commenced a series of examinations which finally led to the knowledge of the second great law of the planetary motions, which may be thus announced: If a line be drawn from the centre of the sun to any planet, this line, as it is carried forward by the planet, will sweep over equal areas in equal portions of time. This law accorded in the most perfect manner with fact, and gave at once the power of following, and, from the mean motion, computing the place of any planet,- -a triumph which all the complexity of older systems had failed ever to accomplish.

Any other mind less adventurous than that of Kepler might have been satisfied with these two great discoveries. The precise curves described by the planets, and a law regulating their motions in their orbits, sufficed to render all the phenomena of the heavenly bodies not only explicable, but susceptible of accurate prediction. There seemed nothing more to be added. Kepler did not think so. He conceived the idea that the solar system was not a mere assemblage of isolated planets revolving about a common centre, but a great associated system, in which some common bond of union existed, which, once found, would present the solar system in a new and true light.

This bond he believed existed in some hidden relation between the times occupied by the planets in describing their orbits, and their distances from the sun. In the history of this remarkable research, we are presented with one of the brightest examples of the fruits of perseverance. If some superior power, some spirit from a brighter world, had revealed to the mind of Kepler the actual existence of some relation between the planet's periods and distances, and had proposed to him to discover this hidden law, there would have been a definite object before the astronomer, and to have persevered in the pursuit of this object would have been within the limits of probability, even if a lifetime were exhausted in fruitless efforts. But to excite in his own mind a faith sufficiently strong in the existence of a law of which there existed not the slightest evidence, and to have persevered in its research for seventeen long years of laborious effort, seems almost incredible.

There is an immense difference between the pursuit which resulted in the discovery of the first two laws of Kepler, and the third one. In seeking for the curve described by the planets, it was looking for that which must have an existence; and in tracing the law of a planet's motion, it was absolutely impossible

to follow a planet, or predict its positions, without such a law. But in seeking for a bond of union among the planetary periods and distances, it was a search for that which, it was believed, had no existence, except in the wild imagination of this extraordinary philosopher. The history of mind scarcely furnishes an example in any degree parallel, if we except, perhaps, the heroic fortitude which marked the career of Columbus. Yet even the great Genoese was in possession of solid facts on which to base his reasoning. He saw evidences of the existence of another hemisphere, which the superficial could never realise. Kepler, more bold, more grand, more sublime, dreamed of nothing less than a brotherhood of worlds, a mighty and magnificent scheme of vast revolving orbs. Should success crown his efforts, the most brilliant results would follow. The distance of a single planet from the sun once obtained, and the periodic time of all being known, the distances might then be found for each individual in the entire system, without even directing an instrument to the heavens. Here then was a prize to reach which no time, or pains, or labour could be misapplied. Its return would be a hundredfold.

But where was the prize to be sought? Even admitting that some common bond did bind the circling worlds into one harmonious system, did it exist in some hidden relation between their periods of revolutions, their distances, their magnitudes, their densities? or was it to be sought in some analogy between the distances and periodic times? After long and deliberately pondering this great problem, Kepler decided that the strongest probability suggested that the distances of the planets, and their periods of revolution, would in some way contain the mysterious bond of union. Here then did this daring mind concentrate its energies; and his purpose once fixed, he marches steadily forward in his research with a courage which no defeat could daunt, and a perseverance which knew no limit but success.

Before announcing the final result, let me explain two terms employed in its statement. The square of any quantity results by multiplying it by itself. The cube comes from multiplying the square by the number. The square of a planet's period, or the cube of its distance, are known the moment we know the period and distance, by applying the simple rules of arithmetic. After Kepler had exhausted all simple relations between the periods and distances of the planets, in no degree shaken in his

lofty faith, he proceeded to try all possible relations between the squares of the periods and distances, but with as little success. Nothing daunted, he proceeded to investigate the possible relations between the cubes of the periods and distances. Here again he was foiled; no law exhibited itself. He returned ever fresh to the attack, and now commenced a series of trials involving the relations between the simple periods and the squares of the distances. Here a ray of hope broke in upon his dim and darkened path.

No actual relation existed, yet there was a very distant approximation, enough to excite hope. He then tried simple multiples of the periods and the squares of the distances: all in vain. He finally abandoned the simple periods and distances, and rose to an examination of the relations between the squares of these same quantities. Gaining nothing here, he rose still higher, to the cubes of the periods and distances; no success: until, finaliy, he tried the proportion existing between the squares of the periods in which the planets perform their revolutions ard the cubes of their distances from the sun. Here was the grand secret; but, alas! in making his numerical computation, an error in the work vitiated the results, and with the greatest discovery which the mind ever achieved in his very grasp, the heart-sick and toil-worn philosopher turned away almost in despair from his endless research.

Months rolled round, and yet his mind, with a sort of keen instinct, would recur again and again to this last hypothesis. Guided by some kind angel or spirit, whose sympathy had been touched by the unwearied zeal of the mortal, he returned to his former computations, and with a heaving breast and throbbing heart, he detects the numerical error in his work, and commences anew. The square of Jupiter's period is to the square of Saturn's period as the cube of Jupiter's distance is to some fourth term, which Kepler hoped and prayed might prove to be the cube of Saturn's distance. With trembling hand he sweeps through the maze of figures; the fourth term is obtained; he compares it with the cube of Saturn's distance. They are the same! He could scarcely believe his own senses. He feared soine demon mocked him. He ran over the work again and again; he tried the proportion, the square of Jupiter's period to the square of Mars' period as the cube of Jupiter's distance to a fourth term, which he found to be the cube of the distance of

Mars; till finally full conviction burst upon his mind: he had won the goal, the struggle of seventeen long years was ended, God was vindicated, and the philosopher, in the wild excitement of his glorious triumph, exclaims:

"Nothing holds me. I will indulge my sacred fury! If you forgive me, I rejoice; if you are angry, I can bear it. The die is cast. The book is written, to be read either now, or by posterity, I care not which. It may well wait a century for a reader, since God has waited six thousand years for an observer!"

More than two hundred years have rolled away since Kepler announced his great discoveries. Science has marched forward with swift and resistless energy. The secrets of the universe have been yielded up under the inquisitorial investigations of god-like intellect. The domain of the mind has been extended wider and wider. One planet after another has been added to our system; even the profound abyss which separates us from the fixed stars has been passed, and thousands of rolling suns have been descried, swiftly flying or majestically sweeping through the thronged regions of space. But the laws of Kepler bind them all; satellite and primary, planet and sun, sun and system, all with one accord proclaim, in silent majesty, the triumph of the hero philosopher.

DISCOVERY OF THE GREAT LAWS OF MOTION AND GRAVITATION.

HE remarkable discoveries which had rewarded the researches of Kepler, confirmed in the most perfect manner the doctrines of Copernicus, flowing as they did from his prominent hypothesis, the central position of the sun. Having reached to the true laws of the planetary motions, the whole current of astronomical research was changed. New methods were demanded, and more delicate means of observation must be brought into use before the data could be furnished for new discoveries.

Henceforward astronomy could only advance by the aid of kindred sciences. Mathematics, optics, and, above all, mechanical philosophy, were to become the instruments of future conquests.

The philosophy of Aristotle, though very far from deserving it, wielded quite as extensive an influence over the age as did the astronomy of Ptolemy. It appears, indeed, that the followers of Aristotle regarded their master as absolutely infallible, and gave to his doctrines a credence so firm, that even the clearest experiments, the most undeniable evidence of the senses, were sooner to be doubted than the doctrines of the divine Greek. To attack and destroy a system so deeply rooted in the prejudices of the age, required a mind of extraordinary courage and power, a