was as close as possible to the surface of the planet so as just to graze it, is one of peculiar interest. The moon so circumstanced would have to hurry round its vast circle in something less than three hours. If its pace fell short of that the body would fall into the planet. Were it greater, then the body would fly off into a different path altogether. If a satellite were situated at a distance from Jupiter exactly equal to the radius of the planet at its equator, then the time of revolution would be just a little more than eight hours. With every increase in the distance there is a corresponding increase in the period. I need not follow the matter into any further detail beyond stating that if the distance of the satellite were ten times the radius of the planet, then the periodic time would be about 92 hours.
There is, however, one special case of so much interest that it must not be passed over. We have hitherto said nothing as to the rotation of Jupiter on its axis. Were Jupiter a rigid body throughout its mass, and did it contain neither oceans nor an atmosphere, then the speed at which the planet rotates would have no significance so far as the movements of the satellites were concerned. But, of course, the supposition just made is anything but correct with regard to the constitution of Jupiter. It is doubtful if there are any parts of its vast globe which could be described as rigid, while it is certain that it is enveloped by a prodigious atmosphere. In other words, Jupiter is composed of materials which are liable to tidal influence. This being so, the speed of Jupiter's rotation on his axis is a very important element in the consideration of the movement of his satellites. We may take the period of rotation at 9 hours 5512 minutes. This
