176 
PROFESSOR KARL PEARSON, MATHEMATICAL 
The formulfe foi’ stature reconstruction, whether obtained with a consciousness of the 
theory of regiession, as in the present paper, or indirectly by taking the means of 
small groups, as by M. Manouveiee, are based upon averages, and involve the 
standard-deviations, the variabilities of distribution of each organ. Hence, the fact 
that individual variations may be greater than ethnic valuations does not touch the 
real point at issue, for the formulm depend on the proportions of macroskely and 
microskely in each race, and these undoubtedly change. The individual variation 
being greater than the ethnic, is not a valid argument for applying a formula, based 
on the observation of one local race straight away to a second. 
The validity of applying the formula for one local race to a second depends, I 
think, upon very different considerations. In the first place, the validity is not 
general. If we endeavoured to reconstruct the radius, for example, of Aino or 
Naqada races from the femur or tibia by a regression formula obtained from measure¬ 
ments on the French, the results would, we might a pi'iori expect, not be so 
satisfactory as for stature.'* 
The validity depends on our conceptions as to “local races.” While the problem 
of local races is dealt with at length in my memoir on artificial and natural selection, 
and 1 do not want to anticipate the results there stated, it is still needful to cite 
here a theorem reached in that memoir. When a sub-race is established bv the 
selection out of a primary race of a group having p organs distributed with given 
variabilities and given correlations about given means, we shall speak of its establish¬ 
ment as due to a direct selection of these p organs. But this direct selection is shown 
to alter also the sizes of all the remaining organs of the organism, the variabilities of 
all those organs, and the correlations among themselves of the non-directly selected as 
well as their correlations with the selected organs. We shall speak of this result as 
* Allowing, as in my page 193, for cartilage and shrinking, I find the following formulie from the 
French measurements for tlie reconstruction of radius in centimetres : 
R = 7-839 -h •367F, 
R = 5-715 + -508T. 
Aino race. 
Naqada race. 
Calculated. 
Observed. 
Calculated. 
Obsei’ved. 
Reconstruction of R from F 
Reconsti’uction of R from T 
22-799 
22-9.34 
22-913 
22-913 
24- 692 
25- 494 
25-697 
25-697 
In the case of the Ainos, the prediction is within -5 per cent, of the observed value. In the case of 
the Naqada I’ace, the prediction from the femur diffei’s by 1 ceuiim., or 4 per cent, fi-om its true value. An 
error of 6 to 7 centiins. in the prediction of stature of a local race uhich would correspond in 
magnitude is hardly likely to occur. The explanation is that the radius is a nuich differentiated hone. 
