tlie Rotation- Energy of Molecules. 81 



As, however, he could only take into consideration the one 

 arithmetic series, and, besides, had no true value for v, it 

 seems to me to be of interest to repeat the calculations. Of 

 special interest, too, will be the investigation in the case of 

 hydrochloric acid, from which, on account of the simpler 

 chemical composition, more exact values may be expected. 



If, in formula (1), we insert the frequency v = 20' 15 x 10 11 , 

 calculated from the maximum of the absorption-band, and 

 observe that the maximum coincides with the third of the 

 lesser maxima (see fig. 4) — ?z = 3, therefore — we get for 

 hydrochloric acid, 



nh 3 x6-548x10-" 5 . lxl0 -„ 

 27T 2 v-2 7r 2 x2&15xl0 n -° 1X1U ' 



According to the Kinetic theory of Gases the mean rota- 



tion energy of a diatomic molecule is kT, where A=« = 1*346 



X 10~ 16 . If now for the calculation we employ the value (v), 

 obtained from the maximum of the absorption-band, which is 

 approximately correct, we get 



T_ JLL. 1-346 x10-»x 290 . 0x1() . 4O> 



i(2irv) 2 i{27rx 20-15 x 10 1 



As we see, the correspondence is very satisfactory. It 

 must, however, be pointed out that the value of v inserted in 

 the last equation is very uncertain. Were the absorption 

 proportional to the number of the absorbing molecules, inde- 

 pendently of the frequency, the mean of the squares of the 

 frequencies ought to be greater than (20' 15 x 10 11 ) 2 , but 

 probably the intensity of the absorption increases with the 

 frequency. If we insert in the formula? a p-value=JS8x 10 11 , 

 which in fig. 4 has a corresponding frequency, lying between 

 the fourth and the fifth maximum, we get a moment of 

 inertia half as large, or 2*5 X 10~ 40 — a value that agrees with 

 Ehrenfest's formula 



V = JttU ^ Page )' 



For water-vapour we get the two moments of inertia 1*9 

 and 4-4xl0~ 4t) from formula (1), using the above-mentioned 

 frequency-differences. From the kinetic formula E=|j&T, 

 we can naturally only calculate the mean moment of inertia, 

 and the calculation is very inexact, too, since from the 

 absorption measurements we can scarcely conclude more than 



Fhil. Mag. S. 6. Vol. 28. No. 163. July 1914. G 



