201 



meteors indicate, he observes, a height of forty or fifty miles, at 

 which the atmosphere is dense enough to reflect a sensible quantity 

 of light. At the height of about 25,000 miles the centrifugal force 

 would become equal to the gravitation of the air, and the equilibrium 

 would be no longer possible. 



But the great reason that prevents our supposing an atmosphere 

 infinitely extended, is the coldness of the upper regions. Mr. Ivory 

 considers the elastic force as disappearing from the effect of cold 

 upon the temperature, is 266 centigrade degrees below the freezing 

 point ; and he observes, that if the decrease uniformly amounted to 

 a degree in 95 (English) fathoms, as it appeared to do in Gay Lus- 

 sac's aerostatic observation, the whole height ought not to exceed 

 29 miles ; consequently he thinks that the thermometer must fall at 

 a slower rate in the higher than in the lower parts of the atmosphere. 

 Mr. Ivory proceeds to investigate the motion of light according to 

 the laws of central forces, and to the experiments of Hauksbee and 

 others on the refractive density of the air. He first shows that the 

 formula employed by the French astronomers, as far as 74 from the 

 zenith, is deducible from any imaginable law respecting the consti- 

 tution of the atmosphere ; and he gives, for example, the mode of 

 obtaining it from that of Cassini. 



He next considers the case of an equable variation of temperature 

 in ascending, which he thinks is rendered probable, as the law of 

 nature, by observations of Gay Lussac and others ; and he inquires 

 into the general methods of integrating the expressions of the re- 

 fraction in such cases, according to the methods already employed 

 by Kramp and Laplace. He examines, on various suppositions re- 

 specting the height of the atmosphere as connected with various 

 laws expressing the progressive temperatures, beginning always from 

 that which is observable at the earth's surface the amount of the 

 horizontal refraction, which he finds not so materially affected by 

 these suppositions as to enable us to decide with certainty, from ob- 

 servation, which of them ought to be preferred. 



Upon these foundations the author investigates the actual mag- 

 nitude of the refraction under different circumstances, by means of 

 several infinite series, of which he computes the values ; and he com- 

 pares his results with those which have been observed by astrono- 

 mers. The ingenious hypothesis of Laplace, he remarks, gives us a 

 height of 59^ fathoms for a depression of a centigrade degree, or 

 197 feet for 1 of Fahrenheit, which, he says, is little more than two 

 thirds of the height actually corresponding to this depression ; and 

 the French table, he says, was computed for the foregoing point, and 

 then altered proportionally throughout its extent for a difference of 

 10 centigrade degrees. As far as 86 from the zenith, Mr. Ivory's 

 computations agree very accurately with those of Bessel ; and further, 

 this celebrated astronomer does not recommend the adoption of his 

 table. The comparison of the new table with the observations of the 

 French Astronomers, and of Dr. Brinkley, appears to be highly fa- 

 vourable to the accuracy of Mr. Ivory's results. 



