450 On the Inheritance of Coat-Colour in Cattle 
larger number than this of pedigree great-grandparental relations *, we have 
simply classified into great-grandparents and (i) male, (ii) female descendants, with 
0, 1, 2, and 3 changes of sex. This required the preparation of 8 instead of the 
full 16 tables. If we write the pedigree in the following manner: 
8(^=9? 10(^=11? 12(?=13? 14(^=15$ 
4(? = 5? 6c? = 7? 
L ^ 1 L ^ 1 
2<? = 3? 
I I 
I ^ , J 
0$ 1? 
then : 
8 with 0 I 
;ave Table 
P of 
great-grandsire and $ offspring, 
no sex change 
15 with 1 
Q 
,, gran dam and $ 
55 55 
8, 12, 14 with 1 
K 
„ grandsire and 
one „ 
9, 11, 15 with 0 
JJ 
S 
,, gran dam and ^ 
)) 
55 51 
10, 12, 14 with 0 
)1 
T 
„ grandsire and ^ 
55 
two changes 
9, 11, 13 with 1 
51 
U 
„ grandam and 9 
55 
55 5) 
10 with 1 
)5 
V 
,, grandsire and $ 
55 
three „ 
13 with 0 
?1 
W 
,, grandam and (J 
55 
51 11 
The results obtained, still by the method of mean square contingency, are given 
in the table below : 
TABLE VI. 
Great- Grandparental Inheritance in Shorthorns. 
Sex change 
Resemblance 
Great-Grandsires and ^ Offspring ... 
0 
■20 
11 51 11 55 
2 
•12 
)5 51 ? 55 
1 
■18 
)) 51 51 51 
3 
■17 
Great-Grandams and ^ Offspring ... 
1 
•15 
11 55 51 . 15 
3 
■15 
51 11 9 15 
0 
•26 
51 11 55 51 
2 
•12 
Mean =-17 
These results are irregular, and not very conclusive ; probably large enough 
numbers were not taken in several of the cases, but the tabulation of great-grand- 
parents in large numbers is by no means an easy task, as in a pedigree stock high 
ancestors tend to be repeated many times. But in both grandsires and grandams, 
if we do not club together J' and $ offspring we find that no change of sex is 
* The process throughout has been the same in all the ancestral tables ; the produce is taken once 
only, and the same ancestor occurs on an average not more than three times, although individuals occur 
much more frequently, because as we go back there is much repeated blood owing to the fashion in 
bulls, and it would be almost impossible labour to reach 1000 independent great-great-grandsires. This 
method was adopted to avoid overweighting the tables with any particular individuals. The same 
principle was also used in the horse tables. 
