The thing of real interest is the fact that the moon does turn the same face towards us; _i.e._ has ceased to rotate with respect to the earth (if ever it did so). The stability of this state of things was shown by Lagrange to depend on the shape of the moon. It must be slightly egg-shape, or prolate--extended in the direction of the earth; its earth-pointing diameter being a few hundred feet longer than its visible diameter; a cause slight enough, but nevertheless sufficient to maintain stability, except under the action of a distinct disturbing cause. The prolate or lemon-like shape is caused by the gravitative pull of the earth, balanced by the centrifugal whirl. The two forces balance each other as regards motion, but between them they have strained the moon a trifle out of shape. The moon has yielded as if it were perfectly plastic; in all probability it once was so. It may be interesting to note for a moment the correlative effect of this aspect of the moon, if we transfer ourselves to its surface in imagination, and look at the earth (cf. Fig. 41). The earth would be like a gigantic moon of four times our moon's diameter, and would go through its phases in regular order. But it would not rise or set: it would be fixed in the sky, and subject only to a minute oscillation to and fro once a month, by reason of the "libration" we have been speaking of. Its aspect, as seen by markings on its surface, would rapidly change, going through a cycle in twenty-four hours; but its permanent features would be usually masked by lawless accumulations of cloud, mainly aggregated in rude belts parallel to the equator. And these cloudy patches would be the most luminous, the whitest portions; for of course it would be their silver lining that we would then be looking on.[24] Next among the investigations of Lagrange and Laplace we will mention the long inequality of Jupiter and Saturn. Halley had found that Jupiter was continually lagging behind its true place as given by the theory of gravitation; and, on the other hand, that Saturn was being accelerated. The lag on the part of Jupiter amounted to about 34-1/2 minutes in a century. Overhauling ancient observations, however, Halley found signs of the opposite state of things, for when he got far enough back Jupiter was accelerated and Saturn was being retarded.