208 
A Contribution to the Problem of Homotyposis 
necessarily mean that there are any specific biological factors influencing the 
number of seeds developing or the number of ovules failing in all of the pods of 
the same individual in a similar manner. The observed values of correlations 
for (semi)dependent characters may be merely the resultant of independent 
variables with which they are correlated. 
To remove the influence of To^o^ upon r^^^^ we have recourse to the partial 
correlation coefficient for two variables, i.e. and o.^, constant. In our notation 
this is 
"^(1 '^OlO-? ^0281^ ^OlSl^ ~l~ 2^0i02^0lSl*'o2Sl) '^(-^ ^OlOj ^02S2 OlS-^ ~^ '^'^OlOl'^OiS-i'^ OiS^) 
But since we are dealing with symmetrical tables we may write* 
d'o'^s's: - I_y,,2_y,,2_y2i2r,,rr,, ' 
'00 'OS 'OS ' ^'oo'os'os 
where the correlations without dashes are those for the same pod and those with 
dashes are for the relationships between difierent pods. 
In applying this formula to the actual data, the values of Tgg for the individual 
pods are essential. These have been deduced from Tables X, XI below and 
Tables VI, VII of a former paper f. 
Meramec Highlands. 
6000 pods, = -6855 ± '004:6, 
2912 pods, r,, = -6936 ± -0065, 
Sharpsburg, Ohio, r^^ = -4553 ± -0086, 
Lawrence, Kansas, = -6032 ± -0091. 
The partial correlation coefficients for seeds per pod for constant numbers of 
ovules per pod are: 
Series 
0 0" S S 
o'o" s's' 
Meramec Highlands 
112 Trees 
•1063 
■2617 
•397 
60 Trees 
•0700 
•2306 
•304 
Sharpsburg, Ohio ... 
•1645 
•1798 
•915 
Lawrence, Kansas 
•0582 
•2019 
•288 
These give a mean value of -0998 as compared with the mean relationship 
uncorrected for the influence of ovules per pod, r^v = -2164. 
Apparently, there are specific physiological % factors which tend to differentiate 
* Biometrika, Vol. vii. p. 328. For original see K, Pearson, Phil. Trans. A, Vol. cc. p. 31, 1902. 
t Bull. Torr. Bot. Club, Vol. xli. pp. 243-266, 1914. 
J Under the term physiological as used here are included (a) the ecological factors which determine 
whether an ovule shall receive a sperm, (6) the nutritional factors which determine the availability of 
food materials, and other environmental prerequisites for development, and (c) the innate vigour or 
other physiological characters of the individual which determine whether a fertihzed ovule shall develop 
into a seed. 
