It is scarcely necessary to mention the speculations of Huygens, Cassini, Gregory, and Michell, respecting the distances and magnitudes of the fixed stars, as deduced from a comparison of the quantities of the light of the Sun and of the Stars. There is too much conjecture in them to obtain much confidence. All Michell's notions, how ever, are entitled to great respect. He computes, that were the sun moved to such a distance that his parallax on the diameter of the Earth's orbit should be 2', he would appear at least as bright as Saturn, which he considers to be nearly equal to that of the brightest fixed star. This conjecture turns out nearly the same as recent observations appear to point out for a Lyrx.
It may be remarked, that at this distance, the diameter of the Sun would be less than 1-100th of a second. Sir Wil liam Herschel supposes the apparent diameter of a Lyra equal to 3-10ths of a second. These deductions, at first sight, seem opposed to each other. If we adopt the dou ble parallax of a Lyrx to be 2", and its apparent diame ter 3- 10ths of a second, its magnitude would be above three thousand times greater than that of the Sun. In this there is nothing very improbable.
Sir William Herschel himself appears to have attended a good deal to the inquiry which is the subject of this arti cle. He resumed Galileo's method of observing the an gular distance of two near fixed stars. He has explained this method at considerable length in the Philosophical Transactions. Sir William Herschel's discoveries as to the double stars offered great facilities of practising this method, but he does not appear to have obtained any re sults of importance. It is not satisfactorily explained why astronomers have not obtained more decisive information from this method. A comparison of observations, made in one part of the year after the end, and at the opposite season before the commencement, of twilight, appears to promise much. It is against all probability that two near stars of very unequal magnitudes should in general be equally distant. It may indeed happen in a few instances.
It remains now to give an account of the recent observa tions that have been made on the zenith distances of cer tain stars for examining this question.
M. Piazzi, observing at Palermo with a vertical circle, four feet in diameter, constructed by the late Mr. Rams
den, conceived he had observed a parallax in several stars. This great astronomer has given an account of his results in the 12th volume of the 111,.moirs of the Italian Society. But several circumstances tend to show that his instru ment was not perfect enough for this purpose, and that the number of observations were too few for decisive re sults.
He makes the parallax of a Lyrx about 2", that of a Arcturus is somewhat less. Procyon appeared by his in strument to have a parallax of 3" in declination. This shows the unexactness of his conclusions ; had Procyon a parallax of in declination, the parallax of the diameter of the earth's orbit would be 20", a quantity that would Iong ago have been discovered by observations of right ascension. The application of an instrument to stars, where the parallax in declination is but a small part of the whole, serves for a criterion of its exactness. If for these stars the parallax in declination appear considerable, the conclu sion must be, that the change of place arises not from parallax, but is an illusion either of the instrument or of the observations.
M. Piazzi, in his great catalogue of 7646 Stars, pub lished in 1814, attributes a parallax cf l".3 to the pole stars, from observations in right ascension. In this catalogue he attributes a parallax of 3" only to Procyon. He could determine nothing with respect to Arcturus. The paral lax of a Lyrx, he continues at 2", and the observations that he had then made of this star appear sufficient as to number.
None of his results agree with the observations that have since been made by Dr. Brinkley at the observatory of Trinity College, Dublin. The nearest approach is that of the parallax of a Lyrx, which, according to Dr. Brink ley, is t".1.
The observations of Dr. Brinkley have been made with an instrument superior to those employed in the attempts of former astronomers, and have been far more numerous, so that at last we have arrived at an appearance of certainty in this interesting subject, and may conclude that all the fixed stars are not at immeasurable distances.
It is right however to state, that his results have not been confirmed by the observations at Greenwich, by the astro nomer royal, Mr. Pond. On the contrary, the observa tions of the latter appear quite opposed to those made at Dublin.