Sir Isaac Newton’s BookII.

218

4.2. T hus the inclination of the orbit is greatest, whenthe line drawn between the moon’s nodes will pass throughthe fun; and least, when this line lies in the quarters, especial-ly if the moon at the tame time be in conjunction with thefun, or in the oppolition. In the first of these cafes the nodeshave no motion, in all others, the nodes will each monthhave receded : and this regressive motion will be greatest,when the nodes are in the quarters; for in that cafe the nodeshave no progressive motion during the whole month, but inall other cafes the nodes do at some times proceed forward,viz. whenever the moon is between either quarter, and thenode which is less distant from that quarter than a fourthpart of a circle.

4.3. It now remains only to explain the irregularities inthe moon’s motion, which follow from the elliptical figureof the orbit. By what has been said at the beginning of thischapter it appears, that the power of the earth on the moonacts in the reciprocal duplicate proportion of the distance:therefore the moon, if undisturbed by the fun, would moveround the earth in a true ellipfis, and the line drawn fromthe earth to the moon would pass over equal spaces in equalportions of time. That this description of the spaces isaltered by the fun, has been already declared. It has alsobeen shewn, that the figure of the orbit is changed each.month; that the moon is nearer the earth at the new andfull, and more remote in the quarters, than it would be with-out the fun. Now we must pass by these monthly changes,and consider the effect, which the fun will have in the differ-ent