178 
PEOFESSOR KARL PEARSON, MATHEMATICAL 
direcbly selected, however widely changed by indirect selection, (ii.) that the formulge 
involve cdl the directly selected organs closely correlated with stature, or that the 
selection has been principally one of size, and not of variability of, or correlation 
between, these organs. The real test of the applicability of the formulae is whether 
or not they give for another local race of which we know d priori the stature, results 
in agreement with themselves and with the known stature. I take it that the justi¬ 
fication required for applying our formulae to palaeolithic man is not the statement that 
ethnic are less than individual iutra-racial variations, but is to be drawn from the 
fact that our formulae, based upon measurements on the French, give results very fairly 
consistent among themselves aud with observaition for such a divergent race as the 
Aino. Such results seem to indlcaite that racial differences in stature are not the 
result of direct selection of stature, and that the selection of the long bones has been 
rathei’ a selection of their absolute and relative sizes than a selection, in the first 
place, of their degrees of variation and correlation, although these ha.ve to some extent 
undoubtedly changed. 
tion has taken place. Suppose there has been a selection of femur and tibia, but not 
of humerus and radius. Then the regression formulre for statui'e'on femur and tibia, 
and for stature on femur and tibia together with one or both of the other two, humerus 
and radius, ought to give identical results ; but these results ought to differ from 
those given by the furmulee for stature on humerus or on radius, or on both together. 
Practically, however, we have in many cases so few bones to obtain our meaus from (and 
these bones themselves parts of different skeletons), that the probable errors of these 
means quite obscure the deviations in stature as obtained from vmrious formulae and due 
to the influence of selection. From this standpoint a partial practical justification can be 
found for taking the mean of the divergent reconstructions of stature given by a series 
of regression formulae, at any rate for the case when the divergences are not very large. 
These divergences maiy be due to errors in the mean lengths of the long; bones, or 
to selection directly of one or more of the long bones, or even to some small direct 
selection of stature. But as in our ignorance of these sources of errors we can onh^ 
suppose some positive and some negative, the mean of all the formulae ma,y to some 
extent eliminate these quite unknown and unascertaiiicible divergences (see p. 175). 
Generally, however, I should expect the stature in which two or more formulae agree, 
to be more probable than the mean of several divergent formulae. 
(5.) On the Data availahle for Stature Regression Formulw .—The only data avail¬ 
able for the cadculation of the correlation between stature and long bones occur in the 
measurements made by Dr. Rollet on 100 corpses in the dissecting room at Lyons.'"'" 
This material has already been made use of by Miss Alice Lee and mj'self in our 
memoir, “ On the Relative Correlation of Civilised and Uncivilised Races,”t so that 
‘ ,De la Mensuration des Os Longs des Membres,’ par Dr. Etienne Rollet, Lyons, 1889. 
t ‘ Roy. Soc. Proc.,’ toI. 61, p. 343 
