508 PHILOSOPHICAL TRANSACTIONS. [ANNO 1600. 



that ray, though taken from what was perhaps not far from its greatest extent 

 might possibly have reached to some distance beyond the apparent bounds of the 

 milky way: but if there had been any considerable difference in these determinations 

 we should remember that some of the data by which I have now calculated are only 

 assumed. For instance, if the opening of the iris, when we look at a star of the 

 7 th magnitude, should be only -^ of an inch and a half, instead of 2, then a, in 

 our formula, will be = 1.5 ; which, when resolved, will give a penetrating power 

 of 81.58 ; and therefore on this supposition, our telescope would easily have shown 

 stars 571 times as far from us as Sirius ; and only those at 653, 734, or 8 16 times 

 the same distance, would have been beyond its reach. My reason for fixing on T * T , 

 rather than a lower quantity, 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 show, 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 telescope will 

 show stars of the 1342d 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 — ^-i = D;* which, 

 on computation, comes out to be above 1 If millions of millions of millions of miles! 

 A number which exceeds the distance of the nearest fixed star, at least 300000 

 times. 



From the above considerations it follows, that the range for observing, with a 

 telescope such as my 40-feet reflector, is indeed very extensive, we have the inside 

 of a sphere to examine, the radius of which is the immense distance just now as- 

 signed to be within the reach of the penetration of our instruments, and of which 

 all the celestial objects visible to the eye, put together, form as it were but the 

 kernel, while all the immensity of its thick shell is reserved for the telescope. It 

 follows, in the next place, that much time must be required for going through so 

 extensive a range. The method of examining the heavens, by sweeping over space, 

 instead of looking merely at places that are known to contain objects, is the only 

 one that can be useful for discoveries. In order therefore to calculate how long a 

 time it must take to sweep the heavens, as far as they are within the reach of my 

 40-feet telescope, charged with a magnifying power of 1000, I have had recourse 

 to my journals, to find how many favourable hours we may annually hope for in 

 * d = 1 1,765475,948678,678679 miles.— Orig. 



