Ethel M. Elderton 
73 
the possibility that the inheritance of the type may not be from like finger to 
like finger alone, but that the type may be ti-ansferred to some other finger of the 
oflfspring. And it is fairly easy to demonstrate that there is an associaticjn not only 
between the types of like fingers in parent and child but also between the types of 
unlike fingers. In other words if a very rare type, say, occurs on the forefinger of 
the parent, it may more frequently appear on the same finger of the offspring, but 
should it appear on another finger of the offspring, we cannot pass it by and assume 
that its appearance is independent of heredity. Clearly we should not do so if Poly- 
dactyly occurred in the right hand of a parent, but in the left hand or even either foot 
of the offspring ! We must therefore suppose a correlation p^g between like fingers in 
parent and offspring and- another correlation p^^' between unlike fingers. Our treat- 
ment thus far would only be satisfactory provided pss' = 0. If this were true descent 
would be from like finger to like finger. If p.,.,- = ps.< descent would be indifferent as 
to finger. A priori we should anticipate that psg- would not be zero but < p^g, or there 
would be some bias in favour of the type being transferred to like finger. In col- 
lecting a large mass of material by voluntary help it was cleai'ly needful to reduce 
to the utmost the desiderata. But in the present case Galton's restriction of his 
data to the simplicity of forefinger prints has sadly limited the possibility of our 
determining the real strength of finger-print inheritance. Like all preliminary in- 
quiries, however, it has sufficed to indicate what we need at the next stage, namely 
complete sets of family finger-prints, and it is to the heavier task of such a collection 
that the Galton Laboratory is now addressing itself. The theory of the general 
inheritance of finger-prints may be attacked in the following manner. 
Let u be a variable which depends on 10 other variables a-',, x.,... x^^ (i-e. the 
finger-print types of the ten fingers) and u' be the like variable in a second 
individual. Now if we suppose the variability in type of each finger to be the 
same — which is only approximately true— and each finger to contribute equally 
to u, we can take as appropriate values : 
U = (i/'i + x.. + . . . -I- ^'lo), 
= TU + + . . . -I- .^''lo)- 
We will further suppose all our variates measured from their means. 
Then will be the correlation between the characters u and u' in the two 
individuals. 
Further if a denote a standard deviation : 
If rgs- be the mean value of = 4V (''.« ). we have 
supposing u and u are individuals in a stable population. 
= TTm W'x-, + 0-'^2 + • • • 
16 f 10 ]■ 
