SECT. 18.] Modes of establishing the Groups or Series. 93 



numbers do not show a steady gradual approach towards 

 what might be considered in some sense a limiting value, 

 but, on the contrary, fluctuate in a way which, however it 

 may depend upon causes, shows none of the permanent uni 

 formity which is characteristic of games of chance. This 

 fact, combined with the obvious arbitrariness of singling out, 

 from amongst the many and various antecedents which pro 

 duced the observed regularity, a few only, which should con 

 stitute the objective probability (if we took all, the events 

 being absolutely determined, there would be no occasion for 

 an appeal to probability in the case), would have been suf 

 ficient to prevent any one from assuming the existence of 

 any such thing, unless the mistaken analogy of other cases 

 had predisposed him to seek for it. 



There is a familiar practical form of the same error, the 

 tendency to which may not improbably be derived from a 

 similar theoretical source. It is that of continuing to accu 

 mulate our statistical data to an excessive extent. If the 

 type were absolutely fixed we could not possibly have too 

 many statistics; the longer we chose to take the trouble 

 of collecting them the more accurate our results would be. 

 But if the type is changing, in other words, if some of the 

 principal causes which aid in their production have, in regard 

 to their present degree of intensity, strict limits of time or 

 space, we shall do harm rather than good if we overstep 

 these limits. The danger of stopping too soon is easily seen, 

 but in avoiding it we must not fall into the opposite error of 

 going on too long, and so getting either gradually or sud 

 denly under the influence of a changed set of circumstances. 



18. This chapter was intended to be devoted to a 

 consideration, not of the processes by which nature produces 

 the series with which we are concerned, but of the theoretic 

 basis of the methods by which we can determine the existence 



