part and pass through the earth's umbra.

But the moon does not always cross the ecliptic where the sun is, nor
uniformly in the same part.

Its crossing-place is different at each succeeding revolution.

[Illustration]

Since the limits of this article will not allow an extended explanation
of the manner of mathematically predicting eclipses, we will apply the
foregoing statements in showing that there will occur an eclipse of the
sun in July, 1851.

The first diagram on page 240 represents the relative positions of the
sun and moon at the time of new moon in June, July, and August, 1851,
calculated for Greenwich.

It is probable that there will be but few among the millions who may
thus behold these wonderful phenomena who will not understand their
causes.

However, an article explaining the manner of predicting these eclipses
with diagrams illustrating the path of the moon's shadow in the solar
eclipse across the United States and upon the whole earth, may not be
acceptable.

Since the earth and moon are solid opaque bodies, they intercept the
light passing from the sun through the heavens; or, in other words, they
cause the existence of shadows.

Hence, if the moon, in its revolution pass directly between the sun and
the earth its umbra will fall upon the earth, and cause a total eclipse
of the sun.

If the moon passed through the heavens in exactly the same path as the
sun, there would result eclipses of both sun and moon at each
revolution; for it would pass directly over the disc of the sun, and
through the centre of the earth's umbra.

But it was long since discovered that the path of the moon is inclined
to the sun's path, or the ecliptic, about 5 deg. (5 deg. 8' 48").

This results from the fact that these crossing-places (which for
convenience and according to astronomical usage we shall call the
_nodes_), are in motion upon the ecliptic, from east to west.

Therefore, the moon may cross the ecliptic at such a distance from the
sun, that when it passes between the sun and the earth, it will appear
to pass above or below the disc of the sun; also, in the opposite part
of its orbit, it may cross at so great distance from the earth's umbra,
that it will pass above or below the umbra, as represented in the
following diagram.

In June, the moon is seen below the sun, passing upward to the ascending
node, and beyond the limits within which eclipses can occur.

While the moon is completing anothe