MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
95 
III.—Table of Bay Ranges. 
Relative Pair. 
Bay Range. 
Probable Error of Median. 
X. 
y■ 
U x o*. 
U' X (Ty . 
X. 
y■ 
Sire. 
Colt .... 
l'46943o* 
1-280190^ 
+ •0160 
+ -0183 
Sire. 
Filly .... 
1-64075 0 * 
1-361490^ 
+ •0159 
+ ■0192 
Dam. 
Colt .... 
L36645o* 
1-29819 o- y 
+ -0196 
± -0206 
Dam. 
Filly .... 
1-381650* 
1-24845 <r y 
±■0193 
±•0214 
Maternal grandsire . 
Colt .... 
l-69694o* 
1-192930^ 
+ •0158 
+ -0224 
Maternal grandsire . 
Filly .... 
l-65021o* 
1-26702 (Ty 
±•0162 
±•0211 
Colt. 
(Half 
Colt .... 
siblings) 
l"23953o* 
1-239530;, 
±•0153 
±•0153 
Colt. 
(Whole 
Colt .... 
siblings) 
l-27688o* 
1 -276880,, 
±•0148 
±•0148 
Filly ...... 
(Half 
Fiily . . 
siblings) 
l-39619o* 
1-396190,, 
±•0135 
±•0135 
Filly. 
(Whole 
Filly .... 
siblings) 
l-34684o* 
1-346840,, 
±•0140 
±•0140 
Filly. 
(Half 
Colt .... 
siblings) 
l-33479o* 
1-282290;, 
± -0202 
± -0208 
Filly. 
(Whole 
Colt .... 
siblings) 
1 "41501o* 
1-35207o„ 
±•0189 
±•0198 
To explain the last double column I note that Mr. Sheppard has shown (‘ Phil. 
Trans.,’ A, vol. 192, p. 134) that the probable error of the median equals 
•84535 cr/v/N. 
Hence in terms of the bay range we have 
probable error of median 
length of bay range 
■84535/(w v /N). 
I have found that this simple result gives a value close to but slightly larger than 
the probable error of the quantity g (p. 82), from which I have determined the 
position of the mean in the bay range. It is much easier to calculate, but of course 
not so exact, as we take no account of possible errors in the bay range itself or 
their correlation with errors in the median. I have accordingly tabulated its values 
in the last double column as a rough guide to the errors made in the numbers 
upon which the statements in the previous section depend. I shall return to the 
consideration of the probable errors below. Turning to columns 3 and 4 of our 
Table II., we can draw the following conclusions as to the variability of sex and 
class:— 
(a.) I he Younger Generation is more Variable than the Old. —Thus, foals are more 
variable than their sires, and, looking at the expressions in Table I II. for the bay range, 
