PAPER BY PROF. BEZOLD. 233 



at the entrance into the hail stage, theu according to what has just 

 been said, 



x'i-\-x i =x n 2 +x 2 

 or 



X" 2 =X / l — {X 2 — X l ) 



or finally, making use of the equation (18), 



x" 2 =x' l -~J^(v 2 -v 1 ) (23) 



If we substitute this value in equation (21) then after an easy trans- 

 formation we find 



AR x a\og ^ ^ r °'\ > l)eo (v 2 -v 1 )=lx f 1 .... (24) 



From this we can now first find v 2 by trial ; the value thus found can be 

 substituted in equation (23), whence in this manner x" 2 is f ound. 



If we are justified in the assumption that all the vapor of water 

 originally present is also after the condensation carried along until the 

 entrance upon the hail stage, as appears to be the case in heavy hail- 

 storms, then we have x'i=x a , and this is certainly large with respect to 

 x } and # 2 , and therefore so far as concerns the absolute value of x" 2 we 

 may briefly put x' i =x" 2 ,s'uiue the difference x 2 —x x no longer comes into 

 consideration. In cases in which this difference is appreciable, as for 

 instance in the determination of v 2 , one can of course not make use of 

 the above approximation. 



The equation (23) also shows in a very clear manner that in general 

 the hail stage can only occur when liquid water is suspended in the air, 

 that is to say, when x'^0 and that it acquires a greater extent the 

 greater this value of x' h that is to say, the greater the quantity of sus- 

 pended water that is present. Already, many years ago, Keye showed 

 that on days of thunder storms the conditions are present in a con- 

 spicuous degree for the suspension and carrying up of water. 



D. THE SNOW STAGE. 



If the air, saturated with aqueous vapor, be cooled below 0° C, theu 

 a part of this vapor must be precipitated as snow. The same formula 

 can be applied to this process as that which we have used in the rain 

 stage if only in place of the heat of evaporation r there be inserted the 

 sum r+l where I as above indicates the heat of liquefaction of ice. 

 Therefore we can after small modifications apply to this stage all the 

 equations developed in Section b. I confine myself to the re-writing 

 in this modified form the two equations (10a) and (17); they thus become 

 for the adiabatic 



AR K \ogv + (c v +cx c )\ogT+ ir ^V = C . . • (25) 



