ntific weight whatever。 Their interest in this regard is purely antiquarian； hence from our changed point of view it seems scarcely credible that Tycho Brahe can have been in earnest when he quotes the Hebrew traditions as proof that the sun revolves about the earth。 Yet we shall see that for almost three centuries after the time of Tycho； these same dreamings continued to be cited in opposition to those scientific advances which new observations made necessary； and this notwithstanding the fact that the Oriental phrasing is； for the most part； poetically ambiguous and susceptible of shifting interpretations； as the criticism of successive generations has amply testified。 As we have said； Tycho Brahe； great observer as he was； could not shake himself free from the Oriental incubus。 He began his objections； then； to the Copernican system by quoting the adverse testimony of a Hebrew prophet who lived more than a thousand years B。C。 All of this shows sufficiently that Tycho Brahe was not a great theorist。 He was essentially an observer； but in this regard he won a secure place in the very first rank。 Indeed； he was easily the greatest observing astronomer since Hipparchus； between whom and himself there were many points of resemblance。 Hipparchus； it will be recalled； rejected the Aristarchian conception of the universe just as Tycho rejected the conception of Copernicus。 But if Tycho propounded no great generalizations； the list of specific advances due to him is a long one； and some of these were to prove important aids in the hands of later workers to the secure demonstration of the Copernican idea。 One of his most important series of studies had to do with comets。 Regarding these bodies there had been the greatest uncertainty in the minds of astronomers。 The greatest variety of opinions regarding them prevailed； they were thought on the one hand to be divine messengers； and on the other to be merely igneous phenomena of the earth's atmosphere。 Tycho Brahe declared that a comet which he observed in the year 1577 had no parallax； proving its extreme distance。 The observed course of the comet intersected the planetary orbits； which fact gave a quietus to the long…mooted question as to whether the Ptolemaic spheres were transparent solids or merely imaginary； since the comet was seen to intersect these alleged spheres； it was obvious that they could not be the solid substance that they were commonly imagined to be； and this fact in itself went far towards discrediting the Ptolemaic system。 It should be recalled； however； that this supposition of tangible spheres for the various planetary and stellar orbits was a mediaeval interpretation of Ptolemy's theory rather than an interpretation of Ptolemy himself； there being nothing to show that the Alexandrian astronomer regarded his cycles and epicycles as other than theoretical。 An interesting practical discovery made by Tycho was his method of determining the latitude of a place by means of two observations made at an interval of twelve hours。 Hitherto it had been necessary to observe the sun's angle on the equinoctial days； a period of six months being therefore required。 Tycho measured the angle of elevation of some star situated near the pole； when on the meridian； and then； twelve hours later； measured the angle of elevation of the same star when it again came to the meridian at the opposite point of its apparent circle about the polestar。 Half the sum of these angles gives the latitude of the place of observation。 As illustrating the accuracy of Tycho's observations； it may be noted that he rediscovered a third inequality of the moon's motion at its variation； he； in common with other European astronomers； being then quite unaware that this inequality had been observed by an Arabian astronomer。 Tycho proved also that the angle of inclination of the moon's orbit to the ecliptic is subject to slight variation。 The very brilliant new star which shone forth suddenly in the constellation of Cassiopeia in the year 1572； was made the object of special studies by Tycho； who proved that the star had no sensible parallax and consequently was far beyond the planetary regions。 The appearance of a new star was a phenomenon not unknown to the ancients； since Pliny records that Hipparchus was led by such an appearance to make his catalogue of the fixed stars。 But the phenomenon is sufficiently uncommon to attract unusual attention。 A similar phenomenon occurred in the year 1604； when the new starin this case appearing in the constellation of Serpentariuswas explained by Kepler as probably proceeding from a vast combustion。 This explanationin which Kepler is said to have followed。 Tychois fully in accord with the most recent theories on the subject； as we shall see in due course。 It is surprising to hear Tycho credited with so startling a theory； but； on the other hand； such an explanation is precisely what should be expected from the other astronomer named。 For Johann Kepler； or； as he was originally named； Johann von Kappel； was one of the most speculative astronomers of any age。 He was forever theorizing； but such was the peculiar quality of his mind that his theories never satisfied him for long unless he could put them to the test of observation。 Thanks to this happy combination of qualities； Kepler became the discoverer of three famous laws of planetary motion which lie at the very foundation of modern astronomy； and which were to be largely instrumental in guiding Newton to his still greater generalization。 These laws of planetary motion were vastly important as corroborating the Copernican theory of the universe； though their position in this regard was not immediately recognized by contemporary thinkers。 Let us examine with some detail into their discovery； meantime catching a glimpse of the life history of the remarkable man whose name they bear。
JOHANN KEPLER AND THE LAWS OF PLANETARY MOTION Johann Kepler was born the 27th of December； 1571； in the little town of Weil； in Wurtemburg。 He was a weak； sickly child； further enfeebled by a severe attack of small…pox。 It would seem paradoxical to assert that the parents of such a genius were mismated； but their home was not a happy one； the mother being of a nervous temperament； which perhaps in some measure accounted for the genius of the child。 The father led the life of a soldier； and finally perished in the campaign against the Turks。 Young Kepler's studies were directed with an eye to the ministry。 After a preliminary training he attended the university at Tubingen； where he came under the influence of the celebrated Maestlin and became his life…long friend。 Curiously enough； it is recorded that at first Kepler had no taste for astronomy or for mathematics。 But the doors of the ministry being presently barred to him； he turned with enthusiasm to the study of astronomy； being from the first an ardent advocate of the Copernican system。 His teacher； Maestlin； accepted the same doctrine； though he was obliged； for theological reasons； to teach the Ptolemaic system； as also to oppose the Gregorian reform of the calendar。 The Gregorian calendar； it should be explained； is so called because it was instituted by Pope Gregory XIII。； who put it into effect in the year 1582； up to which time the so…called Julian calendar； as introduced by Julius Caesar； had been everywhere accepted in Christendom。 This Julian calendar； as we have seen； was a great improvement on preceding ones； but still lacked something of perfection inasmuch as its theoretical day differed appreciably from the actual day。 In the course of fifteen hundred years； since the time of Caesar； this defect amounted to a discrepancy of about eleven days。 Pope Gregory proposed to correct this by omitting ten days from the calendar； which was done in September； 1582。 To prevent similar inaccuracies in the future； the Gregorian calendar provided that once in four centuries the additional day to make a leap…year should be omitted； the date selected for such omission being the last year of every fourth century。 Thus the years 1500； 1900； and 2300； A。D。； would not be leap…years。 By this arrangement an approximate rectification of the calendar was effected； though even this does not make it absolutely exact。 Such a rectification as this was obviously desirable； but there was really no necessity for the omission of the ten days from the calendar。 The equinoctial day had shifted so that in the year 1582 it fell on the 10th of March and September。 There was no reason why it should not have remained there。 It would greatly have simplified the task of future historians had Gregory contented himself with providing for the future stability of the calendar without making the needless shift in question。 We are so accustomed to think of the 21st of March and 21st of September as the natural periods of the equinox； that we are likely to forget that these are purely arbitrary dates for which the 10th might have been substituted without any inconvenience or inconsistency。 But the opposition to the new calendar； to which reference has been made； was not based on any such considerations as these。 It was due； largely at any rate； to the fact that Germany at this time was under sway of the Lutheran revolt against the