THE GROWTH OF PHYSICAL IDEAS 91 



existed was sought for but not found because the effect was 

 too small to be detected by the method of observation used. 

 With the development of powerful telescopes, making pos- 

 sible observations very much more accurate than Tycho 

 Brahe's, the effect of the movement of the earth on its orbit 

 can be detected in the displacement of some stars, which we 

 now know to be the nearer ones. The effect is known as the 

 parallax and is used for determining the distance of the stars. 

 Tycho Brahe could not be expected to have realized the enor- 

 mous distance of the stars in comparison even with the size 

 of the orbit of the earth. 



After Brahe removed to Bohemia, Kepler became his as- 

 sistant and on his death succeeded to his position. He could 

 not continue the great campaign of observation to which 

 Brahe had devoted his life; instead, he used Brahe's astro- 

 nomical data to compute the orbits of the planets. He 

 adopted the Copernican theory, however, which by that time 

 had been generally accepted. According to that theory, the 

 orbits of the planets were circles. But when Kepler studied 

 the observations of the planet Mars, he soon realized that it 

 did not revolve about the sun in a circle and that when it 

 was nearest to the sun, its motion was more rapid than when 

 it was farther away. Then he announced that the planets 

 revolved about the sun in ellipses, with the sun at one of the 

 foci. This was his first law. Next he showed that if a line 

 were drawn joining a planet to the sun as the planet revolved 

 in its orbit, the line would sweep out equal areas in equal 

 times. Finally he gave his great third law, that the squares 

 of the periods of revolution of the planets around the sun 

 are proportional to the cubes of their average distances from 

 the sun. These laws were statements of fact that Kepler de- 

 rived from Brahe's observations. 



When Newton took up the matter, he showed that Kepler's 

 third law would be true provided that there were an at- 

 tracting force between the sun and the planet that varied 

 inversely as the square of the distance and that Kepler's 

 second law could be explained by the same assumption. If 



