THE MOON’S MOTIONS.

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Before passing from the consideration of the directaction of the tangential force, it is to be noticedthat this force affects the secular acceleration of themoon. It had long been held that only the radialforce can really be effective in long intervals of time,because the tangential force is self-compensating,—if not in each lunation,* yet at least in the course ofmany successive lunations. But as a matter of fact,inasmuch as the eccentricity of the earth’s orbit isundergoing a continual though very gradual diminu-tion, an element is introduced which renders thiscompensation incomplete,—not merely in many suc-cessive lunations or in many successive years, but inmany successive centuries. So long as the eccen-tricity of the earth’s orbit continues to diminish, therecan in fact be no tendency to exact compensation sofar as this particular element is concerned. Nowthis circumstance had not escaped Laplace whenhe discussed the moon's secular acceleration; butbe was led to believe that its effects would be whollyinsignificant. Professor Adams, however, in re-examining the whole subject, was led to inquirehow far this view of the matter is justified. Theexperience of past inquirers had shown that no causeof variation, and particularly no cause having effects

* Of course, in a thorough analysis of the action of the tangen-tial force, it has to be remembered that, apart from the ellipticity

the moon’s orbit, and the consequent inequality of the sun’s per-turbing action in different quadrants as well as in different halves,the orbit is undergoing a process of continual change, even underthe action of the tangential and radial forces themselves.

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