98 THE GRAMMAR OF SCIENCE 



by Ptolemy (a.D. 140) nearly three hundred years after 

 Hipparchus, who, fixing the spherical earth, considered 

 sun and moon to move in circles yearly round the earth, 

 and the other planets in circles, whose centres again 

 described circles round the earth. The whole of this 

 system revolved daily round the earth with the stars. 

 This, the famous Ptolemaic system, remained for many 

 centuries the current formula, and even to this day the 

 eccentrics of Hipparchus and epicycles of Ptolemy are not 

 without service as elements of the more modern descrip- 

 tion. It would be wrong, I think, to say that the 

 Ptolemaic system was an erroneous explanation, it was 

 simply an insufficient attempt to describe in brief and 

 accurate language a too limited range of phenomena. 

 Then at the end of the Middle Ages came Copernicus, 

 who got rid of the cumbersome sphere carrying the fixed 

 stars by simply considering the earth to rotate round its 

 axis, and of the epicycles, if not of the eccentrics, by 

 treating the sun, not the earth, as the central point of 

 the system. Here was an immense advance in brevity 

 and accuracy of description ; but still more facts remained 

 to be included, more difficulties to be analysed and over- 

 come. This work was largely done by Keppler, who 

 conceived the earth and planets to move in certain curves 

 termedellipses, of which the sun occupied a non-central point 

 termed the focus. The formula of Keppler is one of the 

 greatest achievements of the scientific method ; it was the 

 work of a disciplined imagination analysing a laborious 

 and minute classification of facts.^ A more wide-embrac- 

 ing statement than that of Keppler was not only possible, 

 however, but required ; and this was provided by Newton 

 in a single formula which embraces not only the motion 

 of the planets, but that of their moons and of bodies at 

 their surfaces. This formula is the well-known law of 

 gravitation, but it is just as much a description of what 

 takes place in planetary motion as Keppler's laws are a 



1 The elaborate observations of Tycho Brahe. Keppler not only stated 

 the form of the planetary path but the mode of its description in his famous 

 three laws. 



