Feb. a, 1934 
Tissue Fluids in Cotton 
289 
values. For purposes of comparison it is desirable to reduce these to a 
percentage basis by dividing all of the absolute differences (X100) by 
the values for the Upland cotton. 14 The resulting percentage differences 
appear in column 10. 
The second set of differences—those entered under the average con¬ 
stants for the first and second collections of Egyptian and Upland cot¬ 
tons, respectively, in columns 5 and 6, under the first and second corre¬ 
lation coefficients in column 7, and under the differences between Egyp¬ 
tian and Upland cotton in the first and second series in column 8—shows 
the relative values of the constants secured in the first and in the second 
series of determinations. 
All of these differences are taken— 
(constant for second series) minus (constant for first series). 
All of the differences have been taken algebraically, with regard to the 
signs of the constants compared. 
Since the physical constants for the two types of cotton (columns 5 
and 6) are both positive values, a positive sign indicates a higher value 
of the physical constant in the second series. Since the correlations 
(column 7) and the differences between the two types of cotton (column 
8) may theoretically be either positive or negative (and actually differ 
with regard to sign in some of the subsequent tables), it is necessary in 
interpreting these differences to bear in mind the signs of the constants 
for the first and second series between which comparisons are being 
drawn. 
The ratios of these differences to their probable errors (when probable 
errors have been determined) are shown below the differences (opposite 
Diff./E diff .). 15 
In determining the probable errors of differences between the means 
for the two series (columns 5 and 6) the correlation between the con¬ 
stants of the first and second series of determinations must be considered. 
The standard deviations of the differences are calculated from the formula 
° (2-1) = ** + *** ~ 2r ‘ 2 <Ti 
where the sigmas denote standard deviations and r the correlation coeffi¬ 
cient measuring the relationship between the first and second series, as 
designated by the subscript numerals. 16 
The differences between the differences between Egyptian and Upland 
cotton in the first and second series (column 8, opposite “Diff., (2)-(i)”) 
show whether the two types show greater or less differentiation at the 
time of the second than at the time of the first collection of samples. 
The probable errors of the increase in the differences between the two 
kinds of cotton have been calculated as follows: 
Let E. U. denote Egyptian and Upland plants, of the first or second 
series as may be indicated by subscript numerals. Then the differences 
are E x — Uj and E 2 — U 2 . The numerical value under consideration in 
14 In the case of hydrogen-ion concentration (Table XIII) the value of the deviation of the Ph for the Up¬ 
land cotton from neutrality has been used in the calculation of the percentage difference between the two 
types. 
15 These values, like the ratios mentioned immediately above, have been computed from the original 
constants carried to a larger number of places than those given here, and are consequently slightly more 
accurate than those which may be recomputed from the constants as given in these tables. 
38 The coefficients of correlation, [r]ir, are given for each of the physicochemical constants considered, and 
for the different subcultures, in Table XXI. These coefficients will be considered later (p.313). For the 
moment they are of interest merely as a means to the calculation of the probable errors of the differences 
between the constants for the first and second series of determinations. 
