ii2 THE WORLD MACHINE 



sometimes guess aright. Listen then to what Archimedes 

 says : 



" Aristarchus of Samos, confuting the hypotheses of the 

 astronomers, concludes that the world is yet many times greater 

 than the estimate we have just given (about 1300 earth radii). 

 He supposes indeed that the stars, like the sun, remain im- 

 mobile ; that the earth revolves, following the circumference 

 of a circle, round the sun as a centre, and that the sphere of 

 the fixed stars, having this same sun for a centre, is of such 

 vastness that the circle in which the earth moves, has to the 

 distance of the fixed stars, the same proportions as the centre 

 of a sphere to its surface" that is to say, a circle millions of 

 miles across, looked at from the fixed stars, would be but a 

 point in immensity ! 



This was in the third century B.C. At the beginning of the 

 seventeenth century A.D., when Tycho Brahe, Kepler, Galileo, 

 and a host of others, were debating the theory of Coppernicus, 

 the objection brought by Tycho, as we have already noted, 

 was that if the earth does revolve, then the stars would shift 

 a little in their relative positions. That point Galileo could 

 not meet. Though he sought eagerly to find a parallax, if 

 only for a single star, he sought in vain. It was not until some 

 seventy years ago that such a shift of position was conclusively 

 demonstrated ; and with it the last link set in the chain of 

 proof which establishes the Coppernican theory. Two thousand 

 years before Tycho, Aristarchus had met this objection in the 

 only way it could be met, and had divined the truth. 



He had divined, had guessed, rather than demonstrated. 

 Was there, then, any way to prove this idea of the distance 

 of the fixed stars ? 



In the opening of Coppernicus' work there is to be found a 

 theorem of amazing simplicity which does offer this proof. But 

 it did not originate with the Polish astronomer ; he copies it 

 from the Almagest of Ptolemy ; it is in the treatise of Cleomedes ; 

 where Cleomedes got it we do not know. Both appear to have 

 been chiefly compilers. Moreover, the idea is such a one as 

 might readily have occurred to the earliest of those who had de- 

 monstrated that the earth is round. It was doubtless very old. 



The chapter in Coppernicus is entitled, " Considerations on 

 the Immeasurable Extent of the Heavens in Comparison with 

 the Size of the Earth," and his theorem is this : 



