PAPER BY PROF. BEZOLD. 227 



The first case corresponds to ci super-saturation limited only by the 

 original amount of water, or, as I will briefly call it, the " maximum 

 super-saturation ;" the second case corresponds to the " normal satura- 

 tion," rejecting any supersaturation. 



For the quantity of heat dQ=d(J\-\-dQ3 communicated to the mixture 

 we obtain therefore two equations, namely : 



(1) For " maximum super-saturation:" 



dQ={c,.+x^,)dT+TdQ^^+AR^T^^' (8) 



(2) For the "normal saturation:" 



dQ=c,dT+xdT+Td(^''^^^ + AKATp. ... (9) 



If we jnit dQ=0 then we obtain the ditfereutial equations of the 

 adiabatics for the two limiting cases. But in doing this we ought uot 

 to overlook the fact that strictly speaking in satisfying the condition 

 dQ=0 we have to do with an adiabatic in the ordinary sense of the 

 word only in one of these limiting cases, namely, that of maximal 

 supersaturation. For if we establish for the adiabatic the single con- 

 dition that for the given change of condition heat shall be neither 

 gained nor lost, then we have in both cases true adiabatics to deal with. 

 If however we define the adiabatic change of condition as one in 

 which not oiih' all exterior work shall be done at the cost of the energy, 

 but also where the whole loss of energy shall be consumed in exterior 

 work then will the definition for the second limiting case and also for 

 all intermediate cases corresponding to values of x'yo and x'<.x„—x' 

 equally agree with changes of condition that satisfy the condition 

 dQ=0. 



When, namely, the condensed water separates from the mass the 

 energy diminishes not only by the quantity needed for the performance 

 of exterior work, but also further by that quantity which is carried 

 away by the water that has precipitated at a given temperature. I 

 will therefore call those changes of condition for which dQ—i) but x+x' 

 <.r,„ that is to say, those changes for which th*^ water wholly or partly 

 separates the "pseudo-adiabatic," and especially that curve which 

 obtains for the complete discharge of the water of condensation, the 

 "pseudo-adiabat." 



Corresponding to this method of distinction the equation 



{c,,+xjdT-^Tdj^+AR,T~=0 (9) 



obtains for the adiabat and the equation 



{c.+x)dT^Td (^'^) + AR,t'^^=0 .... (10) 

 obtains for the pseudo-adiabat. 



