SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 403 



whence 



then will 



and hence 



de . p 



d dt +rq \- rq '- dli 4- ^dh = 0, 



1 +rqj-^ 



J- p 



dt__ 



(ifi~ , , , -.1 de ' 

 c'J^rqJ--^^ 



This derivation of the law of cooling of moist air is due to Peslin, 

 who first gave it in his memoir "Sur les Mouvements G6n6raux de 1' At- 

 mosphere; Bull. Hebd. de I'Association Scientifique de France, torn, iii, 

 1868." Even before him, Sir William Thomson, in 18C2, deduced a very 

 similar relation, but the derivation given by Peslin is somewhat shorter 

 and more elegant. 



dt 

 The quotient ^ represents the diminution of temperature in the 



ascending moist mass of air for an elevation of one unit of length. The 

 diminution of temperature is now dependent upon the quantity of vapor 

 contained in the air, and is therefore variable according to the tem- 

 perature at which the air is saturated with vapor. For r = 0, that 

 is to say, in case no condensation occurs, the equation resolves itself 

 into that already above given for dry air, as it should do. 



In order to attain a more accurate insight into the changes of tem- 

 perature of moist ascending air at different initial temperatures and 

 different altitudes, it appears to be most convenient to compute and pre- 

 sent in one table the values of-rj- for various values of e and q, which 



latter quantity also depends upon the pressure of the air. Previously, 

 however, we must more closely consider the quantities that enter into 

 the composition of the formula. The product r.(/J^ represents the me- 

 clianical equivalent of the latent heat of all the aqueous vapor contained 

 in a kilogram of moist air, and its computation is subject to no difficulty ; 



- is a constant; if the density at the temperature Oo and at the normal 



pressure of one atmosphere (10333) is denoted by J> = 1.29277, then, since 



P P 



p — D pjis 6.09730 the value of the logarithm - • Finally, the factor 



1 de 



- • ^ is computed most simply by means of the formula given by Magnus 



for the maximum tension of vapor for any temperature t. This for- 

 mula reads: 



at 



6 = 4.525x10*+' 



