THE POPULAR EDUCATOR. 



central place, with the moon and sun revolving round it, while 

 all the planets revolved round the sun. 



The Copernican system, however, was, we must remember, at 

 this time a mere theory unsupported by proof, and the main 

 reason of Brahe's rejection of it was that, if the earth revolved 

 in a large orbit, he thought the fixed stars ought to appear in a 

 different position when seen from one extremity of the orbit to 

 that which they occupied when seen from the other extremity ; 

 and not being able to observe this change, he concluded that the 

 earth must be at rest. The principle of this argument was 

 right, and in reality there is a minute difference in the appearance 

 of the stars ; it is, however, too minute to be observed, except 

 by the most delicate instruments. The reason why it is not 

 more clearly seen is that, great as is the diameter of the earth's 

 orbit, the distance of even the nearest fixed star is so immensely 

 greater that the change produced is scarcely visible. We may 

 notice this same effect as we are carried rapidly along in a train ; 

 the objects situated near to the line of railway seem to move 

 past us very rapidly, those further off have a less apparent 

 speed, while lofty objects in the distance scarcely seem to move 

 at all. Every minute changes the apparent position of those 

 which are near, while it is only after the lapse of some little time 

 that we perceive the motion of those at a distance ; and, sup- 

 posing the line of rails were perfectly straight, we might travel 

 on for hours, and not be able to detect the slightest alteration in 

 the apparent position of the sun. We see thus that the con- 

 clusion which Brahe arrived at was wrong, though his premises 

 were right ; and we shall find further on the great importance 

 which is attached to this change of position, or "parallax," as 

 it is called, all the distances of the heavenly bodies being deter- 

 mined by means of it. 



His fame, however, as an astronomer rests upon the care and 

 accuracy of his observations. A new star which appeared in the 

 year 1572, and continued visible for about a year and a half, 

 was specially observed by him, and he recorded a large number 

 of very careful observations on the planets and stars, some of 

 which are of great use for reference at the present time. To him, 

 too, we are indebted for a catalogue of many of the fixed stars, 

 which, though it contained a much smaller number than that of 

 Hipparchus, was greatly superior to it in accuracy. 



A table showing the allowance to be made in the apparent 

 position of the heavenly bodies, on account of the effect 

 produced by the refraction of the air, was also calculated by 

 him. The nature of this refraction will be fully explained further 

 on. We may mention, however, that it causes all bodies near 

 the horizon to appear at a greater altitude than they really have 

 attained ; and hence, in important observations, allowance must 

 be made for its action. 



About the year 1575 Tycho Brahe attracted the attention of 

 Frederick II. of Denmark, who gave him a small island on the 

 Baltic, and an annual allowance. Here he built himself a large 

 house and observatory, which he called Uraniborg, the " Castle 

 of the Heavens," and in this he lived for years, occupied with 

 his favourite science, and assisted by the best instruments which 

 could be procured. After the king's death, some of those who 

 were envious of his honours succeeded in depriving him of his 

 allowance and his observatory. He did not, however, despair, 

 for soon after he was received at Prague by the emperor, 

 and an observatory erected for him and his pupils. Here he 

 remained until his death, which happened a few years later. 



Among his pupils was Kepler, to whom we have already 

 referred. He acquired from Brahe the habit of accurate observa- 

 tion, and was far more successful than his master in the theories 

 which he formed. Naturally he was possessed of a quick and 

 lively imagination. He commenced with careful observation, and 

 then formed his theories in accordance with the facts ; and pro- 

 ceeding in this way, he soon made several important discoveries. 



The task to which he now devoted his time and energies was 

 to discover the nature of the paths described by the planets. 

 Starting with the hypothesis of the sun being in the centre of 

 the system, he began to watch attentively their places, and, to 

 simplify matters, he confined himself at first to the motions of 

 the planet Mars. 



