190 A Short History of Astronomy [Cn. vn. 



upper and lower row respectively, agree completely for as 

 many decimal places as are given, except in the cases of 

 the two outer planets, where the lower numbers are slightly 

 in excess of the upper. For this discrepancy Newton after- 

 wards assigned a reason (chapter ix., 186), but with the 

 somewhat imperfect knowledge of the times of revolution 

 and distances which Kepler possessed the discrepancy 

 was barely capable of detection, and he was therefore 

 justified from his standpoint in speaking of the law as 

 "precise."* 



It should be noticed further that Kepler's law requires 

 no knowledge of the actual distances of the several planets 





** 



Saturnus Jupiter Mars fere Terra 



f 



Venus *"* Mercunus Hie locum habetctiam> 



FIG. 62. The " music of the spheres," according to Kepler. 

 From the Harmony of the World. 



from the sun, but only of their relative distances, i.e. the 

 number of times farther off from the sun or nearer to the 

 sun any planet is than any other. In other words, it is 

 necessary to have or to be able to construct a map of the 

 solar system correct in its proportions^ but it is quite 

 unnecessary for this purpose to know the scale of the map. 



Although the Harmony of the World is a large book, 

 there is scarcely anything of value in it except what has 

 already been given. A good deal of space is occupied 

 with repetitions of the earlier speculations contained in the 



* There may be some interest in Kepler's own statement of the 

 law: "Res est certissima exactissimaque, quod proportionis quae 

 est inter binorum quorumque planetarum tempora periodica, sit 

 praecise sesquialtera proportionis mediarum distantiarum, id est 

 orbium ipsorum," Harmony of the World, Book V., chapter in. 



