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them with the voluntary motions of their own bodies, 

 and supposed that the celestial motions were also 

 voluntary, until, in time, a certain regularity of these 

 celestial motions suggested a mechanical instead of 

 a volitional syntax. The early Greek astronomers 

 held that the moon and sun, the planets and the 

 stars were fixed upon hollow crystal orbs, or spheres, 

 one outside the other, and that by the movement 

 of these hollow orbs the visible heavenly bodies 

 were carried round in orbits, of which the earth was 

 the centre. This would, in a way, account for any 

 movements which they were able to observe, but 

 would not supply a convenient basis for calculation, 

 since the movements of the hollow orbs could not 

 be taken as uniform rotations about fixed axes 

 through the earth's centre. Hipparchus, however, 

 in the second century B.C., brought this mechanical 

 syntax into close, and calculable, agreement with 

 his lunar observations by supposing that the hollow 

 orb carrying the moon revolves uniformly about an 

 axis which does not pass exactly through the earth. 

 Such a supposition introduces the idea of an epicycle ; 

 a mechanical syntax, the use of which was extended 

 by Ptolemy, some two or three hundred years later, 

 for the explanation of the motions of the planets. 

 Concerning this, Mr. W. R. Ball writes, "The idea 

 of eccentrics and epicycles on which the theories of 

 Hipparchus and Ptolemy are based has been often 

 ridiculed in modem times. Xo doubt, at a later 



