660 Lieutenant Eenny on the Constants of 



Being the constant for an atmosphere (consisting of an union or 

 mixture of dry air and vapour of water having an elastic force 

 r' i«^(ii e; (■ (or tension) = 000506 metres, peculiar to the freezing-point, as 



obtained from an approved Table of elastic forces of vapour of 

 water, or otherwise correctly obtained) at level of the sea, of lati- 

 tude 45°, at freezing-point. 

 In order to compare the formula of Bessel (employed by M. E. Plantamour in calcu- 

 lating the height of the Convent of the Great Saint Bernard above the Observatory of 

 Geneva) with my own formula already submitted to the Royal Irish Academy, it is desir- 

 able to prove that the expression (f \/ff', being three-eighths of the square root of the 

 product of the elastic forces of vapour of water, corresponding to the dew-points) is {quam 



25610 

 proxime) equal to aFi of Bessel's formula, in which expression a represents the 



arithmetic mean of fractions of saturation at the stations of observation, and Fi represents 



the elastic force (or tension) of vapour of water, corresponding to the arithmetic mean of 



temperatures of stations, as given by the detached thermometers, obtained from an approved 



table of elastic forces of vapour of water, or calculated by the equation of Bessel (given 



in the Appendix, vide page 661), or otherwise correctly obtained. 



25610 

 In order to prove that (for practical purposes) §\/ff= „„ . -^„ aF^, and that it is a 



matter of indifference, in barometric formulse, whether we make use of the one or the other, 

 I have to remark that the elastic forces of vapour of water corresponding to the dew-points 

 of the atmosphere, are very nearly equal to the elastic forces of the vapour of water of the 

 atmosphere. Now if we consult any approved table of elastic forces of vapour of water (such 

 as that of Dr. Anderson, calculated from experiments by Dalton and Ure), we shall find 

 that the elastic forces form a geometric series (quam proxime) when the corresponding tem- 

 peratures form an arithmetic one, consequently ^ff' indicates the elastic force of vapour of 

 water belonging to a stratum of the atmosphere, situated half-way between the upper and 

 lower stations of observation. But as Fi indicates the elastic force of vapour of water corre- 

 sponding to the arithmetic mean of temperatures of stations, belonging to a stratum half-way 

 between the stations of observation (obtained from an approved table of elastic forces of 

 aqueous vapour, which supposes a state oi saturaiioii), it is obvious that to obtain the actual 

 elastic force we must multiply Fy by the fraction of saturation represented by a. Doing 

 so, we have the expression aFi. Therefore (quam proxime), V iff) = o-^i- -Buti ^Y trial, it 

 is easily discovered that (quam proxime), we have — 



, 25610 , „ , , _, 25610 „ , . , 



* " 67407 ' ^^^^^^^°^^ I v// = 67407 "^' (^"''"' P™'^""«)- 



Seeing that these expressions are very small in quantity, it is an affair of perfect indif- 

 ference whether we employ the one or other, in barometric formulas. In my paper on 



