MOON. 
increases whilst the sun is moving from his 
apogee to his perigee, and decreases wliilst 
he moves from his perigee to his apogee ; 
and the greatest difference of the periodic 
times is found to be about twenty-two mi- 
nutes and a half. The mean periodic time 
of the moon is 27“* 7'* 43 ll", 5; this is 
called her sidereal revolution, being the 
mean time from her leaving any fixed star, 
till her return to it again. Now it is found 
by observation that the mean time from 
her leaving her apogee till she returns to it, 
is 27"* 13'' 18' 4" ; hence, the moon is longer 
in returning to her apogee than she is in mak- 
ing a revolution in her orbit, and therefore 
her apogee must move forward. The mean 
time from her leaving her node till she returns 
to it again, is 27“* 5'“ 5' 33", 6, and this be- 
ing less than her mean periodic time, it 
follows tiiat she returns to her no.de before 
she has completed her revolution, and there- 
fore her nodes must have a retrograde mo- 
tion. The time between two mean con- 
junctions of the sun and moon, or from 
new moon to new moon, supposing their 
motions had both been uniform, is found 
by multiplying the periodic times of the 
earth and moon together, and dividing by 
their difference ; taking therefore the mean 
periodic time of the moon and sun as 
already stated, we get the mean time 
from conjunction to conjunction to be 29“* 
12*' _44' 2 ', 8, and this is called her sy- 
nodic revolution. The true time from new 
to new moon will be sometimes greater and 
sometimes less than this. 
'The apparent diameter of the moon is 
found continually to vary; now the appa- 
rent diameter of any very distant body, va- 
ries inversely as its distance. Hence, as 
the apparent diameter of the moon in- 
creases, she must approach the earth ; and 
when it decreases, she must recede from 
the earth. This variation of her apparent 
diameter agrees exactly with what ought to 
be the case, if the moon moved in an ellipse 
about the earth in one of its foci ; we con- 
clude therefore that the moon moves in an 
ellipse about the earth situated in one of its 
foci, as no other supposition will agree with 
the observed variation of the moon’s diame- 
ter. From the variation of the sun’s dia- 
meter, it appears in like manner, that the 
earth must revolve in an ellipse about the 
sun, having the sun in one of the foci. 
The earth moving in an ellipse about the 
sun in its focus, the nearer the earth comes 
to the sun, the more it is attracted by him, 
and this attraction increases in the same 
VOL. IV. 
ratio as the square of the distance' dimi- 
nishes ; and on tlie contrary, it decreases as 
the square of the distance increases. As 
therefore the earth approaches the sun all 
the time it moves from the aphelion to the 
perihelion, the attraction increases, and con- 
spiring partly with the earth’s motion, it 
accelerates the motion of the earth ; and 
when the earth moves from perihelion to 
aphelion, the attraction acts partly against 
the earth’s motion, and diminishes its mo- 
tion. Thus, the velocity of the earth in- 
creases whilst it moves from the aphelion to 
perihelion, and decreases as much whilst it 
moves fi'om perihelion to aphelion. 
As the moon moves in an ellipse about 
the earth in its focus, she must, in like man- 
ner, by the earth’.s attraction, have her 
velocity increased from her apogee to peri- 
gee, and decreased as much from her peri- 
gee to apogee. These are the principal 
causes of the variation of the velocities of 
the earth and moon. But as the sun at- 
tracts the moon, as well as the earth at- 
tracts it, the attraction of the sun wilt 
cause another variation of the moon’s velo- 
city. Thus the moon being attracted boUi 
by the sun and earth, they will cause great 
irregularities in her motion ; and hence, it is 
very difficult to compute the place of the 
moon. After finding the mean place of 
the moon, that is, the place where she 
would have been if her motion had been 
uniform, it requires not less than twenty 
corrections, in order to get the true place 
to a sufficient degree of accuracy. SU- 
I. Newton was the first person who pointed 
out the sources of these irregularities; but 
they are of a nature too difficult to admit 
of a proper illustration. When we view 
the moon with a telescope, we find that 
her surface is very rough with mountains 
and cavities; this appears from the very 
jagged boundary of the light and dark 
parts. Also, certain parts are found to 
project shadows always opposite to the 
sun ; and when the sun becomes vertical to 
any of them, they are observed to have no 
shadow; these therefore must be moun- 
tains. Other parts are always dark on that 
side next the sun, and illuminated on the 
opposite side ; these therefore must be 
cavities. Hence the appearance of the 
moon constantly varies, from its altering its 
situation in respect to the sun. 
The tops of the mountains on the dark part 
of tlie moon, are frequently seen enlight- 
ened at a distance from the confines of the 
illuminated part. The dark parts have, by 
Ll 
