A. Bahrington and K. Pearson 
445 
great-great-grandparents of the calves on these schedules, and (c) a special scries 
of matings taken from the early volumes of the Herdhook. Thus we have measures 
of the extent to which breeders now, 15 or 20 years ago, and perhaps 50 years 
ago, have mated like with like. The Tables each contain about 825 matings, and 
are given as Tables A, B, C of the Appendix. The general measure of the 
deviation from random mating was obtained by calculating the mean square con- 
tingency coefficient. The results were as follows : 
Table of Assortative Mating Coefficients. 
Recent Times : -2030 
15—20 Years ago : -1912 
50 Years ago: -1219 
It will thus be seen that the tendency of breeders to mate like with like has 
been very sensible for many years, and has now reached a value comparable with 
the unconscious assortative mating in the case of man*, or with that which breeders 
of fancy mice consciously or unconsciously produccf. This selective action ought 
to be taken into account when we endeavour to estimate the resemblance of parent 
to offspring. 
(8) On Direct Inheritance. Fird Degree. 
The usual four tables, sires and dams with bull and cow calves, were formed. 
These tables will be found as D, E, F, and G of the Appendix. They were worked 
out by mean square contingency, and, for the sake of comparison and control, also 
by mean contingency and by fourfold tables. In order to provide material, on which 
it might be possible to consider Mendelian formulae. Tables 11. and III. are 
provided, giving both sire and dam for over 1000 biUl and 1000 cow calves 
respectively. These tables have been already used in the previous section. They 
differ from the mating Table A, in that the same cow and bull are repeated 
not more than three times, while in the mating tables they are entered as often 
as they occur on the schedules. 
A word must be said here about the contingency method as applied to these 
tables. The coefficient of mean square contingency is an absolute measure of the 
dependence of the offspring upon the parents, as long as we stick to the five 
groups now dealt with, but it would most probably be increased in value if we 
subdivided these groups — for example, divided the reds and roans into light 
and dark reds and roans. It has been pointed out elsewhere that this sub- 
division, without we immensely increase the number of individuals dealt with, 
must be limited, or we shall obtain very large contributions to the contingency 
from isolated units, which cannot of course be subdivided. Experience in com- 
paring tables reduced by different methods seems to indicate that 25- to 49-fold 
contingency tables approach closely in average value to the results reached 
by 4-fold table methods:]:. It would have been a great advantage in the case 
* Biomclrika, Vol. iii. pp. 37;i and 487. t JJiumctrika, Vol. iii. p. 20. 
J Biometrika, Vol. in. p. 253. 
