The four chief satellites of Jupiter have special interest for the mathematician, who finds in them a most striking instance of the universality of the law of gravitation. These bodies are, of course, mainly controlled in their movements by the attraction of the great planet; but they also attract each other, and certain curious consequences are the result. The mean motion of the first satellite in each day about the centre of Jupiter is 203 deg..4890. That of the second is 101 deg..3748, and that of the third is 50 deg..3177. These quantities are so related that the following law will be found to be observed: The mean motion of the first satellite added to twice the mean motion of the third is exactly equal to three times the mean motion of the second. There is another law of an analogous character, which is thus expressed (the mean longitude being the angle between a fixed line and the radius to the mean place of the satellite): If to the mean longitude of the first satellite we add twice the mean longitude of the third, and subtract three times the mean longitude of the second, the difference is always 180 deg.. It was from observation that these principles were first discovered. Laplace, however, showed that if the satellites revolved nearly in this way, then their mutual perturbations, in accordance with the law of gravitation, would preserve them in this relative position for ever. We shall conclude with the remark, that the discovery of Jupiter's satellites afforded the great confirmation of the Copernican theory. Copernicus had asked the world to believe that our sun was a great globe, and that the earth and all the other planets were small bodies revolving round the great one. This doctrine, so repugnant to the theories previously held, and to the immediate evidence of our senses, could only be established by a refined course of reasoning. The discovery of Jupiter's satellites was very opportune. Here we had an exquisite ocular demonstration of a system, though, of course, on a much smaller scale, precisely identical with that which Copernicus had proposed. The astronomer who had watched Jupiter's moons circling around their primary, who had noticed their eclipses and all the interesting phenomena attendant on them, saw before his eyes, in a manner wholly unmistakable, that the great planet controlled these small bodies, and forced them to revolve around him, and thus exhibited a miniature of the great solar system itself. "As in the case of the spots on the sun, Galileo's announcement of this discovery was received with incredulity by those philosophers of the day who believed that everything in nature was described in the writings of Aristotle. One eminent astronomer, Clavius, said that to see the satellites one must have a telescope which would produce them; but he changed his mind as soon as he saw them himself. Another philosopher, more prudent, refused to put his eye to