51. AS soon as the apogeon is passed the conjunction with the sun or the opposition, the progressive motion thereof abates, and with it the proportion of the greatest distance of the moon from the earth to the least distance will also diminish; and when the apogeon becomes regressive, the diminution of this proportion will be still farther continued on, till the apogeon comes into the quarter; from thence this proportion, and the eccentricity of the orbit will increase again. Thus the orbit of the moon is most eccentric, when the apogeon is in conjunction with the sun, or in opposition to it, and least of all when the apogeon is in the quarters. 52. THESE changes in the nodes, in the inclination of the orbit to the plane of the earth’s motion, in the apogeon, and in the eccentricity, are varied like the other inequalities in the motion of the moon, by the different distance of the earth from the sun; being greatest, when their cause is greatest, that is, when the earth is nearest to the sun. 53. I SAID at the beginning of this chapter, that Sir ISAAC NEWTON has computed the very quantity of many of the moon’s inequalities. That acceleration of the moon’s motion, which is called the variation, when greatest, removes the moon out of the place, in which it would otherwise be found, something more than half a degree[201]. In the phrase of astronomers, a degree is 1/360 part of the whole circuit of the moon or any planet. If the moon, without disturbance from the sun, would have described a circle concentrical to the earth, the sun will cause the moon to approach nearer to the earth in the conjunction and opposition, than in the quarters, nearly in the proportion of 69 to 70[202]. We had occasion to mention above, that the nodes perform their period in almost 19 years. This the astronomers found by observation; and our author’s computations assign to them the same period[203]. The inclination of the moon’s orbit when least, is an angle about 1/18 part of that angle, which constitutes a perpendicular; and the difference between the greatest and least inclination of the orbit is determined by our author’s computation to be about 1/18 of the least inclination[204]. And this also is agreeable to the observations of astronomers. The motion of the apogeon, and the changes in the eccentricity, Sir ~ISAAC NEWTON~ has not computed. The apogeon performs its revolution in about eight years and ten months. When the moon’s orbit is most eccentric, the greatest distance of the moon from the earth bears to the least distance nearly the proportion of 8 to 7; when the orbit is least eccentric, this proportion is hardly so great as that of 12 to 11.