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THE MOON’S MOTIONS.

or is about one-383rd part of the latter. But theearth’s direct action on the moon is, as we have seen,equivalent to about 7-15ths of the sun’s. Hence thesun’s maximum perturbing influence is less than theearth’s mean attraction on the moon, in the proportionof 15 to 7 x 383, or is about one-179th part of thelatter. Thus the force pulling the moon at M x towardsthe sun, would be represented by a line 383 times aslong as M, A, while the force pulling the moon to-wards E would be represented by a line 179 times aslong as M x A. The relations for the perturbing forcesexerted on the moon in other positions, as well for thewhole forces as for their radial and tangential portions,are indicated by the proportions of the lines in figs.19, 22, and 23. When the perturbing force has its leastvalue, or when the moon is at M 2 or M 4 , this force,now wholly radial, is about one-776th of the sun’sdirect action, and about one-358th of the earth’s.

But now we have to consider the circumstance thatthe earth’s path around thq sun is eccentric, and thatthus the sun’s perturbing influence on the moonnecessarily varies in amount. It will be obvious thatthe perturbing forces must all be greater when theearth and her satellite are nearer to the sun. Let usinquire in what degree they will increase.

This question is readily answered. Fig. 19 indi-cates the magnitude of the perturbing forces whenthe line from the sun to E indicates the sun’s directaction. Now to simplify matters let us take an illus-trative case, in order to determine the law according