PROFESSOR KARL PEARSOK AND MR. LESLIE BRAMLEY-MOORE, 
9()9 
W l/ W 
mares in the third quadrant/''' he., of mares and dams of large fertility, the frequency 
is cut off abruptly in this quadrant. The reason for this is fairly clear. We have 
dealt with a limited number of years, about 30, of horse-breeding ; hence, when the 
dam has a long record, her later offspring at any rate cannot possibly have a long- 
one ; when she has a short one, it is possible for them to have a long one. Accord- 
ingly, there has been a process of unconscious selection, which has led to a negative 
correlation of the apparent fertilities. 
To illustrate the point further, two more correlation coefficients were obtained. In 
Table X, are given the apparent fertilities of mares and their dams with a minimum 
of eight coverings. We find : 
M,,--8-6191, M„, = 7-6309, 
= 3-1656, a-,, = 2-8149, 
= “ -0876. 
The probable error is again about -0202. While the mares now form a group with 
their mean fertility almost equal to that of the dams in the previous result, their 
variability is markedly less. Relatively to the dams its reduction is even greater. 
The correlation is sensibly the same. It would thus seem that the anomalous 
selection of mares wdiich thus reduces their variability so markedly below that of 
the dams is not in the low fertilities, 
I now removed from the Table IX. all parts of it concerning mares wfith a fertility 
greater than 8 ; 867 mares and dams remained with a minimum limit of four 
coverings, the mares not having a greater fertility than 8 oft'spring. I found : 
M,, = 7-7636, M,,, = 4-8558, 
o-,; = 3-3983, cr„, = i-9887, 
r = — -0190. 
The probable error of r = -0229. Now the line of regression for dams on mares 
uuoht to be the same, whether we obtain it from this result or from the first results 
in which mares with more than 8 oftspring are included. Yet, in this case, there is 
no sensible correlation at all. In other words, if we exclude the data for large 
fertilities, we should have to conclude that there was no correlation between the 
apparent fertilities recorded for mares and their dams. We are thus forced to conclude 
that apparent fertility is a character depending on the manner in which the record 
is formed, and must be useless for the investigation of inheritance. This investi¬ 
gation strengthens rny d priori reasons for selecting fecundity, not apparent fertility, 
as the character to be investigated. I took the fecundity of a brood-mare to be the 
numl)er of her living ofispring divided by the potential number of her oftspring 
under the given circumstances. Of both numerator and denominator of this ratio 
I must say a few words. 
* Tlie ]jortion of the table cut off by vertical and horizontal Hues through the means of dams and mares. 
