Page:American Anthropologist NS vol. 1.djvu/516

 BOAS] THE CEPHALIC INDEX 457

We call Trap 1—r3prp3 13p «etc, [ frp Tass oe pois pT aap tbe be i@ere. 2p Mea \ Tisp =P aay... pYasp bt 132.. 2. +. . +r ig-na. pM e-nsp (7) i !. ‘Prtpen p= Pras. .pPaw-op HL a32. op %3-1p Fes Flupens.. p

It will be seen that (7) is identical with (6) except insofar as to all the 7 representing correlations between two measurements, the element p has been added, and insofar as the number of equations and of unknown quantities has been decreased by one. We may, therefore, continue a series of successive substitutions which will always result in equations of the same form. The next substitution would be

_ 1) pT (p-nap - = ef onus sesese Facp-0p% (p-vap

The last substitution will give us

Tatas: + py PF ralas + + py 3alas + + PY

¥ 493). 9

T—rascas s+ prt a2as+ + py Thus the coefficients of correlation between p variables may be reduced to those between (pg — 1) variables.

The variability p of the array of x, which is correlated toa series of values for x9, +5

p? = Average of (*, — 9123... 2 — 9132 = Average of (x,7 +9133 .. 2? +9 tee ..

—~ 29193 .. 41 %2 — 29132...

+ 29123... 9132 .. %2%3+

By substituting the values of the types 7 and py? for the averages of the types xx and x? and for g its related 7, according to (5), we find

pra triks trie tee

—~ 27193. . Tis 27132. . Tis +2ries..%ise. Test .--)