VOL. LXXIV.] PHILOSOPHICAL TRANSACTIONS. 469 



at its surface a greater velocity than that of light ; and consequently, supposing 

 light to be attracted by the same force in proportion to its vis inertiae, with other 

 bodies, all light emitted from such a body would be made to return towards it, 

 by its own proper gravity. 



17. But if the semi-diameter of a sphere, of the same density with the sun, 

 was of any other size less than 4Q7 times that of the sun, though the velocity 

 Of the light emitted from such a body would never be wholly destroyed, yet 

 would it always suffer some diminution, more or less, according to the magni- 

 tude of the said sphere ; and the quantity of this diminution may be easily found 

 in the following manner : suppose s to represent the semi-diameter of the sun, 

 and as to represent the semi-diameter of the proposed sphere ; then, as appears 

 from what has been shown before, the square root of the difference between the 

 square of 4Q7s and the square of as will be always proportional to the ultimately 

 remaining velocity, after it has suffered all the diminution it can possibly suffer 

 from this cause ; and consequently the difference between the whole velocity of 

 light, and the remaining velocity, as found above, will be the diminution of its 

 velocity. And hence the diminution of the velocity of light emitted from the 

 sun, on account of its gravitation towards that body, will be somewhat less 

 than a 494000th part of the velocity which it would have had, if no such dimi- 

 nution had taken place; for the square of 497 being 247009, and the square of 

 1 being 1, the diminution of the velocity will be the difference between the 

 square root of 247009 and the square root of 247008, which amounts, as above, 

 to somewhat less than one 494000th part of the whole quantity. 



18. The same effects would likewise take place, according to article 11, if 

 the semi-diameters were different from those mentioned in the last 2 articles, 

 provided the density was greater or less in the duplicate ratio of those semi-dia- 

 meters inversely. 



19. The better to illustrate this matter, it may not be amiss to take a particu- 

 lar example. Let us suppose then, that it should appear from some observations 

 made on some one of those double stars above alluded to, that one of the two 

 performed its revolution round the other in 64 years, and that the central one 

 was of the same density with the sun, which it must be, if its apparent diameter, 

 when seen from the other body, was the same as the apparent diameter of the 

 sun would be if seen from a planet revolving round him in the same period : let 

 us further suppose, that the velocity of the light of the central body was found 

 to be less than that of the sun, or other stars whose magnitude was not suffi- 

 cient to affect it sensibly, in the proportion of 19 to 20. In this case then, 

 according to article 17, the square root of 1A700Qss must be to the square root 

 of the difference between 24/009 ss and aass, as 20 to 19. But the squares of 

 20 and 19 being 400 and 36 1, the quantity 247009« must therefore be to the 



