Raymond Pearl 
251 
In the present case we shall have 
f2 = ''^±^ + l(m-viy. 
Whence substituting in (ii) we have finally 
R = 
which is the desired result. 
acr' r — l {m — 
.(iii), 
In order to save space I have given in the Appendix, in those cases where we 
have both symmetrical and unsymmetrical tables for a given pair of characters, 
only the symmetrical tables in all but a few instances where the others are intro- 
duced for a special purpose. 
We may now turn to the results. In Table XIV. are given the coefficients of 
correlation for what we may call " direct assortative pairing," namely for those 
cases in which the given character — either length, breadth, or index — in one in- 
dividual is correlated with the same character in the other individual of the pair. 
TABLE XIV. 
Direct Assortative Pairing in the Conjugation of Paramecium. 
Coefficient of 
Coefficient of Corre- 
Series 
Characters 
Correlation from 
symmetrical 
Tables 
lation from tables in 
which each pair is 
No. of 
pairs 
tables 
entered but once 
A 
Length of A 
Length of B 
•5327 + -0333 
A 3 and 4 
•5365 + -0469 
105 
Breadth of A 
Breadth of B 
•21 76 ±-0443 
.45 „ 6 
•2956 + •OeOl 
105 
» 
Index of A 
Index of B 
•3487 + -0409 
^7 „ 8 
■4017+ -0552 
105 
C 
Length of A 
Length of B 
■7249+ -0225 
(•3 „ 4 
•7250+ ■0318 
101 
» 
Breadth of A 
Breadth of B 
•3417+ ^0419 
C5 „ 6 
•3492+ ^0589 
101 
>) 
Index of A 
Index of B 
•5095 + •0351 
(77 „ 8 
•5157f0493 
101 
D 
Length of A 
Length of B 
•4302+ -0972 
D\ 
•4355 ± •1366 
16 
B 
A 
B 
•7941+^0509 
B\ 
•9106+ -0333 
12 
AA 
A 
Breadth of A 
B 
•5882+ ^0221 
AA 3 
•5893+ •OSll 
200 
Breadth of B 
•3490+ -0296 
AA 4 
•3533+ ^041 7 
200 
I think it will be granted by all that these results are remarkable. When we 
remember that the highest values which have been so far obtained for the 
coefficients measuring assortative mating in man do not exceed '3, these very high 
values for Paramecium seem at first sight astonishing or even incredible. In only 
one case out of five does the coefficient for the lengths give a value lower 
than "o, and this is in the case of a very small series in which the probable 
error of the determination is about + '1. It should perhaps be stated again that 
these coefficients represent the actual conditions found by making careful measure- 
ments on pairs of conjugants taken entirely at random from three different cultures 
at different times. There can be no doubt, I think, of the existence of a high 
degree of correlation between the same characters in the two members of pairs 
