n6 POPULAR SCIENCE MONTHLY. 



the phenomena, I conceived that I also might take the liberty of trying 

 whether, on the supposition of the earth's motion, it were possible to 

 find better explanations of the revolutions of the celestial orbs than 

 those of ancient times. Having then assumed the motions of the earth 

 that are hereafter explained, by long and laborious observation I found 

 at length that if the motions of the other planets be likened to the 

 revolution of the earth, not only their observed phenomena follow from 

 the suppositions, but also that the several orbs, and the whole system, 

 are so connected in order and magnitude that no one part can be trans- 

 posed without disturbing the rest and introducing confusion into the 

 whole universe." He looked, he here says, for a new theory because 

 the old one was unsymmetric; and his new theory satisfies because it 

 consistently explains the facts of observation and because it was sym- 

 metric. Symmetry of the kind referred to is not essential to a true 

 theory. If any theory explains every fact of observation quantitatively 

 as well as qualitatively, it is to be accepted. Copernicus was not free 

 from hampering presuppositions any more than his predecessors. 



''We must admit," he says, "that the celestial motions are circular, 

 or else compounded of several circles, since their inequalities observe 

 a fixed law, and recur in value at certain intervals, which could not be 

 unless they were circular ; for the circle alone can make that which has 

 been recur again." In writing this passage his mind was closed to 

 every idea but one. Copernicus knew, far better than most of us, that 

 ovals and ellipses might also serve to represent recurring values, but 

 the thought did not even cross his mind in connection with celestial 

 motions. He was committed to circular motions exclusively, from 

 the outset. 



"We are therefore not ashamed to confess," he says, "that the 

 whole of the space within the orbit of the moon, along with the center 

 of the earth, moves around the sun in a year among the other planets; 

 the magnitude of the world (solar system) being so great that the 

 distance of the earth from the sun has no apparent magnitude (is 

 indefinitely small) when compared with the sphere of the fixed stars. 

 . . . All which things, though they be difficult and almost incon- 

 ceivable, and against the opinion of the majority, we, in the sequel, by 

 God's favor, will make clearer than the sun, at least to those who are 

 not ignorant of mathematics." 



The system of Copernicus required thirty-four circles and epicycles 

 — four for the moon, three for the earth, seven for the planet Mercury 

 and five for each of the other planets. Cumbrous as this apparatus 

 appears to us, it was a distinct simplification of the Ptolemaic system 

 as taught in the sixteenth century. Fracastor, writing in 1538, em- 

 ployed sixty-three spheres to explain the celestial motions. 



One word must be said of the theory of trepidation which Coper- 



