PROFESSOR Pearson's contributions to osteology. 469 



of correlation and regression for different pairs of groups, and 

 sexual ratios for M, a-, and V, are also calculated and tabulated. 

 The tables are explained and discussed, and the following are 

 the chief conclusions drawn : — 



(a) That there is a definite amount of assortative mating with 

 regard to height going on in the middle class. 



(b) That as regards reproductivity, mediocre fathers have a 

 greater tendency to sons, and exceptional fathers to daughters. 



(c) That there is a prepotency of heredity of the father. 



It must be clearly understood that these deductions refer only 

 to the single characteristic, height. 



In a subsequent section of this memoir collateral heredity is 

 discussed from further tables based on Mr Galton's statistics. 



(d) Let X and y be two correlated organs. Let m^ and m^, 

 o"! and (T.2, v^ and v.,, be their means, standard deviations, and co- 

 efficients of variation respectively. If z be any funtion of x and 

 y, of which the mean standard deviation and coefficient of varia- 

 tion are 2, M, and V, then it is shown that 



where r = coefficient of correlation between x and y. 



This relation is not limited to any particular law of frequency. 

 By means of it the coefficients of correlation between the length 

 and breadth of the skull may be calculated. In this case z is 

 the ' Cephalic Index.' Professor Pearson gives the results for 

 the skulls of four local races, namely, — 



Professor Flinders Petrie's newly-discovered 



race, 7- = -2705 



Modern German (Bavarian peasants), . . 7" = -2849 



Modern French (Parisians), . . . . r = -0474 



„ ,, (peasants), .... r=-1265 



The numbers show that the coefficient of correlation is not con- 

 stant for all local races. The fact is also brought out that the 

 most variable measure, both relatively and absolutely, is the 

 breadth of the skull rather than the length. 



" On the Relative Variation and Correlation in Civilised and 

 Uncivilised Races" (Miss Alice Lee and Karl Pearson). — For the 



