Eleven years later Tycho published a volume on the comet as a part of a comprehensive astronomical treatise which was, however, never completed. About the same time his royal patron died, and the new administration proved less sympathetic with the great astronomer's work and less indulgent with his extravagance and personal eccentricities.

After a series of disagreements, Tycho withdrew from his observatory in 1597, spent the winter in Hamburg, and after negotiations with different sovereigns, accepted the invitation of the Emperor Rudolph to settle in Prague in 1599. Here he again organized a staff of assistants, including, to the great advantage of himself and of his science, the young Kepler, but his further progress was prematurely terminated by death in 1601, at the age

of 55.

Tycho's chief services to the progress of astronomy consisted first, in the superior accuracy of his instruments and observations, heightened by repetition and systematic correction of errors; second, in the extension of these observations over a long series of years. In both respects he departed from current practice, and anticipated the modern. In point of accuracy his errors of starplaces seem rarely to have exceeded 1' to 2', and he even determined the length of the year within one second. While he recomputed almost every important astronomical constant, he accepted the traditional distance of the sun.

Kepler gave striking evidence later of his confidence in Tycho's accuracy by writing:

'Since the divine goodness has given to us in Tycho Brahe a most careful observer, from whose observations the error of 8' is shewn in this calculation, . . . it is right that we should with gratitude recognize and make use of this gift of God. . . . For if I could have treated 8' of longitude as negligible I should have already corrected sufficiently the hypothesis . . . discovered in chapter xvi. But as they could not be neglected, these 8′ alone have led the way towards the complete reformation of astronomy, and have made the subjectmatter of a great part of this work.' — Berry.

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