350 Mr. Ivory on the Theory of the Astronomical Refractions. 



as likely to represent the phaenomena with greater accuracy. 

 Now in this his reasoning is not much different from the ar- 

 gument afterwards used by Laplace, to prove that the same 

 two atmospheres are limits between which the true atmosphere 

 is contained. 



Newton likewise found that the refractions computed ac- 

 cording to his second method, 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 : 

 " Supposing the atmosphere to be constituted in the manner 

 described in the 22nd proposition 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 va- 

 pours, 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 con- 

 stituted as supposed, so much exceed the observed quantities. 

 When the density is made to depend solely on the incum- 

 bent weight, the air is not rarefied enough ; and the greater 

 density causes a greater refraction. Having correctly esti- 

 mated 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 satis- 

 factory 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 

 pheenomenon, the knowledge of which is to be acquired by 

 experiment; and this appears the only sure way of placing 

 the theory of the mean refractions on its proper foundation. 



5. One of the tables of refraction most esteemed by astro- 

 nomers 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 

 mav be computed by Cassini's method to the extent men- 

 tioned. The French astronomers have been very successful 



