382 SEMI-CENTENNIAL OF TORREY BOTANICAL CLUB 
On =a+b(t+d+7,) 
The average of this series is І [o] = a + b [1]; because as shown 
above || = —dand+d—d=o0 
The value of a thus becomes equal to [o] — b | and of these 
quantities [o] and |Д are determined from the data and are known. 
For the purpose of calculating the value of b another equation 
is needed and this may be obtained by multiplying each of the 
above series of equations by т + 4. Since, however, d is the same 
value throughout we may ignore it and we have: 
ото = {а +b (t + d) }т + brè 
On Tn = {a+b (t + d) }т, + br? 
Averaging and substituting [т] = —d, 
201 = — d bt) — bd? ++ b [7° ; 
3 ж = d (a Жел | mA Multiplying 1 by d gives 3 
4 [от] + d [o] = b [7] — bd? Adding 2 and 3 gives 4 
Solving this equation the value of b is obtained, and sub- 
stituting the value of b in І gives the value of a. 
In TABLE 16 are calculated the values of b and a for the plant 
Ез in 1913 (see TABLE І for values of 0) in order to illustrate the 
method employed. 
It will be more apparent in the presentation of data that fol- 
lows that differences in the rate of decrease throughout the season 
already noted in the general survey of intraseasonal partial 
variability are undoubtedly the source of greatest individual 
variability. The expression (0 |- a + b [/] as developed above 
can be used to express the general behavior of an individual in 
respect to flower number, and from it are determined the values 
of a and 6 to be used in comparisons. 
The values of a and 5 therefore may be discussed further. In 
the plant involved in TABLE 16 the value of b is —0.065. This 
is the value of the amount of decrease per day estimated from all 
the observations. While the actual variation in the rate is more 
or less variable in the data as collected, there is much in the be- 
havior to suggest that until more of the factors contributing to 
this are known and analyzed, it may be treated theoretically as a 
uniform rate in each plant, an assumption which will admit of the 
foregoing mathematical treatment. 
