466 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 1 



In place of the second term in this equation and since 

 Td^ = d{xr)- X rdT 



we may by the application of Clapeyron's equation obtain 



ICY 



-dT = AV dp" 



and since dp = dp' + dp" therefore in this case the thermal equa" 

 tion becomes 



= (c p + ?c) d T + d (xr) - AV dp . . . . (17) 



This form may also be used as the initial theorem and thence 

 inversely the equation first given may be deduced from it. 

 By the combination of equation (17) with the formula 



- (1 + $)dh = Vdp 



we now obtain as the adiabatic hypsometric formula for the con- 

 densation stage 



= ( Cp + £ c) d T + d {xr) + A (1 + £) dh 

 or 



-dh= Cp + ^ C dT + ? d(xr) 



A(l + ?) A (1 + f) 



and by abbreviating 



c p + ^ c = Q 



A (1 + 



and neglecting £ in the second term in the denominator we obtain 

 the equation 



-dh = C 2 dT + Ld(xr) (18) 



where C 2 varies with the quantity of moisture £. In the rain stage 

 c = 1. 01 is the specific heat of water and in the snow stage c = 0.5 

 is the specific heat of ice. We have for example the values 

 given in table E. 



