A CLASSIFICATION OF GROUPS 311 



the use of the technique, presently the number of accented beats 

 increases so that not only is it impossible to use the data obtained 

 in this way, but it " spoils" an otherwise good observer whose 

 habits become continually modified by the instructions given. 

 This condition no doubt obtains generally, particularly in intro- 

 spections, and it was for this reason that the writer not only did 

 not require introspections, assuming them to have value, but 

 hesitated to mention the word introspection lest the habits of 

 his observers might become too radically changed either by 

 actual instructions or by casual references to it. 



Observer Q beat the following series of groups under conditions 

 as above: 



166 81 225. 148 170 



The 166 group was accented on the 83 beat and on the 137th 

 beat. The 83d beat divides the 166 group into two equal parts, 

 namely, two 83 groups. Thus the present observer agrees with 

 others cited in this work. The 137th beat is the 54th beat of 

 the second hypothetical 83 group, thereby dividing this group 

 into the two groups 54 and 29. The 81 group following, which 

 differs only by 2 from the two 83 components of the 166 group 

 is accented on the 54 beat, i.e., thereby separating out another 

 54 group, and dividing it into the groups 54 and 27 which latter 

 group equals 54/2. The 225 group was accented only on the 

 54th beat, and the rest of the series is unanalyzable. 

 The same observer beat the following series: 



66 86 161 117 42 



The group 66 was accented on the 43d beat, i.e., on the 86/2 

 beat, which 86 group follows the 66 group. The group 161 was 

 accented on the 57th beat, thereby dividing it into the groups 

 75 and 86. The 86 groups actually preceded the 161. The 117 

 was accented on the 75th beat, dividing it into the groups 75 and 

 42. The 75 was shown to be a similar component of the pre- 

 ceding group, and the 42 group actually follows the 117 group. 



From the above it would seem possible to conclude that the 

 coefficient y of the general series (6) is definable in terms of 



