254 A Blometrical Stndij of Conjugation hi Paramecium 
B and D have not been determined. For the other series the coefficients are 
shown in Table XV. 
TABLE XV. 
Coefficients of Cross Assortative Pairing in the Conjugation of Paramecium. 
Series 
Characters 
A 
J) 
C 
>» 
AA 
Length of A 
„ B 
A 
„ A 
B 
Breadth of B 
B 
B 
A 
Mean 
Coefficient of 
Correlation 
No. of 
pairs 
■•0360 ±-0657 
■0969 ± -0652 
•0789 ± •0667 
•1 150 ± •0655 
•1740 ±-0463 
•1482±^0466 
105 
105 
101 
101 
200 
200 
Table 
^9 
A 10 
C9 
CIO 
AA 5 
AA 6 
•1082* 
We see that these cross coefficients are, with a single exception, positive, but 
they are all very low. In Series AA alone are the values significant when com- 
pared with their probable errors. The higher values for the cross correlations in 
this series are due, without much doubt, to the higher direct correlation for the 
breadths, and the relatively high organic correlation between length and breadth 
which we have found in this series. The relation of the cross coefficients to the 
direct and organic correlation coefficients will be taken up later. 
With the coefficients of assortative pairing, both direct and cross, for the 
actually occurring conjugant pairs in hand we may attack directly the problem of 
the origin of the high direct correlations. The first question which arises is as to 
whether these correlations represent any true assortative pairing or merely arise 
because conjugation goes on within a limited, differentiated portion of the popula- 
tion, which portion, as has been shown above, is much less variable than the non- 
conjugant population. If the latter is the true explanation then clearly any 
random pairing of conjugants ought to give rise to coefficients of correlation 
equally high within the limits of the probable errors concerned. What then must 
be done is to make from the records pairs of conjugants chosen entirely at random, 
and then determine the degree of correlation for such pairs. This "random pairing" 
has been carried out in the case of the conjugants in the following way. Each 
individual conjugant's measurements were copied on to a small card or ticket, then 
these cards were shuffled together in a convenient receptacle, and drawn out 
blindly, two cards at a time. The two cards so drawn formed a "random" pair 
of conjugants, and by entering each such pair twice {vide supra p. 249) the 
symmetrical random tables were formed. For each series and pair of characters a 
number of these random tables were made. The length-length random corre- 
lations are the only ones which it is necessary to discuss here. Others have been 
This is the mean numerical value, without regard to the sign of the coefficients. 
