In the case of Saturn the diameters of two of the satellites are wanting which we have assumed to be the same as those of the smallest of those nearest to them, and thus have been able to compute the volumes of the whole of them; but we have not been able to find any statement anywhere of their densities, and to get over this difficulty we have reasoned in the following manner.
The density of the moon is very little over two-thirds of that of the earth, while that of the satellites of Jupiter varies from a little more than the same to a little more than twice as much as the density of their primary. Why this difference? To account for it we appeal to the very general opinion of astronomers, that the four inner planets are in a more advanced stage of their development, or existence, than the four outer ones. In this way it is easy to conceive that the earth has arrived at the stage of being more dense than its satellite; while in the case of Jupiter, his satellites being of so very much less volume than their primary, have already arrived at a higher degree of development. Carrying this motion forward to Saturn, we have supposed that from his being considerably less dense than any other of the outer planets--quite possibly from having been formed out of material comparatively (perhaps not actually) less dense than the others--his satellites may not have condensed to a greater degree than his own mass, and we have, therefore assumed their density, that is the density of the volume of the whole of them, to be the same as that of their primary.
To determine some mass for the rings of Saturn, is a much more intricate matter than for his satellites, and presents to us some ideas--facts rather--which had never before crossed our imagination. The most natural way to look upon these rings is to suppose that they are destined to become satellites at some future time. All the modern cosmogonies that have come under our notice are founded upon the idea that rings are the seed, as it were, of planets and satellites, and if those of Saturn have been left, as it has been said, to show how the solar system has been evolved, it cannot be said that the supposition is not well founded. In this way we are led to speculate upon how many satellites are to be made out of the rings before us. Considering, then, that the nearest satellite is 120,800 miles from the centre of Saturn, leaving only 83,500 miles between his surface and that of Mimas, and also that the distances between satellites diminish rapidly as they come to be nearer to their primaries, there is not room to stow away a great number of satellites. On the other hand, seeing that there are at least three distinct rings, we cannot reasonably do less than conclude that three satellites are intended to be made out of them. But let the number be what it may, all that we have to do with them for our present purpose is to assign some mass to them. With this view, we have given, arbitrarily, to each one of the three we have supposed, a volume equal to that of one of the satellites of 500 miles in diameter, that is, about 65,000,000 cubic miles, and we have supposed their density to be the same as that of water, instead of that of the planet. Thus, in the table, we have assigned to the three a mass of 195,000,000 cubic miles at density of water, which would be more than sufficient to make four other satellites for the system of 500 miles in diameter each, and of the same density as the planet.