A CLASSIFICATION OF GROUPS 281 



100 feet of groups and rests, requiring from thirty minutes to as 

 much as five hours to secure, depending upon the speed of the 

 drums. 



Observers were given no other instructions than those given 

 above. In other respects, and in so far as it was compatible 

 with beating groups, they were left to their own devices, free to 

 perform such other activities as studying their lessons, talking, 

 singing, reading, or thinking, and free to have whatever ideas 

 occurred to or in them, of whose nature no record was made 

 or desired. 



i. THE GENERAL SERIES: a~G, b~G, c~G, w~G, x~G, y-G,z~G 



L Groups as stable activities. In order to show that groups 

 are stable or recurrent activities it is only necessary to show that 

 the coefficients a, 6, c, d, etc. are identical, or, that some of them 

 are, and in numbers sufficient to exclude chance identities. In 

 its ideal, i.e. extreme form, the above general series would reduce 

 itself to one of the following forms: 



f (6) a-G, a-G, a-G, a-G, a-G, a-G, etc. 

 \ (7) c-G, c-G, c-G, c-G, c-G, c-G, etc. 

 [(8) etc. 



This would imply, what rarely happens except under extremely 

 well controlled conditions, and certainly never under the condi- 

 tions under which our observers worked, that the same group 

 was always beat. 



Table 1 contains a record of 17 series of groups beat on approxi- 

 mately seventeen succeeding days by observer R. A glance at 

 this table will show that, considering any given series, there are 

 groups which recur several times within that series; and consid- 

 ering the 17 series, that the above groups likewise occur and 

 recur in practically all series. These facts are more conven- 

 iently shown in table 2, which constitutes a table of the fre- 

 quencies of the several different groups beat by this observer for 

 each of the seventeen days of experimentation and which give 

 also (lower row) the total frequencies of all groups for the total 

 of the seventeen days. 



