In case the same rod be balanced on its centre on the finger, it presents an example of an equilibrium of indifference; that is, if it be swayed slightly to the one side or the other, there is no tendency to restore itself, or to increase its deviation.-It remains indifferent to any change. Take the same rod, and suspend it like a pendulum. Now cause it to deviate from the vertical to the right or left, and it returns of itself to the condition of equilibrium. This is an equilibrium of stability. We have already seen that this is the kind of equilibrium which exists in the planetary system. There are constant deviations, but a perpetual effort is making to restore the object to its primitive condition.

Now in case the rings of Saturn are homogeneous, equally thick, and exactly concentric with the planet, their equilibrium is one of instability. The smallest derangement would find no restorative power, and would even perpetuate and increase itself, until the system is destroyed. For a long time it was believed that the rings were equally thick, and concentric with the planet, but when it was discovered that such features would produce an equilibrium of instability, and that there existed no guarantee for the permanency of this exquisite system, an analytic examination was made, which led to this singular result, viz:-To change the equilibrium of instability into one of stability, all that is necessary is to make the ring thicker or denser in some parts than in others, and to cause its centre of position to be without the centre of the planet, and to perform around that centre a revolution in a minute orbit. Finding these conditions analytically, it now became a matter of deep interest to as

certain whether these conditions actually existed in nature. The occasional disappearance of the ring, in consequence of its edge being presented to the eye of the observer, gave a capital opportunity of determining whether it was of uniform thickness. On these rare occasions, in the most powerful telescopes, the ring remains visible edgewise, and looks like a slender fibre of silver light drawn across the diameter of the planet. In the gradual wasting away of the two extremities of the ring, it has been remarked, that the one remains visible longer than the other. As the ring is swiftly revolving, neither extremity can, in any sense, be regarded as fixed, and hence sometimes the one, sometimes the other, fades first from the sight. An exactly uniform thickness in the ring would render such a phenomenon impossible, and hence we conclude, that the first condition of stability is fulfilled, the rings are not equally thick throughout.

The micrometer was now applied to detect an eccentricity in the central point of the ring. Recent examinations by Struve and Bessel have settled this question in the most satisfactory manner. The centre of the ring does not coincide with that of the planet, and it is actually performing a revolution around the centre of the planet in a minute orbit, thus forming the second delicate condition of equilibrium. The analogy of the great system is unbroken in the subordinate one. For more than two hundred years have these wonderful circles of light whirled in their rapid career under the eye of man, and freed from all external action, they are so poised that millions of years shall in nowise affect their beautiful organization. Their graceful figures and beautiful light

shall greet the eyes of the student of the heavens when ten thousand years shall have rolled away.

Thus do we find that God has built the heavens in wisdom, to declare his glory, and to show forth his handy-work. There are no iron tracks, with bars and bolts, to hold the planets in their orbits. Freely in space they move, ever changing, but never changed; poised and balancing; swaying and swayed; disturbing and disturbed, onward they fly, fulfilling with unerring certainty their mighty cycles. The entire system forms one grand complicated piece of celestial machinery;-circle within circle; wheel within wheel; cycle within cycle;-revolutions so swift as to be completed in a few hours; movements so slow that their mighty periods are only counted by millions of years. Are we to believe that the Divine Architect constructed this admirably adjusted system to wear out, and to fall in ruins, even before one single revolution of its complex scheme of wheels had been performed? No.-I see the mighty orbits of the planets slowly rocking to and fro, their figures expanding and contracting, their axes revolving in their vast periods; but stability is there. Every change shall wear away, and after sweeping through the grand cycle of cycles, the whole system shall return to its primitive condition of perfection and beauty.

LECTURE VII.

THE DISCOVERY OF NEW PLANETS.

In the earliest ages of the world, the keen vision of the old astronomers had detected the principal members of the planetary system. Even Mercury, which habitually hovers near the sun, and whose light is almost constantly lost in the superior brilliancy of that luminary, did not escape the eagle glance of the primitive students of the stars. For many thousand years no suspicion arose in the mind, as to the existence of other planets, belonging to the great scheme, and which had remained invisible from their immense distance or their minute dimensions.Indeed the grand investigations which have recently engaged our attention, the mutation of the planetary orbits, their perpetual oscillations and final restoration, the equilibrium of the whole system, had been prosecuted and completed before the mind gave itself seriously to the contemplation of invisible worlds.

The singularly inquisitive genius of Kepler, over whom analogy seems to have ever played the tyrant, in an examination of the interplanetary spaces, finding these to increase with regularity in proceeding outward from the sun, until reaching the space between Mars and Jupiter, which was out of all proportion too great, conceived the idea that an invisible planet revolved in this space, and thus completed the