DISTANCE, SIZE, AND MASS.

35

and .the moon's period are very accurately known,and as the moon’s distance has been determined byindependent observations, her mass may be inferredby the consideration of her observed motions ; in fact,precisely as, in the method for determining the moon’sdistance, described at page 24, we infer the distancewhen the mass is known; so, if the distance be inde-pendently determined, we can infer the mass.* Andit is to be observed that although, if these twomethods alone existed for determining the mass anddistance, they would leave both problems indeter-minate ; yet, as other methods exist, these tw r o affordvery useful tests of the accuracy of the results deducedby the other methods.

Laplace, adopting the value 5 T 12 /,- 03 for the lunarparallax, deduced for the moon’s mass, by this method,the value A ; the earth’s mass being unity.

Another method for determining the moon’s massis based on the theory of the tides. If the heightof the tides at any place be observed carefully for along period of time, and then the mean height of thespnng tides be compared with the mean height ofthe neap tides, we can infer the relative efficiencyof the sun and moon when acting together to raisethe tidal wave, and when their actions are opposed.

* It is easily seen that, on the assumptions made in the note atPP. 25, 26, the equations (i) and (ii) can either he used to give theresult there stated, or to give the result

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