39. PERTURBATIONS.--In what precedes we have considered the motion of a planet under the influence of no other force than the sun's attraction, while in fact, as the law of gravitation asserts, every other body in the universe is in some measure attracting it and changing its motion. The resulting disturbances in the motion of the attracted body are called _perturbations_, but for the most part these are insignificant, because the bodies by whose disturbing attractions they are caused are either very small or very remote, and it is only when our moving planet, _P_, comes under the influence of some great disturbing power like Jupiter or one of the other planets that the perturbations caused by their influence need to be taken into account. The problem of the motion of three bodies--sun, Jupiter, planet--which must then be dealt with is vastly more complicated than that which we have considered, and the ablest mathematicians and astronomers have not been able to furnish a complete solution for it, although they have worked upon the problem for two centuries, and have developed an immense amount of detailed information concerning it. [Illustration: THE LICK OBSERVATORY, MOUNT HAMILTON, CAL.] In general each planet works ceaselessly upon the orbit of every other, changing its size and shape and position, backward and forward in accordance with the law of gravitation, and it is a question of serious moment how far this process may extend. If the diameter of the earth's orbit were very much increased or diminished by the perturbing action of the other planets, the amount of heat received from the sun would be correspondingly changed, and the earth, perhaps, be rendered unfit for the support of life. The tipping of the plane of the earth's orbit into a new position might also produce serious consequences; but the great French mathematician of a century ago, Laplace, succeeded in proving from the law of gravitation that although both of these changes are actually in progress they can not, at least for millions of years, go far enough to prove of serious consequence, and the same is true for all the other planets, unless here and there an asteroid may prove an exception to the rule. The precession (Chapter V) is a striking illustration of a perturbation of slightly different character from the above, and another is found in connection with the plane of the moon's orbit. It will be remembered that the moon in its motion among the stars never goes far from the ecliptic, but in a complete circuit of the heavens crosses it twice, once in going from south to north and once in the opposite direction. The points at which it crosses the ecliptic are called the _nodes_, and under the perturbing influence of the sun these nodes move westward along the ecliptic about twenty degrees per year, an extraordinarily rapid perturbation, and one of great consequence in the theory of eclipses.