MATHEMATICAL CONTEIBUTIOHS TO THE THEORY OF EVOLUTION. 
291 
sort and rearrange bis data cards in a variety of ways, but to prepare new cards on 
a different system is practically beyond his jDOwers. 
These remarks are made in order to meet criticism of the method in which my 
data cards were prepared. I could now possibly extract more convenient data, but 
that is only because of the knowledge gained in the process of examining the 
fecundity of several thousand horses. I did not even know, ah initio, the extent of 
variability in equine fertility; I did not even know the immense preponderance 
which would have to be given to certain sires, at any rate I had no numerical 
estimate of it. Nor had I any percentage of the number of cases in which a 
pedigree might end abruptly with an alternative sire."'^ 
I saw at once that the apparent fertility of racehorses was even less close to their 
potential fertility (which I presume to be the inherited character) than in the case 
of man. Mares go at different ages to the stud, they remain—for reasons not 
stated—uncovered for occasional years, or periods of years ; they return to the 
training stable for a time ; they are sold abroad ; they are converted into hunters, 
put into harness, or, as is occasionally recorded, sold to cab proprietors. This by no 
means invariably denotes that their fertility is exhausted ; their offspring may be 
bad racers, or their stock unfashionable. Yery frequently also we find the mare put 
to a cart-horse stallion for a year, a few years, or for the remainder of her career, 
and then no record at all is given of the result. Thus the total fertility recorded 
can have but small correlation with the potential fertility, and I was compelled to 
deal with fecundity. The insufficiency of the apparent fertilities, as recorded in my 
mare index, to solve the problem, may be illustrated in the following manner : 
1100 cases of the apparent fertilities of mares and dams having had at least four 
coverings were tabulated (Table IX.). The following results were calculated from 
this table, the subscript in referring to mare and d to dam :— 
M, 
rr.i 
The probable error of = ’0202, and thus we might argue that a fertile dam 
has, on the average, infertile offspring. But an examination of the above numbers 
shows us that the dams are more variable than the mares,t and yet the dams have 
been theoretically subjected to the greater selection, for they must all be granddams, 
or the fertility of the mares could not have been recorded. We are forced to 
conclude that the mares have been in some manner selected, and the foim of the 
selection is fairly obvious on examining the table. There ajjpears a great defect of 
'* Even tlie pedigree of snch a famous racehorse as Gladiateur is soon checked by the uccuirence of 
alternative sires. His sii’O, Mouarque, was the sou of either The Harou, or Sting, or the Emperor, 
t The vai’iahilily of mares, as a whole, not separated into mares and dams, is (see Art. 19) d'277o. 
2 P 2 
= 7'G655, 
M„ = GT391, 
= 3-3G52, 
(T,„ = 3-1G17, 
•0868. 
