14 On the Scheme of a Perpetual Full Moon. 
then have the proper light and tides; because the moon would 
present the same apparent disk, and its mass would also have the 
a? 
a 
same ratio to the cube of its distance, By substituting [= 
tan (laid 
—1=0, and era H wor 
for y, the equations are 23 + sey 
=2+y; from which eee and y=*01884523: so that 
the moon’s distance from the earth will be 7:35 times as far as at 
present; and its mass 397-2 times what it now is, which is 9°8 
times the mass of the earth, or fully eight times its size. 
Laplace has certainly in this, as well as in some of his other 
pious speculations, extended his researches beyond the bounds of 
truth. Manifold doubtless were the ends of the moon’s creation ; 
and among others, it is manifestly designed and admirably fitted 
for giving light tothe earth. On the other hand, the contrivance 
of a perpetual ful! moon loudly proclaims what a confused inefhi- 
cient system would have resulted, had even so great a man as 
Count Laplace been consulted. 
It appears from both examples, that the common centre of 
gravity of the earth and moon is further from the sun than 1, the 
mean radius of the ecliptic. That this must be the case, what- 
ever be the mass of the moon, is easily shown. For, if possible, 
let the centre of gravity be at the distance unity; then since ¥ 
Yy 
——, we 
Ps: Opus Dy 
is divided n — 
s divided by the centre of gravity into ;— > and 5 
should have r=l—--", and r-y=1+ SAE Hence, the 
sum of the products of the mass of each ab into the sun’s 
@xl w@Ox DAL 
aty  @eay 
, if the centre of gravity were in the 
attraction would be represented by ——~——— 
which will equal nail atest 
ecliptic,and the eveneln exactly eg the i force. 
C= y" OS BE wi 
= x 4y34+ &c. The centre of gra- 
But by performing the division, —————— 
vity must therefore be at a ye distance than unity, other- 
wise the centripetal would overpower the centrifugal force. 
Let 1+v be the distance of the centre of gravity from the 
sun, th — ft. 222. ‘ ne pllinse . 
» then x=1 hose t ysl + 4 +05 and since 
the sun’s attraction must equal the centrifugal force, or x x 1 
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