THE MOON’S MOTIONS.

91

thirds of the moon’s diameter. But the theoreticalsecular acceleration, though its effects are accumu-lative, and in geometrical progression, yet in a cen-tury would only cause the moon to be in advance ofthe place which she would have had, if the accelera-tion had not operated during the century, by one-300th part of her diameter; and the actual secularacceleration only causes the moon to gain about twicethis .distance, or about one-150th part of her diameter,in a century.*

We have next to consider one of the most im-portant perturbations to which the moon is subjected sofar as the rate of her motion in her orbit is concerned.

We have hitherto considered chiefly the radial partof the perturbing force. We must now discuss thevariations in the tangential force. We have alreadyseen how this force can be separated from the radialforce (see p. 82). Let us suppose the method appliedto give a figure of the tangential forces correspond-ing to that already given (fig. 22) for the radial forces.To do this, we have to draw a number of lines obtainedasMC and M' Awere obtained in figs. 20, 21. Whenthis is done (and the reader is recommended not tohe satisfied until he has effected the construction forhimself independently), the force-lines are found toarrange themselves as shown in fig. 23. It will be

* In two hundred years the gain is four times as great, in threehundred years nine times as much, and so on. For the above illus-tration I am indebted to Mr. Wilson’s paper mentioned in thepreceding note.