[ 28 ! 1 
IX. English Reproduction Table. 
By Dr. W. Farr, F.R.S. 
Received January 15,—Read January 29, 1880. 
In the office of reproduction there are concerned the male, the female, and their 
offspring. We represent the males at each year of age by the females by l y , the 
children born of women at each age ( soboles ) by s y ; the children born in wedlock by 
s' y , those born out of wedlock by s" r 
The females are classified into the wives ( uxores ), the spinsters ( Jilice ), the widows 
We take the wives, spinsters, and widows from the English Census of 1871, and 
portion out the P y of the English life table on this basis; the offspring we take from 
Norwegian returns of 1871 and 1872, after reducing the relative proportions of legiti¬ 
mate and illegitimate births to the same as in England in those years. We take the 
statistics of children born to women of the several ages for Norway, because in England 
the age of the mother at the birth of her child is not given at the registry of the 
birth;* and comparing returns from Scotland, Norway, Sweden, and Denmark, that 
from Norway commends itself on the whole as the best adapted to our use. 
The life table represents a stationary female population; and if we reckon the child¬ 
bearing period of life to include all ages between 15 and 5 5 years, we have a constant 
population of 11,248,950 to which to look for the sustentation of a population of the 
uniform strength, including males, of 40,858,184. Of these 11,248,950 women aged 
15 to 55 years, 6,278,749 are waves, 4,265,622 are spinsters, and 704,579 are widows. 
The wives give birth to 1,395,529 children, the spinsters and widows to 55,381 
children; the total annual number of births, therefore, among such a population is 
1,450,910. 
Then by means of the following formulae we can determine the number of children 
born to any given number of women of a specified age: thus 
-p = -08924, and ‘08924x 100,000 = 8,924= the number of children born in or 
mo 
out of w r edlock to 100,000 women aged 20. 
S 20 
V 
20 
= ‘40070, or 100,000 waves aged 20 bear 40,070 children. 
* It is to be regretted that the mother’s age at the birth of her child is not yet included in the par¬ 
ticulars recorded in the English birth registers. 
mdccclxxx. 
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