310 
PROFESSOR KARL PEARSOK AKD MR. LESLIE BRAMLEY-MOORE, 
(ii.) The influence of fictitious values has been shown on pp. 276-277 to chiefly 
affect the coefficient of correlation and not the standard deviation. 
Now the present result is based solely on the calculation of standard deviations, 
or on the variability of fecundity as a whole and in arrays. It is accordingly not 
influenced to nearly the same extent by the existence of fictitious values. Could we 
calculate the variability of the arrays of daughters due to individual mares, we 
should probably get a better result for inheritance in the female line.* 
The above result is so satisfactory that I have little doubt that we have deter¬ 
mined a very good value for ctov/ 1 — p^. Substituting it we find for the correlation 
between half-sisters : 
•66552 
7'09130 + -66552 
•0858. 
The law of ancestral heredity gi\ms for half-sisters r = ‘2, and f of this = ’08. 
Thus we see that the collateral heredity between half-sisters, daughters of the 
same sire, is quite sensible, and is almost what we might have predicted would be 
the result, if we supposed correlation to be weakened, as in the previous cases, to 
f of its value by fictitious records. 
It is worth while to consider the amount of fictitious fecundity suggested by 
the reduction factor f. We have only to suppose the n^/N of our p. 277 to be f. 
Now we may well assume the chance of a fictitious fecundity being recorded to be 
the same for either one of a pair of sisters ; hence we shall have p — <2, a^nd therefore, 
from the result on p. 276, we find {p — = f. This gives us (y) — l)_p = \/’4, 
and (?q + the fraction without fictitious values = (p — t)/p = '6325. Thus 
in order to introduce the reduction factor of f by the occurrence of fictitious values 
of the fecundity, we should have to suppose about 37 per cent, of fictitious values to 
occur. This is, of course, a sort of average ; many values will probably be only 
partially fctitious, i.e., will to some extent approximate to their real values. 
Considering the very artificial character of the thoroughbred brood-mare, and the 
uncertainty of her treatment by breeders, this does not seem such an immense 
percentage that it would force us to the conclusion that the law of ancestral heredity 
cannot be true for the inheritance of fecundity. 
(ii.) To find the Correlation in Fecundity hetween the Sisters of a Sire and his 
Daughters. 
What we want is really the correlation between aunts and nieces, but they 
^ The standard deviations for the arrays of mares in Table XII. Avere indeed -worked out for the 
twelve cases of dams from e to q. The mean of these cases was sensibly the same Avhether the simple 
mean, or the mean weighted Avith the numbers in the array was taken, and equalled 2'8091 or ‘1823. This 
is 0-^(1 — rb't But by p. 48, ctq = '1888, Avheuce Ave deduce r — T375, and the regression equals •1581. 
Thus Ave liaA'e found a substantially larger value for r than that on p. 304 by dealing Avith variabilities, 
and not direct correlations. This gives additional evidence, if any Avere needed, of the inheritance of 
fecundity. 
