Formula for Mountain Heights. 445 



is supposed to be at the level of the sea (which supposition injures Poisson's 

 formula by diminishing its generality), it appears that in systematically taking 

 into consideration the hygrometric state of the atmosphere, our formula differs 

 from that of Poisson only in subtracting the quantity § '/{ff) from the baro- 

 metric observations properly corrected. The constant coefficient, 18336 metres, 

 of Poisson's equation, — which is equal to 60158'6 English feet, having been cal- 

 culated for latitude 45°, without a systematic consideration of the hygrometric 

 state of the atmosphere, — ought to be replaced by a constant obtained from a 

 considerable number of accurate barometric observations, taken in connexion 

 with accurate observations of the wet and dry thermometers. 



5. Let us now consider if we can simplify our formula. Poisson says that the 

 corrections dependent on the height of the stations above the level of the sea, 

 and on the height of one station above the other, may be omitted in calcula- 

 tions not requiring any very great nicety, if we increase the constant ; and 

 thisopinionof Poisson, as well as the pernicious advice given by him, as also by 

 La Place, with a view to allow for the vapour of water of the atmosphere, are 

 adopted in Bayley's Astronomical Tables. Notwithstanding such authority, 

 this advice ought not to be followed, as it sometimes leads to errors greater than 

 the unavoidable errors of observation. In fact, these corrections enter the 



formula in two ways altogether different. In the expression ( 1 -1 • j, 



which is a multiplier of the constant, the correction arises from the height of 



the stations above the level of the sea, and in the expression ^{\-\ ) the 



correction arises from the heisrht of one station above the other. As the calcu- 



O 



lations are not very troublesome, it is desirable, in all nice and accurate baro- 

 metric observations, to retain these corrections ; — to the discretion of the 

 calculator must be left when to retain and when to omit them. 



It is now advisable to make some remarks touching the elastic forces of 

 vapour of water found in our formula. The quantities /and/' (according to 

 our definitions) represent the actual forces or tensions of the vapour of water 

 of the atmosphere of the lower and upper stations. These forces differ from 

 the elastic forces of the dew-points by quantities so extremely small that we 

 shall employ, instead of them, the forces of the dew-points. Hygrometric obser- 



VOL. XXIII. 3 N 



