168 



From the zenith distance to about 80°, k = I and at 90° — 0, 8 

 nearly, but it seems reasonable to suppose, that, whatever be the 

 law of variation of density, which occasions this quantity k to differ 

 from unity, that k is constant, or very nearly so, at tlie same zenith 

 distance, whatever may be the change of density at the surface. 

 For, however great within the usual limits we may suppose the 

 change of density at the surface to be, there is no reason to suppose 

 a material change in the law of density in the atmosphere.* 



Hence, if we obtain the quantity Ll^Hl f ~i~~") ^^^ ^"^ ^^" 



nith distance and density at the surface, we shall easily obtain it for 

 the same zenith distance and any other density, by considering k and 

 tan 6' as constant. It is evidently sufficient to take the mean value 

 of ^ 



,, baiom. / \~ 1,0375 , 



«_1 =(m -1)X 5^ x0-('-5O),OO0i) X j^-^^^—^^—— and 



/ V „ 1+.002()S3 (t— 32) 



1,0375 t 



where m' — 1 and—- are the mean values of m — 1 and — cor- 



a 



responding to Far. Therm. 50 and Barom. 29,60 and which, 



adapted to the French Tables, are 



I' 



m' — \ = 57",72 sin 1" and — = ,00128 



a 



Hence the mean value of 



HjfH^, = 264",02 k tan ^ and of ^^^'""'1'^" ^= 28",S6 k tan *' 

 (I SIR 1 ^ Sin I 



By help of a great nimiber of observations of a given star, we 

 can obtain the refraction correppcnding to the mean of the Baro- 



• This reasoning may be fallacious, and it appears lo be veiy desirable, that the facts should 

 be ascertained by a sufficient number of observations, at given zenith distances near the horizon, 

 for different values of m — 1. > 



I Trans. R. I. Acad. Vol. 12, p. 98, 99. 



