276 Prof. L. Natanson on the Critical 



quoted by Prof. Olszewski, viz. : — 



£ = 273-211 = 62; p c =20atm.; p = S0 atm. ; 



we find f c= :41-7 ; I e. about -231°. 



•- Now, in order to evaluate the error which the omission of the 

 absorption of heat may have introduced, it must be borne in 

 mind, first, that the phenomenon of expansion lasted but one 

 second or two, according to the information with which 

 Prof. Olszewski has favoured us ; and, secondly, that the 

 circumambient temperature was —211°. Moreover, the cri- 

 tical temperature of oxygen may be calculated in the same 

 way. With the data 



t = 170*5, j> c =51 atm., p = 80 atm., 



which are given by Prof. Olszewski, equation (8) yields the 

 result —123° for the critical temperature of oxygen, which 

 is known to be situated at — 118°*8. We should assume, 

 accordingly, that the critical temperature of hydrogen lies at 

 some few degrees above —231°, at —228° for instance. 



II. 



The theory of adiabatic expansion in a system consisting 

 of a liquid and of saturated vapour was originated by 

 Clausius and Rankine, verified by Hirn and Cazin, and has 

 been recently developed by M. Duhem ** and M. Raveauf. 

 In the following pages it will be our object to apply this 

 theory to problems suggested by Prof. Olszewski's beautiful 

 experiments on hydrogen. 



Let m, iv, <r denote the mass, the volume, and the entropy 

 per unit mass for the liquid ; and M, W, 2 the same quantities 

 when referring to the vapour ; let Y be the total volume, and 

 S the total entropy of the system, T its absolute temperature, 

 assumed to be uniform throughout, p the general value of the 

 pressure, and P the saturation pressure corresponding to T. 

 If we write for brevity's sake 



^_ dP-d _ d m 



bt + J£%p~ S say > {l) 



then 



dY = (W-to)dM+(mp s ,+M <i ^)dT, . . . (2) 



tfQ=T(2-<r)tfM + T( m ^+M^W; . . (3) 



* Travaux et Memoires des Facultes de Lille, t. i. no. 5, p. 83, 

 Journal de Physique, [3] i. p. 470. 

 t Journal de Physique, [3] i. p. 461, 



