624 THE PRINCIPLES OF SCIENCE. [CHAP. 



finding endless illustrations. Between things which are 

 the same in number there is a certain resemblance, namely 

 in number ; but in the infancy of science men could not be 

 persuaded that there was not a deeper resemblance im- 

 plied in that of number. Pythagoras was not the inventor 

 of a mystical science of number. In the ancient Oriental 

 religions the seven metals were connected with the seven 

 planets, and in the seven days of the week we still have, 

 and probably always shall have, a relic of the septiform 

 system ascribed by Dio Cassius to the ancient Egyptians. 

 The disciples of Pythagoras carried the doctrine of the 

 number seven into great detail. Seven days are men- 

 tioned in Genesis ; infants acquire their teeth at the end 

 of seven months ; they change them at the end of seven 

 years ; seven feet was the limit of man's height ; every 

 seventh year was a climacteric or critical year, at which a 

 change of disposition took place. Then again there were 

 the seven sages of Greece, the seven wonders of the world, 

 the seven rites of the Grecian games, the seven gates of 

 Thebes, and the seven generals destined to conquer that 

 city. 



In natural science there were not only the seven 

 planets, and the seven metals, but also the seven primi- 

 tive colours, and the seven tones of music. So deep a 

 hold did this doctrine take that we still have its results 

 in many customs, not only in the seven days of the week, 

 but the seven years' apprenticeship, puberty at fourteen 

 years, the second climacteric, and legal majority at twenty- 

 one years, the third climacteric. The idea was reproduced 

 in the seven sacraments of the Roman Catholic Church, 

 and the seven year periods of Comte's grotesque system 

 of domestic worship. Even in scientific matters the loftiest 

 intellects have occasionally yielded, as when Newton was 

 misled by the analogy between the seven tones of music 

 and the seven colours of his spectrum. Other numerical 

 analogies, though rejected by Galileo, held Kepler in thral- 

 dom ; no small part of Kepler's labours during seventeen 

 years was spent upon numerical and geometrical analogies 

 of the most baseless character ; and he gravely held that 

 there could not be more than six planets, because there 

 were not more than five regular solids. Even the genius 

 of Huyghens did not prevent him from inferring that but 



