t any rate； to the fact that Germany at this time was under sway of the Lutheran revolt against the papacy。 So effective was the opposition that the Gregorian calendar did not come into vogue in Germany until the year 1699。 It may be added that England； under stress of the same manner of prejudice； held out against the new reckoning until the year 1751； while Russia does not accept it even now。 As the Protestant leaders thus opposed the papal attitude in a matter of so practical a character as the calendar； it might perhaps have been expected that the Lutherans would have had a leaning towards the Copernican theory of the universe； since this theory was opposed by the papacy。 Such； however； was not the case。 Luther himself pointed out with great strenuousness； as a final and demonstrative argument； the fact that Joshua commanded the sun and not the earth to stand still； and his followers were quite as intolerant towards the new teaching as were their ultramontane opponents。 Kepler himself was； at various times； to feel the restraint of ecclesiastical opposition； though he was never subjected to direct persecution； as was his friend and contemporary； Galileo。 At the very outset of Kepler's career there was； indeed； question as to the publication of a work he had written； because that work took for granted the truth of the Copernican doctrine。 This work appeared； however； in the year 1596。 It bore the title Mysterium Cosmographium； and it attempted to explain the positions of the various planetary bodies。 Copernicus had devoted much time to observation of the planets with reference to measuring their distance； and his efforts had been attended with considerable success。 He did not； indeed； know the actual distance of the sun； and； therefore； was quite unable to fix the distance of any planet； but； on the other hand； he determined the relative distance of all the planets then known； as measured in terms of the sun's distance； with remarkable accuracy。 With these measurements as a guide； Kepler was led to a very fanciful theory； according to which the orbits of the five principal planets sustain a peculiar relation to the five regular solids of geometry。 His theory was this： 〃Around the orbit of the earth describe a dodecahedronthe circle comprising it will be that of Mars； around Mars describe a tetrahedronthe circle comprising it will be that of Jupiter； around Jupiter describe a cubethe circle comprising it will be that of Saturn； now within the earth's orbit inscribe an icosahedronthe inscribed circle will be that of Venus； in the orbit of Venus inscribe an octahedron the circle inscribed will be that of Mercury。〃＇3＇ Though this arrangement was a fanciful one； which no one would now recall had not the theorizer obtained subsequent fame on more substantial grounds； yet it evidenced a philosophical spirit on the part of the astronomer which； misdirected as it was in this instance； promised well for the future。 Tycho Brahe； to whom a copy of the work was sent； had the acumen to recognize it as a work of genius。 He summoned the young astronomer to be his assistant at Prague； and no doubt the association thus begun was instrumental in determining the character of Kepler's future work。 It was precisely the training in minute observation that could avail most for a mind which； like Kepler's； tended instinctively to the formulation of theories。 When Tycho Brahe died； in 1601； Kepler became his successor。 In due time he secured access to all the unpublished observations of his great predecessor； and these were of inestimable value to him in the progress of his own studies。 Kepler was not only an ardent worker and an enthusiastic theorizer； but he was an indefatigable writer； and it pleased him to take the public fully into his confidence； not merely as to his successes； but as to his failures。 Thus his works elaborate false theories as well as correct ones； and detail the observations through which the incorrect guesses were refuted by their originator。 Some of these accounts are highly interesting； but they must not detain us here。 For our present purpose it must suffice to point out the three important theories； which； as culled from among a score or so of incorrect ones； Kepler was able to demonstrate to his own satisfaction and to that of subsequent observers。 Stated in a few words； these theories； which have come to bear the name of Kepler's Laws； are the following： 1。 That the planetary orbits are not circular； but elliptical； the sun occupying one focus of the ellipses。 2。 That the speed of planetary motion varies in different parts of the orbit in such a way that an imaginary line drawn from the sun to the planetthat is to say； the radius vector of the planet's orbitalways sweeps the same area in a given time。
These two laws Kepler published as early as 1609。 Many years more of patient investigation were required before he found out the secret of the relation between planetary distances and times of revolution which his third law expresses。 In 1618； however； he was able to formulate this relation also； as follows： 3。 The squares of the distance of the various planets from the sun are proportional to the cubes of their periods of revolution about the sun。
All these laws； it will be observed； take for granted the fact that the sun is the centre of the planetary orbits。 It must be understood； too； that the earth is constantly regarded； in accordance with the Copernican system； as being itself a member of the planetary system； subject to precisely the same laws as the other planets。 Long familiarity has made these wonderful laws of Kepler seem such a matter of course that it is difficult now to appreciate them at their full value。 Yet； as has been already pointed out； it was the knowledge of these marvellously simple relations between the planetary orbits that laid the foundation for the Newtonian law of universal gravitation。 Contemporary judgment could not； of course； anticipate this culmination of a later generation。 What it could understand was that the first law of Kepler attacked one of the most time…honored of metaphysical conceptionsnamely； the Aristotelian idea that the circle is the perfect figure； and hence that the planetary orbits must be circular。 Not even Copernicus had doubted the validity of this assumption。 That Kepler dared dispute so firmly fixed a belief； and one that seemingly had so sound a philosophical basis； evidenced the iconoclastic nature of his genius。 That he did not rest content until he had demonstrated the validity of his revolutionary assumption shows how truly this great theorizer made his hypotheses subservient to the most rigid inductions。
GALILEO GALILEI While Kepler was solving these riddles of planetary motion； there was an even more famous man in Italy whose championship of the Copernican doctrine was destined to give the greatest possible publicity to the new ideas。 This was Galileo Galilei； one of the most extraordinary scientific observers of any age。 Galileo was born at Pisa； on the 18th of February （old style）； 1564。 The day of his birth is doubly memorable； since on the same day the greatest Italian of the preceding epoch； Michael Angelo； breathed his last。 Persons fond of symbolism have found in the coincidence a forecast of the transit from the artistic to the scientific epoch of the later Renaissance。 Galileo came of an impoverished noble family。 He was educated for the profession of medicine； but did not progress far before his natural proclivities directed him towards the physical sciences。 Meeting with opposition in Pisa； he early accepted a call to the chair of natural philosophy in the University of Padua； and later in life he made his home at Florence。 The mechanical and physical discoveries of Galileo will claim our attention in another chapter。 Our present concern is with his contribution to the Copernican theory。 Galileo himself records in a letter to Kepler that he became a convert to this theory at an early day。 He was not enabled； however； to make any marked contribution to the subject； beyond the influence of his general teachings； until about the year 1610。 The brilliant contributions which he made were due largely to a single discoverynamely； that of the telescope。 Hitherto the astronomical observations had been made with the unaided eye。 Glass lenses had been known since the thirteenth century； but； until now； no one had thought of their possible use as aids to distant vision。 The question of priority of discovery has never been settled。 It is admitted； however； that the chief honors belong to the opticians of the Netherlands。 As early as the year 1590 the Dutch optician Zacharias Jensen placed a concave and a convex lens respectively at the ends of a tube about eighteen inches long； and used this instrument for the purpose of magnifying small objectsproducing； in short； a crude microscope。 Some years later； Johannes Lippershey； of whom not much is known except that he died in 1619； experimented with a somewhat similar combination of lenses； and made the startling observation that the weather…vane on a distant church…steeple seemed to be brought much nearer when viewed through the lens。 The combination of lenses he employed is that still used in the construction of ope