26
assuming the moon’s mass to be -gr, found for themean lunar parallax the value 57' 3"'l, correspondingto a distance of 238,792 miles.
We shall throughout the rest of this work assumethat the moon’s mean equatorial horizontal parallax is57' 2" - 7, and her distance, therefore, 238,818 miles,the earth’s equatorial diameter being assumed equal jto 7,925 - 8 miles. j
Now it follows from this that, as seen from the jmoon at her mean distance, the earth’s equatorial jradius subtends an angle of 57' 2"'7; that is, theequatorial diameter of the earth covers on the heavensan arc of 1° 54' 5" - 4, as seen from the moon at hermean distance. If the moon’s orbit were circular,
(in other words, with the assumed units of time and space, <7 = 32’2).Then the moon’s velocity in her orbit
2*\D
;
and the accelerating force of gravity exerted by the earth on themoon, is therefore
D
4tt 2 D
P 2
But the attraction g, first increased so as to take the moon’s massinto account, and then reduced according to the law of the inversesquare
where M is the earth’s mass, m the moon’s, and r the earth’s radius.Hence, equating the expressions (i) and (ii) we find
g (M + m) P 2 r 2 ) J
4M77*