238 A Biometriccd Study of Conjugation in ParameGium 
TABLE VII. 
Differentiation of Govjvgants from Non-Conjugants. Index. 
Series 
Group 
Mean 
Standard 
Deviation 
A 
1) 
Non-Conjugants ... 
Conjugants 
27-848 + -116 
26-338 ±-126 
2-502+ -082 
2-697 ±-089 
5) 
Absolute Difference 
Eelative „ 
1-510+-171 
5-4 7„ 
-•195+ -121 
7-8 % 
C 
Non-Conjugants ... 
Conjugants 
25-911 ±-106 
24-495 ±-113 
2-238 + -075 
2-390 ± -080 
Absolute Difference 
Eelative „ 
1-416 + -155 
5-5 % 
--152 + -110 
6-8 % 
We also note that, in passing from Series A to Series C, the index is lowered 
for both conjugants and non-eonjugants about two points (actually the difference 
for non-conjugants is 1-937 and for conjugants 1-843). The individuals in the 
culture at the time Series G was taken have become narrower in proportion to 
length than they were when Series A was taken. 
After Series G was taken from the culture the environmental conditions 
changed rapidly, and with this change, as has been mentioned, a vigorous 
growth of algae began. At the same time the shape of the Paramecia changed 
markedly in the reverse direction to the change which had occurred in the 
interval between Series A and G. Thus in Series E the index (for non-conjugants, 
of course,) had risen to a mean value of 2.9"508 + •125, and the variability of the 
index had decreased to 2'132. 
The variabilities of the indices show a relation which at first sight appears 
paradoxical. In both series the index is more variable in the conjugants than 
in the non-conjugants, in spite of the fact that both length and breadth, on 
which the indices are based, are more variable in the non-conjugants. This 
greater variability of the index in the conjugants, however, really arises from 
the fact that, as we shall see, the coefficient of correlation between length 
and breadth is much lower in the conjugants than in the non-conjugants. This 
point will be much clearer if we consider the general formula for the standard 
deviation of an index. It has been shown by Pearson* that if Xi and w-^ be the 
absolute sizes of two correlated characters, Vi and ^3 their coefficients of variation 
— , ^- , r-i. the coefficient of correlation between and x-,, and i-,. be the mean 
value of the index ~, and its standard deviation, then 
2i3 = ^/ (^'i' + - 27-13^1^3) (i). 
* Boy. Soc. Proc. Vol. 60, p. 492. 
