CHANCE, AND ITS ELIMINATION. 375 



as often, we may be s^re that some law is concerned ; either there is some 

 cause in nature which, in this cHmate, 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 produces it ; and though it may still rain much oftener 

 with a westerly wind than with an easterly, so far would this be from prov- 

 ing any connection between the phenomena, that the connection proved 

 would be between rain and an easterly wind, to which, in mere frequency 

 of coincidence, it is less allied. 



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 coin- 

 cidence that must of itself bring about, without supposing any connection 

 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 connec- 

 tion ; 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 tliat 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 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 any thing remains, what does remain is the residual 

 fact Avhich 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 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 connection 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 co-exist, 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 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 ev- 

 ery twice, there is some cause in existence which tends to produce a con- 

 junction between A and B. 



