the opposition of his preceptor and family. He travelled to Germany, where he formed connections of correspondence and friendship with the most distinguished persons who pursued astronomy either as a profession or amusement, and particularly with the Landgrave of Hesse-Cassel, who received him in the most flattering

manner.

On his return to his own country, he was fixed there by his sovereign, Frederic, who gave him the little island of Huena at the entrance of the Baltic. Here Tycho built a celebrated observatory, which was called Uranibourg: and during an abode of twenty-one years, accumulated a prodigious mass of observations and important discoveries. At the death of Frederic, envy, then unrestrained, compelled Tycho to leave his retreat. His return to Copenhagen did not appease the rage of his prosecutors; the minister, Walchendorp (whose name, like that of all men who have abused the power entrusted to them, ought to be handed down to the execration of all ages), forbad him to continue his observations. Fortunately, Tycho found a powerful protector in the Emperor Rodolph II. who settled on him a considerable pension, and lodged him commodiously at Prague. He died suddenly at this city, on the 24th of October, 1601, in the midst of his labours, and at an age when astronomy might have expected great services from him.

The invention of new instruments, and new improvements, added to the old ones a much greater precision in observation; a catalogue of stars very superior to those of Hipparchus, and Ulugh Beigh; the discovery of that inequality of the moon, which is called variation; that of the inequalities of the motion of the nodes, and of the inclination of the lunar orbit; the interesting remark, that comets are beyond this orbit; a more perfect knowledge of astronomical refraction; finally, very numerous observations of the planets, which have served as the basis of the discoveries of Kepler. Such are the principal services which Tycho Brahe has rendered astronomy. Struck with the objections which the adversaries of Copernicus made to the motion of the earth, and perhaps influenced by the vanity of wishing to give his name to an astronomical system, he mistook that of nature. According to him, the earth is immovable in the centre of the universe; all the stars move every day round the axis of the world; and the sun, in its annual revolution, carries with it the planets. In this system, already known, the ap

pearances are the same as in that of the motion of the earth. We may, in general, consider any point we chuse; for example, the centre of the moon is immovable, provided we assign the motion with which it is animated in a contrary direction to all the stars.

But, is it not physically absurd to suppose the earth immovable in space, while the sun carries with it the planets in which it is included? How could the distance from the earth to the sun, which agrees so well with the duration of its revolution in the hypothesis of the motion of the earth, leave any doubt of the truth of this hypothesis, in a mind constituted to feel the force of analogy. It must be confessed that Tycho, though a great observer, was not fortunate in his research after causes; his unphilosophical mind had even imbibed the prejudices of astrology, which he tried to defend.

It would, be, however, unjust to judge him with the same rigor as one who should refuse at present to believe the motion of the earth, confirmed by the numerous discoveries made in astronomy since that period.

The difficulties which the illusions of the senses oppose to this theory, were not then completely removed. The apparentdiameter of the fixed stars, greater than their annual parallax, give to these stars on this theory, a real diameter, greater than that of the terrestrial orbit. The telescope, by reducing them to luminous points, make this improbable magnitude disappear. It could not be conceived how these bodies, detached from the earth, could follow its motion. The laws of mechanics have explained these appearances; they have proved, what Tycho had again made doubtful, that a body, falling from a considerable height, and abandoned to the action of gravity alone, ought to fall very nearly in a vertical line, only deviating to the east, by a quantity difficult to estimate accurately by observation from its minuteness, so that at present there is as much difficulty in proving the motion of the earth by a direct experiment, as formerly existed to prove that it should be insensible.

In his later years Tycho Brahe had Kepler for a disciple and assistant. He was born in 1571, at Viel, in the duchy of Wirtemberg, and was one of those extraordinary men whom nature grants now and then to the sciences, to bring to light those great theories which have been prepared by the labour of many centuries.

The career of the sciences did not appear to him proper to sa

tisfy the ambition he felt of rendering himself illustrious; but the ascendancy of his genius, and the exhortations of Maestlinus, led him to astronomy: and he entered into the pursuit with all the activity of a mind passionately desirous of glory.

The philosopher, endowed with a lively imagination, and impatient to know the causes of the phænomena which he sees, often obtains a glimpse of it, before observation can conduct him to it. Doubtless he might, with greater certainty, ascertain the cause from the phænomena; but the history of science proves to us, that this slow progress has not always been that of inventors.

What rocks has he to fear, who takes his imagination for his guide!

Prepossessed with the cause which it presents to him, instead of rejecting it when contradicted by facts, he alters the facts to make them agree with his hypothesis; he mutilates, if I may be allowed the expression, the work of nature, to make it resemble that of his imaginatiou, without reflecting that time destroys with one hand these vain phantoms, and with the other confirms the results of calculation and experience.

