244 = Professor Dean’s investigation of the apparent motion 
ing toward C. After half a revolution it will appear, by Prop. 4 and 
7, in N moving towards D. After three quarters of a revolution it 
will, by Prop. 1 and 8, be in E moving towards A. ‘Therefore when 
the moon’s apogee is in the greatest north latitude, the earth observed 
from the moon seems at each revolution to describe an oval 12° 36/ 
broad from east to west, and 13° 18’ long from north to south, passing 
the north towards the east. 
Next, let the moon’s apogee be 180° from the ascending node, and 
the moon still in the apogee.as in Fig, 10, the centre of the earth, by 
Prop. 3 and 5, will be in the mean place Z Fig. 11, moving north and 
west. After one quarter of a revolution, by Prop. 4 and 6, it must be 
nearly stationary at C. After half a revolution, it must by Prop. 1 
and 7 be again at Z, moving south and east. After three quarters of 
a revolution, it appears, by Prop. 2 and 8, to be nearly stationary in A. 
Thus when the apogee is in the descending node, during each revo- 
lution of the moon, the earth seems, as before, twice to describe a 
line more than 18° in length and passing through the point Z, but ly- 
ing N W and S E. 
Lastly, let the moon’s apogee be 270° before the ascending we 
as in Fig. 12, and the moon in the same place, the centre of the earth 
by Prop. 4 and 5 will be found in N, moving towards C, Fig. 13. 
Having performed one quarter of a revolution by Prop. 1 and 6, it will 
be in W, moving towards B. After half arcvolution by Prop. 2.and 
7, it will be in S, moving towards A. After three fourths of a revo- 
lution, it will be by Prop. 3 and 8 in E, moving towards D. There- 
fore when the moon’s apogee is in the greatest south latitude, the earth 
observed from the moon seems at each revolution to describe an oval, 
similar and equal to the former, but in the contrary direction, passing 
the south towards the east. 
When the line of apsides is oblique to the line of nodes, the path 
