CHANCE, AND ITS ELIMINATION. 63 



data. The coincidences occurred in certain places 

 and times, and within those we can estimate the fre- 

 quency 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 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 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 coexist 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. 



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 ascertain what these are, we could frame 

 a generalization which would be true without restric- 

 tion of place or time : but until we can do so, the fact 



