Brinkley on Refractiun. 365 



II. Read January, 1820. 



Although observations of zenith distances, when the object 

 is near the horizon, are frequently affected by irregularities of 

 refraction, that seem not capable of being reduced to any law, 

 yet there is reason to suppose that the effect of these irregula- 

 rities will disappear in a mean of a great number of observations ; 

 and thus a mean refraction for any altitude may be obtained, 

 depending only on the mean zenith distance, and the corre- 

 sponding heights of the barometer and thermometer. The 

 investigation of the law of these regular refractions, as they 

 may be called, has much engaged the attention of astronomers. 



This inquiry .has led to the extremely complex but elegant 

 mathematical researches of Kramp, Laplace, and Bessel. Their 

 investigations are nearly related to each other. Dr. Young has 

 also recently, by an entirely different method, and with gi'eat 

 analytical skill, obtained an equation expressing the I'elation 

 between the refractive force of air and the refraction at any 

 zenith distance 



It is the object of this paper to deduce, by help of a modifi- 

 cation of the result of the hypothesis of a density decreasing 

 uniformly, by an extremely simple investigation, the refraction, 

 at any low altitude corresponding to any heights of the barometer 

 and thermometer. The tables thence resulting, for zenith dis- 

 tances, between 80° and the horizon, will, I conceive, be found 

 as convenient as can be desired. They scarcely yield in 

 simplicity to the French tables, and enable us to obtain the 

 quantity of refraction, as changed by the weight and tempera- 

 ture of the atmosphere, in which, near the horizon, the French 

 tables appear entirely to fail. 



The first tables in which this has been attended to, as far as 

 the horizon, if I mistake not, were those of INIr. Bessel. 



In our ignorance of the law of variation of density, we can 

 only verify any hypothesis that we adopt, by a comparison of 

 its results with those obtained by direct observation. In this 

 way, by help of Dr. Bradley's observations, Mr. Bessel has 



