236 
Duration of Life and Number of Offspring 
TABLE IV. 
Table of Regression ForviuUe. 
^ = Duration of Life. «/ = Size of Family. 
(1) 
For 
lives of Fathers under 60 years of age 
-2-6570 + -ISSgLr. 
(2) 
For 
lives of Fathers, 60 years of age and over 
?/ = 5-39489 + -01328.};. 
(3) 
For lives of Mothers under 45 years of age 
y = -3-71792 + -2172ar. 
(4) 
For 
lives of Mothei-s, 45 and under 70 years of age 
«/ = 3-6866 + -04335X. 
(5) 
For 
lives of Mothers, 70 years of age and over 
?/ = 8-1546--02537.*.-. 
Note : — Origin at birth, and unit x = \ year. 
These lines, which are shown on the diagrams by broken lines, must be 
regarded as admirable representations of the statistics in all the series. Cubical 
parabolas were also computed for both sexes, but in neither case can it be said 
that the curves nearly as accurately represent the statistics as the regression 
straight lines. Adopting Professor Pearson's method* (mid-ordinate formula) the 
following equations for parabolas of the third order were obtained : 
For Males ij = 6 18673 + -MSQSx - ■Q4idUx^ - •00078a;^ 
„ Females 3/= 6 29315 + -looGo^ - •04839;r'^ + -OOIDDa'', 
the origin in the male curve being at 62'5 years, and in the female 60 years. 
The theoretical maximum fecundity in males was found to be at 78'925 years, 
and that in females at 69 075 years. Referring to the regression straight lines 
it is seen that in the case of males the coefficient of correlation in both series 
is positive ; in the females in the first two periods it is positive, but in the 
period beyond 70 years of age it is negative. In all cases the coefficient is high 
and the probable error is very small. Thus it is seen that in man increased 
longevity is associated with increased fertility, whilst in women this association 
only exists up to about age 70, after which increased longevity is associated with 
diminished fertility, thus confirming Professor Pearson's suspicion that extreme 
fertility is not in all cases favourable to a maximum longevity. In man up to 
age 55 — 60, as might of course have been suspected, the association is well 
defined, but beyond that period it is not so pronounced. The association during 
the first period requires no explanation, being so intimately connected with the 
first or child-bearing period of women. But in the second period the connection 
between longevity and fertility is possibly more apparent than real. Many men 
who become widowers during that period contract subsequent marriage with 
* Biometrika, Vol. ii. Part i. pp. 16 and 17. 
