398 RECORD OF SCIENCE FOR 1887 AND 1888. 



If we assume that all the water formed by condensation continues in 

 suspension, we Lave for the difltereutial equation of the adiabatic 



(C+^J^T+Td(^^^ + AE,T^=0 (8) 



where c„ designates the specific heat of the air at a constant volume, 

 x^ is the quantity of aqueous vapor at the moment when the rain stage 

 begins, x is the quantity of aqueous vapor at any given moment during 

 the rain stage, r is the latent heat of vaporization or quantity of heat 

 required to vaporize a unit mass of water at the temperature T, and the 

 pressure j> or approximately, COG at 0° C and varying with the tempera- 

 ture 5 A and Ra, known constants, as before used. We have moreover 

 x^=x-\-x', where x' designates the mass of condensed water that re- 

 mains in suspension. We could have given another form to the preced- 

 ing equation by choosing as variables |> and T in place of v and T. 



Integration furnishes the equation of the adiabatic under a finite 

 form. If we pass from an initial condition designated by the subscript 

 1 to a final condition designated by the subscript 2 the equation of the 

 adiabatic is 



AR.log^+K+^Jlog^+^^p-^^p=0 (9) 



Psei( do adiabatic. — When the condensed water is separated wholly or 

 in part from the mass of air, exterior work is done, and consequently 

 there is a loss of heat. The changes of condition in this case are called 

 pseudo- adiabatic by Bezold. He gives this name especially to the curve 

 described by the indicator when all the water that is formed falls to 

 the ground without increasing the energy of the mass of gas and with- 

 out other loss than that just mentioned ; actually the fall of rain does 

 communicate some energy to the air. 



The differential equation of the pseudo- adiabatic is 



(c„+a^)^T+T6?(^^) + ARAT'|^=0 (10) 



This equation is independent of x^ or the quantity of saturated vapor 

 that existed at the moment when the rain stage began ; it is also inde- 

 pendent of the quantity of water formed, and consequently on our 

 hypothesis, fallen to the ground since the beginning of the rain stage. 

 In equation (10) x represents the quantity of saturated vapor that exists 

 at any given moment. 



Integrating this equation between an initial condition designated by 



the subscript 1 and a final condition designated by the subscript 2 we 



obtain 



AD 1 ^'2, , T, P'xdT x^r-i aV'i_.. ,,.. 



ARa log - +c„ log rj.^-1- / -r|,-+ rp- — ^=0 .... (11) 



The integration can not be completely effected so long as the relation 

 between the variables is uot givpu under an explicit formj but we may 



