GENERALIZATION. 279 



besetting error of most first attempts at scientific research. 

 The faculty to generalize accurately and philosophically 

 requires large caution and long training ; and is not fully 

 attained, especially in reference to more general views, 

 even by some who may properly claim the title of very 

 accurate scientific observers in a more limited field. It 

 is an intellectual habit which acquires immense and 

 accumulating force from the contemplation of wider 

 analogies. 



Hasty and superficial generalizations have always been 

 the bane of science, and there would be no difficulty in 

 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 Egyptian*. 

 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 



