PART III.--RINGS OF SATURN.

+-----------------------------+--------------------------+ | | | Rings. | Diameters of Rings | Areas of Rings | | in Miles. | in Square Miles. | ---------+-----------------------------+--------------------------+ Outer { | Outer | 172,240 | } 5,252,035,427 | { | Inner | 151,590 | } | | | | | Middle { | Outer | 148,100 | } 6,919,075,757 | { | Inner | 114,560 | } | | | | | Dark { | Outer | 110,060 | } 3,040,689,488 | { | Inner | 90,993 | } | | | | | | | Total | 15,211,800,672 | ---------+----------+------------------+---------+----------------+ |Thickness | | | Volume at | Rings. | of Rings | Volume of Rings |Density. |Density of Water| | in Miles.| in Cubic Miles. |(Water=1)|in Cubic Miles. | ---------+----------+------------------+---------+----------------+ Outer { | | | | | { | | | | | | | | | | Middle { | | | | | { | | | | | | | | | | Dark { | | | | | { | | | | | | | | | | | 90 | 1,369,062,060,480| ·0001425| 195,000,000 | ---------+----------+------------------+---------+----------------+

(4) All of these bodies, planets, satellites, and rings were supposed to revolve around their primaries, and to rotate on their axes, in the same direction viz., from right to left, in the opposite direction to the hands of a watch.

In addition to the above definition it is necessary to give some sort of description of the various parts of the machine or system which has to be made out of the nebula, with their positions, dimensions, and details. This we believe will be made plain enough, in the simplest manner, by Table No. I., taken and calculated from the elements of the solar system given in almost all astronomical works, from which we have selected what we believe to be the most modern data.

The construction of this table requires some explanation on account of its being made to show complete results from incomplete data. There has been no difficulty with the sun, the major planets, and the satellites of the earth and Jupiter, but for the minor planets, the satellites of the three outer planets, and the rings of Saturn, we have been obliged to exercise our judgment as best we could.

There being almost no data whatever of the dimensions and densities of the minor planets, to be found, we have been driven in order to assign some mass to them, to imagine the existence of one planet to represent the whole of them (in fact Olbers's planet before it exploded), which we have supposed to be placed at the mean distance of 260,300,000 miles from the centre of the sun; and we have given to it a mass equal to one-fourth of the mass of the earth, that being, in the opinion of some astronomers, the greatest mass which the whole of them put together could have. This assumption we shall explain more fully at a more suitable time.

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.

For the table referred to we have calculated the areas of the three rings to be 152,110,800,172 square miles, and we have assumed the thickness as 90 miles, that is about two-thirds of that estimated by Chambers in his handbook of Astronomy, but almost the same as that given by Edmund Dubois; nevertheless their total volume comes up to 1,369,062,060,480 cubic miles, which reduces their average density to 0·0001425 that of water, to make up the mass of 195,000,000 cubic miles at the density of water, which we have adopted for the three. This density corresponds to very nearly one-tenth of that of air, which, however strange it may appear to us, may be considered to be a very full allowance, seeing that we shall find, later on, that the planet itself was formed out of matter whose density could not have been more than one twenty-six millionth part of that of air. All the same, it is hardly matter that we could liken to brickbats. After being driven to this low estimate of density, which startled us, we referred to an article in "Nature" of Nov. 26, 1886, on Ten Years' Progress in Astronomy, where we find what follows:--"He (Newcomb) finds the mass of Titan to be about 1/12,000 that of Saturn. It may be noted, too, that Hall's observations of the motions of Mimas and Enceladus indicate for the rings a mass less than 1/10 that deduced by Bessel; instead of being 1/100 as large as the planet, they cannot be more than 1/1000, and are probably less than 1/10,000." (We make them 1/791514). Thinking over the numbers herein given we cannot help being surprised by them. If Titan be 1/12500 of the mass of Saturn, we cannot conceive how the mass of his rings can be so much greater than that of Titan. We cannot pretend to fit even one satellite of that size, mechanically, into a space of 83,500 miles wide, while Titan revels in an ample domain with a width of 332,000 miles. But we shall not pursue this part of our speculations any further. Astronomers may be able to demonstrate that the rings are of a totally different nature to those out of which the planets and their satellites are supposed to have been made, or that the nebular hypothesis or anything resembling it is no better than a foolish dream. All that we have pretended to do has been to give them their due place in the hypothesis we are attempting to analyze, and to look upon them in a practical and mechanical light, as an unfinished part of the solar system.

To determine masses for the satellites of the two outer planets, we have to be more empirical even than we have yet been. A little trouble will show that the whole mass of all the satellites and rings of Saturn put together is about 1/7820th of the mass of the planet, and we shall avail ourselves of this proportion to assign masses for the satellites of the remaining planets, the numbers and names of which are the only data we have been able to find. Considering then, that Uranus has only four satellites and no rings, we think if we give them 1/15,000th of the mass of their primary, it will be a very fair allowance; and with the same empiricism we have adopted for the solitary satellite of Neptune 1/40,000th of the mass of its primary.

However rude and crude these approximations may be, we have the satisfaction of thinking that the masses obtained by their means, can have no appreciable effect upon the operations into which they are to be introduced, whilst they enable us to deal with a complete system or machine. But for these we have another Table No. II. to present, a _résumé_ of the foregoing one, for greater facility of reference.

TABLE II.--VOLUMES OF THE VARIOUS MEMBERS OF THE SOLAR SYSTEM AT THE DENSITY OF WATER. ---------+------------+-------------------+-----------------------+ | | Volume in | Total Volume in | Name. |Designation.| Cubic Miles at | Cubic Miles at | | | Density of Water. | Density of Water. | ---------+------------+-------------------+-----------------------+ Sun | | |482,169,000,000,000,000| | | |-----------------------| Mercury | Planet | | 92,735,000,000| Venus | " | | 1,131,960,000,000| Earth | " | 1,471,169,000,000| | Moon | Satellite | 18,141,236,000| 1,489,310,236,000| | |-------------------| | Mars | Planet | | 160,728,460,000| ---- | Asteroids |One fourth of Earth| 367,792,000,000| Jupiter | Planet |479,292,741,000,000| | " |4 Satellites| 76,180,317,000| 479,368,921,317,000| | |-------------------| | Saturn | Planet |154,351,000,000,000| | " |8 Satellites| 19,539,774,315| | " | 3 Rings | 195,000,000| 154,370,734,774,315| | |-------------------| | Uranus | Planet | 25,874,664,000,000| | " |4 Satellites| 1,724,977,600| 25,876,388,977,600| | |-------------------| | Neptune | Planet | 29,107,237,000,000| | " |1 Satellite | 727,680,925| 29,107,964,680,925| ---------+------------+-------------------+-----------------------+ Total of Planets, Satellites and Rings | 691,966,535,445,840| ------------------------------------------+-----------------------+ Dividing 482,169,000,000,000,000 by 691,966,535,445,840 makes the mass ofthe whole of the members to be 1/696·86th part of the mass of the sun, instead of 1/700th as generally stated by astronomers.