Ball — On Stars with a Lavffc Annual Parallax. 217 



By the aid of this formula the working list was arranged. For a 

 given date the values of a', 8' are known, and the above formula gives 

 a relation between a and 8. Taking lengths proportional to a, 8 as 

 abscissas and ordinates, respectively, twenty curves were plotted on a 

 plane corresponding to dates uniformly distributed over the year. 

 These curves, of course, agree in passing through the point which 

 corresponds to the pole of the ecliptic. By the aid of these curves, 

 when the right ascension and declination of an object are known, it is 

 easy to see at a glance when the object is 90° from the sun. The two 

 critical dates were thus found for each of the objects in the working 

 list, and the observations Avere always made as nearly as possible at 

 these critical dates. 



The instrument employed was the South Equatorial, with the 

 Pistor and Martin's micrometer. The mode of observation was 

 almost identically that adopted by Dr. Briinnow in his observations of 

 a Lyrse and its companion (see Dnnsink Observations, Part I.). The 

 following is the method by which the observations have been reduced, 

 and the different corrections applied : — 



We shall denote the two stars by >S^, S', the two wires of the 

 micrometer by /, II, and the two possible positions of the micrometer 

 \)j A, B : then, the expression, AIS', for example, denotes the 

 reading of the screw I. when placed upon the star S', the micrometer 

 having the position A. A complete measure of the distance of the 

 two stars is obtained by placing one wire on each star, reading off the 

 screws, then interchanging the wires, and reading again. A complete 

 series of measures consists of four such pairs, two being taken in the 

 position A, and two in the position £. Each of the four complete 

 measures are computed separately, the two first by the formula 



^ (AIS - AIS') + ^- {AIIS' - AIIS). 



the two last by the formula 



^ {£IS' - £IS) + ^ (BUS - BUS'), 



Ti, To denote the values of a revolution of screws I., II., respectively, 

 expressed in seconds of are. These values have been computed from 

 the expressions found by Dr. Briinnow — 



^3= 1-001337 n, 



n = 8"-9927 - 0".0002922 (t - 50°), 



where t is the temperature Fahrenheit. In each observation the 

 temperature is read off upon a thermometer, which, for convenience, 

 is screwed to the finder of the telescope, the bulb of the thermometer 

 being sixteen inches distant from the eye-piece of the telescope. For 

 convenience in reducing the observations a table is used, which gives 

 log rx - log 2 and log r-i - log 2 for each degree. XUi^.u-' | 



The direction of the daily motion, or the "parallel," was deter- 

 mined as follows : — "Wire / was set to the middle of the field, the 



