and on Astronomical Refractions. 437 



nish so complete a test of the accuracy of any formula professing to 

 give the relation between the pressure and the temperature in ela- 

 stic fluids, as observations of the temperature of the vapour of water 

 and other substances, which can be carried through a greater range 

 of the therniometric scale, and above all through the low pressures 

 where the character of the curve is more decided. 



M. Biot has dwelt with reason upon the importance of intro- 

 ducing into the theory of Astronomical Refractions a greater con- 

 formity with the conditions of the problem than has hitherto been 

 attempted : and he has also noticed the imperfection in principle 

 of the present mode of calculating heights by observations of the 

 barometer, a method which must of course be abandoned (at least 

 in any accurate exposition of this theory) whenever the discovery 

 of the true connexion between the temperature and the pressure of 

 the higher regions of the atmosphere renders it possible to adopt 

 a move rigorous mode of eliminating the density from the differ- 

 ential equation which connects d p and d %. The correct expres- 

 sion which connects the difference of altitude with the pressures at 

 the upper and lower stations ought to be the foundation of the 

 theory of Refractions. Considering on the one hand the notions 

 upon which my formula is ultimately founded, its identity with 

 the results offered by the observations of steam and other vapours, 

 and moreover the agreement afforded by the direct comparison 

 with the observations of M. Gay Lussac, there can be no doubt 

 that it represents the density of the atmosphere at different altitudes 

 with greater fidelity than any hypothesis which has up to the 

 present time been made the basis of the theory of Astronomical 

 Refractions. 



I think that my table of mean refractions represents the observed 

 quantities within the limits of their probable errors, and I have 

 obtained this result without any arbitrary alterations of the con- 

 stants. 



In the higher regions of the atmosphere the cold is intense*, 

 depriving the air of its elasticity and converting it into a liquid 

 or solid substance. My formula of course is only applicable 

 as long as the air continues in the state of an elastic vapour ; 

 and if at any altitude it ceases to maintain that condition, the 

 density must be represented by a discontinuous function. But the 

 density of this frozen air must be extremely small, and it probably 

 has little effect upon the amount of Refraction. 



I am indebted to Mr. Russell for his kind assistance in the nu- 

 merical calculations which accompany this treatise. 



29, Eaton Place, March 2, 1840. 



* See Poisson, Tlieorie de la Chaleur, p. 460. 



