On the almospherkal Refradion. 405 



nishing him with exact determinations of the necessary constant 

 quantities. As far as 80° from the zenith, or even as far as S5°, 

 a greater degree of perfection can hardly be expected in this part 

 of astronomy. But within 5° of the horizon, the Table is con- 

 fessedly incorrect in theory, and does not agree so well with ob- 

 servation. The author of the Mecanique Celeste, by a single 

 artifice of calculation, both overcame the analytical difficulties of 

 the problem, and hit upon a law of the decrease of heat, which 

 affords a determination of the quantity sought, simple in its ex- 

 pression and approaching very near the truth. But the consti- 

 tution of the atmosphere thus adopted deviates from the case of 

 nature in a twofold manner : first, the initial rate of the decrease 

 of heat is too great; secondly, the rate of decrease becomes 

 slower as the elevation increases; whereas, in nature, it is either 

 uniform or accelerated. By means, however, of tliis double de- 

 parture from the true law, a compensation is effected to which 

 we muse, in a good measure, ascribe the great exactness of the 

 result. For in the atmosphere of Laplace the heat, at any given 

 elevation, is at first greater than in the case of nature; but, as 

 the rate of decrease continually lessens, the former quantity ap- 

 proaches the latter as the height increases, and, at a certain ele- 

 vation, will coincide with it ; beyond which limit the heat in the 

 supposed atmosphere will become less than the true quantity, as 

 at first it was greater. 



In mv formula there is no hypothesis implied, except that of a 

 uniform' decrease of heat. The expression of the refraction is a 

 converging series rigorously integrated upon that hypothesis. The 

 elevation necessary for depressing the thermometer one degree 

 depends upon the magnitude of the horizontal refraction ; and a 

 very small addition to the latter quantity would make my theory 

 agree entirelv with observation. Now there are good grounds 

 for thinking that the horizontal refraction in the French Tables 

 is rather too small. In the first place, when these Tables are 

 compared with exact observations near the horizon, the errors 

 in defect are found to be nearly double the errors in excess*: in 

 the second place, the refraction of the star Lyra, at 87° 42' 10" 

 from the zenith, is determined, by the observations of Mr.Briiikly, 

 to be 1 7' 26"-5, or 5 " more than according to the same Tables f : 

 and thirdly, in the Table published by Mr. Groombridge from 

 his own observations, all the refractions very near the horizon are 

 greater than in the French Tables ; particularly the horizontal 

 refraction is M' 28 "-13 in place of 33' 4()"-3.t Tlie determina- 

 tion of Mr. Groombridge appears to be fully sufficient to make 

 mv theory quadrate entirely with observation as to the cynstitu- 



• Conn, lie* Tcm, 1821, p. 341^. t I"sh Trans. 1815. 



* I'liil. Trans. IHll. 



tiun 



