14 Penetration into Space by Tilef copes. 



It is remarkable that, from very difFerent principles, I have formeilly determined the 

 length of the vifual ray of my 20-feet telefcope upon the ftars of the milky way, fo as to 

 agree nearly with the calculations that hai-e been given *. The extent of what I then 

 figuratiyely called my founding line, and what now appears to anfwer to the power or 

 penetrating into fpace, was (hewn to be not Icfs than 415, 461, and 497 times the dlf- 

 tance of Sirius from the fun. We now have calculated that my telefcope, in the Newto- 

 nian form, at the time when the paper on the Conftru(Stion of the Heavens was written, 

 pofleflcd a power of penetration, which exceeded that of natural vifion 61,18 times; and, 

 as we have alfo fliewn, that ftars at 8, 9, or at mod 10 times the diftance of Sirius, mud 

 become invifible to the eye, we may fafely conclude, that no fingle ftar, above 489,551, 

 or at moft 612 times as far as Sirius, can any longer be feen in this telefcope. Now, the 

 greateft length of the former vifual 'ray, 497, agrees nearly with the lowed of thefe prefent 

 numbers, 489 ; and the higher ones are all in favour of the former compatation ; for that 

 ray, though taken from what was perhaps not far from its greateft extent, might poflibly 

 have reached to fome diftance beyond the apparent bounds of the milky way : but, if there 

 had been any confiderable difference in thefe determinations, we fhould remember that . 

 fome of the data by which I have now calculated are only aflumed. For inftance, if the 

 opening of the iris, when we look at a ftar of the 7th magnitude, fliould be only one-tenth 

 of an inch and a half, inftead of two, then a, in our formula, will be zz 1,5 ; which, 

 when refolved, will give a penetrating power of 81,58; and therefore, on this fuppofition, 

 our telefcope would eafily have fliewn ftars 571 times as far from us as Sirius; and only 

 thofe at 653,734, or 816 times the fame diftance, would have been beyond its reach. My 

 reafon for fixing upon two- tenths, rather than a lower quantity, was, that I might not 

 run a rilk of over-rating the powers of my inftruments, I have it however in contem- 

 plation,, to determine this quantity experimentally, and perceive already, that the difEcul- 

 tits which attend this fubjedl: may be overcome. 



It now only remains to fliew, how far the penetrating power, 192, of my large refle£l:or, 

 will really reach into fpace. Then, fince this number has been calculated to be in pro- 

 portion to the ftandard of natural vifion, it follows, that if we admit a ftar of the 7th 

 magnitude to be vifiUe to the unaflifted eye, this telefcope will fticw ftars of the one 

 thoufand three hundred and forty-fecond magnitude. 



But, as we did not ftop at the fingle ftars above mentioned, when the penetration of the 

 natural eye was to be afcertalned, fo we muft now alfo call the united luftre of fidereal 

 fyftems to our aid in ftretching forwards into fpace. Suppofe therefore, a clufter of 5000 

 ftars to be at one of thofe immenfe diftances to which only a 40-feet refleftor can reach, 

 and our formula will give us the means of calculating what that may be. For, putting S 



- • Phil, Tranf. Vol. LXXV. page 14 7, »48- 



for 



