76 Royal Society, 



the hypothesis of the sun's translation. Unfortunately, we have 

 no observations made in the southern hemisphere in the last century 

 equal in precision to those of Bradley, but the catalogue given by 

 Lacaille in his * Astronomise Fundamenta,' furnishes a means of 

 comparison of considerable value in reference to the present in- 

 quiry. In Mr. Johnson's 'Catalogue of 606 Stars in the Southern 

 Hemisphere' (London, 1835), there are sixty-one which, on com- 

 paring their places in 1830 with those of Lacaille reduced to the 

 same epoch, appear to have sliifted their positions not less than 8" 

 in space in the interval of eighty years between the epochs of the 

 catalogues, or to have an annual proper motion of not less than 

 one-tenth of a second in space. Prof. Henderson's catalogue (Mem. 

 11. Astron. Society, vols. x. and xv.) furnishes thirty-six stars, which, 

 on a like comparison, appear to have an annual proper motion ex- 

 ceeding the same limit. Of these, however, thirty-two are contained 

 in Mr. Johnson's catalogue, but Henderson gives the proper motions 

 of sixteen other stars (in the southern hemisphere), from the com- 

 parison of his own places with those of Bradlej'-. On the whole, 

 therefore, the two catalogues furnish eighty-one different stars whose 

 proper motions are given both in right ascension and declination. 

 The method of investigation is the same as that of Argelander. From 

 the differences of M. and Dec. given by comparison of the cata- 

 logues, the direction of the apparent motion of each star is com- 

 puted. It is then assumed that the sun is moving towards a point 

 whose right ascension A=259° 46'*2 and declination D=-f-32° 

 29'*6 ; and the direction in which each star would appear to move, 

 if it were itself at rest, is computed on this hypothesis. The differ- 

 ence of these two directions is treated as an error of observation, 

 and its numerical value substituted for the differential of the angle 

 which determines the direction of the parallactic motion ; this diffe- 

 rential being expressed by a formula containing the differentials of 

 A and D multiplied by known coefficients. An equation is thus 

 obtained of the form 



= ac? A -fMD+w, 

 in which a, b, and n are known quantities. Each star furnishes a 

 similar equation ; and the equations, being first multiplied respec- 

 tively by the sine of the star's distance from the point assumed as 

 the apex of the sun's motion, in order to give them all the same 

 weight, are solved by the method of least squares, and the result- 

 ing values of c? A and dT) applied as corrections to the assumed 

 values of A and D. The results are as follows: — the whole of the 

 eighty-one equations give (for 1790) as co-ordinates of the point 

 towards which the sun's motion is directed, 



^=263° 38'-0 + 5° 14'-5 ; Dec.=:-f 37° 15'-0+6° 17'-6. 



But two of the stars compared with Lacaille move in a direction so 

 nearly opposite to that of their motion on the assumed hypothesis, 

 that (in one case especially) a slight error of observation would 

 change the sign of n in the equations of condition. It therefore 

 appears necessary to reject those two stars ; and a further reason 



