30G 
PROFESSOR KARL PEARSON AND MR. LESLIE BRAMLEY-MOORE, 
The probable error of the correlation is '0213, and of the regression *0213. Thus 
these results are not significant in themselves, but they are exactly what we might 
expect on the above hypothesis. Taken with the other five tables which we have 
worked out for the inheritance of fecundity, they are significant, for every one of 
them gives a positive correlation, however small it be, and thus adds to the accu¬ 
mulated evidence that fecundity is a heritable character. 
(vi.) It remains to test our results by the theory developed onpj). 2G9 et. seq. But 
a difficulty comes in here. Turning to (xviii.) and (xix.) on p. 268, we cannot feel 
justified in putting Mi = IVB, for there is a secular difference in the fecundity of mares 
and dams, owing to the fecundity of the older brood-mares being based on a longer 
period and liable to the disturbing causes so markedly manifest in the correlation of 
mares and granddams (see my remarks, p. 305). If we combine (xviii.) and (xix.) 
we find 
M'h - Mb = r ^(M'd - MM. 
o-i 
Now r is small, and it will accordingly be legitimate to put M'l = M'j and cti = cr, 
on the right, we have then 
(M"^ - rM"0/(l - r) = 
From this we deduce for the results in (ii.) on p. 304 
Mb = -0321. 
Turning now to (xix.), it may be written 
M'b = I -f 
/o / 0 
i/o-i 
Mf Vl + 
The second term in the curled brackets is small, and in it we may put to a first 
approximation cr'i = o-^ = cto and Mj = Mb- We then have 
or. 
W\ = M'l X 1-0666. 
Substituting the value of M'b we find 
M'l = -6118. 
We thus see a difference in the fecundities of the unweio-hted dams and unweio-hted 
O C? 
mares of -6118 and -6321, or about 2 foals more in the hundred appear to survive in 
the later generation. This is very probably due to the causes already indicated as 
affecting the apparent fecundity of the older mares (see p. 298). The influence of 
