278 Prof, L. Natanson on the Critical 



of I superior to unity (of which one only, l=\ m , is given), and 

 lastly the " neutral line " cN, i. e. the curve passing through 



Fio-. 1. 



"~~-— __/=Xzrc 



V 



the points of contact between adiabatics and isopsychrics. 

 The points I and II correspond to the inversion points 

 T* and T** respectively. In portions of the plane situated to 

 the right of the neutral line, expansion ought to be accom- 

 panied by condensation ; in those situated to the left it ought 

 to be accompanied by evaporation ; but since for the masses 

 of liquid and vapour negative values cannot be realized, con- 

 densation for instance will occur within the limits of the 

 shadowed areas only. 



Let us now consider a gas at a temperature T which we 

 suppose to be above the critical temperature. If the gas be 

 submitted to adiabatic expansion, the path of the representa- 

 tive point in the pY-plane w T ill be an adiabatic curve which 

 will begin on the T -isothermal line. Let us suppose that 

 R a , Rd, R c , R<* . . . represent the pressures, and S a , S&, S e , S<* . . . 

 the entropies of the gas (per unit mass) at the points of issue 

 of the adiabatics ; and let Q , Qa, Q c , Qd • . . denote the 

 pressures, and T a , T&, T c , Td . . . the temperatures at the places 

 where they intersect the line of saturation, Q c and T c being the 

 critical values. We shall have 



<r(Qa,T a ) = S ; *(Q b , T 6 )=S„ ^ 



<7(Q c ,Tc)=2(Q c , T C ) = S*, > (8) 



2(Q d , T d )=S d , &c, &c. ) 



Considering two infinitely near adiabatics : — 



ss= (S) 8t= ? st and SQ= (S) 8T ' • - (9) 



