564* Royal Astronomical Society. 



problem by Henderson, Struve, and Bessel, which I shall now pro- 

 ceed more especially to consider. 



It would be wrong, however, not to notice that the first indica- 

 tion of some degree of impression beginning to be made on the 

 problem seems to be found in Struve's discussion of the differences 

 of right ascension of circumpolar stars in 1819, 20, and 21. The 

 only positive result, indeed, of these observations is, that in the case 

 of twenty- seven stars examined, none has a parallax amounting to 

 half a second. But below this, there certainly do seem to be indi- 

 cations in the nature of a real parallax, which might at least suffice 

 to raise the sinking hopes of astronomers, and excite them to further 

 efforts. 



But the time arrived when the problem was to be attacked from 

 a quarter offering far greater advantages, and exposed to few or 

 none of those unmanageable sources of irregular error to which the 

 determinations of absolute places are liable. I mean by the mea- 

 surement of the distances of such double stars as consist of indivi- 

 duals so different in magnitude as to authorize a belief of their 

 being placed at very different distances from the eye ; or, as Struve 

 expresses it, optically and not physically double. This, in fact, was the 

 original notion which led to the micrometrical measurements of double 

 stars ; but not only was anything like a fair trial of the method 

 precluded by the imperfections of all the micrometers in use until 

 recently, but the interesting phenomena of another kind, which 

 began to unfold themselves in the progress of those measurements, 

 led attention off altogether from this their original application, which 

 thus lay dormant and neglected, until the capital modern improve- 

 ments, both in the optical and mechanical parts of refracting tele- 

 scopes, and the great precision which it was found practicable, by 

 their aid, to attain in these delicate measurements, revived the idea 

 of giving this method, what it never before had, a fair trial. The 

 principle on which the determination of parallax by means of mi- 

 erometrical observations of a double star turns, is extremely simple. 

 If we conceive two stars very nearly in a line with the eye, but of 

 which one is vastly more remote than the other, each, by the effect 

 of parallax, will appear to describe annually a small ellipse about 

 the mean place as its centre. These two ellipses, however, though 

 similar in form will differ in dimension ; that described by the more 

 remote star being comparatively much smaller : consequently, the 

 apparent places being similarly situated in each, their apparent di- 

 stance on the line joining these apparent places will both oscillate 

 in angular position and fluctuate in length, thus giving rise to an 

 annual relative alternate movement between the individuals both in 

 position and distance, which is greater the greater the difference of 

 the parallaxes. 



Thus it is not the absolute parallax of either, but the difference 

 of their parallaxes, which is effectively measured by this method ; 

 i, e. by repeating the measurements of their mutual distance at all 

 times of the year. But, on the other hand, aberration, nutation, 



