288 CARL W. BOCK 



quency of the 22 group, and since the 70 and 94 groups each 

 contain several 22 groups, they must recur less frequently, other 

 things being equal. 



Fortunately the proofs for the above equations were found in 

 the records of the observer, but for reasons to be explained, only 

 by chance. Before the records in question (containing the proofs) 

 were made, during the last four days of experimentation, the 

 facts as stated above were well known to the writer, who searched 

 in vain among those records that had been made up to this time 

 for some. objective evidence which might support the conclu- 

 sions to which considerations of frequency, inverse correlations, 

 and numerical relations pointed. At present, after three years' 

 experience the writer prefers not to refer to records for proof 

 except under very particular circumstances because he knows 

 that a record cannot normally contain the facts of analysis un- 

 less accidentally or incidentally, not because the facts of numer- 

 ical analyses do not correspond to behavioral actualities, but be- 

 cause they do not necessarily correspond as would be expected by 

 ordinary habits of thought. The writer will call attention to the 

 facts and reasons of the above at its proper time. 



Consider figure 5 (first part) a fac-simile of one of the many 

 46 groups. 



Figure 5 shows 46 beats of varying amplitudes given in a prac- 

 tically constant tempo. Numerical and other reasons point 

 to the conclusion that the 46 group above consists of two 22 

 groups and a 2 group. Examination of the figure will show that 

 there exist in this figure absolutely no evidence for the assump- 

 tion. It cannot, except very arbitrarily be said, that here (on 

 say the 22d beat) the first 22 group ends, and there (on say the 

 23d beat) the second 22 group begins, and that the last two 

 beats constitute the above 2 group. Not only is it impossible 

 to see in this figure the desired relationship, but any other rela- 

 tionships are equally invisible. The above 46 group corresponds 

 to the generality of the 46 groups which observer R made and 

 yet it can otherwise be shown beyond all possibility of doubt 

 that the relation, 



46 = 22 + 22 + 2 



