THEORETICAL ASTRONOMY. 113 
earth (pl. 10, fig. 4) be opposite the sun, situated in the tropic of Capricorn, 
which it describes on this day, and the moon, as full moon at M, in the 
tropic of Cancer, which she describes ; our horizon, HR, shows that the 
diurnal are of the sun is very small, while the moon traverses by night a 
very large arc. The contrary of this must take place on the night of the 
summer solstice, June 21, the shortest night of the year. Should the moon, 
as full moon in spring and autumn, stand in the equinoxes as the sun, she 
would then be as long above as below the horizon. 
31. If we suppose the moon to be at L’ (pl. 10, fig. 3), in conjunction or 
between the earth and sun, then the centres of these three bodies will be in 
the straight line RE. While the moon is completing a revolution around 
the earth, moving daily about 13° 10’ 35”, the earth will have passed for- 
ward over a certain part of her orbit, about to ¢. The moon will then be 
at n, in a direction, zz, which is parallel to the former, RE. The moon has 
consequently a periodical or tropical revolution completed within 27 days, 
7 hours, 43 minutes, 4;5 seconds. For the moon to return to conjunction, 
however, that is, again to become new moon, it must in addition traverse 
the arc nL, equal to the arc Tt or Rm, described by the earth in its orbit, 
which are amounts to about 27°. To accomplish this the moon requires 
somewhat more than two days; she consequently returns to conjunction in 
29 days, 12 hours, 14 minutes, and 3 seconds. This period is known as the 
lunar month (in its proper sense), and the revolution itself (from conjunction 
to conjunction) is the synodic revolution, or simply the lunation, which may 
also be counted from one full moon to another. Pv. 10, fig. 10, shows 
that the course of the moon projected on the plane of the earth’s orbit, must 
form a kind of serpentine. The moon has yet to pass over the are nv (fig. 
3), to come back to the. same fixed star; this return, accomplished in 27 
days, 7 hours, 43 minutes, and 12 seconds, is called the sidereal revolution 
of the moon. Finally, the revolution of the moon, with respect to the nodes 
of its orbit, occupies 27 days, 5 hours, 5 minutes, and 36 seconds. 
The moon revolving about our earth is forced to accompany her in her 
course round the sun, so that the path traversed by the moon in space is 
properly an epicycloid. This compound motion of the moon is, conse- 
quently, the source of the various phases represented in fig. 5, as already 
explained in sections 7 and 29. Pl. 10, fig. 5, shows, in addition, the 
first, second, third, and fourth octants, as also that the moon, when full, is in 
opposition to, and when new, in conjunction with the sun. The inclination 
of the moon’s orbit to the earth’s equator is very variable, ranging in 19 
years from 18° 19’ to 28° 36’. The inclination of the moon’s equator to the 
ecliptic (1° 28’ 25’’) never varies. The time of the rotation of the moon 
about her axis corresponds precisely with that of her mean revolution 
around the earth, consequently equal to 27 days, 7 hours, 43 minutes, and 
12 seconds. Hence the moon always turns the same side to us, and the 
opposite side is constantly concealed, except the small part of it revealed 
by libration, For this reason the conclusion was early formed, though too 
hastily, that the moon had no rotation. 
ICONOGRAPHIC ENCYCLOPADIA.—YVOL, I. 8 113 
