240 Duration of Life and Nnmher of Offspring 
TABLE VII. 
General Results. 
Period of Life 
Size of Family 
Mean 
Duration 
of Life 
(years) 
Mean 
Size of 
Family 
Standard Deviation 
Correlation. 
Dui'ation of Life 
and Fertility 
Kegression 
Duration of 
Life (Unit 
= 1 year) 
Size of 
Family 
After 45 years 
After 60 years 
After 75 years 
)7 )1 
Oto 8 children 
9 to 17 „ 
0 to 8 „ 
9 to 17 „ 
0 to 8 „ 
9 to 16 „ 
23-1369 
22-8396 
14-1321 
13-1207 
7-3796 
6-8203 
4-2031 
10-7654 
4-2379 
10-7289 
4-2541 
10-6685 
12-2551 
11-4486 
8-7413 
8-3649 
5-3257 
5-0405 
2-7189 
1 -6648 
2-7189 
1 -6825 
2-6810 
1 -5830 
+ -02144 + -00796 
-•01285 -f -01214 
+ -009205 ±-00941 
-•07192 +•01413 
+ •00710 + -01420 
-•08687 +^02240 
+ ^09666 
- -08834 
+ -02959 
- -35757 
+ -01410 
- -27662 
TABLE VIII. 
Regression Farmuke. 
?/ = Duration of Life ; ,r=Size of Family (Origin at 0 children). 
(1) 
For lives 
of Mothers 
of 0 
to 
8 children, after 45 years of age, 
= 22-7306 + -09666A-. 
(2) 
» 
)i 
9 
to 
23-7906- -08834.2;. 
(3) 
)) 
)j 
0 
to 
60 
y = 14-0067 + -02959.27. 
(4) 
)) 
)> 
9 
to 
17 
?/ = 16-9808 --35757X 
(5) 
)) 
)) 
0 
to 
8 
75 
?/= 7-3196 + -01410^. 
(6) 
5) 
)) 
9 
to 
16 
15 51 
y= 9-7714- •27662X 
favourable to longevity, whilst unfavourable beyond that number; secondly, the 
mean family of the 0 to 8 children groups increases with each period, whilst 
the means of the 9 to 17 children groups as regularly diminish ; and thirdly, that 
the mean duration of lives of mothers of the 0 to 8 children groups is consistently 
greater than that of the mothers of larger families. These statistics have also 
been fitted with cubical parabolas (true ordinate formula) with the following 
results : 
For life after age 45, y = 23-32576 - 08538^ - -01864x-- - -0007 lit-', 
„ „ „ „ 60, y = 13-94679 - -21964:c - -02765^- - •00032«3, 
„ „ „ „ 75, y= 7-20525 - •15409^ -•00816a;2 + ^00135a;l 
The origin of the first two curves is at 9 children, and of the latter at 8'5 children. 
The maxima were found to be at 5-790, 4-208, and 3-527 children respectively. 
The statistics, regression straight lines and curves are plotted on Fig. 3. 
Although as has been previously remarked the correlation is not high in 
any of the series, yet in the case of life beyond 60 and beyond 75 for mothers 
of more than eight children, it is sensibly negative within the limits of probable 
error, and this is sufficient to justify the conclusion that even in the case of 
survivors attaining those ages, their future expectation of life has been prejudiced 
by every additional child that had been born to them. But if excessive fertility 