He calculated the place it ought to occupy according to the 

 theory of its revolving in a circular orbit, and soon found that 

 the place it really occupied in the sky differed considerably from 

 that assigned to it. This theory was thus at once shown to be 

 incorrect, and he had therefore to form a fresh one by the com- 



bination of several circular movements ; and again he diligently 

 calculated its position, till, just as he seemed to be on the verge 

 of success, the planet once more wandered away from the path 

 which he had assigned to it ; and once more he had to commence 

 his observations from the beginning. In this way he continued 

 to try one hypothesis after another, submitting each to the test 

 of most careful observation, till at length no fewer than nineteen 

 different theories had been proposed, and the movements of the 

 planets compared with those which were calculated by these 

 theories ; aiid yet the true solution of the problem was still un- 

 i found. His perseverance, however, never failed, and he toiled 

 j on, though eight long years had been occupied in the task. One 

 important negative result he had, however, arrived at, and this 

 was that, whatever was the nature of the curve the planets 

 described, it was not a circle, nor a combination of circles. This 

 was one great step towards the solution of the task. From the 

 very earliest ages it had been assumed that, as the circle 

 seemed the perfection of form, all the heavenly bodies must more 

 i in circles ; but Kepler now cast off this trammel, and then 

 \ applied himself afresh to his task. 



In looking at the greatness of his work we must remember 



, that the difficulty is much increased by the fact that our station 



I of observation is itself in rapid motion. Could we view the 



planets from the sun, we should easily see their courses ; but 



as we cannot do this, allowance has to be made in every calcu- 



| lation for the movement of our standpoint, and this motion was 



not then clearly understood. 



Having discarded the theory of motion in circles, Kepler now 

 proceeded to try other forms, testing them as before, and the 

 first that occurred to him was the ellipse. The same series of 

 calculations was accordingly gone through again, and this time 

 the motion of the planet was found to agree with that assigned 

 to it by the theory. The great problem of the heavens was now 

 solved, and the joy with which Kepler enunciated the first of 

 the laws which bear his name can scarcely be imagined. This 

 law may be stated as follows : The planets revolve around 

 the sun in elliptical orbits, the sun being situated in one of the 

 foci. 



As this is one of the fundamental laws of astronomy, we must 

 explain it rather more fully. In every circle there is a point 

 called the centre, such that all straight lines drawn from it to 

 the circumference are equal. No such point is to be found in an 

 ellipse ; but in the longest diameter two points can be found so 

 situated that, if straight lines be drawn from one to any point in 

 the circumference, and thence to the other, the sum of these 

 lines will always be equal. These points are called the foci. 



Explanations of the practical methods by which the curve of 

 an ellipse may be traced from any two points as foci, have 

 already been given in Problem LVIII. of "Lessons in Geometry " 

 " How to trace the curve of an ellipse by mechanical contri- 

 vances " (see Vol. II., page 252) ; it is therefore unnecessary to 

 repeat them here in detail. It will be needful, however, to call 

 the reader's attention to what is termed the " eccentricity " of 

 an ellipse, as it is a term that is constantly used in speaking of 

 the orbits of the heavenly bodies. In Fig. 84 (Vol. II., page 

 252), G is the centre, and the fraction of which the numerator is 

 G A and the denominator is G c or, in other words, the propor- 

 tion between G A and G c, which is the half of the major axis 

 is called the eccentricity. In the figure, however, this is repre- 

 sented very much greater than it is in orbits of any of the pla- 

 nets, and their paths therefore differ less from a circle. 



The consideration of the remaining two laws of Kepler must 

 be deferred till our next lesson. 



READINGS IN LATIN. II. 



VIRGIL. 



VIRGIL was a Roman poet who was born in the year 70 B.C. and 

 died 19 B.C. He flourished in the period which is known as the 

 " golden age" of Latin poetry, of which he was one of the most 

 brilliant ornaments. The works by which he is best known are 

 (1) the Bucolics, a book of pastoral poetry, consisting of ten 

 eclogues, as they are called ; (2) the Georgics, four books of 

 what is known as " didactic " poetry, containing instructions in 

 the art of agriculture and similar occupations ; and (3) the 

 JEneid, an epic poem in twelve books, each of considerable 

 length, the subject of which is the wanderings of the Trojan 



