A CLASSIFICATION OF GROUPS 



299 



observer R beat, there must be some definite reason or the 

 selection of a given set of groups as the components, i.e., he 

 selection may not be arbitrary; with a possible exception there 

 are no objective proofs to guide in tVe selection of these compo- 

 nents; the frequency criterion is the sole remaining guide, wh : ch 

 points out the groups 3, 7, 8, and 10 as componential possi- 

 bilities of the 22 group because of their recurrence. 



The groups 3, 7, 8, and 10 have relatively high frequencies. 

 This cannot be due to chance and inasmuch as all other groups 

 whose frequencies are above the average have been shown to be 

 related to the 22 group there can be little question that the latter 



FIG. 8 



is related in some way to one or more of the groups 3, 7, 8, and 

 10. A bit of objective evidence which may be offered in support 

 of the conclusion is the fact that the 416 group which has been 

 shown to be a multiple of the 22 group, is made up of fifty-seven 

 6 groups and two 7 groups. A portion of the 416 group is shown 

 in fac-simile in figure 8. 



Whether or not the coefficient a or as in the present example, 

 the 22 group, can be reduced to lower terms is in a certain sense 

 not important. The most important fact about the 22 group 

 is that it is obviously a functional unit and a functional entity 

 of a very definite kind in terms of which many other groups may 

 be expressed. If reducible, the same importance would attach 



