When two bodies move in virtue of their mutual attraction, both of them will revolve in a curve which admits of being exactly ascertained. Each path is, in fact, an ellipse, and they must have a common focus at the centre of gravity of the two bodies, considered as a single system. In the case of a sun and a planet, in which the mass of the sun preponderates enormously over the mass of the planet, the centre of gravity of the two lies very near the centre of the sun; the path of the great body is in such a case very small in comparison with the path of the planet. All these matters admit of perfectly accurate calculation of a somewhat elementary character. But now let us add a third body to the system which attracts each of the others and is attracted by them. In consequence of this attraction, the third body is displaced, and accordingly its influence on the others is modified; they in turn act upon it, and these actions and reactions introduce endless complexity into the system. Such is the famous "problem of three bodies," which has engaged the attention of almost every great mathematician since the time of Newton. Stated in its mathematical aspect, and without having its intricacy abated by any modifying circumstances, the problem is one that defies solution. Mathematicians have not yet been able to deal with the mutual attractions of three bodies moving freely in space. If the number of bodies be greater than three, as is actually the case in the solar system, the problem becomes still more hopeless.