Of all the grand objects of the solar system, Saturn is truly the most wonderful. This magnificent orb, encircled by a system of rings, and accompanied by eight moons, performs a revolution around the sun at the mean distance of 906,000,000 of miles in 10759 1-4 of our days, or in about 20 1-2 years. – When nearest the earth, it is 811,000,000 of miles distant, an interval which could not be traversed by a cannon ball, flying with a velocity of 500 miles an hour, in less than about 184 years. The circumference of its orbit is 5,695,000,000 of miles; a distance so great, that a steam carriage, moving at the rate of 20 miles an hour, would require above 32,500 years to complete the journey. Saturn rolls in silent grandeur around this whole circuit at an average rate of 22,000 miles every hour.

Saturn is nearly as large as Jupiter, being 79,000 miles in diameter; around this stupendous globe are two magnificent rings, situated in the plane of the equator, and concentric with the planet and with each other. The inner edge of the interior ring is several thousand miles distant from the surface of the planet, and consequently has no contact or connection with it. From the inner to the outer edge of the interior ring, or its breadth, is nearly equal to its distance from the planet. The interval between the interior and exterior rings is 1791 miles. From the inner to the outer edge of the exterior ring, or its breadth, is over 10,000 miles. The thickness of these rings cannot exceed 250 miles. These rings have no connection or contact with each other – Let it be understood, that these rings do not encircle the planet in the form of a broad belt or zone, extending several thousand miles each side of the equator, but they encircle that globe in the plane of its equator with their edges directed towards its centre. The dimensions of this extraordinary appendage, as calculated from Professor Straue’s micrometric measures, are as follow:
Exterior diameter of exterior ring,                              176,418
Interior         do                 do                                          155,272
Breadth of                         do                                             10,573
Exterior diameter of interior ring                                151,690
Interior          do                do                                           117,339
Breadth of                         do                                              17,175
Equatorial diameter of the planet                                  79,160
Interval between the planet and the interior ring      19,090
Interval between the rings,                                                1,791
Thickness of the rings not exceeding                                 250

It will be perceived that the thickness of the rings is incomparably smaller than their breadth.—From recent observations it is believed, that the rings are not only double, but that they are separated by four, and, as some observers declare, by six divisions. If these observations can be depended upon, then there must be five, and perhaps seven, rings concentric with each other. The interval between each ring must be exceedingly narrow.

The disc of Saturn appears striped with dark and bright belts, running parallel with its equator.—These belts are broader than those of Jupiter, but the alternations of light and shade are less strongly marked. These belts are, no doubt, produced by a similar cause to that operating upon Jupiter, being the results of the great atmospheric currents, arising from the difference of temperature in different latitudes, and greatly modified in their direction and velocity by the swift rotation of that planet upon its axis.

The axis of rotation is perpendicular to the plane of the rings, and also to the belts. The planet revolves from west to east in a period of 10 hours, 29 minutes, and 17 seconds. The ring revolves around the planet in its own plane in the period of 10 hours, 32 minutes, and 15 seconds; which is almost exactly the same period as the planet’s rotation, there being only 2 minutes and 58 seconds difference. Whether the several rings revolve in the same period, has not been determined by observation, but it is extremely probable from certain mechanical considerations, founded on the laws of force and distance, that there must be a difference in their periods in order that the system may be maintained in a similar state of equilibrium.

It may be enquired, how the rings are prevented from breaking up, and falling down upon the surface of the planet? The answer to this is the great centrifugal force of rotation. If a moon were placed at the distance of 70,924 miles from the centre of Saturn, it would revolve around the planet in exactly the same period that the ring now revolves. – A satellite then, in order to have the same period with the ring, would actually occupy a position in the exterior ring at a distance of 2288 miles from its interior edge, or 8285 miles from its exterior edge. The centrifugal force of a satellite in the exterior ring would be just equal to the centripetal force towards the planet; therefore it would have no tendency to fall towards or recede from the planet.— Now if we suppose two, three, or a hundred moons situated at the same distance from the planet, they would all have the same period, and consequently would be under the same influence of the same two antagonist forces, and would continue to revolve at the same distance. Now, if instead of a hundred moons, we suppose a ring of moons joined side by side, encircling the planet at the same distance from its centre: such a ring of moons would have no more tendency to collapse or fall towards the planet, than one moon would. And further, if every moon in this ring, instead of being spherical, should be flattened out so as to form a ring similar in every respect to the exterior ring that actually surrounds Saturn, such a ring would revolve in the same period and at the same distance as one moon, and would have no disposition to fall towards Saturn, though it were broken into any number of fragments.

