142 DISCOVERY OH. 



the study of mathematics and was appointed professor 

 at Gratz in 1594, being then twenty-four years of age. 

 But five years later he was, as a Protestant, expelled 

 from Styria and went to join Tycho Brahe at Prague, 

 where for a number of years he endeavoured to fit 

 Tycho Brahe's wonderfully accurate observations into 

 the theories then held as to motions of bodies in the 

 solar system. 



In the process of discovery of the three fundamental 

 laws known by his name, Kepler was led to make many 

 fantastic hypotheses. But all through he was guided 

 by the principle that God who made the world had 

 established fixed laws throughout his works, laws that 

 are often so definite as to be capable of expression 

 in exact numerical terms. In accordance with these 

 views he sought for numerical relations in the disposi- 

 tion of the planets and their arrangement, in respect 

 to their number, their times of revolution and their 

 distances from one another. Each hypothesis he made, 

 however fanciful, he tried by a rigorous test whenever 

 possible, and as soon as he found that the facts were 

 not in accordance therewith he abandoned it, and without 

 hesitation proceeded to try others, which he submitted 

 to the same severe ordeal, to share perhaps the same 

 fate. He says, " After many failures, I was comforted 

 by observing that the motions in every case seemed 

 to be connected with the distances ; and that when 

 there was a great gap between the orbits there was the 

 same between the motions." He was at length led to 

 the discovery of his well-known " Harmonic " law (the 

 squares of the periodic times of revolution of the planets 

 are as the cubes of their mean distances from the Sun). 



The misery in which Kepler lived forms a painful contrast 

 with the services which he performed for Science. The pension 



