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accuracy of the calculations and the tables. The results of his cogitations were printed just before his death in an interesting book, De Revolutionibus Orbium Celestium. It is only by careful reading of this book that the true position of Copernicus can be realised. He noticed that Nicetas and others had ascribed the apparent diurnal rotation of the heavens to a real daily rotation of the earth about its axis, in the opposite direction to the apparent motion of the stars. Also in the writings of Martianus Capella he learnt that the Egyptians had supposed Mercury and Venus to revolve round the sun, and to be carried with him in his annual motion round the earth. He noticed that the same supposition, if extended to Mars, Jupiter, and Saturn, would explain easily why they, and especially Mars, seem so much brighter in opposition. For Mars would then be a great deal nearer to the earth than at other times. It would also explain the retrograde motion of planets when in opposition. We must here notice that at this stage Copernicus was actually confronted with the system accepted later by Tycho Brahe, with the earth fixed. But he now recalled and accepted the views of Pythagoras and others, according to which the sun is fixed and the earth revolves; and it must be noted that, geometrically, there is no difference of any sort between the Egyptian or Tychonic system and that of Pythagoras as revived by Copernicus, except that on the latter theory the stars ought to seem to move when the earth changes its position — a test which failed completely with the rough means of observation then available. The radical defect of all solar systems previous to the time of Kepler (1609 A.D.) was the slavish yielding to Plato's dictum demanding uniform circular motion for the planets, and the consequent evolution of the epicycle, which was fatal to any conception of a dynamical theory. Copernicus could not sever himself from this obnoxious tradition." It is true that neither the Pythagorean nor the Egypto-Tychonic system required epicycles for explaining retrograde motion, as the Ptolemaic theory did. Furthermore either system could use the excentric of Hipparchus to explain the irregular motion known as the equation of the center. But Copernicus remarked that he could also use an epicycle for this purpose, or that he could use both an excentric and an epicycle for each planet, and so bring theory still closer into accord with observation. And this he proceeded to do." Moreover, observers had found irregularities in the moon's motion, due, as we now know, to the disturbing attraction of the sun. To correct for these irregularities Copernicus introduced epicycle on epicycle in the lunar orbit. This is in its main features the system propounded by Copernicus. But attention must, to state the case fully, be drawn to two points to be found in his first and sixth books respectively. The first point relates to the seasons, and it shows a strange ignorance of the laws of rotating bodies. To use the words of Delambre,” in drawing attention to the strange conception, he imagined that the earth, revolving round the sun, ought always to show to it the same face; the contrary phenomena surprised him: to explain them he invented a third motion and added it to the two real motions (rotation and orbital revolution). By this third motion the earth, he held, made a revolution on itself and on the poles of the ecliptic once a year...... Copernicus did not know that motion in a straight line is the natural motion, and that motion in a curve is the resultant of several movements. He believed, with Aristotle, that circular motion was the natural one.

* In his great book Copernicus says: “ The movement of the heavenly bodies is uniform, circular, perpetual, or else composed of circular movements.” In this he proclaimed himself a follower of Pythagoras (see p. 17), as also when he says: “ The world is spherical because the sphere is, of all figures, the most perfect” (Delambre, Ast. Mod. Hist., pp. 86, 87).

Copernicus made this rotation of the earth's axis about the pole of the ecliptic retrograde * Kepler tells us that Tycho Brahe was pleased (i.e., opposite to the orbital revolution), and by making it perform more than one complete revolution in a year, the added part being gown of the whole, he was able to include the precession of the equinoxes in his explanation of the seasons. His explanation of the seasons is given on leaf ten of his book (the pages of this book are not all numbered, only alternate pages, or leaves). In his sixth book he discusses the inclination of the planetary orbits to the ecliptic. In regard to this the theory of Copernicus is unique; and it will be best to explain this in the words of Grant in his great work." He says: —

with this device, and adapted it to his own system. * Hist. Ast., vol. i., p. 354.

Copernicus, as we have already remarked, did not attack the principle of the epicyclical theory: he merely sought to make it more simple by placing the centre of the earth's orbit in the centre of the universe. This was the point to which the motions of the planets were referred, for the planes of their orbits were made to pass through it, and their points of least and greatest velocities were also determined with reference to it. By this arrangement the sun was situated mathematically near the centre of the planetary system, but he did not appear to have any physical connexion with the planets as the centre of their motions.

According to Copernicus' sixth book, the planes of the planetary orbits do not pass

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through the sun, and the lines of apses do not pass through to the sun. Such was the theory advanced by Copernicus: The earth moves in an epicycle, on a deferent whose centre is a little distance from the sun. The planets move in a similar way on epicycles, but their deferents have no geometrical Or physical relation to the sun. The moon moves on an epicycle centred on a second epicycle, itself centred on a deferent, excentric to the earth. The earth's axis rotates about the pole of the ecliptic, making one revolution and a twenty-six thousandth part of a revolution in the sidereal year, in the opposite direction to its orbital motion. In view of this fanciful structure it must be noted, in fairness to Copernicus, that he repeatedly states that the reader is not obliged to accept his system as showing the real motions; that it does not matter whether they be true, even approximately, or not, so long as they enable us to compute tables from which the places of the planets amongst the stars can be predicted." He says that whoever is not * “Est enim Astronomi proprium, historiam motuum coelestium diligenti et artificiosa observatione colligere. Deinde causas earundem, seu hypotheses, cum veras assequi nulla ratione possit....... Neque enim necesse est, eas hypotheses esse veras, imo ne

verisimiles quidem, sed sufficit hoc usum, si calculum observationibus congruentem exhibeant.”

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