The Rev. Dr. Robinson on the Constant of Refraction. 191 



The constants v and v' must be computed for the mean refraction of each 

 set of observations ; p from the annual mean temperature and pressure, as the 

 observations for index correction and latitude extend through the year. 



If we observe a star of southern declination, and assume it to have been well 

 determined at some place where it passes near the zenith, we obtain d/i with a 

 much larger coefficient, for we find in the same way, 



^E = d/j, (y -\- f) = d/j, X y^- 



It may be doubted, however, whether anything is gained by the superior mag- 

 nitude of K ; for it is unsafe to argue, as if the results of one set of instruments 

 were identical with those which another would give in the same locality. The 

 refraction used at the southern observatory must also have been carefully verified, 

 as p' the polar constant is in those existing very considerable. 



The process must, of course, be applied to as many stars as possible, both for 

 the sake of accuracy in the final result, and also because the identity of the values 

 of dfi, obtained at different zenith distances, is an evidence of the correctness of 

 the formula used to compute the refraction. Among the various modes of com- 

 bining the partial results, I prefer that which makes the sum of the squares of 

 errors of observation a minimum ; not taking into account those irregular fluc- 

 tuations to which low stars are liable, caused by momentary changes in dfi, or in 

 the law of density, and, therefore, scarcely coming within this application of the 

 theory of probabilities.* This gives the formula, 



_ K X s (dR)-\-K' X s jdR ') 



^ ~ K^ X w + k'- xn' 



The Armagh circle has been described by me in the Memoirs of the Royal 

 Ast. Soc. vol. ix. After using it pretty extensively, during the last six years, I 

 have found no reason to change the favourable opinion of it which is expressed 

 there ; and, in particular, find no trace of the evil which Mr. Airy considers pro- 

 bable in circles divided on the face, namely, great and irregular fluctuations of 

 run in the microscopes, (Mem. R. Ast. Soc. vol. x. p. 266.) So far from this, 

 it is remarkably steady in that respect. A change of 30° alters the mean run of 

 the four microscopes from 0".25 to 0".47 ; the utmost force that can be applied 



* See on this subject, Bessel Ast. Nachrichten, No. 358. 



