Great Astronomers. Robert S. Ball

question, as to whether the earth was animated by any movement of translation. He came to the conclusion that to attribute any motion to the earth would be incompatible with the truths at which he had already arrived. The earth, argued Ptolemy, lies at the centre of the celestial sphere. If the earth were to be endowed with movement, it would not lie always at this point, it must, therefore, shift to some other part of the sphere. The movements of the stars, however, preclude the possibility of this; and, therefore, the earth must be as devoid of any movement of translation as it is devoid of rotation. Thus it was that Ptolemy convinced himself that the stability of the earth, as it appeared to the ordinary senses, had a rational philosophical foundation.

      Not unfrequently it is the lot of the philosophers to contend against the doctrines of the vulgar, but when it happens, as in the case of Ptolemy's researches, that the doctrines of the vulgar are corroborated by philosophical investigation which bear the stamp of the highest authority, it is not to be wondered at that such doctrines should be deemed well-nigh impregnable. In this way we may, perhaps, account for the remarkable fact that the theories of Ptolemy held unchallenged sway over the human intellect for the vast period already mentioned.

      Up to the present we have been speaking only of those primary motions of the heavens, by which the whole sphere appeared to revolve once every twenty-four hours. We have now to discuss the remarkable theories by which Ptolemy endeavoured to account for the monthly movement of the moon, for the annual movement of the sun, and for the periodic movements of the planets which had gained for them the titles of the wandering stars.

      Possessed with the idea that these movements must be circular, or must be capable, directly or indirectly, of being explained by circular movements, it seemed obvious to Ptolemy, as indeed it had done to previous astronomers, that the track of the moon through the stars was a circle of which the earth is the centre. A similar movement with a yearly period must also be attributed to the sun, for the changes in the positions of the constellations in accordance with the progress of the seasons, placed it beyond doubt that the sun made a circuit of the celestial sphere, even though the bright light of the sun prevented the stars in its vicinity, from being seen in daylight. Thus the movements both of the sun and the moon, as well as the diurnal rotation of the celestial sphere, seemed to justify the notion that all celestial movements must be "perfect," that is to say, described uniformly in those circles which were the only perfect curves.

      The simplest observations, however, show that the movements of the planets cannot be explained in this simple fashion. Here the geometrical genius of Ptolemy shone forth, and he devised a scheme by which the apparent wanderings of the planets could be accounted for without the introduction of aught save "perfect" movements.

      To understand his reasoning, let us first set forth clearly those facts of observation which require to be explained. I shall take, in particular, two planets, Venus and Mars, as these illustrate, in the most striking manner, the peculiarities of the inner and the outer planets respectively. The simplest observations would show that Venus did not move round the heavens in the same fashion as the sun or the moon. Look at the evening star when brightest, as it appears in the west after sunset. Instead of moving towards the east among the stars, like the sun or the moon, we find, week after week, that Venus is drawing in towards the sun, until it is lost in the sunbeams. Then the planet emerges on the other side, not to be seen as an evening star, but as a morning star. In fact, it was plain that in some ways Venus accompanied the sun in its annual movement. Now it is found advancing in front of the sun to a certain limited distance, and now it is lagging to an equal extent behind the sun.

      

FIG. 1. PTOLEMY'S PLANETARY SCHEME.

      These movements were wholly incompatible with the supposition that the journeys of Venus were described by a single motion of the kind regarded as perfect. It was obvious that the movement was connected in some strange manner with the revolution of the sun, and here was the ingenious method by which Ptolemy sought to render account of it. Imagine a fixed arm to extend from the earth to the sun, as shown in the accompanying figure (Fig. 1), then this arm will move round uniformly, in consequence of the sun's movement. At a point P on this arm let a small circle be described. Venus is supposed to revolve uniformly in this small circle, while the circle itself is carried round continuously by the movement of the sun. In this way it was possible to account for the chief peculiarities in the movement of Venus. It will be seen that, in consequence of the revolution around P, the spectator on the earth will sometimes see Venus on one side of the sun, and sometimes on the other side, so that the planet always remains in the sun's vicinity. By properly proportioning the movements, this little contrivance simulated the transitions from the morning star to the evening star. Thus the changes of Venus could be accounted for by a Combination of the "perfect" movement of P in the circle which it described uniformly round the earth, combined with the "perfect" motion of Venus in the circle which it described uniformly around the moving centre.

      In a precisely similar manner Ptolemy rendered an explanation of the fitful apparitions of Mercury. Now just on one side of the sun, and now just on the other, this rarely-seen planet moved like Venus on a circle whereof the centre was also carried by the line joining the sun and the earth. The circle, however, in which Mercury actually revolved had to be smaller than that of Venus, in order to account for the fact that Mercury lies always much closer to the sun than the better-known planet.

      

FIG. 2. PTOLEMY'S THEORY OF THE MOVEMENT OF MARS.

      The explanation of the movement of an outer planet like Mars could also be deduced from the joint effect of two perfect motions. The changes through which Mars goes are, however, so different from the movements of Venus that quite a different disposition of the circles is necessary. For consider the facts which characterise the movements of an outer planet such as Mars. In the first place, Mars accomplishes an entire circuit of the heaven. In this respect, no doubt, it may be said to resemble the sun or the moon. A little attention will, however, show that there are extraordinary irregularities in the movement of the planet. Generally speaking, it speeds its way from west to east among the stars, but sometimes the attentive observer will note that the speed with which the planet advances is slackening, and then it will seem to become stationary. Some days later the direction of the planet's movement will be reversed, and it will be found moving from the east towards the west. At first it proceeds slowly and then quickens its pace, until a certain speed is attained, which afterwards declines until a second stationary position is reached. After a due pause the original motion from west to east is resumed, and is continued until a similar cycle of changes again commences. Such movements as these were obviously quite at variance with any perfect movement in a single circle round the earth. Here, again, the geometrical sagacity of Ptolemy provided him with the means of representing the apparent movements of Mars, and, at the same time, restricting the explanation to those perfect movements which he deemed so essential. In Fig. 2 we exhibit Ptolemy's theory as to the movement of Mars. We have, as before, the earth at the centre, and the sun describing its circular orbit around that centre. The path of Mars is to be taken as exterior to that of the sun. We are to suppose that at a point marked M there is a fictitious planet, which revolves around the earth uniformly, in a circle called the DEFERENT. This point M, which is thus animated by a perfect movement, is the centre of a circle which is carried onwards with M, and around the circumference of which Mars revolves uniformly. It is easy to show that the combined effect of these two perfect movements is to produce exactly that displacement of Mars in the heavens which observation discloses. In the position represented in the figure, Mars is obviously pursuing a course which will appear to the observer as a movement from west to east. When, however, the planet gets round to such a position as R, it is then moving from east to west in consequence of its revolution in the moving circle, as indicated by the arrow-head. On the other hand, the whole circle is carried forward in the opposite direction. If the latter movement be less rapid than the former, then we shall have the backward movement of Mars on the heavens which it was desired to explain. By a proper adjustment of the relative lengths of these arms the movements of the planet as actually observed could be completely accounted for.

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