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I would invite the student who wishes really to masterthe subject to consider intermediate cases, carefullymaking the requisite constructions and applying tothem considerations resembling those which will nowbe applied to the four selected cases:—-
Let the major axis of the lunar orbit (or, as it iscalled, the ‘Mine of apsides,”) be directed as in fig. 34,Plate IX., towards the sun, the perigee being nearestto the sun as at p. Then the perturbing forces, forcertain parts of the orbit, are indicated in the figure.At p and a the radial force exerts its maximum out-ward actions; at M and M 4 it exerts its maximuminward actions. Near 0 15 0 2 , O s , and 0 4 the tangentialforce has its maximum values.*
Now, from fig. 30 combined with fig. 34, we see thatthe outward action of the radial force over the perigealarc 0 i pO 1 results in a regression of the perigee ;t
* The student should make tracings from figs. 34,35, 36, and 37,and draw the radial and tangential resolved parts of the forces,precisely as in Plate VI. This will be found to be a most instructiveexercise.
t To prevent misconception I will go through the reasoningleading to this result, leaving to the student to deal inmanner with other cases as they arise. Fig. 34 shows that vehave outward radial perturbing action as the moon is passing h etperigee. N ow, fig. 30 illustrates the effect of outward radial (ornormal) perturbations. In this figure M s M, M, is the perigealarc, and we see that H is shifted towards 8 or 1 or 2, according a®the body is at M„ or M, or M 2 when the perturbation takes place,and in intermediate positions towards intermediate points. Th®perigee then is shifted from M, backwards ; i. e. in the directioncontrary to that indicated by the arrow on the orbit. AV ith ver f