on Ike Theory of the Astrortomical Refractions. 277 



is first provided ; and the occasional deviations of the true 

 places from the mean are ascertained and corrected according 

 to the state of the air, as indicated by the meteorological in- 

 struments. The subject of the astronomical refractions is 

 thus resolved into two parts very distinct from one another; 

 the first embracing the mean refractions, which are an un- 

 changeable set of numbers, at least at every particular obser- 

 vatory; the second relating to the temporary variations occa- 

 sioned by the fluctuations which are incessantly taking place 

 in the condition of the atmosphere. It is the first of these 

 two questions chiefly, or that regarding the mean refractions, 

 of which it is proposed to treat in this paper. 



In order to form a just notion of the mean refractions, we 

 may suppose that some particular star is selected, and assidu- 

 ously observed for a course of time so considerable as to 

 comprehend every possible change in the condition of the 

 atmosphere ; all these observed places being severally reduced 

 to some assumed state of the thermometer and barometer, and 

 being combined so as to eliminate occasional irregularities, 

 will determine the mean refraction of the star. In this pro- 

 cedure it is supposed, what experience confirms, that the re- 

 sult will ultimately be the same for the same altitude above 

 the horizon, provided the observations are numerous enough, 

 and extend over a sufficient length of time. We may in- 

 stance the star « Lyrae observed by Dr. Brinkley ; his obser- 

 vations are forty-four in number, extending over five years ; 

 and the greatest deviation of single observations from the 

 mean quantity may be stated at + 20". The supplementary 

 table, extending from 85° to 89'^^ of zenith distance, publish- 

 ed in Bessel's Tabulce liegiomontance, is one of mean refrac- 

 tions calculated from many observations at every altitude. 

 The table, in the same work, extending to 85° of distance 

 from the zenith, which the supplementary one is intended 

 to complete, may likewise be considered as having the author- 

 ity of actual observation ; for although a theoretical formula 

 was used in the calculations, yet the results have been care- 

 fully corrected by a comparison both with the observations of 

 Bradley and with those made with very perfect instruments 

 in the observatory over which Bessel presides. These two 

 make together a table of mean refractions of the liighest au- 

 thority; and being free from hypothetical admissions, to 

 speak with precision, they form the only table of the kind 

 of which astronomy in its actual state can boast. 



The mean refractions, being a fixed set of numbers at any 

 proposed observatory, are independent of temporary changes 

 in the state of the air. U the general constitution of the at- 



