Effusion of Argon, Helium, and some otlier Gases. 443 



60 milliin., and the initial and final pressures in the gas- 

 reservoir 690 millim. and 484 millim. These numbers are 

 only approximate and intended merely to show the pressure- 

 conditions under which the experiments were conducted . 



The Joule- 1/iomson Effect. 



As foreseen by the theory, the rate of effusion of argon, 

 when compared with that of oxygen, is very considerably 

 greater than the value as calculated by the law of the inverse 

 square root of the density. The foregoing experiments agree 

 uniformly in showing that the deviation amounts to 3| per cent. 

 On the other hand, the results obtained with helium, although 

 not very uniform, show pretty conclusively that its behaviour 

 is unlike that of argon. According to the theory, however, 

 it should behave in an exactly similar manner. These facts 

 seem to point to the omission of some factor or factors in 

 the basis of the theory. 



Now it will be observed that the theory assumes that the 

 gases obey the ideal gas laws, and hence excludes anything 

 of the nature of the Joule-Thomson effect. It therefore 

 appeared of interest to examine the question of the effusion 

 of an imperfect gas, with special reference to the Joule- 

 Thomson effect. 



An application of the equation of continuity and the law 

 of conservation of energy to the issuing jet yields the well- 

 known fundamental equation : — 



ig 2 + U +pv -- const., 



where q = velocity, 



U = internal energy per unit of mass, 



v = specific volume, 



p = pressure. 

 It is possible * to find an approximate expression for U by 

 making use of the equation given by Joule and Thomson f, 

 namely: — 



dT=^dp . (1) 



Choosing p and T as independent variables, we have 



^(U+pv)dp + ^- t (U+pv)dT=0. . . (2) 



* Cf. Poincare, Thermodynamique. 



t For the present purpose it was not thought necessary to use the 

 formulas recently proposed by Rose-Innes (Phil. Mag. March 1898), and 

 by Love (Proc. Phys. Soc. vol. xvi. Dec. 1899, p. 454). 



