J. A. Harris 461 
the squares of yields directly from Professor Wilson's table and enter the totals for 
each bull in Table XI. This gives 
r^ 2 = -126f076. 
The probable error is based on the actual number of daughters, n = 76, not the 
weighted number, 
fl[n(n-l)] = 538. 
Whether or not this slight correlation in yield (y) is statistically significant, the 
case illustrates a very convenient method of dealing with such problems. I hope 
to discuss the biological sides of the question in more detail elsewhere. 
TABLE XI. 
Milk Yield in Daughters of Various Bulls. 
Sire 
Number of 
Daughters 
Total Yield 
2(2/') 
(n-l>Z(yO 
2 (</'') 
(»- 1)2(2/ 2 ) 
Maxi 
11 
8900 
89000 
7310000 
73100000 
Stamfadern 
9 
8000 
64000 
7195000 
57560000 
Braendekilde Max 
4 
3800 
11400 
3625000 
10875000 
Vigfus 
6 
5900 
29500 
6090000 
30450000 
Osvald Ejersminde 
6 
5500 
27500 
5120000 
25600000 
Gunnar 
3 
2650 
5300 
2362500 
4725000 
Mazeppa II 
6 
6400 
32000 
6875000 
34375000 
Tordensjold 
5 
4650 
18600 
4372500 
17490000 
Trym 1 
7 
6500 
39000 
6165000 
36990000 
Taurus IV 
13 
11350 
136200 
10022500 
120270000 
Ambrosias III ... 
6 
5300 
26500 
4765000 
23825000 
76 
68950 
479000 
63902500 
435260000 
S[n(n- 1)] = 538, ,S [Total yield] 3 = 491477500. 
B. Gross Intra-Glass Relationships. 
If x and y be two measures on the same individual, and if correlation be 
determined between the individuals of the m sub-groups or classes constituting 
the general population, then as pointed out above, r XiXj , r y0s are direct intra-class 
correlations while r XlVi is a cross intra-class relationship. 
The number of combinations will in both direct and cross intra-class relation- 
ships be $[«(«,— 1)], since in the direct correlations one cannot correlate between 
a measure and itself and in the cross correlations one must not -include the 
relationship between the % and y of the same individual — the organic correla- 
tion, r xy . 
The value of this direct organic correlation is given by the moment coefficients 
S[t(x')]/S(n), S[t(x'->)]/S(n), 8&(y')]IS (n), S[$ (y")]/S(n), ...(x) 
Biometrika ix 59 