The interior ring, if it had the same period of rotation as the exterior, would have a tendency to fall towards the planet; for with the same period the centrifugal force would be less than the centripetal.  To prevent this tendency to fall, the rotation of the interior ring must have its velocity increased in the inverse proportion of the square roots of the distances of the two rings; that is, the middle portion of the interior ring is 67,257 miles from the centre, while the distance of the point in the exterior ring at which a satellite would revolve in the same time as the ring, is 79,924 miles. The square root of the first number is 260; the square root of the second is 283; therefore a point on the middle of the breadth of the interior ring would move 283 miles, while the point in the exterior ring moved 260 miles.

The actual velocity of the nearest point would be 14.326 miles per second; while the actual velocity of the other point would be 13.238 miles per second. If the exterior ring revolves in 10h 32m 15s, the interior ring should revolve in 8h 11m 37s nearly 21m sooner. With these velocities, neither of the rings would have any tendency to collapse.

The quantity of matter towards which the outer ring gravitates is a trifle greater than the quantity towards which the inner one gravitates; therefore, for this reason, the inner ring must move a very small degree slower than it otherwise would. I have made the necessary allowance in the foregoing calculations, though I have omitted the minute fractions.

Although the great centrifugal force of rotation is calculated to preserve the rings from contracting until they finally coalesce with the surface of the planet, providing that the centres of gravity of the rings and planet exactly coincide, –yet if these centres, from any external causes whatsoever, become separated by ever so small an amount, it can be demonstrated, that the derangement will go on increasing more and more until the edge of the ring nearest to the centre of the planet, will finally come in contact with its surface. An equilibrium of instability is the name given to this kind of mechanical conditions; it may be exemplified by balancing a rod upon the tip of the finger. While the rod stands in an exact vertical position, it maintains itself in a state of equilibrium, and has no tendency to fall, but this equilibrium is unstable; for the slightest deviation from the vertical will constantly be increased until the rod falls, and the equilibrium is destroyed.

There is another species of equilibrium that may be called the equilibrium of indifference; for instance, let a rod be suspended by its centre of gravity upon an axle, if it be turned in any position in a vertical plane, it will have no tendency to restore itself to its original position, or to increase its deviation, but will remain entirely indifferent to any change. If this rod be suspended like a pendulum, and be made to deviate from the vertical, it immediately seeks to return again to its original position, as is manifested by its oscillations on each side of its centre of gravity. This is an equilibrium of stability. All derangements from this kind of equilibrium, are not permanent; neither do they go on increasing, but are counteracted by the constant tendency to return to the primitive condition of equilibrium.

In case the rings of Saturn were equally thick and homogeneous, (that is, composed of matter of equal density) whether they were exactly concentric with the planet or not, the system would be in a condition of indifferent equilibrium, and therefore would, with the slightest derangement, speedily destroy itself.

To construct an equilibrium of stability, three things are necessary; first, one part of the ring must be thicker or denser than other parts; second, the centre of position of the ring must be without the centre of the planet; and, third, the centre of the ring must revolve around the centre of the planet in a minute orbit. It can be analytically demonstrated, that with these three conditions, the system would be in a state of stable equilibrium. By observation, it is found that these conditions do actually exist. The ring is actually observed to be thicker in some parts than in others; it is also actually observed that the ring is not concentric with the planet, and it is further observed that the centre of the ring does revolve around the centre of the planet. Through these causes, therefore, the system will be maintained through indefinite ages without any danger of permanent derangements, arising from the slight deviations, occasioned by the unequal action of the satellites, or by other causes.

The mutual gravitation of the rings and planet would have no tendency to derange their relative positions; for it can be demonstrated, that if a particle were placed any where within a spherical shell of matter, of equal density at all equal distances from the centre, it would be in a state of indifferent equilibrium, and would have no tendency to move in any direction.

Now if the planet Saturn were actually enclosed within a spherical shell of matter whose interior surface was at the same distance as the interior edge of the ring, in all positions that it might be placed within the same, it would be in a state of equilibrium, having no tendency to move in one direction more than in another. Now if we take away all this spherical shell with the exception of a thin ring, encircling the equator, it is quite evident that the mutual gravity exerted between the planet and each part of the ring would be exactly equal in every position of the planet within this ring whether their centres coincided or not. Even if the surface of the planet were placed in contact with the inner edge of the ring, they would not adhere together with the least force; for the tendency to the opposite part of the ring would be exactly equal to its tendency to that part with which it might be placed in contact. Therefore, the mutual gravitation exerted between a planet and any number of circular rings with which it may be enclosed, (if of equal thickness and density at equal distances) can never alter in the least degree their relative positions, whether their centres coincide or not. This, therefore, is an equilibrium of indifference, so far as their mutual gravitations are concerned.

