of Heights by the Barometer. 411 



The pressures p and p are measured by the height of the mer- 

 curial column in the barometer at the two stations. If H and 

 H denote these heights reduced to the freezing-point, g and g 

 the gravity at the same stations, A the density of the mercury, 

 we shall have 



J»o=.?o AH o- P=ff&K> 

 and 



■=*(# 



The pressures ot and -sr of the vapour contained in the atmo- 

 sphere at the upper and lower stations are known from observa- 

 tions of the dew-point, or of the temperature of a thermometer 

 with a wet bulb. 



The constant c is given when we know the density of the air 

 corresponding to a given temperature. It has been found by 

 Regnault that the relative density of mercury and dry air at the 

 freezing-point, under a barometrical pressure of m, 76, at the 

 sea-level and at 45 degrees of latitude, is 10517*3. Assuming 

 for the absolute zero —274° C, we shall have, in metrical 

 measure, 



C= pt ~ -VUT~ 374 -t 29 172 > G; 



and in English measure, 



c=(53*173)G, 



G = 9 m -80601 = 32*172 feet (Bessel), being the gravity at the 

 level of the sea in latitude 45°. 



If X be the latitude of the place of observation, we shall have 

 for the gravity there 



g =G(l -0-0026 cos 2\) (-Y, 



where R = 6,366,786 ra = 20,888,780 feet (Arago, Astr. Pop. 

 vol. iii. p. 341) is the earth's radius at the latitude of 45°. 

 Therefore the complete formula for the measurement of heights 



. 2 . H — H f — J 



r-r = A(l+ 0-0026 cos 2\)Qj (J-) — 



H _m*7o + 



Kf) 



mrj 



t t 



r) and 7} denoting the elastic force of vapour in metres or inches 

 according to the measure employed. The constant 



A = 58-344 in metrical measure, 

 = 106*346 in English measure. 



