H. L. RiETZ 
109 
with the most remarkable records of ancestry would make the latter appear to be 
better producers than the former. In the case of dams and offspring under con- 
sideration, we have examined the back records of dams, so as to correlate the 
records when darns and corresponding offspring are most nearly equal in age. 
If M, a, V, and r represent mean, standard deviation, coefficient of variability, 
and coefficient of correlation respectively, the results are : 
M a V 
Offspring, 10-687 + 0-057, 2136 ± 0 040, 19-99 ± 0-38, 
Dams, 10-605 ± 0 057, 2-141 + 0-040, 2019 ± 0-38, ~ - 
(h) Offspring and dams over four years old at time of test (Table III.). If the 
dividing line between mature and immature cows is drawn at 4-75 years as appears 
desirable from Table I., too few variates for our purpose fall into the division of 
mature cows. By making the dividing line at four years, the numbers in the two 
groups are nearly ef]ual. In the above study of immature cows, the parent and 
corresponding offspring may differ in ages at the time of their respective tests by 
any amount less than one year ; and there is no reason why a small change in the 
dividing line should affect the point as to whether the heredity coefficient is the 
larger during growth or after maturity. 
For these reasons, we have, for the present purpose, classed cows above four 
years old as mature. The results are: 
M cx V 
Offspring, 15-316 + 0070, 2-543 + 0049, 16-60 + 0-33, _ 
Dams, 15-368 ± 0-070, 2-646 ± 0 051, 17-22 ± 0-34, ~" " ' 
(c) It may be noted that the group of cows under four years old yields 
a coefficient 0-344, while the group over four years old gives r = 0-284 ; but the 
value r = 0-344 is, as we shall show presently, much greater than the correlation 
for a group of parents and offspring of one age, say two or three years old. We 
have used a method of correspondence which much increases the coefficient for 
cows in the period of growth. For the purpose of establishing this point, we 
have first made a direct test based, to be sure, on only 219 pairs of variates 
(Table IV.). This table represents records when animals are under 2-25 years old 
at the time of their respective tests. This material gives 
r = 0-145 + 0-045. 
While the probable error is large, we shall in {d) present an argument to show 
that for offspring and dams two or three years old, it is highly probable that 
r 5 0-145. This will be shown by regarding the result r = 0-344 as arising from 
a combination of material of two sub-groups. 
{d) Combination of sub-groups of a population. To illustrate the combination 
of sub-groups, we first combine data from Tables II. and III. to form a table in 
which corresponding dams and offspring differ by less than one year in age at 
