VOL. XXXI.] PHILOSOPHICAL TRANSACTIONS. 457 



in a less proportion, the one being as the distances, and the other as their 

 squares, reciprocally. Add to this, that the more remote stars, and those far 

 short of the remotest, vanish even in the nicest telescopes, by reason of their 

 extreme minuteness ; so that, though it were true, that some such stars are in 

 such a place, yet their beams, aided by any help yet known, are not sufficient 

 to move our sense; after the same manner as a small telescopical fixed star is 

 by no means perceivable to the naked eye. 



Of the Number, Order, and Light of the fixed Stars. By the same. 



N° 364, p. 24. 



At the last meeting of the society, I adventured to propose some arguments, 

 that seemed to me to evince the infinity of the sphere of fixed stars, as occupy- 

 ing the whole abyss o^ space, or the to Trxv, which at present is generally un- 

 derstood to be necessarily infinite; and thence I laid down what may seem a 

 very metaphysical paradox, viz. that the number of fixed stars must then be 

 more than any finite number, and some of them more than at a finite distance 

 from others. This seems to involve a contradiction ; but it is not the only one 

 that occurs to those who have undertaken freely to consider the nature of in- 

 finite, to which perhaps the very narrow limits of human capacity cannot 

 attain. 



Since then, I have attentively examined what might be the consequence of 

 an hypothesis, that the sun being one of the fixed stars, all the rest were as 

 far distant from one another, as they are from us; and by a due calculation I 

 find, that there cannot, on that supposition, be more than ]3 points in the 

 surface of a sphere, as far distant from its centre, as they are from one another: 

 and I believe it would be hard to find how to place ] 3 globes of equal magni- 

 tude, so as to touch one in the centre; for the 12 angles of the icosaedron 

 are from one another very little more distant than from its centre; that is, the 

 side of the triangular base of that solid is very little more than the semi- 

 diameter of the circumscribed sphere, it being to it nearly as 21 to 20; so that 

 it is plain that somewhat more than 1 2 equal spheres may be posited about a 

 middle one; but the spherical angles or inclinations of the planes of these 

 figures being incommensurable with the 36o degrees of the circle, there will be 

 several interstices left, between some of the 12, but not such as to receive in 

 any part the 13th sphere. 



Hence it is no very improbable conjecture, that the number of the fixed stars 

 of the first magnitude is so small, because this superior appearance of light 

 arises from their nearness; those that are less showing themselves so small by 

 reason of their greater distance. Now there are in all only l6 fixed stars, in 



VOL. VI. 3 N 



