472 MR ROBERT \VORTHINGTO^f. 



The author then proceeds to establish the general theorem, 

 that the constants of this equation — viz., the ' partial regression 

 coefficients ' Co, c, etc. — are those which alone yield the 

 minimum probable error. This theorem immediately finds 

 an important application. For it follows that the custom of 

 taking the average of the results obtained from the several 

 regression formulte for a number of organs, considered in- 

 dividually, is not theoretically so good a method as that of 

 considering the organs collectively and using the 'compound' 

 regression formula. 



The determination of the best value to be assigned to an 

 unknown organ in an individual when the values of n other 

 organs are known is thus dependent on a knowledge of the 

 regression coefficients for the race to which the individual 

 belongs. To ascertain these may perhaps be impossible, 

 especially in the case of extinct races whose remains are but 

 scant. The question therefore arises as to how far the 

 regression formuke for one race can be extended to a second. 

 This point is discussed by the author with reference to the 

 changes in regression coefficients brought about by selection 

 of particular organs. We may quote from his conclusions : 

 " thus we see that the extension of the stature regression 

 formulae for one local race — say, modern French — to other 

 races — say, palaeolithic man — must be made with very 

 great caution. The extension assumes (i.) that stature itself 

 has not been directly selected, however widely changed by 

 indirect selection ; (ii.) that the formulae involve all 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 formuke is whether or not they give for 

 another local race of which we know djJ'^'wri the stature, results 

 in agreement with themselves and with the known stature," 



The only data available for the calculation of the correlation 

 between stature and the long bones being Eollet's measure- 

 ments on one hundred corpses at Lyons (already used in the 

 memoir " On the Eelative Correlation of Civilised and Uncivilised 

 Eaces "), Professor Pearson is confined to these for the calcula- 

 tion of reconstruction formulae. The following cases of recon- 



