movements of the satellites are so rapid that the different phenomena we have referred to are repeated frequently, and many of them can be discerned with a comparatively small telescope.
But the Jovian system of satellites has also a claim on those astronomers who devote themselves rather to mathematical research than to telescopic observation. Each of the moons is, of course, mainly guided in its movement by the attraction of the great globe itself. If there were only a single moon and if there were no other interference, then the determination of its movement would be a comparatively simple matter, and the places occupied by the satellite at every date could be predicted with complete confidence. In no one of the planets, however, can so simple a condition of things as we have supposed be realised. It is no doubt true that the earth is attended by but a single moon, but then the movement of the earth's companion is rendered highly complex by the fact that the attraction of the sun constantly tends to make it swerve from the simple elliptic path which it would otherwise pursue. The movement of our moon, however embarrassing a problem it may present to mathematicians, is, nevertheless, simplicity itself in comparison with the movement which has to be performed by one of Jupiter's moons. In the case of each of these little bodies there is not only a force exerted by the sun with the effect of disturbing the satellite's motion, but each one of the four globes attracts each one of the others, and is in turn attracted by it.
The consequence of this is that the movements of Jupiter's satellites form one of the most troublesome problems which the mathematical astronomer has ever
