THE MOON’S MOTIONS.

73

and the influence of their respective distances fromthe moon. We thus have^rst, the proportion 315,000to 1, in which the sun’s attraction exceeds the earth’sat equal distances ; and secondly, the proportion(238,800) 2 to (91,500,000) 2 in which the attractiondue to the sun’s distance falls short of that due tothe earth’s. Thus we have this relation,—the sun’sactual influence on the moon bears to the earth’sthe proportion which 314,500 x (238,800) 2 bears to(91,500,000) 2 , or approximately a proportion of 15to 7.* Thus the sun’s influence on the moon is morethan twice as great as the earth’s.

It may be asked, then, how it is that the moon doesnot leave the earth’s company to obey the sun’ssuperior influence ? In particular it might seem thatwhen the moon is between the earth and the sun (oras placed at the time of a total eclipse), our satellitebeing then drawn more than twice as forcibly fromthe earth towards the sun as she is drawn towards theearth from the sun, ought incontinently to pass awaysunwards and leave the earth moonless.

The answer to this enigma is, simply, that the sunattracts the earth as well as the moon, and with almostthe same degree of force, his pull on the earth some-times slightly exceeding, at others slightly fallingshort, of his pull on the moon, according as the dis-tance of the moon or earth from him is greater at the

* The actual proportion, is 2'1421 correct to the fourth decimalplace. The proportion 15 to 7 is equal to 2'1429, which for ordi-nary purposes is sufficiently near.