PAPER BY PROF. BEZOLD. 223 



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

 moreover the equation 



holds good also for the adiabatic liues, when p l and v x relate to a definite 

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



The constant n 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 - 8 is the entropy, then the equation of the adiabatic lines re- 

 ceives the following form 



(c p + xc*) log % _ A (R k + X B S ) log? = 

 U p x 



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

 stant pressure is indicated by c*. 



If one knows the path 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 v 2 : 



Q iy2 = A>R* T\og^ 



where, for the sake of simplicity, we put R\ + xR s = R* 

 Therefore we have 



% = 4iJ.log5 (5) 



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

 tropy in the isothermal expansion from the volume ^ to v 2 . 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 i\=v and v 2 =v+Av, and then make Av=vv, where v 

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

 ing manner we put AQ for Q and AtS for the difference of the entropy, 

 we find 



AS = ^=AR* log (1+r) 

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



" For the problems here presented, as is clone by Zeuner in the application of the 

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



