40 Mr. E. C. Snow. Correlations between Collaterals [June 3, 
uncle than to his uncle’s son. This point is illustrated in the present paper 
from the investigation of the collateral correlations of a simple Mendelian 
population mating at random because that determinantal theory is much in 
vogue to-day. It will’be used here to indicate that the facts reached by 
observation as to the degrees of resemblance between an individual and his 
ascendants and collaterals, and considered by some to be paradoxical, are 
curiously enough legitimate developments of Mendelian theory. If they are 
paradoxes of biometric observations, they are also paradoxes of Mendelian 
theory, and highly probably of other determinantal hypotheses which may 
hereafter be developed. 
(5) The three first degrees of collateral relationship are worked out in 
the following paragraphs, viz. :— 
(A) The correlation of siblings, 2.¢. of brethren regardless of sex. 
(B) The correlation of uncles and aunts with nephews and nieces.* 
(C) The correlation of cousins regardless of sex. 
The algebra presents no special difficulties beyond laboriousness. 
(6) Starting with the population of the form 
p? (AA) + 2pq (Aa)+¢ (aa), 
after 16sf random matings of pairs of individuals of each class, the types of 
families produced will be those given in the square brackets in Table I. The 
frequencies of the families will be the factors which multiply the expressions 
within the brackets. Thus, for example, the mating of the p? individuals 
possessing the protogenic constituent (AA) with the 2pq possessing the 
hybrid (Aa) gives rise to 2p%q families, in each of which 8s individuals 
have the protogenic constituent (AA) and 8s the hybrid constituent (Aq). 
* The word “siblings” has been reintroduced and largely accepted as a convenient 
term for brethren of both sexes, but no like terms are in use to denote uncle or aunt and 
nephew or niece regardless of sex. Prof. Pearson has suggested eldersib for uncle or 
aunt and sebmag for nephew or niece as convenient Anglo-Saxon names. 
t The number of matings is taken of the form 16s in order to ‘prevent fractions 
occurring later on in the paper. See Table IV. 
