4o | -Mr.Micuent on the Means of diftovering the 
“in the duplicate ratio of their femi-diameters inverfely ; for by — 
the laft cor. the denfity of the central body remaining the 
fame, ‘the rectangle RC will be in the duplicate. ratio of CD;. 
in order therefore that the rectangle RC may always remain the 
fame, the line RD mutt be inverfely, as CD, and confequently 
the denfity inverfely, as the {quare of CD. 
12. Cor. 5. Hence the quantity of matter contained in thofe 
bodies muft be in the fimpie ratio of their femi-diameters di- 
rectly ; for the quantity of matter being always in a ratio com- 
pounded of the fimple ratio of the denfity, and the triplicate 
ratio of their femi-diameters, if the denfity is in the inverfe 
duplicate. ratio of the femi-diameters, this will become the dire@ 
triplicate and inverfe duplicate, that 1s, when the two are com- 
pounded together, the fimple ratio of the femi-diameters, 
13. The velocity a body would acquire by falling from an in- 
finite height towards the fun, when it arrived at his furface, 
being, as has been {aid before in article 3d, the fame with that 
of a comet revolving in a parabolic orbit in the fame place, 
would be about 20,72 times greater than that ofthe earth in 
its orbit at its mean diftance from the fun ; for the mean dif- 
tance of the earth from the fun, being about 214,64 of the 
fun’s femidiameters, the velocity of fuch a comet would be 
greater at that diftance than at the diftance of the earth from 
the fun, in the fub-duplicate ratio of 214,64 to 1, and the ve- 
locity of the comet being likewife greater than that of planets, 
at their mean diftances, in the fub-duplicate ratio of 2 to 13 
thefe, when taken together, will make the fub-duplicate ratio : 
of 429,28 to1, and the {quare root of 429,28 is 20,72, very: - 
nearly. 
14. The. 7 
