formally promulgated, and ordered to be publicly read in the universities. In Florence, the adherents of Galileo were ordered to attend in the Church of Santa Croce to witness his disgrace. After a short imprisonment in the jail of the Inquisition, he was ordered to Arcetri, and confined in his own house. Here severe misfortunes awaited him; his favourite daughter died; he fell into a state of melancholy; an application that he might go to Florence for the sake of medical advice was refused. It became evident that there was an intention to treat him with inexorable severity. After five years of confinement, permission was reluctantly accorded to him to remove to Florence for his health; but still he was forbidden to leave his house, or receive his friends, or even to attend mass during Passion Week without a special order. The Grand-duke tried to abate this excessive severity, directing his ambassador at the court of Rome to plead the venerable age and ill health of the immortal convict, and that it was desirable to permit him to communicate certain scientific discoveries he had made to some other person, such as Father Castelli. Not even that was accorded unless the interview took place in the presence of an official of the Inquisition. Soon after Galileo was remanded to Arcetri. He spent the weary hours in composing his work on Local Motion, his friends causing it to be surreptitiously published in Holland. His infirmities and misfortunes now increased. In 1637 he became totally blind. The calamiIn a letter he plaintively says, referring to this ties of his old calamity, "So it pleases God, it shall therefore age. please me also." The exquisite refinement of ecclesiastical vengeance pursued him remorselessly, and now gave him permission to see his friends when sight was no longer possible. It was at this period that an illustrious stranger, the author of "Paradise Lost," visited him. Shortly after he became totally deaf; but to the last he occupied himself with investigations respecting the force of percussion. died, January, 1642, in the seventy-eighth year His death; of his age, the prisoner of the Inquisition. is refused True to its instincts, that infernal institution followed him beyond the grave, disputing his right to make a will, and denying him burial in consecrated

burial.

He

ground. The pope also prohibited his friends from raising to him a monument in the church of Santa Croce, in Florence. It was reserved for the nineteenth century to erect a suitable memorial in his honour.

Steady ad

Copernican system.

The result of the discoveries of Copernicus and Galileo was thus to bring the earth to her real position vance of the of subordination and to give sublimer views of the universe. Mostlin expresses correctly the state of the case when he says, "What is the earth and the ambient air with respect to the immensity of space? It is a point, a punctule, or something, if there be any thing, less." It had been brought down to the condition of one of the members of a family-the solar system. And since it could be no longer regarded as holding all other bodies in submissive attendance upon it, dominating over their movements, there was reason to suppose that it would be found to maintain interconnexions with them in the attitude of an equal or subordinate; in other words, that general relations would be discovered expressive of the manner in which all the planetary members of the solar system sustain their movements round the sun.

Kepler, his

Among those whose minds were thoroughly occupied with this idea, Kepler stands pre-eminently mode of in- conspicuous. It is not at all surprising, conquiry. sidering the tone of thought of those times, that he regarded his subject with a certain mysticism. They who condemn his manner of thus viewing things do not duly appreciate the mental condition of the generation in which he lived. Whatever may be said on that point, no one can deny him a marvellous patience, and almost superhuman painstaking disposition. Guess after guess, hypothesis after hypothesis, he submitted to computations of infinite labour, and doubtless he speaks the melancholy truth when he says, "I considered and reflected till I was almost mad." Yet, in the midst of repeated disappointment, he held, with a truly philosophical determination, firmly to the belief that there must be some physical interconnexion among the parts of the solar system, and that it would certainly be displayed by the discovery of laws presiding over the distances, times, and velocities of

the planets. In these speculations he was immersed before the publications of Galileo. In his "Mysterium Cosmographicum" he says, "In the year 1595 I was brooding with the whole energy of my mind on the subject of the Copernican system."

In 1609 he published his work entitled "On the Motion of Mars." This was the result of an attempt, Discovery of upon which he had been engaged since the Kepler's laws. beginning of the century, to reconcile the motions of that planet to the hypothesis of eccentrics and epicycles. It ended in the abandonment of that hypothesis, and in the discovery of the two great laws now known as the first and second laws of Kepler. They are respectively that the orbits of the planets are elliptical, and that the areas described by a line drawn from the planet to the sun are proportional to the times.

In 1617 he was again rewarded by the discovery which passes under the designation of Kepler's third law: it expresses the relation of the mean distances of the planets from the sun with the times of their revolutions-" the squares of the periodic times are in the same proportion as the cubes of the distances." In his "Epitome of the Copernican Astronomy," published 1622, he showed that this law likewise holds good for the satellites of Jupiter as regards their primary.

