Mechanics.

*5 9

of those Bodies can fall; which is the Rea-son of many very surprising Appearances

in

to revolve about itself, it will follow that the Point Cis that which must: describe the Circle (or Orbis Magnus)about the Sun ; because no other Point between A andB can keep always at the fame Distance from the Sun,on Account of the mutual Revolutions of those Bodiesabout that Point at the fame Time they are carried aboutthe Sun.

5. But to illustrate this Matter further, let S be theSun, and CD EF a Part of the annual Orbit; A andB the Earth and Moon in her Conjunction at C, in herQuadrature at D, in her Opposition at E, and in herlast Quarter at F ; during all these Motions from C toF, the Centres of the Earth and Moon will describeCurves of the Cycloid Kind, every where concave to theSun ; and though this may appear a Paradox, yet it iscapable of a Geometrical Demonstration, and may bealso shewn by Experiment. In the common Astrono-mical Tables, the Centre of the Earth is supposed todescribe the Orbis Magnus , and the Place and Distanceof the Sun or Earth is computed accordingly ; but thesewill be different from the true ones, which must becomputed from the Circle which the Earth does monthlydescribe about the common Centre of Gravity ; andthis Difference is call’d the Menstrual Paral-lax.

6. The Point C is that in which the Force of eachBody A, and B, is exerted ; and therefore every Actionof that Point is the fame as it would be if both theBodies were there united in one; thus if A and B weretwo Chain-Shots, the Point C in the Chain, and noother, would strike an Obstacle with the greatest Force,or that of a Body equal to the Sum of A and B.

7. If therefore a Wire be inserted in the Point C,and at the other End any Body D were affixed, thecommon Centre of Gravity of all the three Bodies A,B, and D, may be found as before ; for let the BodyC = A+B; then will C + D : D : : CD : CE; orA-pB+DiD:: CD: CE; and thus E will be

2 the

PI. VII.Fig. 14.

Fig. 13.