270 Mathematical Elements Book IV.CHAP. XVIII.

‘The physical Explanation of the Motion of theAxis of the Earth.

F jT^ HAT the Nodes of the Moon go back)*1 341 JL that are mov'd in antecedentia*, and that#i 347 the Inclination of its Orbit is liable to change*?we have already demonstrated ; let us conceiveseveral Moons to be at the fame distance, revol-ving,in equal Times about the Earth, in a Planeinclin’d to the Plane of the Ecliptic, it is plainthey will all be agitated by the fame Motions;let us conceive the Number of the Moons to beincreas’d, so as to touch one another, and form,a Ring, whose Parts cohere ; whilst one part ofthe Ring is attracted, to increase the Inclination?the other part is agitated by a contrary motion?*1345 to diminish its Inclination*; the greater Force1377 in this Cafe prevails, that is, in the motion of theLine of Nodes , front the Quadratures towards theSyzygies, the Inclination of the Ring is diminifh’d W*1349 each of its Revolutions *,. and it is the least <f all'when* 35 ° the Line of Nodes is in the Syzygies ; on the contra-ry, its Inclination is increas’d when the Line of. Nodesis carried front the Syzygies towards the Quadra-*1351 tures*, and it is the greatest of all when the-Line of1 3 7 8 the Nodes is in these last *; the Line of the Nodes is*«' 3 ' 5 ' 2 continually carried i-r antecedents, unless when it is1344 at re fi hi the Syzygies*.

i 379 V the Quantity of Matter in the Ring he dinn-nifh’d, its Motions will mt be chanstd, because theydepend upon Gravity, which acts equally upon*1027 every Particle of Matter*. r,-