1910] HARRIS—FERTILITY IN CERCIS 125 
and the length of the pod. The partial correlation coefficient gives 
the correlation between two characters, say seeds (s) and length (/) 
for constant values of a third character, number of ovules (0). 
A necessary preliminary is to determine the correlation between 
number of ovules per pod and number of seeds developing per pod. 
We find 7,,.=0.7297+0.0058. Clearly with such a large value 
for the correlation between ovules and seeds we would expect some 
relationship between the number of seeds developing and the length 
of the pod, having no direct physiological significance whatever, but 
due merely to the fact that since number of ovules and number of 
seeds are closely correlated, and number of ovules and length of pod 
are correlated, number of seeds and length of pod must also be corre- 
lated. It is the influence of the ovules which we wish to remove by 
means of the partial correlation coefficient. The familiar formula 
is 
¥31—Toslol 
oe 2 
y ay —fo 
Psi = 
? 
which gives 
py=0.3128+0.0111.7 
I think this is a rather significant result. It not only shows that 
there is a physiological or morphogenetic relationship between the 
number of seeds developing and the length of the fruit independent 
of the correlation for ovules and length, but tells us the intensity of 
the interdependence as well. 
There is still another way in which the influence of the ovules may 
be, to some extent at least, cleared away. Instead of correlating 
between the actual number of seeds maturing per pod and the length 
of the pod, the correlation between the relative number of seeds devel- 
oping per pod (that is, the ratio or index seeds/ovules per pod) and 
the length of the pod may be found: r,;=0.2906+0.0113. This 
constant indicates very clearly that there is a real interdependence 
of number of seeds developing and fruit length, which is independent 
of the correlation for number of ovules and length of fruit. 
7 The probable error of pg is from the formula Epsi=0.67449.1—psi//#- Mr. 
Davip HERON, of University College, London, tells me that he has recently demon- 
trated the correctness of this formula and has the proof in press. 
