ON THE FIXED STARS. 4£)l 



larger than the sun. Those stars which are below the sixth magnitude arc 

 scarcely visible without the help of telescopes. The distances of all the stars 

 from us and from one another are so great, as not to be capable of being im- 

 mediately compared with their diameters; for no star subtends an angle large 

 enough to be ascertained by direct observation. The more perfect the instru- 

 ments that we employ, the smaller are the apparent diameters of the fixed 

 stars. Dr. Herschel found that one oi' the stars of the first magnitude, when 

 viewed in his best telescopes, appeared to be about one third of a 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 perhaps be for ever im- 

 possible 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 consequence 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. Herschel 

 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 bright- 

 est 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 inequality in their dimensions. At 

 any rate there is little doubt, that the diversity of their apparent magnitudes 

 is principally owing to their different distances ; perhaps none of them are 



