The supreme controlling power in the solar system is the attraction of the sun. Each planet of the system experiences that attraction, and, in virtue thereof, is constrained to revolve around the sun in an elliptic path. The efficiency of a body as an attractive agent is directly proportional to its mass, and as the mass of the sun is more than a thousand times as great as that of Jupiter, which, itself, exceeds that of all the other planets collectively, the attraction of the sun is necessarily the chief determining force of the movements in our system. The law of gravitation, however, does not merely say that the sun attracts each planet. Gravitation is a doctrine much more general, for it asserts that every body in the universe attracts every other body. In obedience to this law, each planet must be attracted, not only by the sun, but by innumerable bodies, and the movement of the planet must be the joint effect of all such attractions. As for the influence of the stars on our solar system, it may be at once set aside as inappreciable. The stars are no doubt enormous bodies, in many cases possibly transcending the sun in magnitude, but the law of gravitation tells us that the intensity of the attraction decreases as the square of the distance increases. Most of the stars are a million times as remote as the sun, and consequently their attraction is so slight as to be absolutely inappreciable in the discussion of this question. The only attractions we need consider are those which arise from the action of one body of the system upon another. Let us take, for instance, the two largest planets of our system, Jupiter and Saturn. Each of these globes revolves mainly in consequence of the sun's attraction, but every planet also attracts every other, and the consequence is that each one is slightly drawn away from the position it would have otherwise occupied. In the language of astronomy, we would say that the path of Jupiter is perturbed by the attraction of Saturn; and, conversely, that the path of Saturn is perturbed by the attraction of Jupiter. For many years these irregularities of the planetary motions presented problems with which astronomers were not able to cope. Gradually, however, one difficulty after another has been vanquished, and though there are no doubt some small irregularities still outstanding which have not been completely explained, yet all the larger and more important phenomena of the kind are well understood. The subject is one of the most difficult which the astronomer has to encounter in the whole range of his science. He has here to calculate what effect one planet is capable of producing on another planet. Such calculations bristle with formidable difficulties, and can only be overcome by consummate skill in the loftiest branches of mathematics. Let us state what the problem really is.