DR. RARE ON THE CONSTRUCTION OE LIEE-TABLES. 
849 
(3) that the mean date of all the births in the two years 1848, 1849 was immediately 
before January 1, 1849. The half of the births in those two years will consequently 
represent pretty accurately the number of births out of which the deaths of children 
under one year of age happened in the year 1849. And the deaths and survivors can be 
followed by this method year by year, as is evident in the annexed scheme : — 
Age 
0 
1 
9 
\ (births 1848, 1849)=:mean annual births of which the mean date is January 1, 
[1849. 
minus deaths under age 1 in 1849 
= surviving on January 1, 1850. 
minus deaths age (1 to 2) in 1850 
= surviving on January 1, 1851. 
minus deaths age (2 to 3) in 1851 
3 =surviving on January 1, 1852. 
minus deaths age (3 to 4) in 1852 
4 =surviving on January 1, 1853. 
minus deaths age (4 to 5) in 1853 
5 = surviving on January 1, 1854. 
By commencing with the mean number of births in the years 1849, 1850, and deducting 
the deaths, a similar series may be obtained ; and thus a succession of similar series 
may be deduced, the mean of which will supply the ordinary series 4? l%-, 4? 4^ 4 of 
a Life-Table. 
These series are liable to various disturbances. If all the births are not registered, 
the rate of mortahty is overstated. If all the deaths are not registered, or if the chil- 
dren are carried off as emigrants, the decrements of life are understated. The annual 
number of births fluctuates, and now increases in England ; they are in excess also in the 
early months of the year. Several of the disturbances are slight, and some of them are 
in opposite directions. The results can also be, and have been, checked by the results 
of the other method. The value of m.^ and m ,2 are deduced by dividing the annual 
deaths at the ages 5 to 10 and 10 to 15 by the mean population at those ages. The inter- 
polation of the series from to >^20 succeeds ; taking kp^, kp^^, and as the 
flxed points of the series, and being adjusted to allow for the turn of the curve. 
The Tables A, B, and C supply the data from which the Life-Table of Healthy 
English Districts was deduced. One or two arithmetical examples of the application of 
the method adopted in the earlier ages are also supplied. 
III. INTERPOLATION. 
We have therefore determined the values of kp^ at certain ages. The values of kp^ at 
the interwening ages may be determined by changing the value of r, and making z suc- 
cessively 1, 2 10 irr the formula (p. 846). They may also be irrterpolated for every 
year of age by the method of finite diflerences ; and upon the whole this method is 
