HEIGHTS DETERMINED BY THE BAROMETER. 127 



It must be observed that p is the sum of the pressures 

 due to the air itself, and to the aqueous vapor which is 

 mixed with it ; i. e., the quantity kp in (2) is the sum of 

 the two, Tcp, k'p', where p : and p' are the densities of the air 

 and .the aqueous vapor, respectively. 



Considering t constant as before, and equal to the mean 

 of the temperatures at the two stations, and integrating (8), 

 we have 



i Ioff PL^ fi. ff* I*-*) (Q} 



* p -(l + 0(r + *)(r+*') 



As before, let /*,&', and 7, T', be the observed barometric 

 heights and temperatures, and o the density of mercury at 

 a temperature zero ; then from (2) of Art. 52, by substitut- 

 ing formats vilue from (6.), we have 



= ,.*' a-"). 



p -- Vr+y/ 1 *?* : 

 Substituting (10) in (9), and solving for z z, we have 



z z' = 



(11) 

 Since 6 is very small (Art. 52), we have 



(Calculus, Art, 61.) 



