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HISTORY OB’ PHYSICAL ASTRONOMY.

faintest stars seen in a telescope of given aperture, with the distance ofthose barely visible to the naked eye *.

The subject of the visibility of the stars has been fully considered bySir William Herscliel, in an admirable paper which appears in one of thevolumes of the Philosophical Transactions f. By a series of photometricalexperiments, he determined the quantity of light lost in telescopes of dif-ferent forms of construction. Assuming, moreover, that the pupil of theeye was equal to two-tenths of an inch in diameter, he compared the dis-tance at which a star would be barely visible in a telescope of given aper-ture with the distance of the smallest stars visible to the naked eye, con-sidered as the linear unit. The former of these distances was termed byhim the space-penetrating power of the telescope. Herscliel, in accord-ance with these principles, determined the space-penetrating powers ofvarious telescopes, differing either in construction or aperture, which heemployed in his observations.

Since the brightness of a star seen in a telescope depends upon themagnitude of the aperture, it follows, that by gradually diminishing thelatter, the image of a star may be reduced to any degree of faintness weplease. Hence, if two stars of unequal brightness be observed with twotelescopes exactly similar in all respects, and if the aperture of the tele-scope directed to the brighter star be reduced until both stars appear ofthe same brightness, it is manifest that the absolute quantity of lightemitted by each star to the earth, will be in the inverse ratio of the aper-ture of the telescope through which it is thus seen. Now, knowing therelative quantities of light emitted by the two stars, their relative dis-tances may be readily determined, supposing, as before, that both starspossess the same degree of intrinsic brightness. Sir William Herschel applied these principles to the determination of the relative distances ofthe stars l and clusters of stars § visible in his powerful telescopes. It isimpossible within the limits to which we are confined, to give any accountof the sublime results to which he was conducted by his labours on thisoccasion.

The question with respect to the absolute distance of the stars from theearth, is one which has excited a high degree of interest among astrono-mers ever since the re-establishment of the true system of the world byCopernicus . This might be ascertained in any case by a simple and directprocess, if the star exhibited a change of position depending on the mo-tion of the earth in her orbit, but such a parallactic displacement was longfound to be insensible. Another mode of effecting the same object wasfounded upon a knowledge of the apparent diameter of the star. Assum-ing the star to be equal in absolute magnitude to the sun, it is clear thatthe distance of the sun from the earth would be to the distance of the starfrom the same body, as the apparent diameter of the star to the apparentdiameter of the sun. This mode of determining the distance of a starwas less satisfactory than that founded upon a knowledge of its parallax,seeing that it involved an arbitrary assumption with respect to the mag-nitude of the star; but still it was exceedingly desirable to arrive at someprobable conclusion upon the subject. It was soon found, however, thatthe measurement of the apparent diameter of a star was an object of asgreat delicacy as the detection of its parallax. The earlier astronomers,indeed, supposed that the principal stars possessed an apparent magnitude

* Phil. Trans., 1767, p. 234, et scq.J Ibid., 1817, p. 302, et seep

f Ibid., 1800, p. 49, et seq.

§ Ibid., 1818, p. 429, et seq.