PAPER BY PROF. BEZOLD. 223^ 



In this stage the isodyuamic lines are also equilateral hyperbolas, and 

 moreover the equation 



holds good also for the adiabatic lines, when pi and I'l relate to a definite 

 initial condition, but p and v to an arbitrary final condition. 



The constant k can be adopted without notable error the same as for 

 dry air, namely, u = 1.41. The quantity of vapor therefore disappears 

 entirely from the formula and the adiabatics have the same course in 

 all the planes corresponding to the different values of x. If now the 

 adiabatic curves are considered as lines of constant entropy and we 

 therefore take the equation S-Si = as the fundamental condition 

 where — >S' is the entropy, then the equation of the adiabatic lines re- 

 ceives the following form 



(c, + xc/) \os-^ -A{R, + xRs) logP- = 

 -'i Pi 



where the capacity for heat of superheated aqueous vapor under con- 

 stant pressure is indicated by e*. 



If one knows the jjath of any one adiabatic in the dry stage, then it 

 is easy to construct any given number of others by means of it. To 

 this end we consider that for any further progress along one and the 

 same isotherm, according to well-known propositions, the following for- 

 mula holds good for the quantity of heat needed in the expansion from 

 Vi to Vi : 



where, for the sake of simplicity, we put B\ + xBs = R* 

 Therefore we have 



^f = AR*log^^ (5) 



But the quotient -^^ is nothing else than the diminution of the en- 

 tropy in tlie isothermal expansion from the volume rj to v^. If, there- 

 fore, we start from a line of constant entropy (an adiabatic), and pro- 

 ceed along various isotherms that cut this curve, so that the ratio of 

 expansion remains constant, then we attain to points on a second adi- 

 abatic. 



If now we put Vi=v and V2=v-\-^v, and then make Jv = vVy where y 

 is a constant (an appropriate proper fraction), and if in a correspond- 

 ing manner we put JQ for Q and ^jS for the difference of the entropy, 

 we find 



JS = '^=AR* log (l+v) 

 Therefore as soon as the course of one adiabatic line is known (just 



* For the problems here presented, as is done by Zeuner in tbe application of the 

 mechanical theory of heat to machines, it is recommended to give the positive sign to 



L 



