THE MOON’S MOTIONS.

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and tangential forces at M' are represented by thelines M' B' and M' C'; and so on, for all positions.

Leaving the tangential forces for subsequent con-sideration, let us suppose the above constructionextended so as to give the radial forces exerted atpoints all around the moon’s orbit. We should thenhave the result pictured in fig. 22,—the radial forcesall exerted outwards from 0 4 to Ox, and from 0 2 to 0 3 ,while they are all exerted inwards from Ox to 0 2 , andfrom 0 3 to O t . We see that the former forces largelyexceed the latter.

The first great result, then, from the considerationof the moon’s perturbing action, is this,—it tendsto draw the moon on the whole outwards from theearth, reducing.the earth’s influence to a certain extent.

We can compare the actual amount of the radialforce (or of the perturbing force generally) with theamount of the earth’s attraction; and it is importantthat we should do so in order that we may judge howthe forces acting on the moon are related as respectsmagnitude.

Bor it will be remembered that the construction forobtaining fig. 19 is based on the supposition that theline from E to the sun represents the sun’s directattraction on the earth or moon. Now, the line fromthe earth to the sun is about 91,500,000 miles long;while the line Mj A is equal to the diameter of theearth’s orbit, or to 238,800 miles. So that the sun’smaximum perturbing action on the moon is less thanBis direct action, in the proportion of 2,388 to 915,000,a 2