THE NEW COSMOLOGY 



as well as correct ones, and detail the observations 

 through which the incorrect guesses were refuted by 

 their originator. Some of these accounts are highly 

 interesting, but they must not detain us here. For 

 our present purpose it must suffice to point out the 

 three important theories, which, as culled from among 

 a score or so of incorrect ones, Kepler was able to 

 demonstrate to his own satisfaction and to that of 

 subsequent observers. Stated in a few words, these 

 theories, which have come to bear the name of Kepler's 

 Laws, are the following: 



1. That the planetary orbits are not circular, but elliptical, 

 the sun occupying one focus of the ellipses. 



2. That the speed of planetary motion varies in different 

 parts of the orbit in such a way that an imaginary line drawn 

 from the sun to the planet that is to say, the radius vector 

 of the planet's orbit always sweeps the same area in a 

 given time. 



These two laws Kepler published as early as 1609. 

 Many years more of patient investigation were re- 

 quired before he found out the secret of the relation 

 between planetary distances and times of revolution 

 which his third law expresses. In 1618, however, he 

 was able to formulate this relation also, as follows : 



3. The squares of the distance of the various planets from 

 the sun are proportional to the cubes of their periods of 

 revolution about the sun. 



All these laws, it will be observed, take for granted 

 the fact that the sun is the centre of the planetary orbits. 

 It must be understood, too, that the earth is constantly 

 regarded, in accordance with the Copernican system, 

 as being itself a member of the planetary system, sub- 



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