234 Till-: Mi:cH.\\ics of the earth's atmosphere. 



and for the pseiido ailiabatic 



< 7-, I , , . SI ^ x(r-\-l) ("^c(x.—x)dT ^ 



AB;,\ogv + {c„+cx,)logT+^ ^^-J ^ ^ .^/ =C . . (26) 



where x, is tbe quautity of vapor at tlie begmning of the snow stage 

 and tbe limits a and T are introduced into tbe integral, because in the 

 bail stage, as in tbe beginning of tbe snow stage, T=a=273;c is tbe 

 specific beat of ice. Since x is always smaller witb diminisbiug T and 

 finally approximates to 0, therefore in tbe snow stage tbe deeper tbe 

 temperature falls tbe more does tbe adiabatic approximate to tbat of 

 tbe dry stage. 



In the investigation just finished, attention has been especially di- 

 rected to the course of the adiabatics, as bad also been done in the above- 

 mentioned older investigations. Bat in truth the adiabatic expansion 

 and compression constitutes only a rare, exceptional case, as is already 

 shown by the fact that tbe vertical tem[>erature diminution computed 

 under this assumption (according to tbe so-called couvective equilib- 

 rium) results considerably larger than is given on the average by ob- 

 servations. It is therefore important to deduce tbe quantity of heat 

 absorbed or emitted for given changes of condition, as determined by 

 the values simultaneously observed of pressure, temperature, and mois- 

 ture. In this process tbe method of geometrical j)resentation here de- 

 veloped is applied with great advantage. First, a glance at tbe man- 

 ner in which the curve representing any given change of condition 

 cuts tbe adiabatic suffices to give a decision as to whether in this change 

 one has to do with a gain or loss of beat. Moreover the curve puts one 

 in a position to deduce the quantity of heat exchanged by graphic 

 planimetric methods or by a combination of computation with plani- 

 metric measures. According to what was said in the beginning tbe 

 equation 



Q=A[U2-L\] + A ['"''pdv 



holds good also for tbe processes here considered witb three independ- 

 ent variables, and therefore also for a closed cyclic process 



(J = AF, 



where F is the surface inclosed by the projection of the points that are 



imagined to be upon the Pl^plane. Assuming that 



<^ ^— ,....;;^ any change of condition is given by its projection on 



\^ ^^3 this plane and is represented by tbe line between 



N. \ the points a and b in Fig. 31, then we obtain tbe 



^N^ quantity of beat Cj>„,, involved in this change easiiy 



-p.„ 3^ in the following manner: Onedraws through a (Fig. 



31) any curve of change of condition for which it 



may be easy to compute the increase or diminution of heat; also draw 



