632 J. ARTHUR HARRIS 
modal frequency of two flowers per pedicel in the abnormal pedicels 
and other shrubs which have a modal frequency on a higher number 
of flowers in the secondary umbels, as we may for convenience call 
them, is shown at once by an examination of the frequency distri- 
butions for number of flowers per pedicel in the abnormal pedicels 
of the individual shrubs. This is given in Table IV. From these 
data it appears that 16 of the 18 individual plants which contributed 
Diagram 4. Frequencies of number of pedicels in Spiraea. 
to the total series of 2,792 abnormal rays upon which the polygon for 
1909 in diagram 4 is based, show a distinct secondary mode on 2 
flowers per pedicel. 
The two plants which are exceptions to this rule are represented 
by only 20 and 37 pedicels each. These numbers are entirely too 
small to justify any conclusion concerning the nature of the distribu- 
tions. Had larger, series of countings from these individuals been 
available, they might have shown the same bimodal condition as the 
other sixteen. 
