338 On Hypsometrical Measurements. [No. 4. 



I. — Barometrical Measurements. 

 1. The most recent and complete investigation of the theory of the 

 measurement of heights by aid of observations with the barometer, 

 is that of Bessel in the Astronomische Nachricliten* This formula 

 may be written in a general form, thus : — 



P {g){h'—h) ( (l-<0p) 



h) C 



Log — = I i— 



at)t 



F L (1 + flOt </TF ) 



where — 



P is the weight or pressure of the atmosphere at the lower sta- 

 tion, and P' that at the upper, the unit of pressure bein<>- that 

 exerted by a column of mercury of 336.905 Paris lines or 29.9218 

 English inches at the sea-level in latitude 45°. 



h is the approximate height of the lower station, and h' of the 

 upper, above the level of the sea ; so that if H, and H" respectively 

 represent the true altitudes of the stations and r the radius of the 

 earth, then — 



r H' r H' 



7i = — -——j and h' = >, 



r + H. r -f H' 



{g) is the ratio of the force of gravity at the sea-level in the latitude 

 X, of the two stations to that at the sea-level in latitude 45°. 



a, denotes the fraction of mean saturation of the stratum of air 

 between H and H', and taking the fractions of mean saturation at 

 the two stations, we may use for that of the stratum i (a -f- a'.) 



a is the co-efficient of dilatation of the air for an increase of 1* 

 of temperature, t denotes the mean temperature of the stratum 

 reckoned from freezing point. 



d is the density of vapour in terms of that of air ; 



P, the tension of vapour of the temperature t. And 



L, a constant dependant on the relative density of the air and of 

 mercury. 



2. But, in order to obtain accurate results by means of this formula, 

 it is of importance that the constants should be determined as accu- 

 rately as possible. 



* See Selminucher's Ast. Nach. No, 356. Taylor's Mem. Vol. II. 



