106 Miss Lee, Miss Lewenz, and Prof. Pearson. [Nov. 3, 



" On the Correlation of the Mental and Physical Characters in 

 Man. Part II." By Alice Lee, I). Sc., Marie A. Lewenz, 

 B.A., and Karl Pearson, F.K.S. Received November 3, — 

 Eead November 20, 1902. 



(1.) In a first paper on this subject* we gave a brief account of our 

 material — Miss Beeton's copies of the Cambridge anthropometric 

 measurements with degrees added at the University Begistry, and the 

 school measurements carried out by assistance from the Government 

 Grant Committee. This material will take years to exhaust, but the 

 present notice gives further conclusions to be drawn from Dr. Lee's 

 and Miss Lewenz's later reductions from this great mass of raw 

 statistics. 



(2.) In the first place we may refer to certain matters which arise 

 directly from the first paper. In the discussion which followed the 

 reading of that paper it was suggested that we ought not to correlate 

 intelligence with absolute measurements on the head, but with their 

 ratio to the size of the body. The answer made on that occasion was 

 based on data not then published, namely, that there is no sensible 

 correlation between intelligence and the absolute size of the body. 

 Hence the correlation between intelligence and any ratio of body 

 lengths must also be small. To show this algebraically let X\ and x 2 

 be any two measurements, and the ratio X\\x 2 \ let r^ y% denote 

 the coefficient of correlation of any two characters yi, y 2 ; let v x be the 

 coefficient of variation of the quantity x, i.e., be 100 times its standard 

 deviation divided by its mean.f Then we have the following 

 formulae J : — 



v% =. v 2 + v 2 - 2v v r (i), 



Vi X^X. 2 X l X 2 X t X 2 X 1 X 2 



where i denotes intelligence and x\, x 2 any other characters. 



Clearly when n Xi and are both small cannot be large. Let 



L be length of heaol, B be breadth of head, and S be stature. Then in 

 the case of the Cambridge graduates 



Vjj = 3-1839, r LS = 0-2816, r ih = 0-0861, 

 v B = 3-2836, , r K s = 0-1529, r m = 0-0450, 

 % =-- 3-6958, r LB = 0-3448, ?\s = -0-0056. 



* " On the Correlation of Intellectual Ability with the Size and Shape of the 

 Head," 'Roy. Soc. Proc.,' vol. 69 (1902), pp. 333— 342. 

 t ' Phil. Trans.,' A, vol. 187, p. 276. 



X Ibid., -p. 279. (ii) is deducible by simple algebra in the method often indi- 

 cated in this series of papers. 



