456 MK ROBERT WORTHINGTOX, 



Pearson recently remarked in a letter to Nature^ " because in 

 biological investigation an exact A cannot be associated with 

 an exact B, and an exact C observed (as we can do in physics), 

 biology requires a much more refined logic, much more subtle 

 mathematics than the simplest branches, at any rate, of physical 

 inquiry do. There is nothing more full of pitfalls than 

 ' ordinary reasoning ' applied to problems of association. The 

 biologist observes that some A is associated with B, and that 

 some C is associated with B. But if he wishes to discover 

 whether the relation between A and C is causal, he will need 

 all the refinements of symbolic logic, a mathematical analysis, 

 which is analogous to the geometry of hyperspace, before he can 

 come to a definite logical couclusion on the possible relationship 

 of A and C. He may observe as much as he will, but he will 

 not find out whether the association is confirmable or non- 

 confirmable without this higher logic." 



The object of the present paper (the outcome of some stray notes 

 put together for a friend) is to give some account of that portion of 

 Professor Pearson's work which bears on osteology as a branch of 

 physical anthropology, in such a manner as shall be intelligible to 

 ' non-mathematical ' readers. In any attempt of this kind, it 

 would, I think, be impossible to describe more than the general 

 principles of the mathematical argument. I shall hope, how- 

 ever, to make the lines of the argument sufficiently intelligible 

 to enable the reader to understand what the results really are ; 

 and possibly to induce him to turn again to such papers as 

 " Eegression, Heredity, and Panmixia," or " On the Eeconstruc- 

 tion of the Stature of Prehistoric Paces," where the mathematics 

 had hitherto proved a stumbling-block. 



The chief work published by Professor Pearson and his col- 

 laborators, which has to do with bones, is, so far as I am aware, 

 to be found in the following memoirs : — 



Mathematical Contributions to theTheory of Evolution. " II. 

 Skew Variation in Homogeneous Material." By Karl Pearson. 

 Phil. Trans., vol. 186 A. 



Do. do. " III. Eegression, Heredity, and Panmixia." By 

 Karl Pearson. PJiil. Trans., vol. 187 A. 



Do. do. " On the Eelative Variation and Correlation in 



^ Nature, Jan. 17th. . - 



