The growth of the bacteria (
Escherichia coli) was measured using the photoelectric turbidimeter, and the fitness to logistic curve (4) introduced by VERHURST was examined. The results were as follows;
I. (i) The variable
y in the equation (4) has been defined as
y=
Y+ε, where
Y is the bacterial turbidity (log) established so that the turbidity at the time of the inoculation may be zero, and ε is
L/(1+
era).
Y is observable but ε is unknown.
(ii) The equation (6) of finite differences derived from the equation (4) is used to examine the graphical goodness of fitting to the logistic curve (4). The points on this diagram of finite differences (Fig. 4) are on a straight line, and this fact means the graphical good fitness.
(iii) Parameters
L,
r and ε are calculated diretcly from the value of
P1,
Q1,
P2, and
Q2, but the estimate of ε is adopted from the value of the
L/(1+
era). By means of Interpolation,
a is estimated.
II. According to the method of the least squares presented by W. E. DEMING, the minimum value of the sum of the weighted squares was calculated.
In order to determine the weights in
y-coordinate, the standard deviations of the errors caused by incubation and measuring were estimated experimentally (Fig. 5). As the result of chi square test in which
x0
_??_=min
S/σ
_??_=49.949, degree of freedom=8, and
Pr {
x2≥
X0
2}<0.001, it cannot be allowed that the growth curve of the bacteria follows the logistic curve (4).
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