404 
PHYSIOLOGY: H. S. REED 
Proc. N. a. S. 
taken as the value of a. By a series of approximations it was found that 
the value of k is near 0.095. We may then write: 
X = 210 {l-e'-""^'') (5) 
The values of x corresponding to values of t were determined and are 
given in table 2, together with the observed length of the shoots. 
While there is a general harmony between the calculated and observed 
length of the branches at the weekly intervals, the values are not suffi- 
ciently close to be satisfactory. An examination of the figures shows that 
during the first seven weeks the computed length of the branches is fairly 
correct; from the 8th to the 20th week the computed values are too large; 
from the 20th week to the end of the season, the two sets of values agree 
fairly well. 
The formula appears to fit the growth in the initial and latter part 
of the season, but growth lags behind the calculated values from the 8th 
to the 20th weeks. 
This leads us to consider the possibility that the length-growth of these 
apricot branches follows the course of a reaction which consists of two 
consecutive unimolecular reactions, one of which at first accelerates and 
later retards the other. (The dynamics of such reactions have been 
discussed by Mellor, Chemical Statics and Dynamics (1914).) It is, 
therefore, necessary to increase the previously obtained values of x by 
some quantity which will be large when t is small and which will be com- 
paratively small when t is large. 
The nature of this quantity was ascertained by shifting all the values 
of t toward the ordinate, which was done by substituting ^ — 1 for ^ in each 
case. The values by which the resulting determinations differed from the 
observed values were then computed and the differences were found to 
be periodically alternately positive and negative. (Compare columns 2 
and 3 in table 3.) An appropriate form expressing these fluctuating 
differences may be a function of / involving the cosine. This will equal 
1 when the value of the angle is 0, will decrease as the angle increases, then 
be negative as the angle increases from 90° to 270°, and become positive 
again in the last quadrant. By trial it was found that the difference 
between the observed values and those of the exponential function could 
be approximately expressed by 
19.1 [e--'''' cos f J] 
14 
The equation as used was then 
X = 210 [1-^-"^^ ^'-'^] + 19.1 [f -^'"' cos (6) 
The values of x corresponding to the time intervals from 0 to 28 are given 
in the fifth column of table 3. The root-mean-square deviation 
