328 Morpliolofpi of the Fruit of Saiuiiilnana Canadensis 
Again we have recourse to the partial correlation coefficient as in the investi- 
gation of the influence of peduncle length upon the relationship between the length 
of the fruit and its fertility characters. Here the more complex formula for four 
variables must be used. 
The partial correlation, rj^,,,, for constant values of Oi and O2 is given by 
the formula* 
^ ^ (1 - ?-o,„;-) - ro,,.^ - r„,^s, + (ro^,r„^s, + W^W) 
where Oj and 0.,, and s., are the ovules and seeds on the hrst and second placenta. 
But since our tables have been rendered symmetrical 01 = 0^, 5, = and we may 
write 
* 1 — '',/(/" — i'u'/ — r„s- + 2ro',/ VosVo-s' 
where the correlations without dashes are those for the same placenta and those 
with dashes are for the relationships between different placentae. 
Substituting constants for these formulae we find : — 
For 190G, r,v = -590, 
For 1907, r,.y = -714. 
Remembering that our gross correlations were ?- = -801 for 1906 and r = '844 for 
1907 it is clear that :— 
(a) A certain amount of the correlation between the number of seeds 
developing is due to the correlation between the number of ovules formed on the 
two placentae. 
(6) The correlation is mainly due, however, to the physiological factors upon 
which the development of ovules into seeds depends. 
Under the term physiological as used here are comprehended, (a) the ecological 
factors which determine whether an ovule shall receive a sperm, and the availability 
of food material and other requisites for growth, (6) the innate vigor or other 
physiological characters of the individual which determine whether a fertilized 
ovule shall develop into a seed. 
The foregoing analysis shows, I believe, that the main bulk of the correlation 
between the number of seeds on the two placentae is due to a complex of ecological 
and physiological causes, and is not merely a necessary statistical result of the 
correlation for ovules. Some of the biological factors may have an influence on 
both the number of ovules formed and the proportion of these ovules which shall 
develop into seeds. Experimental data in quantity and form for statistical treat- 
ment are desirable. 
* Pearson, K., Phil. Trans. A, Vol. cc. p. 31, 1902. 
