454 AMERICAN ANTHROPOLOGIST [n. s., i, 1899
��I Supposing two types which have the measurements l l$ / 2 , . . •
j 4, and X lf A 9 , . . . A,,, respectively, inhabit the same area, so
1
i that it is impossible to determine to what type each individual
1 belongs. If the component types are not known, we should find
for the whole series the averages L lt L 8 , . . . Ln with the varia- bilities Mj, M a . . . M 8 , and the coefficient of correlation calculated according to the method given above would be
If we divide this sum into two groups, the one embracing all the individuals of one type, the other those of the other type, we may substitute for the former
Lj -+- Xj = l x -f~ «*i» X t = /, L, -f~ x \
L n ~T~ **-n = 'n I «*n » «&n == 'n L n -f~ # n
for the latter
Lj + X t = A t + £j X, = Aj — I M + £, L n + X n = A n -f- S n X n = A n — L n + S a
R _ 2{x x +l x — L 1 )(x, + / ,— L B ) , 2 (g, + A , — L,) (£, + *»» — U ) nMjMn «M X M„
— ■?5j5 n __i ?Jil n _ 1 ** (A — I'i )(4i — L n ) -f ;/ t (A t — I n ) ( A. n — L„ )
"«M 1 M n +»M 1 M„+ »M,Mn
and by substituting the values of r lt r n and of
��L =
��n
��p _ n x n x n n nt ^j'Hn' , »i « g (/i — A t ) (/ n — A n )
K " r i»M,"M„T rn «MiM n "•" » ! M,M«
Supposing that in the component elements of the series r x and r n , ft t and /*/, /* and /*„' are equal, we have
p __ ^1 //n l *> " » (/ l "" Al)^n — A n )
K — r M,M,+ """»!« M, M n
It will be noticed that whenever the second term of this sum
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