Mathematical Contributions to the Theory of Evolution. 413 



" Mathematical Contributions to the Theory of Evolution. 

 On the Inheritance of the Cephalic Index." By Miss 

 Cicely D. Fawcett, B.Sc, and Karl Pearson, M.A., F.R.S., 

 University College, London. Received January 27, — Read 

 February 17, 1898. 



(1) The cephalic index, when used to test any theory of heredity, 

 possesses many merits, and at the same time one or two defects. 

 In the first place it is supposed to be a marked racial character, and 

 therefore might be considered to be strongly inherited. In the next 

 place it remains sensibly constant after two years of age; thus the 

 strength of inheritance can be ascertained by measurements on 

 young children, whose parents are more frequently alive than if we 

 have to wait for measurement till the offspring are of adult age. 

 Further, although the cephalic index requires a more trained 

 hand to measure it than some other measurements on the living 

 subject, the trained observer will always deduce sensibly the same 

 results;* on the other hand, stature measurements vary sensibly 

 with the hour of the day, and with the observer. The need of a 

 moderately trained observer is the chief defect of cephalic index 

 measurements ; it hinders the rapid collection of numerous family 

 measurements ; the difficulty, further, of satisfactorily measuring the 

 female head without some derangement of the toilet is a further 

 hindrance. t The merits of the cephalic index, however, as a test of 

 heredity far surpass its demerits. A well-organised measurement of 

 the cephalic index in pairs of relatives would probably give the best 

 results available for the laws of inheritance. The cephalic index 

 measured on the living head is of course not so satisfactory as that 

 measured on the skull, but the latter may be considered, even with 

 the aid of Rontgen rays, as at present quite out of the question. The 

 following paper has been worked out, not on very good material or 

 on material collected with the present end in view, but on the only 

 material that seemed at present available. It suffices to justify the 

 view that the inheritance of the cephalic index offers a most satisfac- 

 tory method of testing the laws of heredity. 



(2) Owing to the kindness of Mr. Francis Galton the Department 

 of Applied Mathematics in University College, London, was placed in 

 communication with Dr. Franz Boas, of the American Museum of 

 Natural History, who is well known for his elaborate system of 



* This has been tested by frequent measurements of the same heads. 



f The recent establishment of an anthropometric laboratory at Newnhani College 

 will, it may be hoped, remove the difficulty about head measurements on female 

 students felt by the Cambridge Anthropometric Committee. 



