418 Prof. Karl Pearson. 



3. The first stage in advance was taken when Rollet published his 

 measurements made in the Anatomical Theatre at Lyons, of the 

 stature and long bones of 100 corpses. Rollet's attempt to establish 

 ratios on the basis of his measurements is not very satisfactory, but 

 to him belongs the credit of having first provided a respectable, if not 

 large amount of data. Rollet's work was followed by a very able 

 memoir on the reconstruction of stature by Manouvrier. Rejecting 

 about one half Rollet's data, he constructed tables giving the average 

 stature for certain ranges of each of the six long bones, and farther 

 what he terms coefficients moyens ultimes, for ascertaining the stature 

 corresponding to long bones lying outside the limits of his tableau 

 bareme. There are many traces in Manouvrier's paper of the old view 

 of a " coefficient " by which the long bone must be multiplied in order 

 to obtain the stature. Beyond this view, it cannot be said to contain 

 any theory, and it suffers from certain marked defects. In the 

 first place, proper allowance does not seem to be made for cartilage 

 and the disappearance of animal matter from the bones. The 2 mm. 

 allowed on each bone appear by no means sufficient. In the second 

 place, Manouvrier does not seem to. me to justify his extension of 

 results obtained from the French to very divergent races. He merely 

 remarks that individ ual variations are greater than ethnic. Even if this- 

 extension be made, it must be done with hesitation, and with a full 

 recognition of the assumptions made. Lastly, we may note that the 

 statures obtained from the different long bones by Manouvrier's table 

 for particular races, are often rather widely divergent among them- 

 selves, and no attempt is made to account for this divergence. 



4. Manouvrier's memoir was rapidly followed by an excellent piece 

 of work from Rahon, who collected measurements of the long bones of 

 a very wide series of local races of man, and reconstructed their 

 stature by aid of Manouvrier's tables. This memoir will remain of 

 first-class importance even if better reconstruction formulae than those 

 of Manouvrier are adopted. Manouvrier's tables have been used in 

 recent German memoirs, as those of Kitsch e and Kollmann on the 

 skeletons of the Row Graves and of the Schweizersbild. They are 

 accepted at present as the standard tables for the reconstruction 

 of stature. 



5. The present memoir starts with the theory of probability, which 

 the author has already applied to other problems in evolution,, 

 and deduces the most probable stature for any combination of the four 

 long bones. It is shown that for a population with normal correlation,, 

 the relation between stature and one or more long bones is always 

 linear. A general theorem is proved to show that no linear function 

 of the long bones can give the probable stature with so small 

 a probable error as the regression formula of the theory of probability. 

 From this result the following conclusions are obtained : 



