40
Now the value of the moon’s mass which we shouldinfer from the mean (6" - 51) of these two estimates,will depend on the value we assign to the solarparallax. If we estimate the mean equatorial hori-zontal solar parallax at 8" - 91, it would follow that thedistance of the centre of gravity of the earth andmoon from the earth’s centre is -filths of the earth’sequatorial semi-diameter, or filths of 3,963 miles;that is, about 2,895 miles. Thence it follows thatthe moon’s mass is to the sum of the masses of theearth and moon as 2,895 to 238,818, or
Moon’s mass : Earth ’s mass :: 2895 : 235923:: l: 81-5*
that is, the earth’s mass exceeds the moon’s 811times.
In calculating the sun’s distance from the solarparallactic inequality, Mr. Stone adopted ^ for themoon’s mass. Leverrier adopted the value 8 -2_ (origi-nally, owing to an error of calculation which Mr.
* The actual relation may be given approximately thus :—LetR be the earth’s equatorial radius, D the moon’s distance, P thesun’s parallactic inequality, and n the sun’s mean equatorial hori-zontal parallax, /t being the moon’s mass when the earth’s is repre-sented by unity ; then
ja PE PR
—— = - • or ii -
M+i n d • nD-PR
But the former form is more convenient for calculation.
R
Leverrier takes — as 0-016620 ; Newcomb adopts the value
0-0I646I. The value resulting from the equatorial radius and themoon’s distance adopted in the present work is 0-016593.