434 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



is the ratio of the specific heat of dry air under constant pressure 

 to the specific heat of dry air under constant volume; 

 c p = 0.2375; c v = 0.1685 therefore 



k = 1.41 and w = -. : = 3.441* 



k — 1 



The equation of Poisson is here written in the form usually used 

 in thermodynamics where the "specific pressure p" in kilograms 

 per square meter corresponds to the weight of a column of mercury 

 having the height b and the sectional area of one square meter, 

 therefore we have p = 13.6 b or, still better, 



p = 13.596 b f- 

 £45 



where g is the acceleration of gravity at the location in question 

 and g a corresponds to the acceleration of gravity at sea-level and 

 45 latitude. 



Since in this equation there occurs only the ratio p/p of the 

 pressures therefore instead of specific pressure we may introduce 

 the heights of the corresponding columns of mercury, which is 

 always done in the following memoir. 12 



If now the air contains aqueous vapor, then for adiabatic expan- 

 sion we must take into consideration the condensation of the 

 aqueous vapor at the different stages of expansion according as 

 the result of the condensation and precipitation is liquid (i. e., 

 rain) or solid (i. e., ice and snow), and these stages are best charac- 

 terized by the terms introduced by Hertz as the dry stage, the rain 

 stage, the hail stage, and the snow stage. 



According to this system the first stage is that in which the cool- 

 ing of moist air by virtue of adiabatic expansion proceeds without 

 saturating the air with aqueous vapor. So long as this condition 

 holds good there is no precipitation of water, wherefore this stage 

 is called the dry stage. 



The second stage begins as soon as saturation occurs in con- 

 sequence of diminishing temperature. If the expansion is pushed 

 further and the cooling goes on with it, then the aqueous vapor is 



* Lummer and Pringsheim make k = 1.4025 for dry air. — C. A. 

 12 It may here be remarked that the notation here used generally agrees 

 with that of Guldberg and Mohn in their "fitudes." 



