[ 33 1 
as was fuppofed, in the ratio of x-\-i to x- y that Is, 
■t xX =VH±Ixx. 
X 
Sir Ifaac Newton, from th z phenomena of the tides, 
eftimated the ratio of to x to be that of 
40.788 to 39.788. In that cafe, the cubic root of 
— will have for its logarithm 0.0035934; which 
added to 1.7787954, the logarithm of X computed 
for an immoveable earth, gives 1.7823888, the lo- 
garithm of 60.5883 femidiameters of the equator. 
And the Moon’s horizontal parallax, for this diftance, 
is 56' 44", 07. 
IV. 
On the other hand, if we had obfervations of the 
Moon’s parallax (and diftance) which could be 
reckoned exad: enough for the purpofe, we might 
thence determine the ratio of a; to 1, that is, the ra- 
tio of the quantities of matter in the Earth and 
Moon. 
For having J = and ; likewife 
A. X X*. ^ X 
T being given from obfervation, and X computed as 
above ; it is manifeft that the ratio of x 1 to at, 
and, by divifion, that of x to 1, or of the mafs of 
the earth to that of the Moon, is given. 
For example, if it fhould be concluded from good 
obfervations, that T, the Moon’s mean diftance, is 
604. femidiameters of the equator ; for the logarithm 
of this diftance, which is 1-7317554, take the lo- 
garithm of X, or 1.7787954, thrice the remainder 
Vol. LIV, F will 
