384 SEMI-CENTENNIAL OF TORREY BOTANICAL CLUB 
are sufficient data to enable the determination of a more adequate 
expression for the behavior with respect to flower number; namely, 
the theoretical value for the first day of bloom (a) and the rate of 
decrease per day (5). 
It is, however, evident that the rate of decrease is influenced 
by a large number of factors such as length of blooming period, 
position of heads on branches, kinds of heads, whether terminal 
or lateral, etc., points which will be brought out later in the paper, 
and that it is in consequence not uniform throughout the season. 
The data, while sufficient to give us an approximate value for the 
rate of decrease, are not sufficient to determine it absolutely, and 
it must be borne in mind that the expression for flower number 
used in this paper is not considered to be absolute, but merely the 
most adequate to be obtained from the material at hand. This 
value can be determined from all the data in the manner developed 
above. : 
The value of a can also readily be determined on the basis of 
the observations. Іп the case of the data in TABLE 16, а = 18.6- 
[(—0.065) 31] = 20.6. This is a computed value for the flower 
number of the first date of bloom. 
It will be seen that two plants which start with the same flower 
number per head and show the same rate of decrease must have a 
different average number of flowers per head for the whole season 
if their blooming periods are of different leagths. The average 
will be lower the longer the blooming period. Just so the standard 
deviation will be the greater the longer the blooming period. Оп 
the other hand, if the two plants show differences in the rate of 
decrease the average number of flowers per head for the whole 
season may be the same in the two plants. The following com- 
parison should make the point quite clear. The plant E; (TABLES 
I and 2) bloomed 74 days in 1913 with an average flower number 
for the season of 18.6 and a standard deviation + I.9. In 1914 
it bloomed 91 days with an average flower number of 19.2 and 
standard deviation of + 1.5. Does this mean that in 1914 Es 
started with a higher number of flowers per head than in 1913, 
and maintained this characteristic throughout the season, or was 
the starting point in the two years the same with a difference in the 
manner of decrease? In using the method described above, for 
