4/0 PHILOSOPHICAL TRANSACTIONS. [ANNO 1784. 



difference between this quantity and aass, in the same proportion, that is as 

 24700c) to 222g25.62 ; and aass must consequently be equal to 24083.38.?*, 

 whose square root 1552* nearly, or, in round numbers, 155 times the diameter 

 of the sun, will be the diameter of the central star sought. 



20. As the squares of the periodic times of bodies, revolving round a central 

 body, are always proportional to the cubes of their mean distances, the distance 

 of the two bodies from each other must therefore, on the foregoing suppositions, 

 oe l6 times greater in proportion to the diameter of the central body, than the 

 distance of the earth from the sun in proportion to his diameter ; and that 

 diameter being already found to be also greater than that of the sun in the pro- 

 portion of 155.2 to 1, this distance will consequently be greater than that of the 

 earth and sun from each other in the proportion of 16 times 155.2, that is 

 2483.2 to 1. 



21. Let us further suppose, that from the observations, the greatest distance 

 of the two stars in question appeared to be only 1 second ; we must then mul- 

 tiply the number 2483.2 by 20t)264.8, the number of seconds in the radius of 

 a circle, and the product 512196750 will show the number of times which such 

 a star's distance from us must exceed that of the sun. The quantity of matter 

 contained in such a star would be 155.2 3 or 3738308 times as much as that con- 

 tained in the sun ; its light, supposing the sun's light to take up 8 m 7 s in coming 

 to the earth, would, with its common velocity, require 79 00 years to arrive at 

 us, and 395 years more on account of the diminution of that velocity ; and sup- 

 posing such a star to be equally luminous with the sun, it would still be very 

 sufficiently visible, I apprehend, to the naked eye, notwithstanding its immense 

 distance. 



22. In the elements employed in the above computations, I have supposed the 

 diameter of the central star to have been observed, in order to ascertain its den- 

 sity, which cannot be known without it ; but the diameter of such a star is 

 much too small to be observed by any telescopes yet existing, or any that it is 

 probably in the power of human abilities to make ; for the apparent diameter of 

 the central star, if of the same density with the sun, when seen from another 

 body, which would revolve round it in 64 years, would be only the 1717th part 

 of the distance of those bodies from each other, as will appear from multiplying 

 107.32 the number of times the sun's diameter is contained in his distance from 

 the earth, by \6, the greater proportional distance of the revolving body, cor- 

 responding to 64 years, instead of 1. Now the 1717th part of a second must 

 be magnified 309060 times in order to give it an apparent diameter of 3' ; and 

 3', if the telescopes were mathematically perfect, and there was no want of dis- 

 tinctness in the air, would be but a very small matter to judge of. 



23. But though there is not the least probability that this element, so essen- 



