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At m 3 slie is again in advance of her mean place by amaximum amount, and at w 4 she is again behind hermean place by a maximum amount.
This inequality of the moon’s motion is called theVo.ri-ation. It is so marked that at the points correspondingto TOj and m 3 the moon is in advance of her mean placeby an amount equal to about her own diameter, whileat m 2 and m i she is by a similar amount behind hermean place. The range of the variation is thus equalto about twice the moon’s diameter. The period ofthe variation is on the average half a lunation, sincein that time the moon passes from her greatest re-tardation (due to this cause) to her greatest advance,and so back to her greatest retardation. We owe toTycho Brahe the discovery of this inequality in themoon’s motion.*
And now, precisely as we had, after considering theannual equation, to discuss an associated but much lessconsiderable inequality, so there is an inequality asso-ciated with the variation, but much smaller in amount.It is, however, more interesting in many respects,precisely as the secular acceleration of the moon is amore interesting inequality than her annual equation.
We have hitherto not taken into account the cir-cumstance that though the sun’s distance enormously
* It will be evident that the ancients, who trusted chiefly toeclipses to determine the laws of the moon’s motion, were pre-cluded from recognizing the remarkable displacement due to tbevariation; since eclipses necessarily occur when the moon is on theline passing through the earth and sun, or when the moon is atM, or M„ at which points the variation vanishes.