A CLASSIFICATION OF GROUPS 287 



the 94 group four times, one of the maxima for this group which 

 is not beat on the thirteenth day. Similarly, the maxima for 

 the 70 group occurs one day later, i.e., on a different day from 

 that of the 46 group on which day the frequency of the latter 

 group approaches a minimum. On the tenth day a maximum of 7 

 obtains for the 22 group while the 70 group is beat but once 

 and the 46 group twice. On the fifteenth when the 94 group 

 has a maximum, all other groups practically have minimums. 



Apparently an inverse correlation of some kind obtains be- 

 tween the frequency maxima of these four groups, and in this 

 case some kind of a relationship must exist among the four 

 groups. Consider finally the four numbers 22, 46, 70, and 94: 

 the following numerical relations obtain: 



22 = 22 



46 = 22 + 22 + 2 

 70 = 46 + 22 H- 2 

 94 = 70 + 22 + 2 



These relations are the counterpart of the apparent periodicities 

 previously referred to on the graph. If the above numerical 

 relations correspond to actual facts it would mean that 



22-G = 22-G 



46-G = 22-G + 22-G + 2-G 

 70-G = 46-G + 22-G + 2-G 

 94-G = 70-G + 22-G + 2-G 



and it would explain the periodicity of the maxima that obtain on 

 graph 1 for the frequencies of the above four groups as well as the 

 otherwise inexplicable fact that an organism can beat a certain 

 group with progressively increasing frequency, or perform an 

 activity of any kind in the same manner and suddenly for no 

 apparent reason cease to perform it at all. The explanation is 

 that the observer does not cease to beat the 22 group he merely 

 beats it several times in succession, hiding thereby its identity 

 as such in the guise of an apparently new or different group. 

 The above equations explain also why the frequencies of such 

 groups as the 70 and 94 is relatively so small. They do not 

 represent frequencies of different groups but rather the fre- 



