VOL. XC.] PHILOSOPHICAL TRANSACTIONS. 587 



take it for granted, that a certain idea of brightness, attached to the stars which 

 are generally denominated to be of the 2d magnitude, may be added to our expe- 

 rimental knowledge; for, by this means, we are informed what we are to under- 

 stand by the expressions — , . . , z , -pp — ^.* We cannot wonder at the im- 

 mense difference between the brightness of the sun and that of Sirius; since the 

 first 2 expressions, when properly resolved, give us a ratio of brightness of more 

 than 170 thousand millions to 1; whereas the latter 2, as has been shown, give 

 only a ratio of 4 to 1 . What has been said will carry us, with very little addition, 

 to the end of our unassisted power of vision to penetrate into space. We can have 

 no other guide to lead us a 3d step than the same before-mentioned hypothesis; in 

 consequence of which however it must be acknowledged to be sufficiently probable, 

 that the stars of the 3d magnitude may be placed about 3 times as far from us as 

 those of the 1st. It has been seen, by my remarks on the comparative brightness 

 of the stars, that I place no reliance on the classification of them into magnitudes; 

 but in the present instance, where the question is not to ascertain the precise 

 brightness of any one star, it is quite sufficient to know that the number of the 

 stars of the first 3 different magnitudes, or different brightnesses, answers, in a 

 general way, sufficiently well to a supposed equally distant arrangement of a 1st, 

 2d, and 3d set of stars about the sun. Our 3d step forwards into space, may there- 

 fore very properly be said to fall on the pole star, on y Cygni, t Bootis, and all 

 those of the same order. As the difference, between these and the stars of the 



preceding order, is much less striking than that between the stars of the 1st and 2d 



aH Q.H 



magnitude, we also find that the expressions — = — ?—, and . . )t J are not in the 



high ratio of 4 to 1 , but only as 9 to 4, or 2^ to 1 . 



Without tracing the brightness of the stars through any farther steps, I shall 

 only remark, that the diminution of the ratios of brightness of the stars of the 4th, 

 5th, 6th, and 7th magnitudes, seems to answer to their mathematical expressions, 

 as well as, from the first steps we have taken, can possibly be imagined. The cal- 

 culated ratio, for instance, of the brightness of a star of the 6th magnitude, to 

 that of one of the 7th, is but little more than 1 £ to 1 ; but still we find by expe- 

 rience, that the eye can very conveniently perceive it. At the same time, the faint- 

 ness of the stars of the 7th magnitude, which require the finest nights, and the 

 best common eyes to be perceived, gives us little room to believe that we can pene- 

 trate much farther into space, with objects of no greater brightness than stars. 

 But, since it may be justly observed, that in the foregoing estimation of the pro- 

 portional distance of the stars, a considerable uncertainty must remain, we ought 

 to make a proper allowance for it, and, in order to see to what extent this should 

 go, we must make use of the experimental sensations of the ratios of brightness 

 we have now acquired, in going step by step forward; for, numerical ratios of 



* The names of the objects, ©, Sirius, 0Tauri, are here used to express their distance from us. 

 — Orig. 



4 P 2 



