THE GEEAT ECLIPSE OF AUGUST 17 , 1868. 
265 
paratively small portion of the earth’s surface ; so that a solar 
eclipse is not visible over any very large extent of country. 
Hence it happens that, in any one place, solar eclipses are far 
less frequent than lunar ones. 
Let us next consider the motions of the sun and moon, as 
they would be seen by an observer supposed to be placed at the 
earth’s centre. The sun and moon are continually circling 
round the celestial sphere, the sun on the ecliptic in the space 
of one year (the diurnal motion may be left out of consideration 
altogether at present) the moon, once in a sidereal lunar month, 
in a path which is inclined about 5° 8' (sometimes a little more, 
sometimes a little less) to the ecliptic, but which is not other- 
wise fixed in position. The nodes of the moon’s orbit, or the 
points in which it intersects the ecliptic, are continually shift- 
ing, sometimes advancing along the ecliptic, at other times 
retrograding, but on the whole retrograding at such a rate as 
to go once round the ecliptic in somewhat less than nineteen 
years. 
Now if we consider these motions we shall see that, supposing 
the sun and moon both to start from a node, the sun will have 
gone some distance from the node when the moon has come 
round to that point, and yet a little further before the moon 
has overtaken him, i.e. before the end of one lunation. There- 
fore, when the two bodies are in conjunction, they are separated 
from each other by a slight interval. This interval has increased 
at the end of the next lunation ; and clearly, it will first increase 
and then decrease, until the time comes when the two bodies 
are in conjunction near the other node. Were it not for the 
slight motion of the nodes already mentioned, this node would 
be half a circumference of the ecliptic from the other; but 
under the actual circumstances the distance is somewhat less 
than the semi-circumference of the ecliptic ; that is, than the 
'distance traversed hy the sun in six months. The same is of 
course the case if we consider the motion of the moon with re- 
spect to the point directly opposite the sun, that is, with respect 
to the moving centre of the earth’s circular shadow, as supposed 
to be projected on the interior surface of a sphere surrounding 
the earth at the moon’s distance. 
Now it is clear that, for an eclipse of the sun, the moon must, 
when in conjunction with the sun (that is, at the time of new 
moon), be close to a node. As seen from e (fig. 1) the moon 
must lie between m' m', the sun beiug supposed to lie in the 
direction e m. And for an eclipse of the moon, the moon must, 
when in opposition to the sun — that is, at the time of full moon 
— be also close to a node ; or, as seen from e, the moon must lie 
within the dark part of the cone, between m and m. Hence, it 
follows, from what was shown in the preceding paragraph, that 
