74 
Weight of Seed and Characteristics of Plant 
between weight of seed planted and ovules per pod, r„,o, and between weight 
planted and number of seeds matured per pod, The partial correlation 
coefficients, 
^!(io ' wp ^ po _ ^ws "^ ps 
Vl-?%Vl-rV. Vl-rV,,Vl -rV. 
showing the correlation for weight (w) and ovules (o) and weight and seeds (s) for 
constant numbers of pods (p) per plant are also given. These require in addition 
to the correlations here given Vup, rp„ and r^,,., the correlations between the number 
of pods per plant and the number of ovules and seeds in these pods. Values 
of ru,p are available from the preceding paper (Biometrika, Vol. ix. p. 21, Table 
VII) and from a supplementary table giving nine additional constants*. For the 
reader's convenience these are reprinted in this table. The values of r^o and r^,, 
will be published in connection with another problem. 
The probable errors have all been calculated on the basis of the number of 
pods examined as N. There is considerable question whether the actual number 
of seeds planted should not have been used instead ; the degree of trustworthiness 
of a constant is perhaps not greater than is indicated by the lowest number of 
actual measurements (irrespective of the number of associated measures taken). 
The point is not of the greatest practical importance for the present case, since the 
number of series is so large that conclusions can be drawn from the run of the 
constants as a whole and too much weight need not be given to individual series. 
A glance at the table shows that the correlations are low throughout. The 
suggestion naturally arises that some of the extremely low values may be due to 
non-linear regression. The regression straight line equations and the results of 
Blakeman's testf are given in Table II. Here r, rj and the straight line equation 
for the regression of ovules and seeds per pod on weight planted (in working units) 
are determined by the conventional formulae. The final two columns give the 
values of 
when f = 7]- - r- and Xi = "67449/^/-^. 
All the straight lines are shown in Diagram 1. The empirical means are 
indicated in all of the cases where it can be done without confusion. The slope is 
very slight and the agreement of observed and predicted means not very close, 
especially near the ends of the i-ange, wJm'e the number of observations is small. 
There is, however, no clear indication that a curve of a higher order would describe 
the results better than a straight line. This irregularity is precisely what is to be 
expected in cases of low correlation. 
Harris, J. Arthur, "An Illustration of the Influence of Substratum Heterogeneity upon Experi- 
mental Results." Science, N. S. Vol. xxxviii. pp. 34-5—346, 1913. 
t Blakeman, J., Biometrika, Vol. iv. pp. 332—850, 1905. 
