390 LECTURE XLI. 



second in diameter. But there is always a limit to the perfection of the 

 focus of the telescope and of the eye, and, however accurate both may be, 

 the image of every radiant point will occupy on the retina a space of a 

 certain magnitude, not depending on that of the object : so that it will per- 

 haps be for ever impossible to measure any angle, which is only a very 

 small fraction of a second. (Plate XXXI. Fig. 453, 454.) 



There is, however, reason to suppose, that the angle subtended by the 

 nearest stars is in reality more than a hundred times less than the angle 

 measured by Dr. Herschel, for it may be conjectured that our distance 

 from the nearest stars is about a hundred million million miles ; taking 

 about one third of a second for the annual parallax of the earth, that is, 

 for the change of the apparent places of some of the fixed stars in conse- 

 quence of the earth's annual motion.* This seems to be nearly the' utmost 

 amount of an annual parallax that could wholly have escaped observation ; 

 for Dr. Herschelf supposes that, by means of double stars, a parallax of 

 one tenth of a second only might become sensible, and even this has never 

 yet been discovered ; on the other hand, if the parallax were really much 

 smaller than this, it would be necessary to suppose the actual magnitude or 

 splendour of the brightest stars to be incomparably greater than that of the 

 sun ; for at the distance of a hundred million million miles, our sun would 

 appear, according to Lambert's calculations, but about one fourth as bright 

 as Saturn, or like a star of the second or third magnitude only. Perhaps, 

 indeed, the stars may differ as much from each other in magnitude as the 

 planetary bodies, but it is somewhat more natural to imagine them more 

 nearly equal, until we have some reason for supposing any material inequal- 

 ity in their dimensions. At any rate there is little doubt, that the diversity 

 of their apparent magnitudes is principally owing to their different dis- 

 tances ; perhaps none of them are much nearer to each other than the 

 nearest to us ; and there may still be a very great variety in their actual 

 dimensions. There can be only twelve points on the surface of a sphere as 

 far from each other as from the centre J ; in a sphere of twice the radius, 

 there may be about 50 points at the same distance ; in a sphere of three 

 times the radius, more than 100 : and it has been observed that these 

 numbers do not greatly differ from the actual numbers of the stars of the 



* The accuracy of modern instruments establishes the existence of a sensible paral- 

 lax to one star at the least. By means of an excellent heliometer, Bessel has obtained 

 a series of distances of the two stars which constitute the double star 61 Cygni, 

 from which he concludes that this star has a sensible parallax of about one-third of a 

 second. Other astronomers have attacked the subject with vigour, and amongst the 

 rest, Mr. Henderson has made out a highly probable parallax to a Centauri. A dis- 

 cussion of this subject will be found in Fockens's Commentatio Ast. de annua stel. 

 paral. Lugd. 1835 ; and in Mr. Main's Report on the present State of our Know- 

 ledge of the Parallax of the fixed Stars, Trans, of the Astron. Soc. vol. xii. 



See also Clairaut, Hist, et Mem. 1739, p. 358. Schubert, Bode's Jahrbuch, 1796. 

 Piazzi, Mem. della Soc. Ital. 1805, xii. 1809. Calendrelli, Opusc. Astr. 1806. 

 Brinkley, Ir. Tr. 1815, p. 25. Ph. Tr. 1821. Ast. Soc. vol. i. Pond. ibid. 1817. 

 J. Herschel, Ph. Tr. 1826, p. 266 ; 1827. Struve, Introd. to Duplicium Mensura, 

 &c. fol. Dorpat, 1827. Bessel, Astronomische Nachrichten, vol. xvi. Taylor, 

 Madras Obs. vol. ii. Airy, Ast. Soc. vol. x. Henderson, ibid. vol. xi. 



t Ph. Tr. 1782, Ixxii. 82. 



I Halley, Ph. Tr. 1720, p. 22. Kastner, Dissert. Math. 



