would be the periodic time of a satellite which was situated at a distance above the surface of the planet which was about one and a quarter times as much as his radius; more accurately, this magnitude would be 2·273 equatorial radii of the planet distant from the centre of Jupiter. A satellite which revolved in this critical orbit would occupy quite an exceptional position, as the time of its revolution would equal that of the planet's rotation, so that the satellite would be constantly over the same spot of the planet. The planet would, in fact, always bear the same face towards an observer situated on the satellite, just as the moon always turns the same face to the earth. It is, however, certain that the new satellite is somewhat outside this critical position.
The fact that the period of revolution of the new satellite happens to be so near twelve hours leads to a somewhat singular difficulty in determining its movements. It is plain that to find the orbit which it pursues with any precision it would be desirable to combine observations made when it was now at one side and now at the other side of Jupiter. Let us suppose that' at midnight the satellite is at its greatest distance to the east of the planet. It can then, of course, be observed under the most favourable circumstances. Six hours later the satellite, having accomplished half a revolution, will be at the greatest elongation west; but then Jupiter will be so placed that it cannot be observed. Daylight, of course, follows, and in twenty-four hours after the first observation the satellite will have resumed the position which it had at midnight the preceding night. It thus follows that at one observatory it can only be possible for many nights in succession to observe the satellite at one of the sides of Jupiter. If