Let it be distinctly understood, that this equilibrium has reference to the ring as a whole, and not in regard to its different parts. Every part of the ring gravitates towards the planet, and if each of these parts were detached or loose, they would fall to it, unless prevented by the centrifugal force of rotation. But our reasonings were grounded on the assumption that the matter composing the ring was solid, and adhering to the ring with a cohesive force greater than its gravity towards Saturn. In such a case, it is evident that they could not be affected by gravity, without effecting the whole ring; but the affections of the whole ring are equal and opposite; therefore, the whole cohesive ring will maintain its relative position to the planet while the loose parts will, if not prevented by centrifugal force, be precipitated or fall towards the surface of the planet.

Although the equilibrium of indifference, which we have now explained, could not be deranged by the mutual gravitations of the cohesive ring and planet, yet their relative positions might and would be deranged by the unequal action of the satellites upon the rings and planet which would in a short time bring them into immediate contact, were it not for the three principles of stable equilibrium to which we have previously referred. How wonderful are these adjustments!  What wisdom is displayed in this grand, though anomalous system!

And then again, when it is known that the interval between the rings does not exceed 1800 miles, how exquisite must be the adjustments, to prevent them from collapsing! Neither of the rings or planet, if of equal thickness and density, would alter their relative positions by their own mutual gravitations; but one ring, in the course of a very short time, might be precipitated upon the other by the operation of some external force, unless prevented by the three conditions which we have already specified as necessary to their stability.

The velocity of the rotation of the rings is much greater than their orbitual velocity around the sun. The circumference of the exterior edge of the outer ring is over 554,000 miles; it must revolve, therefore, over 52,000 miles every hour; while the velocity in the orbit around the sun is only about 22,000 miles per hour. During their midnight, the absolute velocity of that point of the ring the most distant from the sun, resulting from both of these motions, will be 74,000 miles per hour to the east; while that point of the ring nearest the sun, will be moving with an absolute velocity of 30,000 miles per hour to the west. From their noon till their midnight, — a period of only about 5 1-4 hours, there must be an average change of absolute velocity of about 20,000 miles per hour.

The inclination of the orbit of Saturn to the plane of the ecliptic is equal to 2deg. 29m. 35.7s. The inclination of the equator and ring to the plane of its orbit is equal to 28 deg. 11m. The plane of the ring in the year 1852 intersects the plane of the ecliptic in two points, namely, 167deg. 33m. 14.9s. and 347deg. 33m. 14.9s. of longitude. The nodes of the ring are not quite stationary, but advance on the ecliptic about 46 462s. per annum.

The variety of seasons upon Saturn and his rings will be somewhat more striking than with su, because the inclination of his equator to his orbit is greater than ours. Summer, winter, spring, and autumn, will each be about 7 1.2 years long. Every 15 of our years the sun will apparently pass through the equinoxes of Saturn, at which time it will be vertical to the outer edge of the ring. The sun will apparently recede to the south side of the rings as far as the southern tropic or about 30deg. south, and then return back again, crossing the equator or plane of the ring, and continue 30deg. north or to the northern tropic; therefore the sun shines 15 years on the southern side of the rings, and then the same length of time on the northern.  Each side of the rings, therefore, have alternately 15 years day and 15 years night.

Saturn’s rings are not always visible in consequence of their relative positions in regard to the sun and earth. There are three causes for their disappearance.

First, when the sun is vertical to the edge of the ring, the edge will be the only illuminated part; the sides of the ring, therefore, will be invisible; and as the edge is so very thin, it will also be invisibly to all telescopes, but those of the most extraordinary power. This disappearance will happen once in 15 years, when Saturn is at or near his equinoxes.—When in this case, the ring is rendered visible by the aid of the most powerful telescopes, it “can only appear as a very narrow straight line of light, projecting on either side of the planet as a prolongation of its diameter.”

Second, when the edge of the ring is presented to the earth, though one of its sides may be obliquely enlightened, yet it will be invisible because of its place being in the direction of the line of vision, and the edge being too thin to be seen. This will never happen only when the planet is within 6 degrees 1min. of either node, –or only once in 15 years.

Third, when the sun and earth are on the opposite sides of the ring, the dark side being towards us, will be invisible. This also can never happen, only once in 15 years, when the planet is within deg. 1m. of either node. In this case, no power of the telescope would render the ring visible; but the aspect of the planet would be very singular, appearing like a bright round disc, striped with belts of darkish shade, and crossed equatorially by a narrow and perfectly black line. This of course would be the projection of the dark invisible ring upon the bright disc.

The ring of Saturn will always be visible, in every part of its orbit, except in a space of about 6deg. 1m. on each side of either node where it may, under the foregoing circumstances, become invisible. Saturn passes through this small arc where the disappearances may happen in about 359 1-2 days, in a little less than one of our years. When Saturn passes over that portion of its orbit between 17 deg. 34m. and 341deg. 32m. of heliocentric longitude, the northern side of the ring is enlightened and visible. When he passes over that portion of his orbit, included between the longitudes of 353 deg. 34m. and 161deg. 32m., the southern side of the ring is enlightened and visible.

