46S 1'HILOSOPHICAL TRANSACTIONS. [ANNO 1784. 



ratio of the semi-diameters, this will become the direct triplicate and inverse 

 duplicate, that is, when the two are compounded together, the simple ratio of 

 the semi-diameters. 



13. The velocity a body would acquire by falling from an infinite height towards 

 the sun, when it arrived at his surface, being the same with that of a comet 

 revolving in a parabolic orbit in the same place, would be about 20.72 times 

 greater than that of the earth in its orbit at its mean distance from the sun ; for 

 the mean distance of the earth from the sun, being above 214.64 of the sun's semi- 

 diameters, the velocity of such a comet would be greater at that distance than at 

 the distance of the earth from the sun, in the sub-duplicate ratio of 214.64 to 

 1, and the velocity of the comet being likewise greater than that of planets, at 

 their mean distances, in the sub-duplicate ratio of 2 to 1 ; these, when taken 

 together, will make the sub-duplicate ratio of 42Q.28 to 1, and the square root 

 of 42Q.28 is 20.72, very nearly. 



14. The same result would have been obtained by taking the line rd pro 

 portional to the force of gravity at the sun's surface, and dc equal to his semi- 

 diameter ; and thence computing a velocity, which should be proportional to the 

 square root of the area rc when compared with the square root of another area, 

 one of whose sides should be proportional to the force of gravity at the surface 

 of the earth ; and the other should be, for instance, equal to 16 feet 1 inch, 

 the space a body would fall through in one second of time, in which case it 

 would acquire a velocity of 32 feet 2 inches per second, The velocity thus 

 found compared with the velocity of the earth in its orbit, when computed from 

 the same elements, necessarily gives the same result. Mr. M. made use of this 

 latter method of computation on a former occasion, as may be seen in Dr. 

 Priestley's History of Optics, p. 787, &c. but he has rather chosen to take the 

 velocity from that of a comet, in the article above, on account of its greater 

 simplicity, and its more immediate connexion with the subject of this paper. 



15. The velocity of light exceeding that of the earth in its orbit, when at its 

 mean distance from the sun, in the proportion of about 103 10 to l, if we 

 divide 10310 by 20.72, the quotient 4Q7, in round numbers, will express the 

 number of times which the velocity of light exceeds the velocity a body could 

 acquire by falling from an infinite height towards the sun, when it arrived at his 

 surface ; and an area whose square root should exceed the square root of the area 

 rc, where rd is supposed to represent the force of gravity at the surface of the 

 sun, and cd is equal to his semi-diameter, in the same proportion, must conse- 

 quently exceed the area rc in the proportion of 247009, the square of 4Q7 to 1. 



16. Hence, according to article JO, if the semi-diameter of a sphere of the 

 same density with the sun were to exceed that of the sun in the proportion of 

 500 to 1, a body falling from an infinite height towards it, would have acquired 



