Ajialytkal investigations respecting ASTRONOMICAL RE- 

 FRACTIONS and the application thereof to the formation of s 

 convenient TABLES together with the results of observations 

 of circumpolar Stars, tending to illustrate the Theory of Re" 

 fractions. 



Bij JOHN BRINKLEY, D. D. M. R. I. A.. F. R.S. andi 

 ANDREWS' Professor of Astronomy, in the University of 

 Dublin. 



Read May 9, 1814; 



A BRIEF detail will explain the objects of this paper.- 

 M. Le Comte Laplace first shewed that the fluxional expres- 

 sion for refraction may be integrated by approximation, as = 

 far as about 74° from the sjenith, without a knowledge of 

 the variation of density in the atmosphere. * 



T. Simpson had deduced by the princi plies of the 8th sec-- 

 fion of the first book of Newton's Principia, the fluxional* 

 expression for refraction, by considering a particle of light: 

 as a body acted on by a force tending to the centre of the 

 earth .-|- He and others since deduced the integral on the 

 hypothesis, that the density of the atmosphere decreased. 



* M^c. c^. Lit. JO. c 1. toni. 4; f Math, Dissertations, p. 51, && 





