CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
iZf) 
rule not just + of the value of the total regression coefficient c/. For example, if 
A 4 wei’e the radius and B stature, ci''' — 3'271, while C 4 is a negative quantity — *187. 
This process of taking means may accordingly screen some most important element, 
like the negative value of the partial regression coefficient of the ra,dius. Tkeoreticallu, 
therefore, as vrell as fiom the standpoint of discovery, the regression formula for n 
organs will give more valuable results than the mean of the results of the n regression 
formulse for the n organs. A practical modification of this principle will be referred 
to below (p. 178). 
(4.) The theory of regression will thus enable us to determine the best value to be 
assigned to an unknown organ, when the values of any other n organs are known, 
supposing the individual to ivhich these organs belong is a member of a race or group 
for ivhich the regression coefficients have been ascertained. 
On what principle, however, can we extend the regression formulse for one race to 
a second \ The regression coefficients depend upon two things, the variability of 
the organs under consideration and their correlation. Now the change in variability 
as we pass from one race to a second has never been questioned. It has been 
suggested that the correlations were I'acial characters, but the divergences in corre¬ 
lations between local races a,re far beyond the probable errors of the observations.* 
Mr. Filon and I have shown that every random selection from a race changes both 
variation and correlation.T have shown in a memoir not yet published that all 
natural and all artificial selection also changes these quantities. How then can we 
hope that a regression formula as applied from one local race to another will give 
accurate results ? Why should the statui’e formula obtained from measurements on 
modern Frenchmen apply to palreolithic man ? 
I think M. Manouvriee, somewhat lightly skips this difficulty in the following 
sentences :—“ Enfin les variations ethniques des proportions du corps seront dans le 
meme cas que les precedentes [les variations individuelles]. H y a des races macros- 
keles et des races microskeles, comme il y des individus de ces deux sortes, et les 
variations individuelles sont bien plus grandes que les variations ethniques les plus 
accusees. Or les coefficients moyens des os de grande longueur tendant a abaisser la 
faille et ceux des os de faible longueur tendant a Telever, il s’ensuit qu’il sera tenu 
compte dans une certaine mesure de la macroskelie des races comme de celle des 
individus dont les os seront absolument longs et de la microskelie des races comme 
de celle des individus ayant des os absolument courts.’’^; If we admit for the 
moment, which I sliould not be prepared to do generally,|| that the individual 
variations in a local race are greater than the “ethnic variations” or divergences 
between the means of local races, M. Manouvrier’s conclusion by no means follows. 
* See ‘Phil. TiVins,” A, vol. 187, pp. 2GG, 280, and ‘Roy. Soc. Proc.,’ vol. 61, p. 3t0. 
t “ On Random Selection,” see ‘ Pliil, Trans,’ A, vol. 191, p. 229, and ‘ Roy. Soc. Proc.,’ vol. 62, p. 173. 
4 Loc. cit., on my page 171. 
[| vSee the results as to the radius referred to on 2 ^. 176 below. 
