GRAVITATION" — BROWN 183 



Briefly, the three laws state that the curves in which the planets move 

 round the sun are ellipses with the sun in one focus; that the time 

 taken to get from one part of the ellipse to another is proportional 

 to the area bounded by the ellipse and the two distances to the sun, 

 and lastly, that the squares of the periods of revolution of the planets 

 around the sun are proportional to the cubes of the lon<^est diameters 

 of the ellipses in which they move. The success of his work was a 

 wonderful achievement, for he had little to guide him; only by 

 persistent trial and error could these results have been obtained at 

 that time. 



Kepler died in 1G30. Isaac Newton, the third and without any 

 question the greatest of the trio who laid the foundations of celestial 

 mechanics, was born in 1642. Through his work the subject was 

 changed from a mass of hypotheses and guesses into a science which 

 was capable of endless development. Kepler had given a geometrical 

 description of the motions of the planets : he had formulated certain 

 empirical laws which had no apparent connection with one another. 

 Newton gave the bases by which he was able to show that these laws 

 were a necessary consequence of properties that are common to all 

 matter. To do so, he had to take new steps in at least three direc- 

 tions. First, the final formulation of the laws under which all matter 

 will move whatever may be the acting forces. Here he had the aid 

 of the work of Galileo, who had been a contemporary of Kepler, but 

 who does not seem to have been in touch with him. Second, the 

 choice of the law or laws of force which would make the planets 

 move in the manner shown by Kepler. Third, the invention of a 

 mathematical device, which would enable him to deduce the con- 

 sequences of the laws of motion and of gravitation, and thus to show 

 that Kepler's laws were precisely what could be expected from the 

 operation of these fundamental properties of matter. 



We are approaching the two hundred and fiftieth anniversary of 

 the year in which Isaac Newton gave the first demonstration that the 

 orderly progress of the bodies that constitute the solar system was 

 due to the existence of certain simple laws apparently obeyed by all 

 matter. These laws, formulated with admirable lucidity in the 

 Principia, remained unchanged for over two centuries. "NMiilc the 

 comparison of their eifects with the observed motions showed small 

 deviations with the gradually increasing accuracy of the calculations 

 needed to show those effects, and of the observations, only in our 

 own time has the theory of relativity given us a new basis from 

 which these properties of matter may be developed. From the point 

 of view of the astronomer who is interested in the comparison of 

 theory with observation in the solar system, the difference between 

 the two methods of approach is philosophical rather than practical. 



