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° (5° 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.