88 MISSOURI BOTANICAL GARDEN. 
empirical means—considering the smallness of the avail- 
able samples. The means for 1906 perhaps suggest non- 
linear regression, but our data hardly justify further sta- 
tistical treatment. The coefficient of correlation, r, may 
without further test be regarded as a fairly satisfactory 
measure of the relationship under consideration. 
Here, as in the inflorescences already studied, we cannot 
be satisfied with the information given by the coefficient 
of correlation for number of flowers and number of fruits 
per inflorescence. The clusters with the larger number of 
flowers would be expected to produce more than the average 
number of fruits, providing that the chances of an indi- 
vidual flowers producing a fruit is not, in some measure, 
dependent upon the number of flowers in the inflorescence 
upon which it is borne. 
The constant which we desire is rz, where z is to be 
read as number of flowers per inflorescence and z as the 
deviation of the number of fruits per inflorescence from 
their probable value, on the assumption that the chances 
of a flower producing a fruit is independent of the number 
of flowers per inflorescence. 
Using the formula 
ma AA 
V 1—tyy? + (Tey —Vz | Vy)? 
‘zz = 
where x denotes number of flowers and y number of fruits, 
I find :— 
For 1905, r,,—= — .387 + .043 
For 1906, r2, = — .3899 + .032 
Difference — .062 + .053 
Again the agreement of the two series is as close as one 
could expect, having regard to the probable errors. The 
signs show that as the number of rays per inflorescence 
increases, the capacity of the individual rays for maturing 
their ovules into seeds decreases, and to a considerable 
extent. 
