On the Scheme of a Perpetual Full Moon, 13 
been expected ; where Laplace is introduced alleging that had 
the moon been made to enlighten the earth, Nature has been 
frustrated in her design, for that end is not answered. Our 
author then, compassionating the weakness of Nature, proposes 
the scheme of a perpetual full moon. With how much wisdom, 
we shall see immediately. 
If the moon were always in opposition, or full, it is evident 
that she would then be a primary planet, and a superior one too; 
for she would revolve about the sun as a centre, and her orbit 
would also include the orbit of the earth. Now, since in this 
case the periods of the earth and moon are equal, the forces with 
which they are urged to the sun must be as their distances from 
it. If, therefore, ©, OG, and )}, be the masses of the sun, earth, 
and moon; 2x the distance of the earth from the sun; and x+y 
the distance of the moon from the sun: Then ae a = may 
ze 2 
i * aa re AS 
denote the force urging the earth to the sun*, and Gisee a3 7m? 
that drawing the moon to the sun; hence BEN aA ae 
nn (x+y)? 
= :2: x+y. But if the distance at which the earth alone 
would revolve about the sun in a year be =], we have also 
»,© © S 
© —: ria: 1, and Grate SB ety]; *s. 33 
ei 1= bai ess a Se orks 
“i aie —1=0, and Gun t or =x2+y. Let ©='333928, 
6=l,and p= — ; then 2=*9998566, and y=:01007544. 
; aol 
The distance of the real moon from the earth is = nearly ; 
so that in this case it would be 3:93 times as far off; and the 
light received from it being inversely as the square of the di- 
; 1 : ; , 
stance, will only amount to ae of what it now is: also, since 
the action of the moon to raise the tides is reciprocally as the 
1 
cube of the distance, we shall only have 55 of the present 
tides. 
1 ] 390,\3 
If ) were such that —— :y?::—-:)= vib 
saat eer aes » WE should 
oh 
* In strictness, the force urging © and © together is ox< + cas - 
©O+) ,8 ,8 
») ; 4 
—~; and that urgin and ) togetheris ——— +, 
~? ging © ) tog (e+yyt a 
is sufficiently accurate for the present purpose. 
+ —. Bui the above 
y* 
then 
