But before we discuss this matter, it will be well to state what is known beyond peradventure about the moon.
Its mean distance from the earth is usually called, for the sake of a round number, 240,000 miles, but more accurately stated it is 238,840 miles. This is variable to the extent of more than 31,000 miles, on account of the eccentricity of its orbit, and the eccentricity itself is variable, in consequence of the perturbing attractions of the earth and the sun, so that the distance of the moon from the earth is continually changing. It may be as far away as 253,000 miles and as near as 221,600 miles.
Although the orbit of the moon is generally represented, for convenience, as an ellipse about the earth, it is, in reality, a varying curve, having the sun for its real focus, and always concave toward the latter. This is a fact that can be more readily explained with the aid of a diagram.
[Illustration: THE MOON'S PATH WITH RESPECT TO THE SUN AND THE EARTH.]
In the accompanying cut, when the earth is at _A_ the moon is between it and the sun, in the phase called new moon. At this point the earth's orbit about the sun is more curved than the moon's, and the earth is moving relatively faster than the moon, so that when it arrives at _B_ it is ahead of the moon, and we see the latter to the right of the earth, in the phase called first quarter. The earth being at this time ahead of the moon, the effect of its attraction, combined with that of the sun, tends to hasten the moon onward in its orbit about the sun, and the moon begins to travel more swiftly, until it overtakes the earth at _C_, and appears on the side opposite the sun, in the phase called full moon. At this point the moon's orbit about the sun has a shorter radius of curvature than the earth's. In traveling from _C_ to _D_ the moon still moves more rapidly than the earth, and, having passed it, appears at _D_ to the left of the earth, in the phase called third quarter. Now, the earth being behind the moon, the effect of its attraction combined with the sun's tends to retard the moon in its orbit about the sun, with the result that the moon moves again less rapidly than the earth, and the latter overtakes it, so that, upon reaching _E_, the two are once more in the same relative positions that they occupied at _A_, and it is again new moon. Thus it will be seen that, although the real orbit of the moon has the sun for its center of revolution, nevertheless, in consequence of the attraction of the earth, combined in varying directions with that of the sun, the moon, once every month, makes a complete circuit of our globe.