588 PHILOSOPHICAL TRANSACTIONS. [ANNO 1800. 



brightness, and sensations of them, as has been noticed before, are very difFerent 

 things. And since, from the foregoing considerations, it may be concluded, that 

 as far as the 6th, 7th, or 8th magnitude, there ought to be a visible general dif- 

 ference between stars of one order and that of the next following, I think, from 

 the faintness of the stars of the 7th magnitude, we are authorized to conclude, 

 that no star, 8, 9, or at most 10 times as far from us as Sirius, can possibly be per- 

 ceived by the natural eye. 



The boundaries of vision, however, are not confined to single stars. Where 

 the light of these falls short, the united lustre of sidereal systems will still be per- 

 ceived. In clear nights, for instance, we may see a whitish patch in the sword- 

 handle of Perseus, which contains small stars of various sizes, as may be ascer- 

 tained by a telescope of a moderate power of penetrating into space. We easily 

 see the united lustre of them, though the light of no one of the single stars could 

 have affected the unassisted eye. Considerably beyond the distance of the former 

 must be the cluster discovered by Mr. Messier, in lj64 ; north following H Gemi- 

 norum. It contains stars much smaller than those of the former cluster; and a 

 telescope should have a considerable penetrating power, to ascertain their brightness 

 properly, such as my common 10-feet reflector. The night should be clear, in 

 order to see it well with the naked eye, and it will then appear in the shape of a 

 small nebula. Still farther from us must be the nebula between » and £ Herculis, 

 discovered by Dr. Halley, in 17 14. The stars of it are so small that it has been 

 called a nebula; and has been regarded as such, till my instruments of high pene- 

 trating powers were applied to it. It requires a very clear night, and the absence 

 of the moon, to see it with the natural eye. Perhaps, among the farthest objects 

 that can make an impression on the eye, when not assisted by telescopes, may be 

 reckoned the nebula in the girdle of Andromeda, discovered by Simon Marius, in 

 1612. It is however not difficult to perceive it, in a clear night, on account of 

 its great extent. 



From the powers of penetrating into space by natural vision, we proceed now to 

 that of telescopes. It has been shown, that brightness, or light, is to the naked 

 eye truly represented by -; in a telescope therefore, the light admitted will be 



expressed by — • Hence it would follow, that the artificial power of penetrating 

 into space should be to the natural one as a to a. But this proportion must be 

 corrected by the practical deficiency in light reflected by mirrors, or transmitted 

 through glasses; and it will in a great measure depend on the circumstances of the 

 workmanship, materials, and construction of the telescope, how much loss of light 

 there will be sustained. 



In order to come to some determination on this subject, I made many experi- 

 ments with plain mirrors, polished like my large ones, and of the same composi- 

 tion of metal. The method I pursued was that proposed by Mr. Bouguer, in his 

 Traite d'Optique, page 16, fig. 3; but I brought the mirror, during the trial, as 



