280 THE PRINCIPLES OF SCIENCE. 



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 system was repro- 

 duced 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 thraldom ; no small part of Kepler's 

 labours during seventeen years was spent upon nu- 

 merical 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 acute genius of Huyghens 

 did not prevent him from inferring that but one satellite 

 could belong to Saturn, because, with those of Jupiter and 

 the Earth, it completed the perfect number of six. A 

 whole series of other superstitions and fallacies attach to 

 the numbers six and nine 1 . 



It is by false generalization, again, that the laws of 

 nature have been supposed always to possess that sim- 

 plicity and perfection which we attribute to particular 

 forms and relations. The heavenly bodies, it was held, 

 must move in circles, for the circle was the perfect figure. 

 Even Newton seemed to adopt the questionable axiom 

 that nature must always proceed in the simplest way ; in 

 stating his first rule of philosophizing, he adds : ' To this 

 purpose the philosophers say, that nature does nothing in 



1 Baring-Gould, ' On the Fatalities of Number,' in ' Curious Myths of 

 the Middle Ages' (1866), p. 209. 

 m ' Principia/ l>k. III. ad initium. 



