218 Proceedings of the Royal Irish Academy. 



micrometer was tumed, approximately, to the right position, and 

 clamped ; the driving clock was set in motion, and the star was 

 brought by the slow motions to coincide with the intersection of I 

 and the fixed wire. The clock was then stopped, and the micrometer 

 was adjusted by the tangent screw so that the star ran along the fixed 

 wire. In a second observation care was taken that the tangent screw 

 was turned the opposite way when making the final adjustment. 

 The observations of position were then made, and at the close of the 

 series two more observations of the parallel were made, with the same 

 precautions as before, but with the micrometer 180° from its position 

 in the first set. The mean of the four observations was adopted as the 

 " parallel." On referring to the observations, it will be seen that on 

 many occasions the set of parallel observations was not so complete 

 as is here described. Such care in determining the parallel as is 

 necessary when the stars are three or four minutes apart would, of 

 course, be thrown away if the stars were comparatively close together. 



In observing the position, the micrometer was turned until the 

 fixed wire was placed over the two stars, and the final adjustment 

 was made with the tangent screw. This observation was then re- 

 peated, the head of the screw being turned the opposite way on the 

 second occasion. The micrometer was then turned through 180°, 

 and two more observations were made, with similar precautions. 

 Thus, a complete determination of the position angle involves four 

 readings of the parallel and four of the position. 



The observations thus made have to be corrected for the effects of 

 refraction, aberration, precession, and nutation. We shall consider 

 them separately. 



Let D be the distance of the two stars, and let p be the position 

 angle ; then, if 2 be the zenith distance, iq the parallactic angle, and h 

 the coefficient of refraction, the correction to be applied to the appa- 

 rent distance for refraction is 



hD{\ -f tan-z cos^ {jj — t])), 



where k is the coefficient of refraction taken from Bessel's Tables, 

 Ast. Unt. Bd. I., p. 198. To facilitate the calculation of % and y], 

 the table suggested by Bessel has been computed, which gives the 

 values of m, and log cot n for each minute of hour angle in the latitude 

 of Dunsink, 53° 23' 13". "We can then readily compute s and 7;from 

 the formulae — 



tan t) = cot n sec (S + m), 



tan s = sec ?7 cot (8 -f in). 



In using these expressions it is supposed that eastern hour angles are 

 negative ; cot n has the sign of the sine of the hour angle, and m has 

 the sign of the cosine of the hour angle. 



In applying the correction for refraction to the observation of the 

 position angle, it is, of course, to be remembered that the reading of 



