312 
PROFESSOR KARL PEARSON AND MR. LESLIE BRAMLET-MOORE, 
three generations from the record is really more stringently selected than the sire 
with only two. We can now form cr and cr' by (xxviii.) and (xxix.), if we adopt 
suitable values of otq and o-'o, p, as we have seen, may with high probability be put 
equal to '3 (p. 309). o-q for groups of daughters, on p. 309, is given as ’1855, but since 
this certainly included a fair number of what are now aunts, it must be somewhat too 
low for (tV We can well put cr'o equal to the ‘1888 of the mares on p. 304. o-q for aunts 
cannot be as low as the standard-deviation of dams on that page, as man}^ of the 
aunts may never appear in the record as granddams,* i.e., they are less stringently 
selected. The mean of the two results for mares and dams may, perhaps, be taken 
as a close enough approximation for our present purpose, or o-q = T765. We then 
deduce 
^=•1739, ^'='1955. 
If we compare the results now found with those for sisters cited on pp. 308 and 309, 
we find :— 
“ Aunts.” 
“ Sisters.” 
“ Nieces.” 
M 
•6199 
•6371 
•6338 
<^a 
•0434 
"0544 
•0761 
1 
(T 
•1739 
•1855 
•1955 
The accordances and divergences are much what we might expect, except in the 
case of a-„. We should, d }}riori, have expected “sisters” to have approached 
nieces more nearly than aunts. The work has been gone carefully through, but I 
have not succeeded in finding any error. In the “ nieces,” of course, the weighting 
of an outlying fecundity-mean due to a sire with but few daughters, may still be 
large, if his sire have numerous daughters ; this cannot occur in the case of “ sisters,” 
as the weighting depends only on the number in the array. The like heavy 
weighting cannot usually occur in the case of “ aunts,” for they are, as a rule (owing 
to selection to the third generation) daughters of old and famous sires, with plent}' 
of material for basing averages upon. We do not get many “nieces” attached to 
“ aunts,” who are not daughters of famous sires. Such is probably the source of 
divergence in 0 -^ between nieces and sisters. 
Using formula (xxviii.), on p. 274, we find 
r = -0114, 
and for the regression coefficient '0123. 
This value is much below the '05 of the law of ancestral heredity, and below the 
reduced value ’02, which we might have expected to reach. Still, it again shows 
* Every dam appears as a granddam, otherwise the fecundity of the daughter could not have been 
found. 
