3 °° 
Journal of Agricultural Research 
Vol. XXVII, No. 5 
in column i, the number of the row in the experimental field in column 
2, the number of samples upon which the statistical constants are based 
in column 3, and the series of collections (first or second) in column 4. 
The average value of the freezing-point lowering for the hybrid form 
appears in column 5. The freezing-point lowering for the parent forms 
is given in column 6. The table is divided into two sections in order 
to distinguish between the Egyptian (upper half of table) and Upland 
(lower half of table) parents. 
The correlation between the parents and the hybrids of the same 
triplet, given in column 7 of Table XV, is essential to the determination 
of the probable errors of the differences between the hybrid and the 
parent forms and will not be discussed in this place further than to note 
that the differences between the correlations for the first and second 
series show greater irregularities than those which were found in the 
coefficients for the two parental forms (p. 288). 
Two sets of differences are given. 
The first is that between the hybrid and parent forms (columns 8-10 
of Table XV). The probable errors of these absolute differences have 
been calculated with due regard to the influence of the heterogeneity of 
the field and of the variations of time and atmospheric conditions upon 
the probable errors, i. e., by the use of the formula 
& 2 (h—p) ~ "h Gp 2 ?hp°’h ar p 
where h= hybrid and p= parent forms, and the other symbols have 
their usual biometric significance. The ratios of the differences to their 
probable errors appear in column 9. 19 
The second set of differences comprises those‘between the means for 
the first and second series of determinations on hybrids and parents 
(columns 5 and 6 of Table XV), between the correlations between parents 
and hybrids (column 7) in the two series, and between the differences 
between the hybrid and the parent forms (column 8) in the first and 
second series, respectively. These differences are all taken with regard 
to signs. The ratio of these differences to their probable errors (when 
probable errors have been determined) are given beneath the differ¬ 
ences. 20 The probable errors of the differences between the first and 
second collections for the hybrid and the parent forms (columns 5 and 6) 
have been computed with due regard to the correlation between the 
determinations for the first and second series, as set forth in Table XXI. 
The probable errors of the differences between the differences between 
hybrid and parent forms (column 8) have been computed with regard 
to the correlation between them (as given in Table XXIII) by means of 
a formula similar to that given in the last paragraph above. 
Considering the results of the determinations (Table XV), it is clear 
that the differences between the hybrid and the parent form are negative 
in sign throughout, thus showing that the hybrid has in all comparisons 
a lower osmotic concentration of tissue fluids than either of the parental 
forms. 
19 These ratios have been computed from means and probable errors carried to a larger number of sig¬ 
nificant figures than it is possible to publish in these tables (Tables XV-XVIII). They are, therefore, 
somewhat more exact than those which may be deduced from the constants as given here. 
80 These ratios, like those referred to in the note immediately above, have been calculated from constants 
carried to a larger number of places. 
