54 INDUCTION. 



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 ; provided neither be con- 

 nected 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 repugnance. 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 causing them 

 both ; in the latter, that one of them, or some cause which 

 produces one of them, is capable of counteracting the produc- 

 tion of the other. We have thus to deduct from the 

 observed frequency of coincidence, 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, enabling 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 

 data. The coincidences occurred in certain places and 

 times, and within those we can estimate the frequency with 

 which such coincidences would be produced by chance. 

 If, then, we find from observation that A exists in one case 

 out of every two, and B in one case out of every three; 

 then if there be neither connexion nor repugnance between 

 them, or between any of their causes, the instances in which 

 A and B will both exist, that is to say will coexist, will be 

 one case in every six. For A exists in three cases out of 

 six : and B, existing in one case out of every three without 



