Chap. 3. PHILOSOPHY. 187

bear one to another, than in respect to the very numbers, thathave been here set down, by reason os the difficulty there isin measuring to the greatest exactness the diameters of the pri-mary planets; as will be explained hereafter, when we cometo treat of telescopes a . By the observations of the foremen-tioned Mr.P ound, in Jupiter the distance os the innermostsatellite should rather be about 6 semidiameters, of the second9-h os the third I y, and os the outermost 2 6 j b y and in Sa-turn the distance of the innermost satellite 4 semidiameters,of the next 6~, of the third 8;, of the fourth 20^, and of thefifth y 9 c . However the proportion between the distancesof the satellites in the fame primary is the only tiling necef-lary to the point we are here upon.

4. But moreover the force, wherewith the earth acts indifferent distances, is confirmed from the following consider-ation, yet more expresty than by the preceding analogicalreasoning. It will appear, that is the power os the earth, bywhich it retains the moon in her orbit, be supposed to act at alldistances between the earth and moon, according to the fore-mentioned rule ; this power will be sufficient to produce up-on bodies, near the surface os the earth, all the effects ascribedto the principle os gravity. This is discovered by the fol-lowing method. Let A (in fig. 94. ) represent the earth,B the moon, BCD the moon’s orbit, which differs little froma circle, of which A is the center. If the moon in B wereleft to it self to move with the velocity, it has in the point B, it

b Newt, Princ. philos. Lib. III. pag. 391.

» Book III. Ch.4.

Bb i

« Ibic*. pagl 592.

would