Formula for Mountain Heights. 447 



The formula (A) is the formula in its most general form, the constant K 

 being calculated for 45° latitude. The formula (B) is a local formula. The 

 formula (C) is also a local formula, and may be employed in England when the 

 upper station is not more than 500 feet above the lower one, or more than 1000 

 feet above the level of the sea, and when the barometric observations are of the 

 rough kind. I strongly recommend, however, the use of formula (B) in all cir- 

 cumstances. 



A new constant is obviously a desideratum in all these formula. 



Before this paper is brought to a conclusion, some remarks in reference to 

 papers on this subject, and published in the second and third volumes of the 

 " Proceedings of the Eoyal Irish Academy," may not be inappropriate. 



In these papers it is assumed, that because the thickness of a portion of dry 

 air, by becoming united to a portion of vapour of water having a tension F, 

 both under a pressure tt, is to the thickness of dry air, previous to its union, 

 under an equal pressure, as -n-.Tr — F; so that dry air necessarily receives an 

 increase of thickness by becoming united with vapour of water, the pressure 

 continuing unchanged. It follows that in employing barometric observations 

 for ascertaining the height of mountains, when we take into consideration the 

 hygrometric state of the atmosphere, we ought to allow a corresponding increase 

 of height in the proportion, tt — F: tt, calculated by summation of variable 

 quantities by means of series, or of the integral calculus. 



Now if the increase of height, in consequence of the atmosphere containing 

 aqueous vapour, were analogous to the increase of height produced by increase 

 of temperature, which causes an increase of the elastic force of the atmosphere, 

 without any addition of material substance, the method pursued in former 

 papers would be substantially correct. But vapour of water, by becoming 

 united to dry air, adds its own weight to that of the dry air. Thus the analogy 

 fails altogether ; so much so indeed, that if the elastic forces of dry air and of 

 vapour of water were equal, the formula for dry air alone would be the same 

 as that for dry air united to vapour of water, notwithstanding that dry air ne- 

 cessarily expands by addition of vapour of water, the pressure continuing un- 

 changed. But the elastic forces of vapour of water and of dry air are to each 

 other as 8 to 5 ; and the increase of height in barometric formulae due to the 



3 N 2 



