290 
Journal of Agricultural Research 
Vol. XXVII, No. 5 
the comparison of the first and second series is (E 2 -*U 2 )-(E 1 -'U 1 ). 
The means, standard deviations and correlations of these differences 
might be determined directly. Since the means and standard devia¬ 
tions of the individual determinations are both available and since the 
correlations between the individual determinations in the first and second 
series may be utilized for another investigation, it seems best to deter¬ 
mine the correlations between the differences in the first series and the 
second series indirectly. The type of formula to be applied has been 
given elsewhere (22) and illustrated in its applicability to growth incre¬ 
ments ( 31 ). 
The formula to be used in the calculation of the probable error of the 
difference between the differences has also been given (23). 
The standard deviations of the difference between the two parental 
forms have been determined in order to test the significance of the 
difference between the types in either the first or second series. We 
require, therefore, merely the correlations between the differences in the 
individual duplets or triplets, in the first series and in the second series. 
In this case the product moment for the correlation between the dif¬ 
ferences, d v d 2 
2 (<!&) = 2 (EA)-2 (EiUJ-S (U 1 E 2 ) + 2 (U.UJ. 
The standard deviation of the differences between the differences in 
the first and second series then becomes— 
tf 2 (d*-dj) = Odi 2 + G d 2 2 “ 2r dld2 <T dl <T <j*. 
The correlations between these differences for the various characters 
appear in Table XXIII. 
Turning now to a consideration of the actual constants in Table X we 
note first of all that the differences between Egyptian and Upland cotton 
(column 8) are without exception positive in sign. Thus they show that 
in all instances the leaf-tissue fluids of the Egyptian cotton have a higher 
osmotic concentration than those of the Upland. The differences in the 
first series are, in all cases but one, at least four times as large as their 
probable errors (column 9). The single exception occurs in the compari¬ 
son between bulk Pima and bulk Meade. In the second series the differ¬ 
ences are from 7.8 to 14.2 times as large as their probable errors. There 
can, therefore, be no question whatsoever concerning the significance of 
the differences between the osmotic concentration of the tissue fluids of 
Egyptian and Upland cotton. Expressing the results in terms of dif¬ 
ferences in atmospheres, P, rather than in freezing point lowering, A, by 
means of the formula 
P= 12.06 A—0.021 A 2 , 
for which tabled constants are available (24), it appears that the differ¬ 
ences range from about 0.07 to 0.62 atmospheres in the first series. In 
the second series the differences range from 0.68 to 1.18 atmospheres. 
The differences between the first and second series of determinations 
(Table X, columns 5 and 6) show that in the second series the osmotic 
concentration is regularly lower than that in the first series. These 
differences are in all cases six or more times as large as their probable 
errors. They show conclusively, therefore, that osmotic concentration 
is lower in the second series of determinations than in the first. 
