Diftance, Magnitude, Ce. of the Fixed Stars, Cc. 47 
24. There is alfo another circumftance, from which perhaps: 
fome little additional probability might be derived, with regard 
to the real diftance of a ftar, {och as that we have fuppofed ; 
but upon which however, it muft be acknowledged, that no 
great ftrefs can be laid, unlefs we had fome better analogy to go 
upon than we have at prefent. The circumftance I mean is the 
greater fpecific brightnefs which fuch a ftar muft have, in pro- 
portion as the real diftance is lefs than that fuppofed, and vice 
versa ; fince, in order that the ftar may appear equally luminous, 
its {pecifie brightnefs muft be as the fourth power of its diftance 
inverfely ; for the diameter of the central ftar being as the 
cube ‘of the diftance between that and ‘the revolving ftar, and 
their diftance from the earth being in the fimple ratio of their 
diftance from each other, the apparent diameter of the central 
-ftar mutt be as the {quare ‘of its real diftance from the earth, 
and confequently, the furface of a {phere being as the {quare of 
its diameter, the area of the apparent ‘dife of fuch a. ftar muft 
be as the fourth power Of ‘its diftahce from the earth; ‘but in 
whatever ratio the apparent dife of the ftar is greater or lefs,. 
in the fame ratio inverfely muft bé the intenfity of its light,. 
in order to make it appear equally luminous. Hence, if its real” 
diftance fhould be greater or lefs than that fuppofed in the pro- 
portion’ of 2 or 3 to r, the intenfity of its light muft be lefs or 
greater, in the ‘icf cale, in the proportion of 16,’ er, ‘in ‘the: 
latter of 81 to t. 
25. According to Monf. Boucuer (fee his Traité d’Optique) 
the brightnefs of the fun exceeds that of a wax candle in no 
lefs a proportion than that of 8009 to 1. If therefore the bright- 
nefs of any of the fixed ftars fhould not’ exceed that of our com- 
mon candles, which, as being fomething -lefs luminous than. 
WAX,, 