The philosopher who is really useful to the cause of science, is he, who, uniting to a fertile imagination, a rigid severity in investigation and observation, is at once tormented by the desire of ascertaining the cause of the phænomena, and by the fear of deceiving himself in that which he assigns,

Kepler owed the first of these advantages to nature, and the second to Tycho Brahe. This great observer, whom he went to see at Prague, and who had discovered the genius of Kepler, in his earliest works, notwithstanding the mysterious analogies of numbers and figures with which it was filled, exhorted him to devote his time to observation, and procured him the title of Imperial mathe

matician.

The death of Tycho, which happened a few years afterwards, put Kepler in possession of his valuable collection of observations, of which he made a most noble use, founding on them three of the most important discoveries that have been made in natural philosophy.

It was an opposition of Mars which determined Kepler to employ himself on the motions of this planet, rather than on any other. His choice was fortunate in this respect, that the orbit of Mars,

being one of the most eccentric of the planetary system, the inequa. lities of his motion are more perceptible, and therefore lead to the discovery of their laws with greater facility and precision. Though the theory of the motion of the earth had made the greater part of those circles with which Ptolemy had embarrassed astronomy disappear, yet Copernicus had substituted many others to explain the real inequalities of the celestial bodies.

Kepler, deceived like him, by the opinion that their motions ought to be circular and uniform, tried a long time to represent those of Mars in this hypothesis. Finally, after a great number of trials, which he has related in detail in his famous work called Stella Martis, he overcame the obstacle, which an error, supported by the suffrage of every period, had opposed to him; he discovered that the orbit of Mars is an ellipse, of which the sun occupies one of the foci, and that the motion of the planet is such, that the radius vector, drawn from its centre to that of the sun, describes equal areas in equal times. Kepler extended these results to all the planets, and published from this theory, in 1626, the Rudolphine tables, for ever memorable in astronomy, as being the first founded on the true laws of the planetary motions.

Without the speculations of the Greeks, on the curves formed from the section of a cone by a plane, these beautiful laws might have been still unknown. The ellipse being one of these curves, its oblong figure gave rise, in the mind of Kepler, to the idea of supposing the planet Mars, whose orbit he had discovered to be oval, to move on it; and soon, by means of the numerous properties which the ancient geometricians had found in the conic sections, he became convinced of the truth of this hypothesis. The history of the sciences offers us many examples of these applications of pure geometry, and of its advantages; for every thing is connected in the immense chain of truths, and often a single observation has been sufficient to show the connection between a proposition apparently the most sterile, and the phænomena of nature, which are only ma thematical results of general laws.

The perception of this truth probably gave birth to the myste rious analogies of the Pythagorists: they had seduced Kepler, and he owed to them one of his most beautiful discoveries. Persuaded that the mean distances of the planets from the sun, ought to be re

gulated conformably to these analogies, he compared them a long time, both with the regular geometrical solids, and with the intervals of tones. At length, after seventeen years of meditations and calculation, conceiving the idea of comparing the powers of the numbers which expressed them, he found that the squares of the times of the planetary revolutions, are to each other as the cubes of the major axes of their orbits; a most important law, and which he had the advantage of observing in the system of the satellites of Jupiter, and which extends to the systems of all the satellites.

We might be astonished that Kepler should not have applied the general laws of elliptic motion to comets. But, misled by an ardent imagination, he lost the clue of the analogy, which should have conducted him to this great discovery. The comets, according to him, being only meteors engendered in ether, he neglected to study their motions, and thus stopped in the middle of the career which was open to him, abandoning to his successors a part of the glory which he might yet have acquired. In his time, the world had just begun to get a glimpse of the proper method of proceeding in the search of truth, at which genius only arrived by instinct, frequently connecting errors with its discoveries. Instead of passing slowly through a succession of inductions, from insulated phænomena, to others more extended, and from these to the general laws of nature; it was more easy and more agreeable to subject all the phænomena to the relations of convenience and harmony, which the imagination could create and modify at pleasure.

Thus, Kepler explained the disposition of the solar system, by the laws of musical harmony. We behold him even in his latest works, amusing himself with these chimerical speculations, even so far as to regard them as the "life and soul" of astronomy. He has deduced from them the eccentricity of the terrestrial orbit, the density of the sun, its parallax, and other results; the inaccuracy of which, now discovered, is a proof of the errors to which we expose ourselves, in deviating from the rout traced by observation.

After having destroyed the epicycles which Copernicus had preserved; after having determined the curve which the planets describe round the sun, and discovered the laws of their motion; Kepler approached too near to the principle from which these laws were derived, not to anticipate it. Attempts to discover this prin