300 
PROFESSOR KARL PEARSON AND MR. LESLIE BRAMLEY-MOORE, 
were all fathered among themselves except in 49 cases. In other words, they were 
tlie sons or grandsons of only 49 sires. Of these 49 sires, there were 12 whose 
pedigree I could not trace,but they were very probably sons of sires already on my 
list or among the remaining 37, In the majority of cases they appeared only as 
the sire of one stallion. The remaining 37, whose pedigree I could trace, were 
descended at once or in very few generations from 9 sires.t Thus both from the 
standpoint of the mares and of the sires we are dealing with a closely in-bred 
stock, and this is one and probably a very important factor in the weakening of the 
fecundity correlation. 
Having regard to these difficulties, if we can succeed in showing that fecundity in 
thoroughbred racehorses is inherited, we can be fairly confident that we have 
onlj^ reached a lower limit of the correlation coefficient, 
(16.) On the Inheritance of Fecundity in the Female Line. 
(i.) A preliminary investigation must here be made, in order to determine the p of 
the formulm given in Proposition III. (p. 269) we want the correlation of fecundity 
with fertility. If be the fecundity, f the apparent fertility, and c the number of 
coverings, twins counting as a double covering, we have ; 
^ = fl^‘> 
whence if we determine the correlation between ^ and f numerous constants will 
follow. Table XI. gives the correlation between fertility and fecundity for 1000 
brood-mares. We found : 
= -6375, M, = 6-515, 
cr,|, = ’1810, cr, = 3*2775, 
p — 5152, 
= lOOo-^/M^ = 28-39, Vj = 100o-,/M, = 50*31, 
where and ly are the “ coefficients of variation.Here b}^ Yule’s Theorem § 
r^j-cr^lo-f is the slope of the line which most closely fits the curve of regression for 
fecundity on fertility. If we supposed this curve to be straight, then the line must 
coincide with it. Now since fecundity vanishes with fertility, the curve passes 
through the origin, and hence, if the regression be linear, tlie line must also pass 
througli the origin. In this case, as is shown on p. 270, = vfv = *5644. The 
difiereiice between *5644 and *5152 may be taken, as it is several times the probable 
error, to indicate that the regression curve between fecundity and fertility is only 
approximately linear. 
The variations in both fertility and fecundity are here large. Accordingly we 
* Stockmar, Sovereign, Andover, Phaeton, Prince Caradoc, Robert Houdin, Pjlades, King of Kent, 
Clarrj- Owen, Calabau, Homily and Taurus. 
t Tramp, Sir Peter Tea/de, Cattoii, Buzzard, Orville, Dionied, Sorcerer, Dr. Syntax, Marske. 
X ‘ Phil. Trans.,’ A, vol. 187, p. 276. 
§ 'Roy. Soc. Proc.,’ vol. 60, p. 477. 
