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UNIVERSE

at the cost of introducing into the system two new circles and two ideal centres of motion. The preces- sion of the equinoxes, discovered by Hipparchus, even lent support to the concept of fictitious pivots. It seemed to swing the pole of the ecliptic around the pole of the celestial sphere. In this shape the Greek system of the heavenly bodies came down to posterity, during the second century of our era, through Ptolemy's "Syntax". The two fundamental proposi- tions of the geocentric system, viz. that the earth has no axial rotation and no translation in space, form the sixth chapter of the first book. The "Syntax" did not pass directly from the Alexandrian school to Europe. Greek astronomy made its round through Syria, Persia, and Tatary, under Albategnius, Ibn- Yunis, Ulugh-Beg. The Ptolemaic system was ac- cepted by the Arabic astronomers without criticism, and was made known in Europe through their trans- lations. An unintelligible Latin "Almagest" had taken the place of the Greek "Syntax", and rested like a tomb-stone on European astronomy.

(2) New astronomical life awoke in the fifteenth century in Germany. Nicholas of Cusa rejected the axioms of Ptolemy; Peurhach and Midler restored the text of Ptolemy's "Syntax", and Copernicus made it his Hfe-work to disentangle the cycles and epicycles of the Greek system. The task of Copernicus was harder than that of his predecessor Aristarchus, on account of the unanimous acceptance of the geocentric system for more than a thousand years. The first book of Copernicus's great work, "On the Revolutions of the Celestial Bodies", is directed against the Ptolemaic axioms on the centre of the universe and the stability of the earth. He rightly observes that the universe has no geometrical centre. He then gives clear defi- nitions of relative and apparent motion and apijlies the Apollonian principle of interchanging the com- ponent motions in the opposite sense of Ptolemy. The complex heavenly machinery was explained by a triple motion of the earth, one around its axis, another around the sun, and a third, a conical motion, around the axis of the ecliptic, in periods of respectively one day, one year, and 2.5,816 years. Ptolemy's negative argimients against a moving earth were answered in a masterly manner. It had been objected that a dis- astrous centrifugal force would be created on the sur- face of the earth. Copernicus retorts that a far greater centrifugal force must be admitted in the outer planets and the fixed stars if they revolved around the earth. The resistance of the atmosphere, which, it was urged, would sweep away every object from a moving earth, was disiiosed of by Copernicus, exactly as it is to-day: each jilanet condenses and car- ries its own atmosphere. A third difficulty was raised about necessary changes in the appearance of the con- stellations, or, in modern language, about largo paral- laxes of the stars, when viewed from opposite points of the earth's orbit. Copernicus correctly thought the stars so far away as to make the terrestrial orbit com- paratively too small to show any effect in the instru- ments then available. The negative arguments of Ptolemy being dispelled, there remained only one pos- itive argument, in favour of Copernicus.

(3) The simphcity of the heliocentric system had sufficient weight to convince a genius like Copernicus. He never called his system an hypothesis. The first who exorcised censorship on the work "Do revolu- tionibus" w.as the Reformer, Osiandor. Dreading the op|)sition of the Wittenberg school, he put the word " Hypothesis" on the title-jjage and substituted for the prefai'c of Copernicus one of his own — all with- out authorization. It was more than half a century later that the Congregation of the Index pointed out nine sentences that had either to be omitted or ex- pressed hypothetically before the book might be read freely by all. The argument of simplicity was greatly strengthened by Kepler, when he discovered the ellip-

ticity of planetary orbits. Copernicus had foimd, by long years' ob.servation, that the inequaUties of plane- tary motion could not be accounted for, after Ptole- maic fashion, by simply placing the circular orbits excentrically. Not being prepared to abandon the circle, he resorted to small epicycles. Their final removal greatly enhanced the simplicity of the Coper- nican system. Then came the discoveries of the aberration of hght and of stellar parallaxes. While they appeared as natural consequences of the orbital motion of the earth, they threw on the Ptolemaic sys- tem the condemnation of an almost infinite com- plexity. The fixed stars were recognized to vibrate in double ellipses, their major axes parallel to the ecliptic, in periods of exactly one year. The double elUpses are the images of the terrestrial orbit, pro- jected on the celestial sphere by the parallactic dis- placement of the stars and by the finite velocity of light. The former kind is much the smaller of the two, and in most cases dwindles to immeasurable di- mensions. Some twelve hundred of them have actu- ally been observed. The aberration-ellipses have their apparent major axes all of equal length. The geocentric system not only has no explanation for these phenomena, but cannot even represent them without two epicycles for each star in the firmament. The Copernican argument of simplicity thereby re- ceived an overwhelming corroboration.

B. Direct Proofs of the Copernican Syslem. — While the argument of greater simphcity is only an indirect criterion between the two opposing systems, me- chanics has furnished more direct proofs. Copernicus actually had them in mind when he maintained that centrifugal force in a daily rotating celestial sphere would have to be enormous, that the atmosphere is condensed around the terrestrial globe, and that single planets cannot revolve around fictitious points that have no physical meaning. Kepler was too much preoccupied with geometrical studies and with the favourite idea of cosmical harmonics {Harmonices mundi) to recognize in the common focus of his ellip- tical orbits a governing power. It was reserved for Newton and Laplace to formulate the mechanical laws of celestial motion.

(1) The annual revolution of the earth around the sun is a necessary consequence of celestial mechanics, (a) Knowing the mathematical expression of centrifu- gal force, Newton computed, from the velocity and distance of our satellite, the amount of attraction that the earth must exerci.se upon it to maintain its orbital revolution. Learning then, from French geometers, the exact dimensions of the earth, he found the force that keeps the moon in her orbit to be identical with terrestrial gravity, divided by the square of the dis- tance from the centre. The discovery led to the com- putation of the masses of sun and planets, inclusive of the earth, the latter turning out more than three hun- dred thousand times lighter than the sun. The me- chanical conclusion is that the lighter body revolves around the heavier, and not the reverse; or, in more scientific language, that both revolve around their common centre of gravity, which, in this case, lies inside the solar sphere.

(b) Our satellite furnishes another more direct proof of the annual revolution of the earth. Carl Braun shows in the " Woehenschrift ftir Astronomie", X (1867), 193, that the moon is attracted nearly three times more forcibly by the sun than by the earth. Our satellite wovdd, therefore, leave us unless we re- volved with it around the sun. The earth is only able to give the annual lunar orbit a serpentine shape, so as to have the satelhte alternately outside and inside her own orbit.

(c) Newton also alludes to comets and shows that, in the Ptolemaic system, each of them needs an epicycle parallel to the ecliptic, to turn its orbit towards the sun. With our present cometary knowl-