HEIGHTS DETERMINE!} BY THE BAROMETER. 129 



feet; representing this numerical quantity by c and substi- 

 tuting it in (14), we get 



k_ ___c 



mg ~ 1 .002588 cos 2A' 



which in (13) gives 



*' / z \ 



-.W*(r'-T)l, (16) 



from which the value of z may be determined by a series of 

 approximations; i. e., an approximate value must be first 



2J 



obtained by neglecting - ; then this approximate value 



y 



must be substituted for z in -.. and a more accurate value 



r 



will be obtained, and the same process may be repeated, if 

 necessary.* 



iy 



Sen. 1. When - is very small, it may be neglected in 



(16). It has been found in practice, however, that in this 

 case the results are more accurate by employing 18,393 

 metres as the value of c. (Duhamel, p. 259.) 



In order that the heights as determined by the barometer 

 may be very exact in practice, certain corrections are neces- 

 sary. For instance, the value of k is modified by the fact 

 that the density of aqueous vapor at a given temperature 

 and pressure is less than the density of dry air under the 

 same circumstances ; and the proportion of aqueous vapor 

 to dry air will generally be different at the two stations. 



* A formula for this is given in Bncy. Brit., Vol. in., p. 386, involving a consid- 

 eration of densities of vapor. 