Humboldt, referring to the movement of Jupiter's satellites, remarks: "It was this which led Kepler, His remonin his Harmonices Mundi,' to state, with the strance with firm confidence and security of a German spirit the Church. of philosophical independence, to those whose opinions bore sway beyond the Alps, Eighty years have elapsed during which the doctrines of Copernicus regarding the movement of the earth and the immobility of the sun have been promulgated without hindrance, because it was deemed allowable to dispute concerning natural things and to elucidate the works of God, and, now that new testimony is discovered in proof of the truth of those doctrines-testimony which was not known to the spiritual judges, ye would prohibit the promulgation of the true system of the structure of the universe.'

Thus we see that the heliocentric theory, as proposed by

Copernicus, was undergoing rectification.

Rectification

The circular

movements admitted into it, and which had burof the Coper- dened it with infinite perplexity, though they nican theory. had hitherto been recommended by an illusive simplicity, were demonstrated to be incorrect. They were replaced by the real ones, the elliptical. Kepler, as was his custom, ingenuously related his trials and disappointments. Alluding on one occasion to this, he says: "My first error was that the path of a planet is a perfect circle -an opinion which was a more mischievous thief of my time, in proportion as it was supported by the authority of all philosophers, and apparently agreeable to metaphysics." The philosophical significance of Kepler's discoveries was not recognized by the ecclesiastical party at first. It is chiefly this, that they constitute a most important step to the establishment of the doctrine of the government of the world by law. But it was impossible to receive these laws without seeking for their cause. The result to which that search eventually conducted not only explained their origin, but also showed that, as laws, they must, in the necessity of nature, exist. It may be truly said that the mathematical exposition of their origin constitutes the most splendid monument of the intellectual power of man.

The philo

sophical import of these

laws.

Before the heliocentric theory could be developed and made to furnish a clear exposition of the solar system, which is obviously the first step to just views of the universe, it was necessary that the science of mechanics should be greatly improved-indeed, it might Necessity for mechanical be said, created; for during those dreary ages science. following the establishment of Byzantine power, nothing had been done toward the acquisition of correct views either in statics or dynamics. It was impossible that Europe, in her lower states of life, could produce men capable of commencing where Archimedes had left off. She had to wait for the approach of her Age of Reason for that.

The man of capacity at last came. Leonardo da Vinci Leonardo da was born A.D. 1452. The historian Hallam, enumerating some of his works, observes, "His knowledge was almost preternatural." Many of his writings

Vinci.

still remain unpublished. Long before Bacon, he laid down the maxim that experience and observation must be the foundation of all reasoning in science; that experiment is the only interpreter of nature, and is essential to the ascertainment of laws. Unlike Bacon, who was ignorant of mathematics, and even disparaged them, he points out their supreme advantage. Seven years after the voyage of Columbus, this great man-great at once as an artist, mathematician, and engineer-gave a clear exposition of the theory of forces obliquely applied on a lever; a few years later he was well acquainted with the earth's annual motion. He knew the laws of friction, subsequently demonstrated by Amontons, and the principle of virtual velocities; he described the camera obscura before Baptista Porta, understood aerial perspective, the nature of coloured shadows, the use of the iris, and the effects of the duration of visible impressions on the eye. He wrote well on fortification, anticipated Castelli on hydraulics, occupied himself with the fall of bodies on the hypothesis of the earth's rotation, treated of the times of descent along inclined planes and circular arcs, and of the nature of machines. He considered, with singular clearness, respiration and combustion, and foreshadowed one of the great hypotheses of geology, the elevation of continents.

movement in

This was the commencement of the movement in Natural Philosophy; it was followed up by the publica- Stevinus contion of a work on the principles of equilibrium by tinues the Stevinus, 1586. In this the author established Natural Phithe fundamental property of the inclined plane, losophy. and solved, in a general manner, the cases of forces acting obliquely. Six years later Galileo's treatise on mechanics appeared, a fitting commencement of that career which, even had it not been adorned with such brilliant astronomical discoveries, would alone have conferred the most illustrious distinction upon him.

The dynamical branch of Mechanics is that which is under most obligation to Galileo. To him is due Discovery of the establishment of the three laws of motion. the laws of They are to the following effect, as given by Newton:

motion.

(1.) Every body perseveres in its state of rest or of