SECT. 19.] Modes of establishing the Groups or Series. 95 



of a series obtained in the first chapter ; for we have found 

 that these series are mostly presented to us in groups. 

 These groups are found upon examination to be formed upon 

 approximately the same type throughout a very wide and 

 varied range of experience ; the causes of this agreement we 

 discussed and explained in some detail. When, however, we 

 extend our examination by supposing the series to run to a 

 very great length, we find that they may be divided into two 

 classes separated by important distinctions. In one of these 

 classes (that containing the results of games of chance) the 

 conditions of production, and consequently the laws of statis 

 tical occurrence, may be practically regarded as absolutely 

 fixed; and the extent of the divergences from the mean 

 seem to know no finite limit. In the other class, on the 

 contrary (containing the bulk of ordinary statistical enquiries), 

 the conditions of production vary with more or less rapidity, 

 and so in consequence do the results. Moreover it is often 

 impossible that variations from the mean should exceed a 

 certain amount. The former we may term ideal series. It 

 is they alone which show the requisite characteristics with 

 any close approach to accuracy, and to make the theory of 

 the subject tenable, we have really to substitute one of this 

 kind for one of the less perfect ones of the other class, when 

 these latter are under treatment. The former class have, 

 however, been too exclusively considered by writers on the 

 subject ; and conceptions appropriate only to them, and not 

 always even to them, have been imported into the other 

 class. It is in this way that a general tendency to an ex 

 cessive deductive or d priori treatment of the science has 

 been encouraged. 



