family that swept in beauty and harmony about their common parent the sun.

The mind now stood upon the first platform of the rocky pyramid which it had been slowly rearing and with which it had been slowly rising, through long centuries of ceaseless toil. One grand point had been gained. Darkness had given way to light, but the great problem of the universe was yet to be resolved, All this long and arduous struggle had only revealed what the problem was. Appearances were now separated from realities, and with a fresh and invigo rated courage the human mind now gives its energies to the accomplishment of definite objects, no longer working uncertainly in the dark, but with the clear light of truth to guide and conduct the investigation.

Possessed of these extraordinary advantages, the advance now became rapid and brilliant, as it had previously been slow and discouraging. That the planets, reckoning the earth as one, constituted a mighty family of worlds, was now manifest-whether linked singly to the sun, or mutually influencing each other, was the grand question. This great problem rested upon the resolution of a multitude of subordinate ones. The actual curve constituting the planetary orbits, the magnitude of these orbits, their actual position in space, the values and directions of their principal lines, the laws of their motion, all these and many more questions of equal importance and intricacy presented themselves in the outset of the examination now fairly commenced. Human skill was exhausted in the contrivance and construction of mechanical aids by which the movements of the planets might be watched with the greater accuracy,

Partial success crowned these extraordinary efforts but there yet remained delicate investigations which with the utmost skill in observing escaped the farthest reach of man's eagle gaze, and seemed to bid defiance to all his powers.

To conquer these difficulties, one of two things must be accomplished: either man must sweep out from earth towards the distant planets, to gain a hearer and more accurate view, or else bring them down from their lofty spheres to subject themselves to his scrutinizing gaze. How hopeless the accomplishment of either of these impossible alternatives. But who shall prescribe the limits of human genius? In studying the phenomena of the passage of light through transparent crystalized bodies, a principle is discovered which lets in a gleam of hope on the disheartened mind. It seizes this principle, converts it to its use, and arms itself with an instrument more wonderful than any that fancy in its wildest dreams ever pictured to the imagination. With the potent aid of this magic instrument, the astronomer no longer is bound hopelessly to his native earth; without indeed quitting in person its surface, his eye gifted with superhuman power, ranges the illimitable fields of space. He visits the moon, and finds a world with its lofty mountains and spreading valleys. The starlike planets swell into central worlds, with their circling moons, and myriads of fixed stars, hitherto beyond the reach of human vision, stand revealed in all their sparkling beauty. It is as if the united ranges of a thousand eyes were all concentrated in a single

one.

A new era now dawns on the world. The delicate

and invisible irregularities of the planetary motions are now fully revealed, and the data rapidly accumu late by means of which the last grand question is to be resolved. The orbitual curves are determined. The laws of the revolving planets are revealed. A mysterious relation between the distances of the planets from the sun and their periods of revolution unites them positively into one grand family group. That they are bound to the sun by some inscrutable power, is certain, and it now remains to determine the law of increase and decrease of this force for all possible distances. This last truth is finally achieved, and the wisdom of God is vindicated in the beautiful structure of our grand system.

The second lofty platform is reached in the mighty pyramid, whose summit is now nearing the stars of heaven. From this elevation the mind looks out upon the circling planets and their revolving satellites, and the mysterious comet, and ventures to propound the question, do these bodies so interfere with the movements of each other, as to affect permanently the structure by which the equilibrium and stability of the entire system is guarantied?

To answer this question, a new train of investigation is commenced, satellite is weighed against planet, and planet against the sun, until the mass of matter contained in each individual of the system becomes accurately known. Then is undertaken the grand problem of perturbations. The telescope reveals the fact that slow and mysterious changes are going on in the mean motions of the moon, in the figure of the planetary orbits, and in the relative ponitions which these orbits hold to each other. Are

these changes ever progressive? If this be true, then does the system contain within itself the seeds of decay, the elements of its own destruction. Slowly but surely as the solemn tread of time, the end must come, and one by one planet and satellite and comet, sink forever in the sun. Long and arduous was the struggle to reach the true answer to this difficult question. The entire solution involved a multitude of parts.

When the mutual dependence of the multitude of bodies constituting our system was discovered, when planet, and satellite, and comet, were found to feel and sway to the influence which each exerted on the other, the simplicity of their movements was gone for ever; orbits once fixed in the heavens, slowly swung away from their moorings; the beautiful precision which had to all appearance marked the planetary curves, was destroyed. The regularity of their motions was changed into irregularity, and a system of complexity which seemed to bid defiance to all effort at comprehension, presented itself to the human intellect.

It was no less than this-given, a system of revolving worlds, mutually operating on each other; required, their magnitudes, masses, distances, motions, and positions, at the close of a thousand revolutions. What mind possessed the gigantic power to grasp this mighty problem? Reason was lost in wandering mazes, and the brightest intellect sunk clouded in gloom.

In this dilemma, the mind turns inward on its own resources. As the physical man climbs some mountain height by successive efforts, rising higher and higher, scaling rock after rock, and mounting precipice after precipice, by the use of strength comparatively

feeble, resting and recruiting as it becomes exausted, was it impossible, to contrive some mental machinery which might give to the reason the power of pros ecuting its difficult researches, in such manner that it might stop and rest, and not lose what it had already gained in its onward movement?

Geometry had invigorated the reason, as exercise toughens and strengthens the muscles of the human frame. But it had given to the mind no mechanical power, wherewith to conquer the difficulties which rose superior to its natural strength. Archimides wanted but a place whereon to stand, and with his potent lever he would lift the world. The astronomer demands an analogous mental machinery to trace out the complex wanderings of a system of worlds. What the human mind demands and resolves to find, it never fails to discover. The infinitesimal analysis is reached, its principles developed, its resistless power, compelled into the service of human reason. I shall not now stop to explain the nature of this analysis. Its power and capacity alone engage our attention at the present. Once having seized on a wandering planet, it never relaxes its hold, no matter how complicated its movements, how various the influences to which it may be subjected, how numerous its revolutions, no escape is possible. This subtle analysis clings to its object, tracing its path and fixing its place with equal ease, at the beginning, middle, or close of a thousand revolutions, though each of these should require a century for its accomplishment.

Armed with this analysis, which the mind had crea ted for its use, giving to it a strength only commensurate with the increased power which had been given