A CLASSIFICATION OF GROUPS 295 



cated by other circumstances. However since they have been 

 found, they do in the present instance furnish the necessary proof 

 for the conclusions that analysis has pointed out, and warrant 

 the assumption that the 46, 70, and 94 groups are compounds of a 

 single group, the 22, and that the several maxima of these 

 groups are therefore conditioned by a common factor and not 

 by four separate factors. The general series (6) thereby suffers 

 the following further modification: 



(7)a-G,(2a+fc)-G,(3a+2/b)-G,(na+(n-l)/b)-G . . . w-G, x-G, y-G, z-G. 



3. The coefficient w. A glance at table 2 and graph 1 will 

 reveal the interesting fact that there occur in the vicinity of the 

 maxima for the groups 22, 46, 70, and 94, groups that are beat 

 relatively more frequently than the average of all other groups, 

 but yet not nearly with the abnormally high frequencies of the 

 above four groups. Their occurrence as such is not significant; 

 their occurrence with the said frequencies is not significant; but 

 their occurrence with their particular frequencies in association 

 with the groups 22, 46, 70, and 94 is significant and raises the 

 question whether the high frequencies of the associated groups is 

 in any manner conditioned by the frequencies of the groups to 

 which they are associated? 



The groups to which reference is made here are the 24, 44, 45, 

 47, 48, 68, 71, and 95. Considering only the 46 group and its 

 associated groups 44, 45, 47, and 48, the facts are as follows: 

 the group 46 occurs with abnormal frequency; the four neigh- 

 boring (in the numerical sense) groups 44, 45, 47, and 48 occur 

 in far greater numbers than the average of all other groups, but 

 yet with not nearly the exaggerated frequencies of the group 46. 

 Each of the four groups 22, 46, 70, and 94 have one or more 

 such exceptional neighbors, and with the exception of the groups 

 3 and 7 of which special mention will presently be made, no 

 other group has a frequency that lies above the average. The 

 question that logically follows is this: why are groups like the 

 44, 45, 47, and 48, that have relatively high frequencies asso- 

 ciated with groups like the 46 group that has an abnormally high 

 frequency? 



