Formula for Mountain Heights. 439 



T, T' be temperatures of the quicksilver of the barometers at lower and upper 



stations, as shown by the attached thermometer. 

 t^a be temperatures of the atmosphere at lower and upper stations, as shown 



by the detached thermometer. 

 H = h' — hbc the required height of the upper station above the lower one. 



Now, according to our definitions, we have 



and whereas the mixture or union of dry air and vapour of water is exposed to 

 a pressure tt, and that the vapour of water sustain a part of the pressure = F, 

 it is obvious that the dry air of the mixture is exposed to a pressure ~ tt — F ; 

 it is, moreover, well known that the densities of dry air and vapour of water, 

 under the same or equal pressure, are to each other as 8 to 5 ; also that, 

 cceteris paribus, the densities of gas vary as the pressures to which it is ex- 

 posed. If, therefore, we assume unity to represent the density of the dry air of 



F 



the mixture, we have ^^ r^to represent the density of the vapour of water 



of said mixture, also 1 + § . ■ -r, = %- to represent the density of the 



mixture itself; but, according to our definitions, this last density is p ; there- 



■K — ^ F . 77 — F 



fore, as S^ ; i ; ; p ; the density of the dry air of the mixture = p . ^-= . 



TT — -T TV — "S" -T 



But the said dry air is under a pressure = tt — F, and as the densities of gas 

 vary cceteris paribus as the pressures to which it is exposed, we have as an ex- 

 pression for the density of the dry air of the mixture under a pressure w the 



TT 



quantity p . j-r^, at the same time that the quantity p indicates the density 



of the mixture itself under an equal pressure tt, and of the same temperature T. 

 The moduli of elasticity {vide Definitions) of different gases, under equal pres- 

 sures, vary obviously as the reciprocals of their densities ; therefore — 



As - : :: A : A . 2_. 



p TT ,r 



PZ — ^V 



— B 



3 M 2 



