MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 309 
Table of Arrays of Mares, which are Half-Sisters, 
Sire. 
No. of mares. 
Mean fertility. 
S.D. of array. 
Specnlam. 
76 
9-697 
2-989 
Sterling. 
52 
10-750 
2 545 
i Scottish Chief. 
67 
9-201 
3-176 
Newminster. 
64 
8-875 
2-497 
Parmesan. 
37 
9-708 
3-076 
Macaroni. 
81 
10-210 
2-770 
King Toni. 
53 
9-689 
2-748 
Lord Clifden. 
41 
9-878 
2-086 
! Hermit. 
79 
9-437 
3-003 
1 Blair Athol. 
87 
9-057 
2-752 
1 Lord Lyon. 
32 
9-125 
3-314 
The Duke. 
35 
9-186 
2-474 
Doncaster. 
37 
9-297 
3 021 
Adventurer. 
58 
10-466 
2-621 
Cathedral. 
43 
9-267 
2-847 
Rosicrucian. 
59 
10-932 
3-094 
Stock well. 
80 
9-131 
2-093 
Rataplan. 
40 
8-222 
2-201 
! Y. Melbourne. 
55 
9-064 
2-301 
. Thormanby. 
41 
9-951 
1-651 
' Totals. 
Mean. 
Ditto in actual units* . 
1117 
55-85 
191-143 
9-55715 
-6371 
53-259 
2-66295 
•1775 
I next took the mean and standard deviation of the 1117 mares to obtaiu o-q. 
The mean fecundity was now found to be 9'5685 and o-q = 2‘7824, or in actual units 
'6379 and ’1855. Clearly only about I- per cent, difference is made whether we 
take the mean fecundity of the 1117 mares, or the mean of the unweighted means 
of the twenty arrays. Knowing croand(To\/l — we can now find p. We have 
almost at once 
p = *2900. 
This is probably the first determination of a coefficient of inheritance between a 
latent character in one sex and a patent character in the other sex. We see that it 
has almost exactly the value required (’3) by the law of ancestral heredity, or we 
conclude, mares inherit from their sires a ^ecimdity governed closely hy the law of 
ancestral heredity. 
If the reader asks why is not the intensity reduced in this case in the same 
manner that we find it reduced in the case of the inheritance from the dam, the 
reply is ; 
(i.) In the case of the dam and mare, both quantities to be correlated are liable to 
fictitious values. In the case of sire and mare, we deal with only one. 
* A fecundity unit is taken to be 1/T5, for tliis is the unit of grouping. 
