PAPEP. BY DR. in:RTZ. 203 



ng from tbe first to the second stage. The values thus obtained are 

 tlien lo be substituted as po J^nd To in equation (2). By substituting 

 T=273o in the equation thus obtained, we obtain that j^,, which occurs 

 n the equations of the third stage. If now we furtlier determine from 

 Llie equation (.3) the final pressure 2>\ of the tliird stage then this 

 pressure and the temperature 273° form the j?o and To of the equations 

 3f the fourth stage. It will frequently happ-n that the temperature 

 lown to which the first stage holds good will lie below the freezing 

 point ; in that case one passes directly over to the fourth stage, omitting 

 the second and third. After we have thus <letermiued for all the 

 equations the coefficients and the limits for which each equation holds 

 gooil we can use them in order to determine the T belonging to any 

 given p or inversely. All these computations can however only be 

 ■executed by successive approximations, and one would do well to take 

 the necessary approximate values from the accompanying diagram. If 

 we have determined /> and Tfor any special condition then the remaining 

 •characteristics are easily found. The density of the mixture follows from 

 the corresponding e(]uation of elasticity. The equation (la) gives the 

 •quantity of water still present in the form of vapor, and therefore also 

 the quantity of water already liquefied. Frequently one desires to 

 know the difference in altitude h that corresponds to the dilferent con- 

 ditions ^0 and 2h under the assum[)ti()n that the whole atmosphere is 

 found in the so-called condition of adiabatic e(piilil>rium. If one de- 

 sires the exact solution of this ])rohlem, it must be attained by the 

 laborious mechanical evaluation of the integral 



j rdp ; 



but s nee it is precisely with regard to this ])oint that an exact deter- 

 mination never has a s|)ecial value, therelbie here one may always 

 abide by the accompanying convenient diagram. 



II. 



If we had to deal only with one mixture whose composition is exactly 

 "tnown for which we therefore can have only one value of the ratio n : A, 

 then we could exactly re-produce the formuhe above developed by a 

 graphic table that Avould enable us to directly perceive the adiabatic 

 changes of the mixture for any condition. 



We should represent pressure and temperature by coordinates in one 

 plane and cover this plane with a system of curves that should con- 

 nect all those conditions together that can adiabatically pass from one 

 to the other. It would then only be necessary to glide from a given 

 initial condition along the curve going through the corresiiondingi)oint 

 in order to i)erceive the behavior of the mixture as it i)asses through all 

 these stages. 



Since however the meteorologist must necessarilv deal with mixtures 