The greatest opening of the ring occurs about 1-2 years after the planet passes either node; when the plane of the ring will be inclined to the line of our vision about 30 deg This will be the greatest angle under which we can ever see the ring. By the effect of perspective, it will then appear like an ellipse whose greatest diameter will be double the shortest. This is the most favorable position for viewing the ring. This occurred in 1839-40, and will occur again in 1854-5. From this most open position, the ring, for 7 1-2 years, continues to change its apparent aspect by becoming more and more narrow until it finally vanishes in a straight line.

All these various phases are only apparent, arising from the relative position of the ring in regard to the eye. These effects may be exemplified by holding a broad thin ring between our eye and one of the walls of this house, and varying its position. It is evident that when held in any given position it will hide a certain portion of the wall; let this portion be marked. Now change the position of the ring, and the portion of the wall obscured will be changed also. If the ring be held with its plane inclined 30 deg with the line of vision, the portion of the wall that will be hid will be an ellipse whose greater diameter will be double the shorter. If the angle of the inclination of the ring be less, the minor axis of the ellipse will be less; and this axis will decrease its length as the inclination decreases.  until finally the ellipse will coalesce into a straight line. Now all these phases actually happen in viewing the ring of Saturn.

The scenery from the surface of Saturn must be grand, imposing beyond conception. The enlightened side of the ring will be seen for 15 years alternately in the northern and southern hemispheres.  It will appear, like a vast arch of light, extending from the eastern to the western horizon. The mountains, vallies, and landscapes will be very distinctly visible; while the difference of the rotations of the planet and ring will be so small, that the ring will appear to them to rotate from east to west once in about 246 of their days; during which time every part of the enlightened side of the ring will successively pass their meridian.

While in one hemisphere they are enjoying the beautiful and sublime scenery of this georgeous ring, in part of the other hemisphere they will be suffering a fifteen years total eclipse, occasioned by the interposition of the ring between them and the sun.

Saturn is accompanied by 8 satellites; all of which revolve around him from west to east. The most distant has its orbit inclined to the plane of the ring 12deg. 14m., which is nearly one half of the angle of inclination between the plane of the ring and that of its orbit. All the rest of the satellites move in or nearly in the plane of the ring. To these satellites the following names have been given, beginning with the nearest to the planet and proceeding outwards, namely:–

Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, and Japetus. The discovery of Hyperion is quite recent, having been made on the night of the 19th of September, 1848, by two different discoverers far separated from each other, namely Mr. Lassell, of Liverpool, and Prof. Bond, of Cambridge, U.S.

The nearest, or Mimas, revolves in an orbit only 5228 miles above the outer ring, or 93,437 miles from the planet’s surface; its period is 22h. 37m. 22.9s.

Enceladus is 131,100 miles from the surface of the planet, and revolves around it in 1d. 8h. 53m. 6.7s.

The distance from the surface of the planet to Tethys is 171,761 miles; its period is 1d. 21h. 18m. 25.7s.

Dione is 231,139 miles from the planet, and revolves around it in 2d.17h. 41m. 8.9s.

Rhea is 338,520 miles distant, and revolves in 4d. 12h. 25m. 10.8s.

Titan is 836,918 miles from the surface of the planet, and revolves around it in 15d. 22h. 41m. 25.2s.

Hyperion is 1,063,669 miles from the planet, and revolves around it in 22d. 12h.

Japetus is 2,507,749 miles from the planet’s surface, and revolves around it in 79d. 7h. 53m. 40.4s.

The first four satellites are nearer to Saturn than the moon is to our earth; and if we suppose them to be as large as our moon, the apparent disc of the first will be about 8 times larger than that of our moon’s: that of the second, 4 times larger; that of the third, over twice as large; that of the fourth will appear about the same size. The first will pass from new to full moon in one of Saturn’s days, and the next day it will pass from full to new moon. The second will pass through all the phases from new to full and from full to new moon in about three Saturnian days. The third will pass through all the same aspects in a little over four of Saturn’s days: and the fourth will undergo the same changes in a little over 6 of Saturn’s days. The four most distant satellites will probably appear somewhat smaller than our moon and each will exhibit all of its phases during the period of its revolution.

How splendid must be the firmament of Saturn. New moons, half moons, full moons, rings, all revolving – all changing – all exhibiting the handy work – the wisdom, and glory of the great Architect of nature who created this superb and magnificent system!

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[Transcribed by Erin T. McAllister, Mauri Pratt, and Rebecca Staker; Jun 2012]

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