316 INDUCTION. 



in the latter, that one of them, or some cause which produces one o 

 them, is capable of counteracting the production 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 re- 

 main 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 coin- 

 cidences occurred in certain places and times, and within those we can 

 estimate the frequency with which such coincidences would be pro- 

 duced 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 be- 

 tween 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 regard to the presence or absence of A, will exist 

 in one case out of those three. There will therefore be, of the whole 

 number of cases, two in which A exists without B ; one case of B 

 without A ; two in which neither B nor A exists, and one case out of 

 six in which they both exist. If then, in point of fact, they are found 

 to coexist oftener than in one case out of six ; and, consequently A 

 does not exist without B so often as twice in three times, nox B with- 

 out A so often as once in every twice ; there is some cause in exist- 

 ence, which tends to produce a conjunction between A and B. 



Generalizing the result, we may say, that if A occurs in a larger 

 proportion of the cases where B is, than of the cases where B is not ; 

 then will B also occur in a larger proportion of the cases where A is, 

 than of the cases where A is not ; and there is some connexion, through 

 causation, between A and B. If we could ascend to the causes of the 

 two phenomena, we should find, at some stage, either proximate or 

 remote, some cause or causes common to both; and if we could ascer- 

 tain what these are, we could frame a generalization which would be 

 time without restriction of place or time : but until we can do so, the 

 fact of a connexion between the two phenomena remains an em- 

 pirical law. 



§ 3. Having considered in what manner it may be deteimined 

 whether any given conjunction of phenomena is casual or the result of 

 some law; to complete the theory of chance, it is necessary that we 

 should now consider those effects which are partly the result of chance 

 and partly of law : or in other words, in which the effects of casual 

 conjunctions of causes are habitually blended in one result with the 

 effects of a constant cause. 



This is a case of Composition of Causes; and the peculiarity of it 

 is, that instead of two or more causes intermixing their effects in a 

 regular manner with those of one another, we have now one constant 

 cause, producing an effect which is successively modified by a series 



