272 Oil the Etf'ect of a Differential Fertilitu on Degeneracy 
gated ; the family of the athletic might be compared with that of the non-athletic; 
and those of the smith and the navvy with those of the cobbler, tailor, and street 
hawker. It would, I think, be quite possible even without a reformed census, for 
which every sociologist should work, to obtain many results of value bearing on 
differential fertility by inquiries of the above nature. 
Each diagram consists of five normal curves. They are worked out on 
Hypothesis (i), i.e. that the fertility of the parentage is equally affected by the 
character in both parents, and that there is an assortative mating in the community. 
The coefficient of parental heredity is taken as "^S and that of assortative mating 
as -20. X is measured from the mean of the character in tlie parentage of the first 
generation. Expressing everything in terms of o-j the variability, say, of males in 
the first generation we have the following curves : 
Diagram I. Representing Illustration I. 
Curve I. Distribution of Males in first generation : 
Curve III. Curve of Fertility of Individual Parentages of first generation: 
Diagrams. 
Curve II. Distribution of Individual Parentages in first generation: 
1 
e 2 (l-55<ri> 
v'27rl-55(r, 
1 (x - l-2603(Ti\2 
y = 6-439 e''i\ 2-5697o-i ) . 
(N.B. Only part of this curve is drawn.) 
Curve IV. Distribution of Effective Parentages in first generation : 
1 Ai-- -33620-1 Y 
^-—-^ e 2 V l-3273<ri ) 
V27r l-3273<ri 
Curve V. Distribution of Males in second generation : 
Diagram II. Representing Illustration II. 
Curve I. Distribution of Males in first generation : 
y = -7=. e ^ ci" . 
Curve II. Distribution of Individual Parentages in first generation : 
