On the other hand, Tycho was not strong on the theoretical side. He was never willing to accept the Copernican hypothesis of rotation and orbital motion of the earth maintaining, for example, that if the earth moved, a stone dropped from the top of a tower must fall at a distance from the foot. Again with reference to the apparent displacement of the stars which would be expected to result from orbital motion of the earth, he says:

A yearly motion would relegate the sphere of the fixed stars to such a distance that the path described by the earth must be insignificant in comparison. Dost thou hold it possible that the space between the sun, the alleged centre of the universe, and Saturn amounts to not even of that distance? At the same time this space must be void of stars.

Sensible, however, of the weakness of the Ptolemaic theory, he devised an ingenious compromise in which the planets revolved about the Sun in their respective periods, and the entire heavens about the earth daily - all of which is not mathematically different from the Copernican theory.

We see in him at the same time a perfect son of the sixteenth century, believing the universe to be woven together by mysterious connecting threads which the contemplation of the stars or of the elements of nature might unravel, and thereby lift the veil of the future; we see that he is still, like most of his contemporaries, a believer in the solid spheres and the atmospherical origin of comets, to which errors of the Aristotelean physics he was destined a few years later to give the death-blow by his researches on comets; we see him also thoroughly discontented with his surroundings, and looking abroad in the hope of finding somewhere else the place and the means for carrying out his plans.

As a practical astronomer Tycho has not been surpassed by any observer of ancient or modern times. The splendor and number of his instruments, the ingenuity which he exhibited in inventing new ones and in improving and adding to those which were formerly known, and his skill and assiduity as an observer, have given a character to his labors and a value to his observations which will be appreciated to the latest posterity. - Brewster.

P

KEPLER. Pierre de la Ramée, or Petrus Ramus, a French mathematician and philosopher, impatient with the cumbrous astronomical hypotheses of the ancients, and unsatisfied with Copernicus' proposed simplification, published a work in 1569 expressing the hope

'that some distinguished German philosopher would arise and found a new astronomy on careful observations by means of logic and mathematics, discarding all the notions of the ancients.'

Within a few months he discussed the matter at length with Tycho Brahe at Augsburg. Without accepting Ramus' views, the young astronomer did make it his life work to lay the necessary foundation for such a new astronomy. Thirty years later, Mästlin, professor at Tübingen, wrote his former student Kepler then aged 28

that Tycho 'had hardly left a shadow of what had hitherto been taken for astronomical science, and that only one thing was certain, which was that mankind knew nothing of astronomical matters.'

Born late in 1571 in Würtemberg, of Protestant parents in very straitened circumstances, Johann Kepler's whole life was a struggle against poverty, ill-health, and adverse conditions. In 1594, abandoning with some hesitation theological studies, for which his acceptance of the new Copernican hypothesis disqualified him, he was appointed lecturer on mathematics at Gratz. Students were few, and his duties included the preparation of a yearly almanac, containing, besides what its name implies, a variety of weather predictions and astrological information. "Mother Astronomy," he says, "would surely have to suffer hunger if the daughter Astrology did not earn their bread."

Becoming thus more interested in astronomy, "there were," he says, "three things in particular: viz., the number, the size, and the motion of the heavenly bodies, as to which I searched zealously for reasons why they were as they were and not otherwise." The first result which seemed to him important, though somewhat fantastic from our standpoint, was a crude correspondence be

tween the planetary orbits and the five regular solids, published in 1596 under a title which may be abridged to Cosmographic Mystery.

The Earth is the circle, the measure of all. Round it describe a dodecahedron, the circle including this will be Mars. Round Mars describe a tetrahedron, the circle including this will be Jupiter. Describe a cube round Jupiter, the circle including this will be Saturn. Then inscribe in the Earth an icosahedron, the circle inscribed in it will be Venus. Inscribe an octahedron in Venus, the circle inscribed in it will be Mercury.

Kepler declared that he would not renounce the glory of this discovery "for the whole Electorate of Saxony." The correspondence of the dimensions of this fantastic geometrical construction with the distances of members of our solar system is in reality far from close, but both Tycho Brahe and Galileo seem to have been favorably impressed by the book.

The difficulties of Kepler's position as a Protestant in Gratz led him, after a preliminary visit, to accept an engagement as Tycho's assistant at Prague.

The powers of original genius were then for the first time associated with inventive skill and patient observation, and though the astronomical data provided by Tycho were sure of finding their application in some future age, yet without them, Kepler's speculations would have been vain and the laws which they enabled him to determine would have adorned the history of another century. - Brewster.

In 1602 Kepler succeeded Tycho as imperial mathematician. Most fortunately, also, he secured possession of his chief's great collection of observations, though not of the instruments, -a matter of less consequence, since Kepler like Copernicus was a mathematician rather than an observer. To the study of these records he devoted the next 25 years. Among all the planetary observations of Tycho Brahe those of Mars presented the irregularities most difficult of explanation, and it was these which, having been originally assigned to Kepler, engrossed his attention for many years, and in the end led to some of his finest discoveries.