and on Astronomical Refractions. 469 



If 



f) 



'\ 7 - i - « _A^_! = -Has before, vol.xvi.p. MO. 



1 -g 



7 



1 _ JE^ 

 The expression for z' may be put into the form 



_fL_ = - k ( l ±Z Q) Nap. log (1 - Hq). 



*xe 



If y = 1-49138 when p' = 0, g = 1, we get for the superiordimit 

 of the atmosphere an altitude of about 24 miles, or 38918 metres. 

 Ultimately the intensity of the cold deprives the air of its 

 elasticity*. The density therefore requires in strictness to be re- 

 presented by a discontinuous function ; for the formula suggested in 

 this treatise is of course only applicable so long as the air exists 

 in the state of an elastic vapour. The freezing point of air is un- 

 known, and we cannot decide when this condition ceases to obtain. 

 Delambre estimates the height of the atmosphere as deduced from 

 the phenomena of twilight t at 70,800 metres; but this calculation 

 is open to objection. See Conn, des Temps, 1841, p. 58. 



I have given the example of the calculation of a height by an ob- 

 servation of the barometer, in order to show how my formula for 

 the densitv may be employed; but however inaccurate in principle 

 the method in use may be, it is sufficiently exact for elevations ac- 

 cessible to man. In all inquiries, however, connected with the con- 

 dition of the higher regions of the atmosphere, and in the various 

 hypotheses which may be made respecting the decrement of tem- 

 perature, the corresponding height must be calculated by an ap- 

 propriate formula, procured agreeably to the hypothesis which may 

 be adopted. Our information respecting the state of the higher 

 regions of the atmosphere is I think more likely to be improved by 

 observations made in aeronautic ascents than by those made on the 



sides of mountains. 



. _ k{\ + *0) 

 Let u = - Nap. log ( 1 - Hq) i - ~ ag iif$ 



i + - 



= a iu. 



* See Poisson, Theorie de la Chaleur, p. 460. « On peut se representer une colonno 

 atmospherique qui s'appuie sur la mer, par example, comme un fluide elastique termine 

 par deux liquides, dont l'un a une densite et une temperature ordinaires, et 1 autre une 

 temperature et une densite excessivement faibles." See also Biot, Conn, des Temps, 



1841. 



f See Delambre's Astronomic, vol. i. p. 337, and Lalande's Ast., vol. ii. art, 2270 



