GENERALIZATION. 247 



Schdnbein. There was a time when the rainbow was an 

 entirely inexplicable phenomenon, a portent, like a comet, 

 and a cause of superstitious hopes and fears. But we find 

 the true spirit of science in Roger Bacon, who desires us 

 to consider the objects which present the same colours as 

 the rainbow ; he mentions hexagonal crystals from Ireland 

 and India, but he bids us not suppose that the hexagonal 

 form is essential, for similar colours may be detected in 

 many other transparent stones. Drops of water scattered 

 by the oar in the sun, the spray from a water-wheel, the 

 dew-drops lying on the grass in the summer morning, 

 all display a similar phenomenon d . No sooner have we 

 grouped together these apparently diverse instances, than 

 we have begun to generalize, and have acquired a power 

 of applying to one instance what we can detect of others. 

 Even when we do riot apply the knowledge gained to 

 new objects and phenomena, our comprehension of those 

 already observed is vastly strengthened and deepened by 

 thus learning to view them as particular cases of one 

 more general property. 



A second process, to which the name of generalization 

 is equally given, consists in passing from a given fact or 

 partial law to a multitude of unexamined cases, which 

 we believe to be subject to the same conditions. Instead 

 of merely recognising similarity as it is brought before us, 

 we predict its existence before our senses can detect it, so 

 that generalization of this kind endows us with a pro- 

 phetic power of more or less probability. Having ob- 

 served that many substances assume, <like water and 

 mercury, the three states of solid, liquid, and gas, and 

 having assured ourselves by frequent trial that the greater 

 the means we possess of heating or cooling, the more sub- 

 stances we can vapourize and freeze, we pass confidently 



d Whewell's ' Philosophy of the Inductive Sciences,' 2nd edit. vol. ii. 

 p. 171, quoting the ' Opus Majus,' p. 473. 



