CHANCE, ANB ITS fiLIMINATION. 



347 



It rains more than twice as often, we 

 may be sure that some law is con- 

 cerned ; either there is some cause in 

 nature which, in this climate, tends 

 to produce both rain and a westerly 

 wind, or a westerly wind has itself 

 some tendency to produce rain. But 

 if it rains less than twice as often, 

 we may draw a directly opposite in- 

 ference : the one, instead of being a 

 cause, or connected with causes, of 

 the other, must be connected with 

 causes adverse to it, or with the 

 absence of some cause which pro- 

 duces it ; and though it may still 

 rain much oftener with a westerly 

 wind than with an easterly, so far 

 would this be from proving any con- 

 nection between the phenomena, that 

 the connection proved would be be- 

 tween rain and an easterly wind, to 

 which, in mere frequency of coinci- 

 dence, it is less allied. 



Here, then, are two examples : in 

 one, the greatest possible frequency 

 of coincidence, with no instance what- 

 ever 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 

 connection between them, provided 

 there be no repugnance ; provided 

 neither be connected with any cause 

 tending to frustrate the other. If 

 we find a greater frequency of coin- 

 cidence than this, we conclude that 

 there is some connection ; if a less 

 frequency, that there is some repug- 

 nance. In the former case, we con- 

 clude 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 cap- 

 able of counteracting the production 

 of the other. We have thus to deduct 



from the observed frequency of coin- 

 cidence as much as may be the effect 

 of chance, that is, of the mere fre- 

 quency 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 distri- 

 bution of the primeval natural agents, 

 of which we can know nothing be- 

 yond the boundaries of human obser- 

 vation, 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 con- 

 fined 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 connection nor re- 

 pugnance between them, or between 

 any of their causes, the instances in 

 which A and B will both exist, that 

 is to say, will co-exist, will be one 

 case in every six. For A exists in 

 three cases out of six : and B, exist- 

 ing 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 there- 

 fore 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 co-exist oftener than in 

 one case out of six, and, consequently, 

 A does not exist without B so often 

 as twice in three times, nor B without 

 A so often as once in every twice, 

 there is some cause in existence which 

 tends to produce a conjunction between 

 A and B. 



Generalising the result, we may say. 



