H. L. RiETZ 
111 
table material of two tables, in one of which offspring and dams are two (1'75 — 
2-25) and in the other three (2-75— 3-25) years old. Take r, ^ n^, then from (6), 
0-344 5r, + (l-r,)^^^-^^^^^ (7). 
?1" O"" 
Values of n^, n.,, n, vii, are obtained from the arrays of Table I., and we 
assign to o- a value 2"34< unfavourable to a small value of 7:,, This gives 
0-344 = r 1(1 ,. (983)(545) (2-36y- 
0 344>/, + (l n) ^^^28)= (2^34)^' 
v., ^ 0-145. 
When this estimate and the value 0-145 for the group of cows under 2-25 years 
old are compared with the value 0-284 for mature cows, it looks as if inheritance 
in the production of butter fat is much greater after maturity than in youth, but 
we avoid drawing conclusions until the corrections for selection are applied 
(see §8). 
(5) Gorrelatiou of Granddams and Offspring — mature Cows (Tables VI. 
and VII.). 
The requirements for entrance to the Advanced Register are stated in § 2. 
A cow may have more than one record, and that one is regarded as " most 
remarkable" which exceeds most the required production of the age at which she 
is entered. We shall take the most remarkable records in dealing with grand- 
dams, instead of the records when the members of a pair are most nearly equal 
in age at the time of their respective tests, since the laborious task of finding back 
records is unnecessary to determine the correlation, as I have found in treating 
dams and offspring for comparison with the methods previously used in this paper. 
Granddams have no official records in many cases where dams and offspring 
have such records, and there is difficulty in securing adequate numbers from our 
data for determining the correlation of granddams and offspring. To overcome 
this difficulty, we have, in order to determine correlation for mature cows, adopted a 
method of transmuting production of immature cows to mature cows. For this 
M 
purpose we multiply the production of any immature cow of age s by , where i/s 
is the mean production of cows of age indicated by the subscript. A good determi- 
M. . . 
nation of -jj is obtained from arrays of Table I. The means, standard deviations, 
and coefficient of correlation obtained from these transmuted values are comparable 
in an average way to the statistical constants obtained from mature cows. 
For the sake of numerical comparison, we have determined the correlation of 
dams and maternal granddams (Table V.) by transmuting to mature cows. The 
results are : 
M a 
Dams, 15-383 + 0-073, 2-377 + 0-052, ^ 
Maternal Granddams, 15-423 ± 0 077, 2-495 ± 0-055, ^ ^ ± " 
