C 30 ] 
3. The Moon’s parallax, as determined by the 
moftfkilful aftronomers, gave him the Moon’s diftance 
in femidiameters of the Earth. 
4. The time of a periodical month gave him the 
ratio of the verfed fine of the arc of the Moon’s orbit 
which fhe defcribes in one fecond j to the radius. 
And from thefe his conclufion was ; that the gra- 
vitation at the Earth’s furface, being diminished as the 
fquare of the diftance from the Earth’s centre increafes, 
would, at the diftance of the Moon, produce a fall 
from reft, in onz /econd, precifely equal to that verfed 
fine. Or, that the gravitation of the Moon toward 
the Earth, being increafed as the fquare of that dif- 
tance is diminiftied, would, at the Earth’s furface, be 
of the fame quantity as that of falling bodies is (by 
the experiment of the pendulum) a&ually found 
to be. 
II. 
Bat the law of gravitation, thus deduced, being 
found to hold univerfally, and reciprocally, amongft 
all the great bodies of our fyftem, fo that even the 
minute anomalies of their motions are explained from 
it ; we may now afiume it as given, and make the 
Moons diftance the quantity fought. 
Thus, writing F for the number of feet which a 
body falling from reft, defcribes, in vacuo> at the 
equator, in one fecond , V for the verfed fine of the 
arc of the moon’s orbit defcribed in the fame time, 
to the radius unity, D for the femidiameter of the 
equator in feet, and the ratio of the diftance of the 
centers of the earth and Moon, to the femidiameter 
of 
