598 THE PRINCIPLES OF SCIENCE. [CHAP. 



that either can be produced by the symmetrical modification 

 of the other, we discover a groundwork of similarity in the 

 crystals, which enables us to infer many things of one, 

 because they are true of the other. Our knowledge of 

 ozone took its rise from the time when the similarity of 

 smell, attending electric sparks, strokes of lightning, and 

 the slow combustion of phosphorus, was noticed by 

 Schb'nbein. There was a time when the rainbow was an 

 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 

 transparent stones. Drops of water scattered by the oar 

 in the sun, the spray from a water-wheel, the dewdrops 

 lying on the grass in the summer morning, all display a 

 similar phenomenon. No sooner have we grouped together 

 these apparently diverse instances, than we have begun to 

 generalise, and have acquired a power of applying to one 

 instance what we can detect of others. Even when we do 

 not apply the knowledge gained to new objects, our com- 

 prehension of those already observed is greatly strengthened 

 and deepened by learning to view them as particular cases 

 of a more general property. 



A second process, to which the name of generalisation 

 is often given, consists in passing from a 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 

 generalisation of this kind endows us with a prophetic 

 power of more or less probability. Having observed 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 and cooling, the more substances we can vaporise 

 and freeze, we pass confidently in advance of fact, and 

 assume that all substances are capable of these three forms. 

 Such a generalisation was accepted by Lavoisier and 

 Laplace before many of the corroborative facts now in our 



