1)K. A. LEE AND PROFESSOR K. PEARSOX ON 
2')0 
Table XXII. 
Race. 
Mean product. 
Product of means. 
Etruscan $ . 
.3,046,886 
3,042,2.32 
Etruscan $ . 
2,746,817 
2,742,818 
German J'. 
3,282,-3.38 
3,280,662 
German $. 
2,860,213 
2,856,6.35 
.. 
2,881,137 
2,886,107 
Xaqada 2 . 
2,619,631 
2,642,039 
Aino $ . 
3,144,287 
3,129,8.31 
Aitio ?. 
2,797,032 
2,786.983 
Thebans $ . 
2,859,374 
2,849,705 
Theljans ?. 
2,589,815 
2,602,057 
Modern Egyptians $ . . 
2,801,990 
2,822,055 
i\Jodern Egyptians ? . . 
2,424,920 
2,468,440 
It will be found that whether w'e use the mean product or the product of the 
means will make only a few cubic centimetres difference in the estimate, something 
under the 1 })er cent., within which we cannot sip^pose our results to be correct. 
Hence for practical purposes we may content ourselves with using the product of the 
means, the determination of which is far less laborious. Our least square formukn 
have all been based on the product of the means. 
(14.) Third Fundamental Problem. To reconstruct from external measurements an 
organ not vieasurcdde on the liuing organism, i.e., the skull capacity from measure¬ 
ments on the living head. 
It has been shown Ijy Karl Pearson (‘ Phil. Trans.,’ A, vol. 192, p. 183) that if 
a' and y be two characters and ni, n, m', n four constants, then the correlation 
coellicient of nix -p n and ni y -f- n' is the same as that of x on y. The regression co¬ 
efficient wall be the same if m = m'. Now in the case of length, breadth, height, 
/, h, and h measured on the living Iiead we have differences from their values as 
measured on the skull depending on the thickness of the living tissues covering the 
skull. These tissues of course vary from individual to individual, but as the thickness 
of the tissues themselves are of the second order of small Cjuantities as compared Avith 
the length, breadth, and height of the skull, Ave may safely assume that their Amriations 
Avill be of the like order compared to those of /, h, and h. AAe shall thus obtain a 
A"ery fair a])proxiniation to the mgression coefficients connecting the skull capacity 
with head-length, breadth, and auricular height, by using those already found for the 
like quantities measured on the skull. Thus aa'c should haAm a formula (9) of the foi’in 
C - Go = a{l - I,) F ^{b - y -f y(A - Ao) .(A) 
Avhere bg, h^ are the mean lengtli, breadth, and auricular height of the liA'ing head, 
and Cg, a, (3, y constants to be determined fi'oni the measurefnent of skulls. 
Further, formula (9) takes the form 
C:^e{/-8,){h-K)(e-S3)-P>7.(B) 
