vii LAW AND PRINCIPLE 167 



on the chariot of truth. By meditation Plato arrived 

 at the doctrine that the planets move at uniform rates 

 in circles. A circle was conceived to be the most perfect 

 figure, therefore it was concluded to represent the 

 appropriate path of a heavenly body, without any refer- 

 ence to actual observation or experience. For fifteen 

 hundred years Plato's principle of uniform motion in 

 circles was not disputed, and even Copernicus, while 

 constructing his revolutionary system, regarded it as 

 an axiom that " The movement of the heavenly bodies 

 is uniform, circular, perpetual, or else composed of 

 circular movements." The difficulties which this tradi- 

 tion introduced in trying to make observation fit theory 

 were explained in one way or other, but there were 

 always errors or defects which could only be accounted 

 for by complicated reasoning. 



When Kepler began his analysis of Tycho Brahe's 

 accurate observations of the positions and motions of 

 heavenly bodies, particularly of the planet Mars, he 

 tried numerous combinations of circles and epicycles 

 with the view of finding a theory to account for them 

 completely. The Copernican theory was sufficient to 

 explain the general aspects of the heavens, but the 

 principle of uniform circular motion postulated by it 

 for the planets was unable to satisfy the standards 

 of precise measurement. Kepler found that when 

 theory was confronted with observation there was 

 always an error of eight or nine minutes of angular 

 measurement, and this amount he believed to be 

 impossible in such careful observations as were made 

 by Tycho Brahe. The amount is about equal to one- 

 fourth the apparent angular diameter of the sun, or to 

 the angle subtended by a halfpenny looked at squarely 

 from a distance of a dozen yards. " Out of these eight 



