MEASUREMENT OF HEIGHTS. 541 



or 



(l+.T)^log«<{^ 



- [424T-0 - 0"^-95 (t + (0)] (1 + ^T)| (t - it)), 

 whence follows 



x-(0< '-^ ^rzn- 



[424-0 -0-95 (t+ (0)] (1 +^T)-^^ ^ 



T — T 



If, then, we know both the last members of the denominator and 

 a, we can compute by this formula a value of t — (^), which, con- 

 tinuing Dalton's supposition, exceeds the difference of tempera- 

 ture between the elevation h and the limit of the atmosphere. 



H' — H 



If we take, forexample^ — __ , = 85 toises and T = 0, and sup- 

 pose the atmosphere at the surface of the earth to be half saturated 

 with aqueous vapour, we obtain approximately r — (^) < 13°'5, 

 which is scarcely equivalent to the usual decrease of temperature 

 in 1200 toises, not to speak of the limit of the atmosphere ; if 

 T — {t)= n . 13°"5, the extreme value of a = \n. Dalton^s sup- 

 position is therefore only reconcilable with a very small quan- 

 tity of aqueous vapour in the atmosphere, and not with that 

 which really exists. If we could, therefore, regard as correct 

 the pre-supposition of the equilibrium of the atmosphere on 

 ■which we have proceeded, the presence of a considerable quan- 

 tity of aqueous vapour in the atmosphere would be a conclusive 

 argument against Dalton's supposition. But this equilibrium 

 never really exists, and I am indebted to Professor Neumann 

 for the remark, that the density of aqueous vapour ascending 

 from the surface of the earth must be increased by the resistance 

 opposed to it by the air. 



8. 



I come now to the examination of the supposition, that the 

 temperature between two elevations at which it has been ob- 

 served varies according to the law which has been assumed by 

 Laplace, Sect. 2. The equation between t and X, which enounces 

 this law, as deducible from Sect. 2, is 



(l + *0* = (l+*-r§!^ + (l+^T')^^^. . (23.) 

 But we have no reason to regard as unreal moderate deviations. 



