282 Mathematical Elements Book IV.

The Force of the Sun is to the Force of the*1419 Moon as 1 to 4,4815* ; the mean apparent Dia-meter of the Sun is 32 Min. 12 Sec. and the meanapparent Diameter of the Moon is 31 Min. i 64Sec. that is, they ar t to one another as 3864 to142 7 3753 > therefore the Density of the Sun is to theMoon's Denfity as 10000 to 48911 ; which Den-sity of the Moon may be corrtpar’d with the Den-*1260 sities of Jupiter , Saturn , and the Earth* ; and theMoon is denser than the Earth.

The Quantities of Matter in two Bodies are toone another in a Ratio compounded of the Densi-* 79 ties and Bulks* ; that is, if the Body be a Sphere,in a Ratio compounded of the Densities and theCubes of the Diameters.

j 42 8 The Densities of the Moon and Earth are to one

*1427 another as 48911 to 39214*, the Diameters as n1260 to 40,2. therefore the Quantities of Matter inthose Bodies are as 1 to 39,13. Tho’ the Densi-ties be discover’d, if you suppose the Bodies to behomogeneous, yet the Quantities of Matter willbe rightly defin’d tho’ the Bodies are not homo-geneous ; for we determine the Density whichthat Body would have, if the Matter of whichthe Body really consists was equally diffus’d allover it.

1429 2 "he Gravities on the Surfaces of the Earth andm Moon are determined by multiplying the Densities

1230 by the Diameters*, that is, they are to one ano-ther as 2,93 to x, or as 407,8 to 139,2 ; whichNumber also does express the relation of Gra-vity on the Surface of the Moon with the Gravity*1258 on the Surfaces of the Sun, Jupiter, and Saturn*.

1430 Dhe common Center of Gravity of the Moon ansEarth, about which both Bodies are mov’d, i®.determin’d; for its distance from the Center ofthe Earth, is to the distance between the Centers

or