OBSERVATIONS FOR TIME AND LONGITUDE, 
179 
the game at 15h., C at 16b., and S that of the star. B, C and S are 
plotted from their differences of right ascension and declination from A. 
A circle described with S as centre and radius equal to the moon’s semi¬ 
diameter, cuts the moon’s path at D and E; these two points are 
positions of the moon’s centre at the times of disappearance and re¬ 
appearance respectively. Should this circle fail to cut the line of the 
moon’s path, it shows that no occupation will take place. The moon 
passes over the distance A B in one hour, and if we assume its motion 
AD 
uniform, we have the time the moon takes to travel over AD = . _ x 60 m. 
’ AB 
The lengths of A D and A B may be measured on any convenient scale. 
In the present instance the point D happens to coincide with B, and 
A D therefore equals A B, and the G. M. T. of disappearance is 15 hrs., 
or, correcting for longitude, the local time is 14 hrs. 40 m. 0 s. 
Similarly, by scaling off B C and C E, their lengths are found to bear 
the proportion of 24 and 4*6, so that the time the moon’s centre would 
take to traverse the distance 
0 E = x 60 min. 
24 
= 11 mins. 30 secs. 
and the G. M. T. of reappearance is 16 hrs. 11m. 30 s., and, applying as 
before the correction for longitude, the local time is 15 hrs. 51 m. 30 s. 
Angles of Disappearance and Reappearance . 
From the North point of the Moon’s limb: —Any lines drawn, on the 
figure, parallel to the direction in which have been plotted the difference s 
in declination will represent portions of celestial meridians, and such a 
line, if drawn through the centre of the moon, will cut its circumference 
at its north and south points. The line PDQ, drawn through the 
centre of the moon D, cuts the circumference at P and Q, which are 
respectively the north and south points, because, in constructing the 
figure, it was assumed that north declination increased from the bottom 
towards the top. The moon’s motion is also plotted in the direction from 
A towards E, and since its motion in the heavens is from west to east, 
B represents the eastern side of the moon’s disc. The angle of dis- 
n 2 
