62 INDUCTION. 



Here, then, are two examples: in one, the greatest 

 possible frequency of coincidence, with no instance 

 whatever to the contrary, does not prove that there 

 is any law; in the other, a much less frequency of 

 coincidence, even when non-coincidence is still more 

 frequent, does prove that there is a law. In both 

 cases the principle is the same. In both we consider 

 the positive frequency of the phenomena themselves, 

 and how great frequency of coincidence that must of 

 itself bring about, without supposing any connexion 

 between them, provided there be no repugnance ; pro- 

 vided neither be connected with any cause tending to 

 frustrate the other. If we find a greater frequency of 

 coincidence than this, we conclude that there is some 

 connexion ; if a less frequency, that there is some repug- 

 nance. In the former case, we conclude that one of the 

 phenomena can under some circumstances cause the 

 other, or that there exists something capable of caus- 

 ing them both ; in the latter, that one of them, or 

 some cause which produces one of them, is capable of 

 counteracting the production of the other. We have 

 thus to deduct from the observed frequency of coinci- 

 dence, as much as may be the effect of chance, that is, 

 of the mere frequency of the phenomena themselves ; 

 and if anything remains, what does remain is the 

 residual fact which proves the existence of a law. 



The frequency of the phenomena can only be 

 ascertained within definite limits of space and time; 

 depending as it does on the quantity and distribution 

 of the primeval natural agents, of which we can know 

 nothing beyond the boundaries of human observation, 

 since no law, no regularity, can be traced in it, ena- 

 bling us to infer the unknown from the known. But 

 for the present purpose this is no disadvantage, the 

 question being confined within the same limits as the 



