H. L. RiETZ 
113 
Although the upper limit for immature cows is thus extended to five years, 
the data are too meagre to give reliable results in the determination of the corre- 
lation of granddams and granddaughters tested during the period of growth. 
However, the material is collected in Tables X. to XII. as it may be of interest in 
showing the poor records of the granddaughters of some fancy granddams, and 
the effect of these extreme variates on the correlation coefficient. These figures 
naturally lead to the question for the breeder as to whether the probability of pro- 
gress with a considerable number of good animals is not greater than with an 
equal investment in fancy animals. 
From Tables X. and XI., 
= 0'062 + 0-046, 
r„ = 0-005 + 0-02G. 
If we exclude the fancy paternal granddams at and above 22, 
r,, = 0-091 + 0-020. 
The variates excluded arise from only six paternal granddams ; this shows how 
adversely a few extreme paternal granddams may influence the correlation coeffi- 
cient when these ancestors are weighted with their offspring. On the question of 
the selection of sires, we have (Table XII.) 
r,, = 0-082 ± 0-048. 
(8) Corrections for Effects of Selection on the foregoing Results. 
The entrance requirements of the Advanced Register are stated in § 2. The 
material used in our study of heredity is subject to the form of double selection 
treated by Pearson*. To make the application, let s be the standard deviation of 
the group of cows which meets the requirements of admission to the Advanced 
Register, a the standard deviation of pure bred Holstein-Friesian cows from 
which those which meet the requirements are selected, Sj the standard deviation of 
dams which meet the requirements, the standard deviation of cows from which 
the selection is made. In our material, a cow may meet the requirements when 
her dam does not, or a dam may meet the requirements when her offspring do not 
meet them. We can enter a pair in the correlation table when and only when 
both variates meet the minimal requirements. 
Let = - , yu, = ^ , then the formula 
R = r , (1) 
VI - r- (1 - ^)}) VI - r^l - ii^-) 
gives the means of correcting the foregoing heredity coefficients for selection, 
where R is the correlation coefficient for the selected group, and r for the total 
group. 
* Biometrika, Vol. vi., pp. Ill, 11'2. 
Biometrika vii 15 
