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



.57.567> a remarkable approximation to that of Bessel. This is, however, for the 

 temperature of the barometer 37° ; but it vs^ill probably avail for 50° also ; as if, 

 on the other hand, the Dublin barometer has a wooden mounting, on the other 

 there is probably a little air in the upper part of the tube which will compensate 

 for its inferior expansion of scale. 



Bessel has given for a or r^T-r* 57-538 at 48°.75, but the barometer at 50°. 



He, however, found afterwards, that the refractions of his table require to be 



multiplied by 1.00l779> which would make it at the normal temperature and 



pressure 57.4993, hence ^ = 57.524. This appears to satisfy the Greenwich 



observations, as well as* those at the Cape of Good Hope ; and its unexpected 



agreement with Brinkley shows how safely it may be depended on. At the same 



time, the very circumstances of that agreement give additional weight to the 



opinion which I have already expressed, that every fixed observatory should 



verify the refractions which it employs, and employ meteorological instruments 



of the best quality that can be made. 



The observed refraction of a star below the pole is obviously (omitting 



degrees) 



R = o — 8, 



o being the observed polar distance, 8 the assumed declination of the star. 

 Calling do and dh the corrections which these require, the true refraction is 



o — 1-\- do — dZ. 



If we put /i X V for the tabular refraction, we have, 



V (/x -|- dfi) ■=. vi -\- do — dl. 



Now, the polar point having been determined with an erroneous refraction, all 

 the polar distances require the correction rf/x X p ; and if we determine the 

 declination by observations above the pole, we have, 



rfo = (^/i X P ; dh-=. — dti.[y'-\-v)\ 

 and hence, 



R — v/t = rfB = c?/i [v — v' — 2p] = c?/x X k. 



* When the necessary corrections for the latitude and the change of the length of the pendu- 

 lum are applied. 



