Of the earth viewed from the moon. 243 
BC, and nearly stationary as to that direction, as the earth has acquir- 
ed its mean motion. 
7. When the moon has arrived at its lower apsis, the earth again 
appears on the circle of declination SN, but its angular motion toward 
the east being greater than that of the moon on its axis, its apparent 
diurnal motion is toward the east. 
8. When the moon has again arrived at its mean distance, the 
earth seen from it is 6° 18’ before or east of its mean place, and will ap- 
pear just as far east of the circle of declination in the line AD, and as 
it has acquired its mean motion that distance will remain some time 
with little variation. 
Now to ascertain the combined effect of these two causes in pro- 
ducing an appareut vibratory motion of the earth as observed frum 
the moon— : 
First, let the moon’s apogee and ascending node be in conjunction 
as in Fig. 6, and the moon in the same point. By Prop. 1 and 5, the 
centre of the earth, observed from the moon, will appear at its mean 
place Z Fig. 7, moving towards the south and west. After one quar- 
ter of a revolution, by Prop. 2 and 6, it will be foundin B. After half 
a revolution, by Prop. 3 and 7, it will be again in Z, but moving north 
and east. After three quarters, by Prop. 4 and 8, it will be nearly at 
rest in D, and the completion of the revolution carries it back to the 
point Z. ‘Thus in the present position of the nodes and apsides, in 
each revolution of the moon, the earth will appear to move twice 
through a line more than 18° long, passing the mean point Z and ly- 
ing N Eand S W. 
Next, let the moon’s apogee be 90° forward of the ascending node 
as in Fig. 8, and the moon again in the apogee, the centre of the earth, 
by Prop. 2 and 5, will appear in S moving towards B, Fig. 9. After 
one quarter of a revolution it will appear by Prop. 3 and 6 in W, mov- 
