NEWTON AND THE COLOURS OF THE SPECTRUM 261 



Any one comparing the accounts given in 1669 and 1704 

 must see that in the earlier year Newton believed that an analogy 

 between the spectrum and the musical scale might contain 

 possibilities of development, but that this belief was not realised. 

 What was the belief due to ? It is probable that Kepler's 

 Harmonices Mundi had something to do with it. This is the 

 book which is memorable as having announced to the world 

 Kepler's third law, that of the relation between the planetary 

 periods and distances, and which must have been known to 

 Newton about 1669 owing to his explanation of the third law. 

 Miss Clerke, the astronomer, in the biography of Kepler in the 

 Encyclopedia Britannica, characterises the book as an extra- 

 ordinary production, and states that its main purport was " the 

 exposition of an elaborate system of celestial harmonies de- 

 pending on the various and varying velocities of the several 

 planets, of which the sentient soul animating the sun was the 

 solitary auditor." Some of the reasoning certainly does appear 

 extraordinary ; Kepler not only makes the Deity anthropo- 

 morphic but also a mathematician. " Cum autem Deus 

 nihil sine Geometrica pulchritudine constituent " (p. 194, 

 Bk. V.) is one of the arguments. But I think it is possible to 

 regard the work more sympathetically than this. 



Any one wishing to " explain " the universe in Kepler's 

 time had not the analogy of the pendulum, the ideas of force 

 and acceleration, electrons, or the mathematics of wave motion 

 or any of the rest of the modern imagery to his hand. He was 

 restricted to the properties of the geometrical figures and to 

 the laws of harmony, i.e. of vibrating strings, which had been 

 discovered by Pythagoras well nigh 2,000 years before. A 

 physical law became necessarily a " harmony " because the 

 first physical laws discovered were those of harmony. Pytha- 

 goras, who was the earliest mathematical physicist, and who 

 probably saw the possibility of nature obeying mathematical 

 laws, lived at a time when ideas were not clearly distinguished 

 from things themselves. So the metaphor ran away with his 

 followers, and by a peculiar confusion of thought it became 

 necessary, for example, for the planets actually to give out 

 musical notes as they revolved in their orbits. But there was 

 enough truth seen in Pythagorism to keep it alive, and it had, 

 of course, an immense tradition. So it is not to be wondered 

 at that Kepler sought to elaborate and restate it. His attempt 



