76 
Weight of Seed and Characteristics of Plant 
Consider in somewhat greater detail the signs and magnitudes of these 
correlations*. 
Of the 26 values of r^u only 4 are negative. The mean value of the 22 positive 
coefficients is + "0073; the mean of the 4 negative is —"0236; the mean of all 
(regarding signs) is + 'OSSS. 
For the relationship between weights of seed planted and number of seed 
matured per pod, r,,,^, 21 constants are positive and 5 are negative. The mean of 
the positive coefficients is + •0502 ; the mean of the negative values is — '0303 ; 
for all 26 correlations the mean (regarding signs) is + "0348. 
Thus both correlations are (as is clear from the diagrams) unquestionably 
positive but very low. 
Apparently the relationship for weight and ovules is slightly closer than that 
for weight and seeds per pod, but tlie difference is too slight to justify any final 
conclusion. 
Consider now the question whether the observed correlations /•,(,(,, r,„s are to be 
regarded as direct biological relationships between the two variables w and o or w 
and s, or whether they are to be looked upon as merely necessary resultants of 
other interdependences. At present, the only other demonstrated correlation 
which might tend to bring about sensible values of r,™ and r^,,, is that between 
number of pods per plant and number of ovules formed and number of seeds 
developing per pod. Since number of pods per plant is known to be correlated 
with weight of seed planted, while both number of ovules and number of seeds per 
pod are correlated with number of pods per plant, some correlation must be 
expected between weight planted and number of ovules and seeds per pod. If 
now the observed values of ?'„,o and which are always small, are merely the 
necessary resultant of the relationships ?-„,yj, r^o, ?Vs' ^'^^ would expect the partial 
correlation coefficients, ^r,,,^, pr^ts, to be sensibly zero. If these partial correlations 
are not sensibly zero, it can only mean that there is a direct (causal) relationship 
other than the one just considered between number of ovules (or seeds) and the 
weight of the seed planted. 
The partial correlations and the correlations are shown side by side in 
Diagrams 3 and 4. The lowering of the degree of interdependence between both 
weight and ovules and weight and seeds by the correction for number of pods per 
plant is clearly marked. In a number of cases in which the correlation coefficient 
is positive the partial correlation coefficient is negative. 
Thus only 4 of the 26 values of i\^„ are negative, while 9 of the partial cor- 
relation coefficients have the minus sign. In only 5 cases is r^^ negative, but in 
11 of the series, the sign of pV^s is negative. The mean values of the partial cor- 
relations are very close indeed to zero. Thus ^r^o = '0186 as compared with 
^wo = "0533 ; pr,(,s='0099 as against r,j,, = "0348. 
* I have already shown (Science, N. S. Vol. xxxviii. pp. 345 — 346, 1913) that the LL, LG and GG 
series are open to question because of the lack of certain pi-ecautions in the cultures ; while they are 
included in the table of fundamental constants to avoid any possible criticism of selection of series they 
will be left out of account in the following discussions. 
