143, 144] 



Kepler s Third Law 



189 



The second and most important of these, published in 

 1619, though the leading idea in it was discovered early 

 in 1618, was regarded by Kepler as a development of his 

 early Mysterium Cosmographicum ( 136). His specula- 

 tive and mystic temperament led him constantly to search 

 for relations between the various numerical quantities occur- 

 ring in the solar system ; by a happy inspiration he thought 

 of trying to get a relation connecting the sizes of the orbits 

 of the various planets with their times of revolution round 

 the sun, and after a number of unsuccessful attempts dis- 

 covered a simple and important relation, commonly known 

 as Kepler's third law : 



The squares of the times of revolution of any two planets 

 (including the earth) about the sun are proportional to the 

 cubes of their mean distances from the sun. 



If, for example, we express the times of revolution of 

 the various planets in terms of any one, which may be con- 

 veniently taken to be that of the earth, namely a year, and in 

 the same way express the distances in terms of the distance 

 of the earth from the sun as a unit, then the times of 

 revolution of the several planets taken in the order Mercury, 

 Venus, Earth, Mars, Jupiter, Saturn are approximately '24, 

 615, i, i'88, 1 1*86, 29-457, and their distances from the 

 sun are respectively -387, 723, i, 1-524, 5*203, 9-539; if 

 now we take the squares of the first series of numbers (the 

 square of a number being the number multiplied by itself) 

 and the cubes of the second series (the cube of a number 

 being the number multiplied by itself twice, or the square 

 multiplied again by the number), we get the two series of 

 numbers given approximately by the table : 



Here it will be seen tha.t the .two series of numbers, in the 



