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major axis of ter actual orbit, we see that the ellipticalarea of her real path is less than that of the supposedcircular orbit. Hence, on the whole, she is nearer tothe sun than if she described a circular orbit in a yearinstead of her elliptical path. It is true that shemoves more slowly when in aphelion, and thus hervirtual yearly distance (so to speak) from the sun isincreased; but this does not compensate for the actualreduction of her orbit-area due to the eccentricity ofher orbit.* Hence the sun’s perturbing influence onthe moon is somewhat greater, owing to the ellipticityof the earth’s orbit. Now this ellipticity is subjectto slow variation, due to the influences of planetaryattraction. At present it is slowly diminishing. Theearth’s orbit is slowly becoming more and more nearlycircular, without, however, any change (or any cor-responding change) in the period of revolution. Thusthe area swept out by the earth each year is slowlyincreasing, and the total of the sun’s perturbing in-fluence on the moon in each year is slowly diminishing.The moon then is somewhat less retarded year afteryear; so that in effect she travels somewhat morequickly year after year. This change is called thesecular acceleration of the moon’s mean motion, orrather an acceleration which is partially accounted for
* The reasoning by which this may be demonstrated corre-sponds precisely with that in pp. 166, 167 of my treatise onSaturn , where I show that a planet receives more heat (luringa complete revolution in an elliptical orbit, than it would receivein revolving round a circular orbit in the same period.