PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 291 
General Formulae for Regression in Stature :— 
h, = deviation of father ; h 3 = deviation of mother. 
Sons :—The mean height of array of sons corresponding to fathers of height h 2 and 
mothers of height ho is 
/q = -41 76 h 2 + -299 7 h s , 
or, 
= -4176 Ao + -2766 (1’08A 3 ). 
Daughters :—The mean height of array of daughters corresponding to fathers of 
height A 2 and mothers of height A 3 is 
h\ = -2895 h. 2 + -2609 A 3 . 
= -3136 (hj 1-08) + -2609 h 3 . 
In the second expressions given with both, formulae, the parental heights are 
exhibited in terms of the equivalent heights of the sex of the offspring. 
Explanation of the Tables .—Table XII. gives the value of the correlation coefficient 
rp _ rp> rp 
as influenced by assortative mating, e.g., -- y. The values of the simple correlation 
1 —rp 
coefficients (rq, r 2 , r 3 ) are taken from Table II. Against each coefficient is placed the 
value of the “ direct ” coefficient, on the supposition that i\ = 0— e.g., r 3 —in order to 
exhibit immediately the influence of assortative mating. 
Table XIII. gives the regression coefficients as influenced by assortative mating, 
e.g. 
1 - rd 
G 2 
(see p. 286), and “direct’"' 
or uninfluenced by such mating, e.g., 
r 3 —; the former are calculated from the values given in Tables XII. and I., and the 
°2 
latter are reproduced from Table III. 
Table XIV. exhibits the decreasing variation in arrays of sons and daughters, 
when w 7 e select (i.) neither father nor mother, (ii.) a mother of given type, (iii.) a father 
of given type, and (iv.) both mother and father of given types; (i.) is taken from 
Table I., (ii.) and (iii.) from Table IV., and (iv.) is calculated from the formula for 
deduced on p. 287. 
(cl.) Conclusions. Prepotency of Father .—These tables bring out the essential 
prepotency of the father in the case of both sons and daughters, the ratio of the 
contributions being 42 to 28 in the first case and 31 to 26 in the second case. A 
prepotency of the father * in other characteristics has been noted by Mr. Galton 
in his “ Hereditary Genius,” but it is there attributed to the greater ease with which 
the male characteristic (genius) makes itself apparent. It deserves, however, to be 
* Prepotency of either parent might, I think, be easily tested statistically in the case of morbid 
inheritance, particularly in tubercular disease. Dr. R. E. Thompson (‘ Family Phthisis,’ pp. 89 and 95), 
indicates a prepotency of the mother in both male and female inheritance of this disease. 
2 p 2 
