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Thus we have an exceedingly simple constructionfor determining the sun’s perturbing action on themoon (as compared with his direct action) when sheis in any given position. We have merely to drawM K square to the line joining B and S, to take K Hequal to twice E K, and to join M H; then M H is theperturbing force, where the line joining M and S repre-sents the sun’s direct action on the moon. *
Let us now figure the various degrees of perturbingforce exerted on the moon when she is in differentparts of her orbit, neglecting for the present the in-clination of her path to the ecliptic; in other words,regarding all such lines as M H (fig. 18) as lying in oneplane. The ellipticity of the moon’s orbit is also for themoment neglected. In fig. 19, Plate VI., this has beendone. To avoid confusion, the different points wherethe action of the perturbing force is indicated havenot been all lettered. Nor has the construction forobtaining the lines indicating the perturbing forcebeen indicated in any instance. The student will,however, have no difficulty in interpreting the figure.M x M 2 M 3 M 4 is the moon’s orbit around the earth at E.The sun is supposed to lie on the right in the pro-longation of E A. At Mj the perturbing force isoutwards towards the sun, and is represented inmagnitude and direction by the line M, A, which is
* Practically M H may be taken to represent the sun’s perturb-ing action on the moon when the line joining E and S representsthe sun’s direct action on the earth ; for the proportion of M S toeither E S or H S, is very nearly unity under all circumstances.