258 A Biometrical Study of Conjnr/atioii i)i Paramecium 
in conjugant pairs means that the differences between corresponding characters 
in the two members of such pairs must be relatively small. It will be of interest 
to examine the difference distributions for the character length in actually con- 
jugated pairs, and in random pairs of non-conjugants and conjugants. The 
difference distributions which follow wei-e made by finding the absolute difference 
(in microns) between the lengths of the two members of a pair, taking the 
differences as always positive, and forming distributions of their frequencies. The 
unit of grouping adopted was in the case of the conjugated pairs and random 
pairs of conjugants 2 microns, and in the case of the random pairs of non- 
conjugants, 4 microns. These difference distributions are shown in Table XVIII. 
It is at once evident from these frequency distributions that the differences in 
length between the members of pairs are absolutely very much less in the case 
of the conjugated pairs than in random pairs of either conjugants or non-con- 
jugants, and also they show less "scatter" about the mean. The great divergence 
between conjugated and random pairs will perhaps not at first sight be evident 
to one unaccustomed to working with frequency distributions, because of the 
difference of the units of grouping used. If we plot these distributions, however, 
as has been done for Series C in Diagram IX., in such a way that the areas and 
base units of conjugant and non-conjugant polygons are the same, the facts are at 
once obvious. 
It is seen that in over 60 per cent, of the conjugated pairs the two members 
differ in length by less than 8 microns, while in more than 60 per cent, of the 
random pairs of conjugants, and in more than 75 per cent, of the random pairs 
of non-conjugants the difference is 8 microns or more. A more precise comparison 
of the groups may be made from the constants of the frequenc}^ distributions 
which are exhibited in Table XIX. 
TABLE XIX. 
Variation Constants for Difference Distributions. 
Series and Groups 
Mean 
Standard 
Deviation* 
Coefficient of 
Variation 
Series A. Conjugated Pairs 
„ A. Conjugants (Random) 
„ A. Non-Conjugants (Random) 
„ C. Conjugated Pairs 
„ C. Conjugants (Random) 
„ C. Non-Conjugants (Random) 
8-943+ -435 
14- 143+ -631 
17-619+ -785 
7-931 ± -448 
15- 673+ -758 
21-010+1-003 
6-610+ -308 
9-593+ -446 
11-924+ -555 
6-681 + -317 
11-297+ -536 
14-939+ -709 
73-914 + 4-978 
67-830 + 4-376 
67 -676 + 4-.359 
84-245 + 6-219 
72-079 + 4-885 
71-105 + 4-785 
We see that the mean difference in the case of the random pairs is very much 
greater than in the case of the conjugated pairs. Also the random pairs give 
a much higher absolute variability. The coefficients of variation are large because 
* In calculating the standard deviations for the distributions, Sheppard's correction was not used, 
because we have no approach to high contact at the lower end of the range. 
