234 THE MECHANICS OP THE EARTHS ATMOSPHERE, 



aud for the pseudo-adiabatic 



AB K \ogv+(c v +ex c )logT+ K J -J a — t~ =C ' ' {2) 



where x e is the quantity of vapor at the beginning of the snow stage 

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

 hail stage, as in the beginning of the suow stage, T=a=213;c is the 

 specific heat of ice. Since x is always smaller with diminishing T and 

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

 temperature falls the more does the adiabatic approximate to that of 

 the dry stage. 



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

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

 mentioned older investigations. But in truth the adiabatic expansion 

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

 shown by the fact that the vertical temperature diminution computed 

 under this assumption (according to the so-called convective equilib- 

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

 servations. It is therefore important to deduce the 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 the method of geometrical presentation here de- 

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

 ner in which the curve representing any given change of condition 

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

 one has to do with a gain or loss of heat. 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 the 

 equation 



Q=A[U 2 -Ur}+A f m pdv 



holds good also for the processes here considered with three independ- 

 ent variables, aud therefore also for a closed cyclic process 



Q = AF, 



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



imagined to be upon the P "P" plane. Assuming that 

 at <T^<>. ai, y change of condition is given by its projection on 



this plane and is represented by the line between 



the points a and 6 in Fig. 31, then we obtain the 



^ quantity of heat Q aJ , involved in this change easily 



Fig.m. i" the following manner: One draws 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 



