It may be worth while to refer to this, as it leads to the recognition of certain important facts in connection with the new discovery. Let us consider, for instance, the innermost of the four well-known satellites of Jupiter. It revolves round its primary in a period which, according to the best determination, may be taken as 1 day, 18 hours, 27 minutes, 34 seconds. We may regard this orbit as circular and the distance of the satellite from the centre of Jupiter as 262,000 miles. In like manner the outermost of the four satellites revolves around Jupiter in a period of 16 days, 16 hours, 32 minutes, 11 seconds, and the length of its radius is 1,170,000 miles. There is a certain relation between the four magnitudes I have named, which is expressed by saying that the squares of the times are proportional to the cubes of the distances. As this law depends upon gravitation it must be obeyed by any new satellite, and here we can foresee that the Barnard moon, whatever else it may do, must at all events revolve in an orbit under such conditions that the cube of its radius bears to the square of the periodic time the same relation as in the case of each of the other satellites.
In estimating the distance of a satellite from its primary, the most natural unit of measurement to adopt is not to be expressed in miles or in thousands of miles. It should rather be given in terms of the equatorial radius of the planet. The sense of proportion is gratified in this way of looking at the matter. This is specially advantageous in the case of Jupiter's moons, and we shall proceed to illustrate it by pointing out the movements that would be appropriate for moons placed at different distances from the centre of Jupiter. The critical case of a moon which
