the true solar year. This difference accumulating every year, had amounted to nearly eleven days in the year 1582. Thus the equinox which, in Julius Cæsar's time, fell on the 21st of March, now took place on the 10th. The Gregorian reformation aimed at two objects: the first was that of preventing the accumulation of the difference in future, by ordaining that the concluding year of the first three out of each four centuries (which would have been bissextile) should be a common year, the fourth remaining bissextile. This diminishes the difference to an amount almost insensible: to make it quite so, Laplace has since suggested leaving the 4000th year a common year. The second object was to restore to the equinox the name of the 21st of March, with a view to the regulation of the festivals of the church, especially Easter. Hence the adoption of what was called the new style, or dating eleven days forward; what was the 10th of March, being now called the 21st. This gave rise to great confusion, as the states opposed to the Pope's authority long refused to adopt it, and two styles prevailed. It was not adopted in England till 1751; nor is it in Russia to this day.

SECTION III.

THE DISCOVERIES OF KEPLER AND GALILEO.

In the period last treated of, we have had occasion to notice the advances which began to be made in the sixteenth century, in the various parts of the abstract science of quantity, and of its application to some of the phenomena of the natural world. We have also seen the commencement of a revolution in opinions on philosophical subjects: an opposition beginning to manifest itself against the Aristotelian dogmas, and an increasing disposition to recur to experiment and observation as the

only legitimate ground of theory. The great problem of the system of the world we have found engaging the attention of two philosophers of pre-eminent celebrity: but one of these, though he laboured in the observatory to obtain accurate measures of the facts, failed in the comprehensiveness of the theory he propounded: the other made a happy adoption of a satisfactory theory, but it was supported only by arguments from analogy and probability, and the demonstrated insufficiency of the old hypotheses. We have now to turn our attention to a train of discoveries in which we shall find the true theory supported on a firm basis of facts, and accordance with observation.

Kepler.

John Kepler was born at Weil, in the duchy of Wirtemberg, December the 21st, 1571. In infirm health from his birth, his life was more than once despaired of, yet he continued to make considerable progress in his studies, both at the school of Maulbronn and at the college of Tubingen, under the tuition of Mæstlin. His time was here occupied, as he has himself minutely related*, in the ardent pursuit of certain astronomical speculations, which evince at once the fertility of his imagination, and the indefatigable perseverance with which he pursued and worked out the most laborious details of calculation required by these theories, which, after all, turned out entirely unsubstantial, and which he discarded without hesitation on finding them so.

Meanwhile he had acquired a reputation which at once recommended him to be appointed professor of astronomy at Gratz. Here, in the intervals of his public duties, he pursued these researches with unabated ardour. "There were three things," he says, "in

His own published correspondence supplies us with the most interesting details of his pursuits. Copious references to the original authorities will be found in Drinkwater's Life of Kepler.

particular, of which I pertinaciously sought the causes why they are not other than they are: the number, the size, and the motion of the orbits." He was delighted with the simplicity of the Copernican system, and was thus anxious to trace numerical relations among its elements, from a firm persuasion that some abstruse principle of numerical harmony pervaded all nature, and regulated the proportions of all its parts. One after another, he proposed, tried, and rejected every sort of numerical relation he could devise. Notwithstanding perpetual failures, he adds, "I was comforted in some degree, and my hopes of success were supported, as well by other reasons which will follow presently, as by observing that the motions in every case seemed to be connected with the distances, and that when there was a great gap between the orbits, there was the same between the motions; and I reasoned that, if God had adapted motions to the orbits in some relation to the distances, it was probable that he had also arranged the distances themselves in relation to something else."

It is far from our intention to follow Kepler through the vast number of speculations which he pursued on these points; we merely refer to them as admirable indications of the spirit and character of his method of philosophising, and as illustrative of the genius of his investigations. The theory which pleased him best, and which, though it deviated considerably from the observed results, yet he regarded as differing only by the errors of observation, was a geometrical construction which determines the proportions of the orbits, by inscribing successively in them the five regular solids, each sphere being drawn to touch internally the sides of the solid inscribed in the preceding. This, with some other supplementary theories, forms the substance of his "Mysterium Cosmographicum," 1596.

In 1597 he withdrew from Gratz into Hungary, and subsequently visited Tycho at Prague. Owing to some dissensions, it seems that he shortly after gave up his appointment at Gratz; and his affairs being in

a state of great embarrassment, he was actually supported by the generosity of Tycho, and appointed his assistant in the office of imperial mathematician to the emperor Rodolph. He was engaged with Tycho in the formation of new astronomical tables, which, it would appear, the emperor patronised almost entirely with a view to the purposes of astrology; and which were to be brought out on a magnificent scale, under the title of the " Rudolphine Tables." Tycho's former assistant, Lomberg (or Longomontanus), had retired into Denmark on an appointment to an astronomical professorship: on Kepler, therefore, devolved the task of discussing Tycho's observations, and more especially those on the planet Mars. This work was, however, interrupted by the death of Tycho; on which Kepler succeeded to the principal situation which he had filled. He now prosecuted his observations; and in particular had the opportunity of examining the new star which appeared in 1604 in Serpentarius. At this time, also, he entered largely into discussions on the pretensions of astrology, in which he appears to have believed in a modified sense; but it is rather difficult to make out precisely what his opinions were, from the extraordinary style in which the statement of them is couched.

His appointment in the emperor's service appears to have been attended with the constant vexation of a difficulty in getting his pension paid. This interrupted the publication of the " Rudolphine Tables; but meanwhile he produced a treatise on Comets, and his

Paralipomena in Vitellionem," in 1604. This work contains many original views, though mixed up with much visionary speculation. It bears unquestionable marks of genius; but, like many of his other writings, much of it is excessively tedious, from the detail in which he gives the account of the whole train of his investigations. It contains two principal researches of interest one relating to the structure of the eye, the other to the law of refraction.

In 1609, Kepler published that great and extraor

dinary work, his "Treatise on the Motions of the Planet Mars." He had devoted himself to this subject at intervals from the commencement of his engagement with Tycho; and the determined perseverance with which he laboured at the most overwhelming arithmetical calculations, is, perhaps, scarcely less surprising than the powerful genius which shines conspicuous in the successful treatment of so arduous an enquiry, or the wonderfully prolific imagination, which was never at a loss in starting a new theory to work upon when the last had been found insufficient. This volume contains, in effect, the developement of two of those great laws of the planetary orbits by which the name of Kepler has been immortalised, and which form the basis of the whole system of Newton. The author seems thoroughly impressed with the importance of the work on which he is entering; and having an eye to the prejudices which had been evinced with respect to the promulgation of the Copernican system, and the views entertained by Tycho, he introduces his subject in the following emphatic terms:

"If any one be too dull to comprehend the science of astronomy, or too feeble-minded to believe in Copernicus without prejudice to his piety, my advice to such an one is, that he should quit the astronomical schools; and condemning, if he has a mind, any or all the theories of philosophers, let him look to his own affairs, and leaving this worldly travail, let him go home and plough his fields; and as often as he lifts up to this goodly heaven those eyes with which alone he is able to see, let him pour out his heart in praises and thanksgiving to God the Creator; and let him not fear but he is offering a worship not less acceptable than his to whom God has granted-to see yet more clearly with the eyes of his mind, and who both can and will praise his God for what he has so discovered."

In the introductory part of the work, the author discusses at length the received opinions respecting gravitation; and after exposing many parts of the