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IV. — On a new Barometric Formula for Mountain Heights, in which the Hygro- 

 metric Condition of the Atmosphere is systematically considered. 5y Heney 

 Laus Renny, M. R. I. A., Lieutenant, Royal Engineers, Retired List. 



Kead January 8th, 1855. 



XN the most approved formiiliE employed in determining the height of moun- 

 tains by means of the barometer, we find attempts to make allowance for the 

 hygrometric state of the atmosphere, which attempts areas loose as they are in- 

 accurate. It is therefore desirable to reconsider systematically the entire question, 

 in order to obtain a formula free from the defects of those at present in use, the 

 necessity of which cannoiJ?e doubtful to any one who is aware that in the for- 

 mula given by La Place and Poissqn, the mode of making allowance for the 

 hygrometric state of the atmosphere increases, instead of diminishing the error 

 whenever the temperature of the atmosphere is below the freezing point ; 

 which circumstance has already been brought before the notice of the Academy 

 in a paper submitted to it by Dr. Apjohn, and published in the " Proceedings 

 of the Royal Irish Academy," vol. ii. p. 563. 



1. The ordinary method of obtaining the fundamental equation for determin- 



ing the height by means of the barometer, viz. h = c log — „ in which h indicates 



the height of one station above the other, c a constant quantity, and j?,j9' the 

 pressures of the atmosphere, which method consists in regarding the heights 

 ofthestationsto vary as the logarithms of the pressures — is mathematically cor- 

 rect, and sufficient for practical purposes, so long as the question has reference 

 to only one elastic gas, such as dry air ; but in a question which has reference to 

 a union or mixture of two elastic gases, such as dry air and vapour of water, 

 having different elastic forces, it is necessary to employ the integral calculus ; 

 and the following calculations are made after the method of Poisson, which 



VOL. XXTII. 3 M 



