PAPER BY DR. HERTZ. 199 



minished indefinitely without addition of heat? We must distinguish 

 different stages. 



First stage. — The vapor is unsaturated ; liquid water is not present. 

 We assume that the unsaturated vapor follows the laws of Gay-Lussac 

 and Mariotte. Let e be the partial pressure of the aqueous vapor ; 

 p — e be that of the dry air ; v the volume of a kilogram of the mixture. 



7? T 1 7? T 



We then have p — e = A : e = u — 1 — where R and Ri are constants 



v ' v 



of well known meaning and value. 



Since now the total pressures is the sum of these two values, there- 

 fore 



pv={AR+juR,)T 



aud this is the so-called equation of condition [equation of elasticity] 

 for the mixture. If further, c,, is the specific heat of air at constant 

 volume and c\ the same for aqueous vapor, then in order to bring 

 about the changes dv and dT, the quantity of heat to be added to the 

 air must be 



dQ^X^c^dT + ART^ } 



Ou the other hand, the quantity of heat to be added to the aqueous 

 vapor must be (see Clausius Mechanische Warmetheorie. 1876, vol. I, 



p. 51.) 



i dv ) 



dQ 2 = ,. l \c' r dT+AR l T~\. 



Therefore for both together, the quantity of heat is 



dv 

 dQ = (Xc v +»c' v )dT+A(XR + !*Ri)T- 



But this quantity of heat must be zero for the adiabatic changes now 

 investigated by us. Iu order to integrate the differential equation 

 arising from putting dQ equal to 0, we divide it by T. From the 

 mechanical theory of heat we know beforehand that by this operation 

 the equation becomes iutegrable, aud we find this confirmed a poste- 

 riori. If we carry out the integration and eliminate v by means of the 

 equation of elasticity, in that we recall that o, + AR is equal to o, or 

 the specific heat under constant pressure there follows 



(Ac, + /ic',)log£-A(A..R+/*Ri)log|=0 . . . (1) 



J. Jfo 



The quantity that forms the left-hand side of this equation has a 

 physical significance. It is the difference of the entropy of the mixture 

 in the two conditions that are characterized by the quantities pTand 

 p T . Moreover the mixture evidently behaves exactly like a gas 



