penetrating into Space by Telescopes. 83 



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

 supposition, our telescope would easily have shewn stars 571 

 times as far from us as Sirius ; and only those at 653, 734, or 

 816 times the same distance, would have been beyond its reach. 

 My reason for fixing upon two-tenths, rather than a lower quan- 

 tity, was, that I might not run a risk of over-rating the powers 

 of my instruments. I have it however in contemplation, to 

 determine this quantity experimentally, and perceive already, 

 that the difficulties which attend this subject may be overcome. 



It now only remains to shew, how far the penetrating power, 

 192, of my large reflector, will really reach into space. Then, 

 since this number has been calculated to be in proportion to the 

 standard of natural vision, it follows, that if we admit a star of 

 the 7th magnitude to be visible to the unassisted eye, this tele- 

 scope will shew stars of the one thousand three hundred and 

 forty-second magnitude. 



But, as we did not stop at the single stars above mentioned, 

 when the penetration of the natural eye was to be ascertained, 

 so we must now also call the united lustre of sidereal systems 

 to our aid in stretching forwards into space. Suppose therefore, 

 a cluster of 5000 stars to be at one of those immense distances 

 to which only a 40-feet reflector can reach, and our formula 

 will give us the means of calculating what that may be. For, 

 putting S for the number of stars in the cluster, and D for its 



distance, we have = D ; * which, on computation. 



* D = 11765475948678678679 miles. 

 M <2 



