MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 185 



reason he gives the preference to the first as likely to represent the phenomena with 

 greater accuracy. Now in this his reasoning is not much different from the argument 

 afterwards used by Laplace, to prove that the same two atmospheres are limits be- 

 tween which the true atmosphere is contained. 



Newton likewise found tliat the refractions computed according to his second me- 

 thod, that is, in an atmosphere with densities decreasing in geometrical progression, 

 are too great near the horizon, on which point he thus writes to Flamsteed. " Sup- 

 posing the atmosphere to be constituted in the manner described in the 22nd propo- 

 sition of my second book (which certainly is the truth), I have found that if the 

 horizontal refraction be 34', the refraction at the altitude of 3° will be 13' 3"; and if 

 the refraction in the apparent altitude of 3° be 14', the horizontal refraction will be 

 something more than 37'. So that instead of increasing the horizontal refraction by 

 vapours, we must find some other cause to decrease it. And I cannot think of any 

 other cause besides the rarefaction of the lower region by heat." Here the true reason 

 is assigned why the refractions near the horizon, in an atmosphere constituted as sup- 

 posed, so much exceed the observed quantities. When the density is made to depend 

 solely on the incumbent weight, the air is not rarefied enough ; and the greater den- 

 sity causes a greater refraction. Having correctly estimated the effect produced by 

 the pressure of the supported air, Newton is unavoidably led to ascribe to heat the 

 greater rarefaction that takes place .in the atmosphere of nature. His words prove 

 that he had no clear conception in what manner the density in the lower region is 

 altered by the agency of heat ; and, to say the truth, nearly the same ignorance in 

 this respect prevails now as in his time. The decrease of density in ascending is a 

 complicated effect of many causes for the most part unknown ; and it seems in vain 

 to expect a satisfactory investigation of it by arbitrary suppositions. But setting aside 

 hypothetical constitutions of the atmosphere, we may consider the rarefaction of the 

 air in ascending as a phenomenon, the knowledge of which is to be acquired by ex- 

 periment ; and this appears the only sure way of placing the theory of the mean re- 

 fractions on its proper foundation. 



5. One of the tables of refraction most esteemed by astronomers is that published 

 annually in the Con. des Temps. It has been already shown that, as far as 74*^ from 

 the zenith, this table is calculated by the simple method of Cassini. There is nothing 

 incidental in this ; for all tables of refraction may be computed by Cassini's method 

 to the extent mentioned. The French astronomers have been very successful in de- 

 termining the constants of the formula. The refractive power of the air was obtained 

 by Delambre from a great number of astronomical observations ; the same quantity 

 was deduced by MM. Biot and Arago from experiments on the gases with the prism ; 

 and the results of two methods, so entirely different, agree so nearly, that there seems 

 no ground for preferring one to the other. The remaining part of the French table, 

 for altitudes less than 16°, is computed by a method of Laplace, which the author 

 has explained, without disguising its defects, in the fourth volume of the Mec. Celeste^ 



MDCCCXXXVIII. 2 B 



