130 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



■where 2.023 is the ratio between the specific heat of the vapor of 

 water and that of dry air. These formulas apply only in so far 

 as the air is not saturated with the vapor of water. At the moment 

 when the air becomes saturated, the decrease of temperature is 

 accompanied by a condensation of vapor and it is necessary to dis- 

 tinguish between the three cases. We will assume that the con- 

 densed vapor remains suspended in the mass of air under considera- 

 .tion. 



(3) The vapor of water is partially transformed into water. 



We will consider a mixture consisting of 1 kilogram of dry air, 

 x kilograms of vapor of water, and y kilograms of water. Express- 

 ing by U', U", and U'" the energies of dry air, of the vapor of water, 

 and of water respectively we have the total energy of the mixture 



U = U' + xU" + yU'" 



The sum of x and y remains constant and writing 



x + y = £ 

 we shall find 



d U = dU' + £ d W" + d(x{U" - £/'")) 



Designating by z/ and v" the specific volumes of the dry air 

 and of the vapor of water and neglecting the volume of the water, 

 we have the volume of the mixture 



V = v' + x v" 

 We can then write 



p d V = (p - f) dv' + fd (x v") 



Expressing the latent heat of vaporization by /, and the specific 

 heats of dry air and of water by c and c' we have approximately, 

 neglecting the volume of water: 



I = {IJ" - U"') + Afv" 



(273 + r) d 



xl 

 3~+TJ 



= d [x (U" - £/'")] + A fd (x v") 



273 



A a 

 cdx =d U' + - - dx 

 g 



c'dr = d U'" 



(p-f)V =- (273 + r) 



/ =606.5 - 0.696 t 



