296 CARL W. BOCK 



When it was shown that the groups 22, 46, 70, and 94 were 

 stable activities by virtue of their recurrence, it was assumed 

 that this implied that the said groups were functional units, or 

 behavioral entities of some kind, such units as reflexes, etc. Now 

 it is well known of these more traditional units that they vary 

 within very wide limits from time to time in their temporal and 

 spatial attributes and in the number and sequence of their ele- 

 ments, as well as in their amplitudes and directions. Such 

 variability is to be expected. Groups like the 46 above do in- 

 deed vary. Of the 62 different 46 groups no two are exactly 

 alike except in the number of their elements from which they all 

 derive their common name. In their other attributes they vary 

 very widely. Particularly do they vary with respect to the 

 amplitudes of their individual beats. The latter are obviously 

 minor variations which, consequently, ought to occur, as they 

 do, very frequently on grounds of probability. But variations 

 of 1, 2, 3, or more beats cannot be said to be minor variations 

 and therefore would not occur as often as amplitude variations, 

 not necessarily because they are essentially different kinds of 

 variations but because they imply greater variations of the 

 same kind. Thus a variation of one beat from the typical 46 

 group implies theoretically only that the 46th beat has an am- 

 plitude which is a greater deviation from the 46 group than 

 45 beats with a normal amplitude plus one beat with an am- 

 plitude of about one-third of the average of the other beats 

 would be. 



Since amplitude variations do occur very frequently and since 

 variations of one beat or more are of the same nature as these, 

 differing in degree only, and since they therefore imply relatively 

 large variations of amplitude, it is to be expected on purely a 

 priori grounds that a typical group, as the 46 group, will have 

 associated with it groups like itself and of the same species 

 whose frequencies will in general be the greater, the greater the 

 frequency of the type group; and the less, the farther the indi- 

 vidual members of the same species are numerically removed 

 from the type group. This is obviously the case in the present 

 instance where the above conditions- are sufficiently fulfilled as 

 on graph 1. 



