Stout & Boas: STATISTICAL STUDIES IN CICHORIUM 403 
ment of this sort is not realized, the strong tendency to such a type 
is more or less evident from the data which show that there is a 
decrease for branches according to the relative time of blooming, 
which merges into and contributes to the general decrease of the 
flower number for the plant as a whole. 
The more absolute calculation of the decrease of average num- 
ber per head, therefore, involves the factor of position of the va- 
rious branches involving their age, length of life, and number. 
This decrease, due to position, may be considered as an unknown 
c and its value calculated in the same manner as that of b. If” 
be used to represent the number of the branch, we may introduce 
these two new factors into the equation which now becomes 
о = a + bt + сп. Threesimultaneous equations can be developed 
by the same methods already used, giving 
(1) [o] = a + b [t] + c [n] 
(2) [ot] = a [t] + b [P] + c [tni 
(3) lon] = a [n] + b [tn] + c [n°] 
In order that the rate of decrease for each branch be given its 
full weight, uninfluenced by the high flower number of the branches 
that begin to bloom later, the data were so arranged that the 
same starting point was taken for all branches; that is, all the 
observations for first day of bloom, second day of bloom, etc. 
were grouped together, regardless of dates. From TABLE 28 the 
values of a, b, and c for the plant (A X Es) ло. 4 were calculated. 
In order to simplify the calculations the observations are put 
down as + and — deviations from 18.0. 
Comparisons show that both series of calculated values cor- 
respond fairly well with the observed values. It does not, of 
course, appear from the data on this one plant that the values 
computed when both time and position are taken into account are 
in better agreement with the observed values than if time alone 
be considered. In order that the reader may judge of the amount 
of agreement, there is presented for comparison in TABLE 29 (1) the 
flower numbers actually observed on various dates after the 
first day of bloom without taking position into account, (2) the 
theoretical values for the same dates with regard to the factor of 
_ time, and (3) the values when both time and position are taken 
into account. 
