y is the ratio of the specific heats of the gas. 



If every molecule has the same number (3 + </) of degrees 

 of freedom, then 



A(Tr)_ 3 



A(To) ~ 3 + ?' 



so 



that 



I (7-1) 



3 



or 



7 = 1 + 



3 + #' ' 3 + ^ 



* Bjerrum, Zeit.f. Electroch. xvii. (1911), and xviii. (1912). 



