456 PHILOSOPHICAL TRANSACTIONS. [aNNO 1720. 



Of the Infinity of the Sphere of fixed Stars. By Edmund Halley, LL. D, 



F.R.S. N°364, p. 22. 



The system of the world, as it is now understood, is taken to occupy the 

 whole abyss of space, and to be as such actually infinite ; and the appearance 

 of the sphere of fixed stars, still discovering smaller and smaller ones, as we 

 apply better telescopes, seems to confirm this doctrine. And indeed, were the 

 whole system finite, though never so extended, it would still occupy no part 

 of the infinitum of space, which necessarily and evidently exists; whence the 

 whole would be surrounded on all sides with an infinite inane, and the super- 

 ficial stars would gravitate towards those near the centre, and with an accelerated 

 motion run into them, and in process of time coalesce and unite with them 

 into one. And, supposing time enough, this would be a necessary consequence. 

 But if the whole be infinite, all the parts of it would be nearly in aequilibrio, 

 and consequently each fixed star, being drawn by contrary powers, would keep 

 its place; or move, till such time, as, from such an aequilibrium, it found its 

 resting place; on which account, some perhaps may think the infinity of the 

 sphere of fixed stars no very precarious postulate. 



But to this I find two objections, which are rather of a metaphysical than 

 physical nature. And first, this supposes, as its consequent, that the number 

 of fixed stars is not only indefinite, but actually more than any finite number; 

 which seems absurd in terminis, all number being composed of units, and no 

 two points or centres being at a distance more than finite. But to this it may 

 be answered, that by the same argument we may conclude against the possi- 

 bility of eternal duration, because no number of days, or years, or ages, can 

 compleat it. Another argument I have heard urged is, that if the number of 

 fixed stars were more than finite, the whole superficies of their apparent sphere 

 would be luminous, for that those shining bodies would be more in number 

 than there are seconds of a degree in the area of the whole spherical surface, 

 which I think cannot be denied. But if we suppose all the fixed stars to be as 

 far from one another as the nearest of them is from the sun ; that is, if we 

 may suppose the sun to be one of them, at a greater distance their disks and 

 light will be diminished in the proportion of squares, and the space to contain 

 them will be increased in the same proportion ; so that in each spherical surface 

 the number of stars it might contain, will be as the biquadrate of their dis- 

 tances. Put then the distances immensely great, as we are well assured they 

 cannot but be, and from thence by an obvious calculus, it will be found, that 

 as the light of the fixed stars diminishes, the intervals between them decrease 



