254 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



If we assume that the initial condition of the air as it ascends from 

 the ground is represented by the point a 

 of the diagram (fig. 31), and that S S 

 is the corresponding saturation-curve, then 

 supersaturation will occur when the adia- 

 bat a a t intersects this curve without 

 being broken at the point of intersection, 

 that is to say, when the cooling takes 

 place according to the same law after pass- 

 ing the point of saturation, as it did be- 

 fig. 31 fore in the dry stage. 



But we attain supersaturation or the 



quantity 



yi = y\ - Jx 



when we seek the curve of saturation belonging to a l and with it the 

 value y t '. Moreover, we can apply to the supersaturated air the 

 conception of relative humidity and put 



y 1 



R = 100 —. 



y{ 



where, of course R > 100. 



If now by reason of any sudden paroxysm the supersaturation 

 should suddenly cease, then an increase in temperature would occur, 

 and since the expansion of the mass of air can only take place gradu- 

 ally there must also be an increase of pressure, that is to say, the 

 curve representing the adiabatic condition must rise suddenly from 

 a t to a 2 . In this process the point a 2 always lies below the satura- 

 tion curve, since a part of the water falls away from the mass when it 

 attains the final condition represented by a 2 , and therefore less vapor 

 is present in a kilogram of the mixture than at the original beginning 

 of the expansion. 



After the cessation of the sudden rise in temperature (which 

 carries the pressure from /? x up to /? 2 ) there will, of course, again begin 

 the process of expansion, but this will now be along the adiabat 

 of the rain-stage or the snow-stage. The graphic method just 

 described may be used to locate the position of the point a 2 for 

 the purpose of determining the conditions corresponding thereto. 



The position of a 2 is found by considering the line drawn vertically 

 through a t as the fundamental line, since the pressures increase with 

 temperature linearly in this direction. We may therefore identify 

 the points a x and a 2 directly with the points T x and T 2 of fig. 30. 



