Temperature of Hydrogen. 277 



here dQ is the quantity of heat absorbed in an elementary 

 reversible transformation. Put 



T S=^ T S= r; (4) 



7 and V will be what is termed the specific heat of saturated 

 liquid and of saturated vapour respectively. Lastly, if L 

 stands for the heat of vaporization per unit mass, consider 

 the quantity 



A= (m + M)y ^ (5) 



(m y + Mr)(W-w)-L(m^+M^) 



If certain assumptions be conceded (which have been 

 advanced by M. Raveau with respect to the specific heats at 

 constant volume), it may easily be proved, as M. Duhem has 

 shown, that A will be positive at every temperature. Taking 

 this for granted, consider the case of adiabatic expansion, so 

 that dV>0 and dQ = 0. From (2), (3), and (5) we obtain 



Cl-K'-B '«» 



the symbols I and X being defined as follows : — 



M y 

 l= ^m~+M ; X= ^T ; (7) 



here X is some definite function of the absolute temperature, and 

 I may be termed the degree of evaporation. We propose to call 

 those curves on the p V-diagram which correspond to given 

 constant values of I isopsychric lines. Equation (6) shows that 

 the isopsychric line l = X is at every temperature a tangent to 

 the adiabatic line ; and from the same equation the relative 

 positions of other isopsychrics and adiabatics,in the neighbour- 

 hood of the points of their mutual intersection, may be inferred. 

 The general nature of the relation between 7, Y and therefore 

 X and the temperature is pretty well known : thus at low 

 temperatures X rises from very small values, possibly from 

 zero, becomes equal to unity at the first point of inversion, 

 which we shall denote by T*; then as the temperature in- 

 creases, X still increases and attains a maximum \ m ; then it 

 begins to decrease, becomes again equal to unity at the second 

 point of inversion T**; lastly, it further decreases and at the 

 critical point becomes probably equal to J, since (as shown by 

 M. Raveau) the ratio 7/T tends there to become equal to —1. 

 In fig. 1 the saturation line AcB is shown, as well as a set of 

 real isopsychrics corresponding to values of I inferior to 

 unity, further imaginary isopsychrics corresponding to values 



