DISTANCE, SIZE, AND MASS.

43

on the moon’s mass, it follows that when its observedvalue is compared with the formula deduced by theory,a means of determining the moon’s mass must neces-sarily be obtained.

Laplace, adopting Maskelyne’s value of the maxi-mum nutation,—namely, 9" - 6, inferred for the moon’smass i (the earth’s being regarded as unity). Pro-fesser Newcomb adopting 9"'223 for the lunar nuta-tion, and 50"‘378 for the annual luni-solar precession,deduces the value -L . Leverrier with the same valuesdeduces . Mr. Stone, in his latest calculation, withthe same values, deduces for.the moon’s mass gH . *

In the present work we adopt 8 -H (or 0 - 01228) asthe moon’s mass, the earth’s being regarded as unity.Taking the moon’s volume as (the earth’s asunity), it follows that the moon’s mass bears a smallerproportion to the earth’s than her volume bears to theearth’s volume, in the ratio of 4,926 to 8,140. Hencethe moon’s mean density must be less than the earth’sin this ratio. So that if we express the earth’s densityby unity, the moon’s will be expressed by 0'6052. Ifthe earth’s mean density be held to be 5'7 times thatof water, the moon’s mean density is rather less than3i times the density of water.

Such are the main circumstances of that long pro-cess of research by which astronomers have beenenabled to pass from the first simple notions sug-

* To these values may be added Lindenau’s estimate andthe estimate obtained by MM. Peters and Sehidlowski,