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PROFESSOR KARL PEARSOK AKD MR. LESLIE BRAMLEY-MOORE, 
deviation in the fecundity is, however, about *191, or about 19 foals in the 63, or 
about 30 per cent.—a. very great variation, so that if fecundity lie inherited, a 
ditferential death-rate of the immature will hardly suffice to check it. 
So much then of the numerator of my ratio. I have spoken immediately above of 
the denominator as if it were the number of times the mare had been covered. 
It is generally this, but in the relatively few cases where the mare has given birth 
to twins, I liave counted that coverino’ ttcice. Had this not been done the fecunditv 
might have been greater than unity, for example even in some exceptional cases 
have risen to two. On the other hand, a loss t)f twins Avould have, been marked by 
no greater change in fecundity than a loss of one foal, or the survival of one twin 
would not have been different in its effect on fecunditv to the birth of a foal. In 
order, therefore, to avoid these difficulties—especially that of isolated individuals 
lying far beyond the fecundity range of 0 to 1—when twins were born the poten¬ 
tiality of the covering was reckoned in the denominator as two. The relative 
infrequency of twins causes, however, this modification of the denominator to havm 
small influence on the result. 
My next step was to form some estimate of the extent to which fecundity thus 
measured was the same for diflerent periods in a mare’s breeding career. I expected 
fecundity to diminish with age as in the case of mankind, but taking out a fair!}' 
large test number of mares, I found that their fecundity for the periods covered by 
two succe.ssive stud-books was in the majority of cases closely the same. With larger 
experience 1 should now lay more weight on the decrease of fecundity with age; and 
I also think fecundity is smaller when the mare first goes to the stud. But even 
thus much of the reduced fecundity of old mares seems to arise from breeders sending 
famous mares to the sire long after their breeding days are passed. I have several 
records of old mares being covered seven or eight times without oflspring. This 
custom of breeders was much more rife in the early days of breeding than it appears 
to be now, when some breeders discard or sell a fairly old mare, even if she is barren 
two or thiee successive years. Clearly the custom gives the mare a fictitious 
fecundity, far below her real value, and probably accounts for granddams having a 
somewhat less fecundity than their granddaughters. 
The next problem to be answered \vas the effect the method of forming my 
fecundity ratios might have on the relative numbers which would be found in 
diflerent element-groups. For example, supposing the element of fecundity to be 
1/10, or the element-groups 0-1/20, 1/20-3/20, 3/20-5/20, . . . 17/20-19/20, 19/20-1, 
would the fact that the fecundity ratio is a ratio of tvhole numbers cause, d a 
greater probability of frequency in one of these element-groups than another ? 
’fo begin with, all estliiiation of fecundity based on less than four coverings was 
discarded. Three coverings give too rough an appreciation of a mare’s fecundity, it 
can only fall into one of the values 0, 1/3, 2/3, and 1. The question then arises, if 
all the fecundities : 
