After this discovery it was possible to watch for still outstanding very minute discrepancies; and so the problem of stellar parallax was attacked with fresh vigour by Piazzi, by Brinkley, and by Struve. But when results were obtained, they were traced after long discussion to age and gradual wear of the instrument, or to some other minute inaccuracy. The more carefully the observation was made, the more nearly zero became the parallax--the more nearly infinite the distance of the stars. The brightest stars were the ones commonly chosen for the investigation, and Vega was a favourite, because, going near the zenith, it was far removed from the fluctuating and tiresome disturbances of atmospheric refraction. The reason bright stars were chosen was because they were presumably nearer than the others; and indeed a rough guess at their probable distance was made by supposing them to be of the same size as the sun, and estimating their light in comparison with sunlight. By this confessedly unsatisfactory method it had been estimated that Sirius must be 140,000 times further away than the sun is, if he be equally big. We now know that Sirius is much further off than this; and accordingly that he is much brighter, perhaps sixty times as bright, though not necessarily sixty times as big, as our sun. But even supposing him of the same light-giving power as the sun, his parallax was estimated as 1"·8, a quantity very difficult to be sure of in any absolute determination. Relative methods were, however, also employed, and the advantages of one of these (which seems to have been suggested by Galileo) so impressed themselves upon William Herschel that he made a serious attempt to compass the problem by its means. The method was to take two stars in the same telescopic field and carefully to estimate their apparent angular distance from each other at different seasons of the year. All such disturbances as precession, aberration, nutation, refraction, and the like, would affect them both equally, and could thus be eliminated. If they were at the same distance from the solar system, relative parallax would, indeed, also be eliminated; but if, as was probable, they were at different distances, then they would apparently shift relatively to one another, and the amount of shift, if it could be observed, would measure, not indeed the distance of either from the earth, but their distance from each other. And this at any rate would be a step. It might be completed by similarly treating other stars in the same field, taking them in pairs together. A bright and a faint star would naturally be suitable, because their distances were likely to be unequal; and so Herschel fixed upon a number of doublets which he knew of, containing one bright and one faint component. For up to that time it had been supposed that such grouping in occasional pairs or triplets was chance coincidence, the two being optically foreshortened together,