Thus from three different quarters, three successful and almost simultaneous assaults were delivered upon a long-beleaguered citadel of celestial secrets. The same work has since been steadily pursued, with the general result of showing that, as regards their overwhelming majority, the stars are far too remote to show even the slightest trace of optical shifting from the revolution of the earth in its orbit. In nearly a hundred cases, however, small parallaxes have been determined, some certainly (that is, within moderate limits of error), others more or less precariously. The list is an instructive one, in its omissions no less than in its contents. It includes stars of many degrees of brightness, from Sirius down to a nameless telescopic star in the Great Bear;[77] yet the vicinity to the earth of this minute object is so much greater than that of the brilliant Vega, that the latter transported to its place would increase in lustre thirty-eight times. Moreover, many of the brightest stars are found to have no sensible parallax, while the majority of those ascertained to be nearest to the earth are of fifth, sixth, even ninth magnitudes. The obvious conclusions follow that the range of variety in the sidereal system is enormously greater than had been supposed, and that estimates of distance based upon apparent magnitude must be wholly futile. Thus, the splendid Canopus, Betelgeux, and Rigel can be inferred, from their indefinite remoteness, to exceed our sun thousands of times in size and lustre; while many inconspicuous objects, which prove to be in our relative vicinity, must be notably his inferiors. The limits of real stellar magnitude are then set very widely apart. At the same time, the so-called "optical" and "geometrical" methods of relatively estimating star-distances are both seen to have a foundation of fact, although so disguised by complicated relations as to be of very doubtful individual application. On the whole, the chances are in favour of the superior vicinity of a bright star over a faint one; and, on the whole, the stars in swiftest _apparent_ motion are amongst those whose _actual_ remoteness is least. Indeed, there is no escape from either conclusion, unless on the supposition of special arrangements in themselves highly improbable, and, we may confidently say, non-existent.