DISCOVERIES IN THE CELESTIAL SPACES. 697 



being of opinion that some were higher and others lower than 

 the r'est. The idea formed of the heaven of the fixed stars 

 was extended to the planets ; and thus arose the theory of the 

 eccentric intercalated spheres of Eudoxus and Menoechmus, and 

 of Aristotle, who was the inventor of retrograde spheres. The 

 theory of epicycles, a construction which adapted itself most 

 readily to the representation and calculation of the planetary 

 movements, was, a century afterwards, made by the acute 

 mind of Apollonius to supersede solid spheres. However much 

 I may incline to mere ideal abstraction, I here refrain from 

 attempting to decide historically whether, as Ideler believes, 

 it was not until after the establishment of the Alexandrian 

 Museum that " a free movement of the planets in space was 

 regarded as possible," or whether before that period the 

 intercalated transparent spheres (of which there were twenty- 

 seven according to Eudoxus, and fifty-five according to Aris- 

 totle), as well as the epicycles which passed from Hipparchus 

 and Ptolemy to the middle ages, were regarded generally not 

 as solid bodies of material thickness, but merely as ideal 

 abstractions. It is more certain that in the middle of the 

 sixteenth century, when the theory of the seventy-seven ho- 

 mocentric spheres of the learned writer, Girolamo Fracas- 

 toro, found general approval ; and when, at a later period, 

 the opponents of Copernicus sought all means of upholding 

 the Ptolemaic system, the idea of the existence of solid 

 spheres, circles, and epicycles, which was especially favoured 

 by the Fathers of the Church, was still very widely diffused. 

 Tycho Brahe expressly boasts that his considerations oil 

 the orbits of comets first proved the impossibility of solid 

 spheres, and thus destroyed the artificial fabrics. He filled 

 the free space of heaven with air, and even believed that 

 the resisting medium when disturbed by the revolving 

 heavenly bodies, might generate tones. The un-imagina- 

 tive Rothmann believed it necessary to refute this renewed 

 Pythagorean myth of celestial harmony. 



Kepler's great discovery that all the planets move round the 

 sun in ellipses, and that the sun lies in one of the foci of these 

 ellipses, at length freed the original Copernican system from 

 eccentric circles and all epicycles.* The planetary structure 



* A better insight into the free movement of bodies, and into the inde- 

 pendence of the direction once given to the earth's axis, and into the 



