of Ammonia, Sulphur dioxide, and, Carbon dioxide. 375 



Keutel (Diss., Berlin, 1910) has shown that no advantage 

 is gained by reducing the results by the method of least 

 squares, and that no correction need be applied for the 

 moisture in the air of the tube, or other impurities in the 

 air. 



From the wave-lengths in the gas and in air, the ratio of 

 the specific heats, K = c p jc v , may be calculated. For an ideal 

 gas: 



u 2 = f { *', (1) 



where u is the velocity of sound in the gas, p the pressure, 



d the absolute density, and k! the ratio c p /c v for an ideal 



gas with constant c v . 



By combining (1) with the general gas equation ^>a?=RT, 



we find 



M 

 «W.^, (2) 



where M is the molecular weight, R the gas constant, and T 

 the absolute temperature. If u is in cm. per sec, 



11 = 8-2 xl0 7 erg/l°. 



If (2) is applied to an actual gas, the value of k ! obtained 

 does not give c p \c vt but is a purely arbitrary number. The 

 true ratio c v \c v may, however, be calculated from k' by the 

 equation 



fc = fc'cf), (3) 



where </> is given by Nernst (Theoretische Chemie, vii. Aun\): 



4> = 1-~7tt(1-6t 2 ) (4) 



This equation is based on the equation of D. Berthelot for 

 the compressibility of gases under pressures not far removed 

 from atmospheric. The values of it and t are calculated 

 from the critical pressure, p c , and critical temperature 

 (absolute), T c , as follows : 



7r =p/p c ; r = T c /T* (5) 



The difference of the two molecular heats is given by 



0^-a=ja(l + ^7TT 3 ); .... (6) 



also based on Berthelot's equation, and given by Nernst 

 (loc. cit.). 



* Mem. du Bureau internat. des Poids et Mesures, xiii. (1907). 



