280 Prof. L. Natanson on the Critical 



variations 8Qj and SQ 2 , as correspond to equal temperatures 

 T 1 = T 2 , we obtain 



and from this it appears that at the critical temperature the 

 value of the ratio SQi/£Q 2 is equal to —1, but that at lower 

 temperatures it rapidly decreases and becomes zero at the 

 second point of inversion T ** : thus in the neighbourhood 

 of the temperature T*"* the differences SQ 2 must infinitely 

 surpass in value the correlated differences SQi. This result 

 furnishes us, I think, with a satisfactory thermodynamical 

 explanation of the phenomena which Prof. Olszewski observed 

 when he submitted to adiabatic expansion hydrogen cooled to 

 — 211°. The pressure he evaluates to be about 80 atm. is 

 evidently what we have called R c ; and 20 atm. indeed is the 

 critical pressure S c or Q c . In order to obtain a numerical 

 illustration, let us assume that the intersection points of the 

 two adiabatics E x — 90 atm. and R 2 = 70 atm. with the line of 

 saturation are comparable with one another ; further on T/y 

 to be equal, say, to — *05 at the temperature of intersection. 

 Then, 8Q 2 being 2 atm., we obtain 8Q l = — *078 atm., and 

 this, as Prof. Olszewski has been kind enough to inform us, 

 is much below the minimum change accessible to observation. 

 Another point of interest is the following. From what has 

 been said above, it will be seen that at the second point of 

 inversion T** (or II in fig. 1) the adiabatic curve is tangent 

 to the line of saturation, and therefore does not penetrate 

 into the domain of vapour and liquid coexistence of which 

 that line constitutes the boundary. Adiabatics then, which 

 begin with smaller initial pressures than the particular adia- 

 batic referred to, will be situated in the domain of superheated 

 vapour ; it is only at a temperature below the first point of 

 inversion T* and at a pressure K inferior to P* that such an 

 adiabatic ' may enter the " domain of coexistence. " And 

 again, such adiabatics as begin with greater initial pressures 

 than the particular adiabatic referred to must twice intersect 

 the line of saturation ; the first time at a pressure Q while 

 entering the domain of coexistence, and the second time at 

 another pressure H while leaving it. Now let us suppose 

 adiabatic expansion to be effected along such an adiabatic 

 curve ; something like a fog or a cloud will obviously 

 appear at Q and again disappear at H. (The pressures Q 

 will increase, and those denoted by H will decrease if the 

 initial pressures R are increasing ; and the two saturation 

 pressures P* and P** will be the limits between which the 



