penetration into Space by Tele/copes. 503 



What has been fald will carry us, with very little addition, to the end of our unafllfted 

 power of vifion to penetrate into fpace. We can have no other guide to lead us a third ftep 

 than the fame beforementioned hypotheGs ; in confequence of which, however, it muft be 

 acknowledged to be fufficiently probable, that the ftars of the third magnitude may be placed 

 about three times as far from us as thofe of the firft. It has been feen, by my remarks on 

 the comparative brightnefs of the flars, that I place no reliance on the claflification of them 

 into magnitudes * ; but, in the prefent inftance, where the queftion is not to afcertain the 

 precife brightnefs of any one ftar, it is quite fufficient to know that the number of the ftars 

 of the firft three different magnitudes, or different brightnefTes, anfwers, in a general way, 

 fufhciently well to a fuppofed equally diftant arrangement of a firft, fecond, and third fet of 

 ftars about the fun. Our third ftep forwards into fpace, may therefore very properly be 

 faid to fall on the polc-ftar, on y Cygrii, f Bootis, and all thofe of the fame order. 



As the difference, between thefe and the ftars of the preceding order, is much lefs ftriking 

 than that between the ftars of the firft and fecond magnitude, we alfo find that the ex- 



prelTions ', and .-, , . ■,- , are not In the high rjitio of 4 to i, but only as 9 to 4, 



*^ UTauri)* Polaris P ° y > -w 



or 2^ to I. 



Without tracing the brightnefs of the ftars through any farther fteps, I fhall only re- 

 mark, that the diminution of the ratios of brightnefs of the ftars of the 4th, 5th, 6th, and 

 7th magnitude, feems to anfwer to their mathematical expreffions, as well as, from the firft 

 fteps we have taken, can pofFibly be imagined. The calculated ratio, for inftance, of the 

 brightnefs of a ftar of the 6th magnitude, to that of one of the 7th, is but little more than 

 if to I ; but will we find by experience, that the eye can very conveniently perceive it. At 

 the fame time, the faintnefs of the ftars of the 7th magnitude, which require the fineft 

 nights, and the beft common eyes to be perceived, gives us little room to believe that we 

 can penetrate much farther into fpace, with objefts of no greater brightnefs than ftars. 



But, fince it may be juftly obferved, that in the foregoing eftimation of the proportional 

 diftance of the ftars, a confiderable uncertainty muft remain, we ought to make a proper 

 allowance for it ; and, in order to fee to what extent this fhould go, we inuft make ufe of 

 the experimental fenfations of the ratios of brightnefs we have now acquired, in going ftep 

 by ftep forward : for, numerical ratios of brightnefs, and fenfations of them, as has been 

 noticed before, are very different things. And fince, from the foregoing confiderations, 

 it may be concluded, that as far as the 6th, 7th, or 8th magnitude, there ought to be a vi- 

 fible general difference between ftars of one order and that of the next following, I think, 

 from the faintnefs of the ftars of the 7th magnitude, we are authorized to conclude, that 

 no ftar, eight, nine, or at moft ten times as far from us as Sirius, can pofBbly be perceived 

 by the natural eye. 



• PhiJ. Tranf, for the year 179*, page 168, i6j. 



The 



