According to Whitmell the greatest possible duration of a total solar eclipse is 7m. 40s., and it can attain this limit only when the eclipse occurs near the beginning of July and is visible at a place 5° north of the equator.
The duration of a lunar eclipse depends mainly upon the position of the moon with respect to the earth's shadow. If it strikes the shadow centrally, as at _M´_, Fig. 33, a total eclipse may last for about two hours, with an additional hour at the beginning and end, during which the moon is entering and leaving the earth's shadow. If the moon meets the shadow at one side of the axis, as at _P_, the total phase of the eclipse may fail altogether, and between these extremes the duration of totality may be anything from two hours downward.
[Illustration: FIG. 34.--Relation of the lunar nodes to eclipses.]
67. RELATION OF THE LUNAR NODES TO ECLIPSES.--To show why the moon sometimes encounters the earth's shadow centrally and more frequently at full moon passes by without touching it at all, we resort to Fig. 34, which represents a part of the orbit of the earth about the sun, with dates showing the time in each year at which the earth passes the part of its orbit thus marked. The orbit of the moon about the earth, _M M´_, is also shown, with the new moon, _M_, casting its shadow toward the earth and the full moon, _M´_, apparently immersed in the earth's shadow. But here appearances are deceptive, and the student who has made the observations set forth in Chapter III has learned for himself a fact of which careful account must now be taken. The apparent paths of the moon and sun among the stars are great circles which lie near each other, but are not exactly the same; and since these great circles are only the intersections of the sky with the planes of the earth's orbit and the moon's orbit, we see that these planes are slightly inclined to each other and must therefore intersect along some line passing through the center of the earth. This line, _N´ N´´_, is shown in the figure, and if we suppose the surface of the paper to represent the plane of the earth's orbit, we shall have to suppose the moon's orbit to be tipped around this line, so that the left side of the orbit lies above and the right side below the surface of the paper. But since the earth's shadow lies in the plane of its orbit--i. e., in the surface of the paper--the full moon of March, _M´_, must have passed below the shadow, and the new moon, _M_, must have cast its shadow above the earth, so that neither a lunar nor a solar eclipse could occur in that month. But toward the end of May the earth and moon have reached a position where the line _N´ N´´_ points almost directly toward the sun, in line with the shadow cones which hide it. Note that the line _N´ N´´_ remains very nearly parallel to its original position, while the earth is moving along its orbit. The full moon will now be very near this line and therefore very close to the plane of the earth's orbit, if not actually in it, and must pass through the shadow of the earth and be eclipsed. So also the new moon will cast its shadow in the plane of the ecliptic, and this shadow, falling upon the earth, produced the total solar eclipse of May 28, 1900.