86
sun are approximately as the numbers 62, 61, and 60;and therefore the perturbing influences on the moonwhen the earth is in aphelion, at mean distance, and inperihelion, are respectively as the numbers 64, 61, and58 (obtained by leaving the middle number 61 un-altered, and making the first and last differ threetimes as much as before from the middle number).
There is, then, an appreciable difference betweenthe perturbing forces exerted by the sun when theearth is in perihelion, or at about the beginning ofJanuary, and when the earth is in aphelion, or atabout the beginning of July. The earth’s'power overthe moon is more considerably diminished in theformer case than in the latter. Now the partialrelease of the moon from the earth’s influence resultsin a slight increase of her mean distance and alengthening of the moon’s period of revolution (werefer of course to her sidereal revolution) around theearth. This will be evident when we consider thatthe earth’s attraction is always tending, though thetendency may not actually operate, to reduce themoon’s distance; so that any cause diminishing thetotal force towards the earth must enable the moon toresist this tendency more effectually than she other-wise would. In winter, then, when the earth is nearperihelion, the moon’s mean distance and her period ofrevolution are somewhat in excess of the average; fo rthe sun’s releasing effect is then at a maximum. I nsummer, on the contrary, the earth being near aphelion,the moon’s mean distance and her period of revolution