PAPER BY PROF. BEZOLD. 219 



like sheets above each other, and iu the study of the changes in condi- 

 tion one can simply adhere to the consideration of the curves described 

 by the projection of the represented points upon the PF plane. There- 

 lore, this plane will frequently hereafter be briefly designated as the 

 coordinate plane. VYe can therefore execute the mental presentation 

 of these processes in this phme, if only certain artifices are used, of 

 which mention will be made hereafter, and when we consider the result- 

 ing curves after a manner similar, as it were, to the lines on a Rie'mana 

 surfoce. The most inii)ortaut result is, that thereby the external work 

 consumed or expended finds its mental representation precisely as in 

 the simple method of Clapeyron. The formula 



d Q = A d U+ Ajidv 



expresses the quantity of heat to be added for an infinitely small change 

 of condition, under the notation* here adopted, and the special assump- 

 tions here considered; or if we pass from an initial condition over to 

 the final condition 



JJ 



Q = A[U2—Ui] + A I pdv. 



In this equation the quantities x, x', x" are contained in the values for 

 the energy, and indeed play a very important part therein ; moreover, 



^ is implicitly contained in v. but notwithstanding this I pan -^vill be 



J'i'2 

 2)dv will 



represented bj- the area included between the curved portion (more 

 accurately, the projection on the PV i)lane of the curve) rei)resenting 

 the change of condition, the initial and the final ordinate and the i)or- 

 tiou of the axis of abscissas lying between these ordinates. 



In the following sections the equations of condition for the individual 

 stadia will now be considered, from them those of the characteristic 

 curves (isotherms, adiabatics, and curves of constant quantities of sat- 

 uration) will be deduced, and finally the course of these in the geo- 

 metrical form of presentation will be investigated. 



A. THE DRY STAGE. 



If we indicate by2>A the partial pressure exerted by the dry air, hy ps 

 the pressure resulting from the vapor and in general distinguish all 

 quantities relating to the air and vapor, in an analogous manner by the 

 same indices then we obtain directly 



RkT ^ RiT 



or, i:>v={Bk-\-xR&)T (1) 



* I adopt Zeuner's method of vrriting as more familiar to me ; that is, I assume that 

 the energy is expressed iu units of work. 



