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XIII. — Tables for Facilitating the Computation of Differential Refraction in 

 Position Angle and Distance. By the Hon. Lord M'Laren. 



(Read 6th December 1886.) 



The annexed tables are intended to facilitate the computation of the cor- 

 rections for refraction which have to be applied to differential measures, such 

 as are made with the micrometer or heliometer. 



Differential measures are of two kinds : — (1) Direct measures of differences 

 of right ascension and declination ; and (2) measures of position angle and 

 distance. In either case the observer only seeks to determine the relative 

 positions of the objects under observation ; and the correction for refraction 

 consists in the applying to each reading a quantity representing the difference 

 of the separate effects of refraction on the apparent places of the two stars, 

 whose relative positions are to be determined. This might be effected by 

 computing separately the displacement of each star caused by refraction, and 

 taking the difference between these quantities for the required correction. 

 But, in practice, the correction for refraction is obtained more easily and more 

 accurately by differentiation. 



When the measures to be corrected for refraction are direct measures of 

 differences of right ascension and differences of declination, the quantities 

 log — and log jj may be tabulated for a given latitude, with the arguments, 

 declination, and hour angle. The numerical values of these co-efficients for unit 

 of arc (or 1") are to be computed for all possible positions above the horizon ; 



7 T> /7 T? 



and then the correction is at once obtained by taking out log j— and log jj 

 from the table and adding to each the logarithm of the number of seconds of 

 arc in the corresponding measure. It is intended, in a subsequent paper, to 

 submit a specimen of such a table prepared for the latitude of Edinburgh. 



The correction for refraction in the case of observations of position angle 

 and distance is a more troublesome matter ; because the various readings of 

 the position angles and distances for any pair of stars are not all taken at 

 the same elevation above the horizon, and therefore each measure must be 

 separately corrected for refraction before it can be combined with the others 

 into a mean position angle or mean distance. 



VOL. XXXIII. PART II. 2 S 



