120 
Miscellanea 
X. Inheritance of the Sex-Ratio in the Thoroughbred Racehorse. 
By DAVID HERON, M.A. 
Mr Cobb in his note in the Miscellanea of this number has defined the sex-ratio of an in- 
dividual as the vakie which the ratio of male to total births tends to assume when his fraternity 
becomes indefinitely large. 
It is suggested that the variability, o-q, actually observed in the sex-ratio as calculated 
in the ordinary way, arises in part from the variability in what he calls the true sex-ratio, o-^, 
and in part from the error due to considering small families, s^^~^ > further that the true 
correlation between the sex-ratios of parent and offspring can be found by multiplying that 
obtained from considering the actual families by a factor {a-J^-'r ■pqln)l<T^. 
It has already been shewn that a-^ is zero, within the limits of probable error, in the case of 
man. We can however test the reality of this factor directly by two methods. We can compare 
the correlation found by considering any group of families with that found after rejecting the 
smaller families, or we can compare the correlation found by considering large completed 
families with that found from sex-ratios defined by, say, the first four members of these families. 
In each case, the larger families ought to give higher correlation. The results of the first 
test have already been given in Prof. Pearson's note. To apply the second test, 1000 mares 
were taken at random from The General Stud Book, and the sex-ratio of their produce and 
that of their dam calculated. Only those cases were considered where each mare had at least 
eight foals, and as only second and subsequent editions of the Stud Book were used, the sex-ratio 
in each case was based on a completed family. From the same families sex-ratios were also 
calculated from the first four members. Tables I and II give the actual correlation tables 
TABLE I. 
Correlation of Sex-Ratios of Mother and Daughter Mares Produce: Completed 
Families. Thoroughbred Horses from The General Stud Book. 
Sex-Ratios of Daughters' Produce. 
1 
1 
1 
i 
1 
• 
1 
1 
?^ 
1 
1 
95 
1 
0 
<p 
1 
Totals 
'-■^ 
0 
-p 
•00— -05 
■05— -15 
3 
4 
2 
1-5 
-5 
11 
■15— -25 
1 
3 
6 
9 
16-5 
7-5 
4 
2 
49 
■25— -35 
1 
2 
7-5 
14-5 
33 
28-5 
24-5 
20 
7 
2 
140 
■85— -45 
1 
10-5 
28-5 
56 
60 
56 
29-5 
14-5 
2 
2 
260 
•45— ^55 
2 
13 
33 
58 
76-5 
68-5 
20-5 
16-5 
3 
291 
■55— ■65 
1 
11 
14 
34 
45 
31 
20 
8 
1 
165 
•65— ^75 
2-5 
8 
10 
23 
12-5 
6-5 
4-5 
67 
■75— ^85 
1 
1-5 
2 
6 
4-5 
1 
16 
•85— •95 
1 
1 
•95—1 -00 
Totals 
7 
48-5 
105-5 
205 
259-5 
207-5 
103 
53 
8 
2 
1000 
o 
C 
03 
O 
Pi 
>i 
