81 



80^, or a very slight modification thereof will be generally used 

 by astronomers. 



The form of the French tables may not be generally adopt- 

 ed, others more convenient perhaps may be derived. The 

 new form given in this paper ^vill serve as a check in the 

 use of the French tables, and may be thought more con- 

 venient than these for observations of the- sun, moon and 

 planets. 



Below 80° zenith distance, a knowledge of the law of va- 

 riation of density is absolutely necessary for computing the 

 quantity of refraction. As this cannot be had, all tables for 

 these zenith distances must be in a manner empirical. 

 The French tables are less so than any others, from the 

 method used by Laplace. But the quantity of refraction 

 varies so much from some unexplained cause, the heights of 

 the barometer and thermometer remaining the same, that 

 observations below 80° can be of little use. This irregularity 

 IS very manifest at 80° 45* in the observed refractions of 

 Capella below the pole. Sixty-five observed refractions of 

 this star are given, and compared with those computed from 

 the formula. 



Forty-two observed refractions of x Lyrac below the pole, 

 (zen. dist. 87° 4^',) are also given. In these the irregu- 

 larities of refraction are very considerable. The mean of the 

 observed refractions serves for shewing that refraction is 

 greater than would result from a density decreasing uni- 

 formly, and less than would result from a uniform tem- 



VOL. XII. N 



