854 
DE. FAEE ON THE CONSTEHCTION OF LIFE-TABLES. 
Table of first differences in the Life-Table of Healthy Districts of England. 
Males. ^ 
Age 
Xla,. 
C2. 
C3. 
0*. 
3 
20 
59 
60 
4-631,5849,0000 
4-584,1951,2769 
4-403,7768,0454 
4-394,3905,1434 
A 
9-993,2422,0000 
9-996,9724,0000 
9-990,6137,0980 
9-989,5894,0000 
ote . — The last seri* 
0-001,2416,1260,934 
9-999,9127,2285 
9-998,9756,9020 
9-998,9460,9820 
3s px was carried backi 
9-999,8012,4393,666 0-000,0141,9648,567 
0-000,0101,9910 9-999,9988,9510 
9-999.9704,0800 9-999,9843,4520 
9-999,9547,5320 9-999,9843,4520 
yards from Xp(^ to \p^^. 
Females. 
3 
20 
57 
60 
4-623,2586,0000 
4-570,6868,3846 
4-405,2189,6826 
4-381,2818,8126 
A 
9-993,2928,0000 
9-996,6528,0000 
9-992,9332,3725 
9-990,2049,0000 
ote . — -The last seri 
0-001,2164,1598,794 
9-999,9241,5455 
9-999,0836,2675 
9-999,0720,4825 
px was carried back 
9-999,7874,2556,561 
0-000,0060,2930 
0-000,0123,2100 
9-999,9637,7950 
tvards from XjOgQ to \p.^ 
0-000,0170,4566,365 
9-999,9994,2530 
9-999,9838,1950 
9-999,9838,1950 
/ * 
A series of the form is reqnhed in rendeiing the Life-Table 
applicable to the solution of questions in Annuities and Life Insurance. 
The logarithms of the series are obtained by making the first term of the new series, 
and the first term of the first order of differences the 
and of the original series remaining unchanged. Taking the interest of money at 
3 per cent. and ?i'y=:l-9871627,753. 
The derivation of the new series from this value of Xv, and from the above Table 
(males), is shown in the annexed example. Any value of v"" may be introduced in the 
same way. 
Age. 
20 0-0000101, 991 
•0000090,942 
^^=9-9999988,951 
9-9999127,2285 
•9999229,2195 
•9999320,1615 
X(vj),r) = P. 
9-9841351,7530 
•9840478,9815 
•9839708,2010 
•9839028,3625 
«0=^(hv'). 
4-3274506 
•3115858 
•2956337 
•2796045 
•2635074 
In describing the first English Life-Table, I ventured to express the belief that the 
chances of life may ultimately be calculated by Mr. Babbage’s machine*. Mr. Bab- 
bage’s conception has been realized in the original and ingeniously constructed machme 
of the Messrs. Scheutz, which was favomrably reported upon by a committee of the Royal 
Society. The first differences to be inserted in the machine can be immediately deduced 
from those given above ; and we may hope ere long to see the logarithms of Life- 
Tables, for single and for joint lives, printed from types cast in moulds stamped by the 
machine now in the course of construction by the Messrs. Doxkix, for Her Majesty’s 
Government, at the instance of the Registrar-General. 
* Letter to the Eegistrar- General, in Appendix (p. 352) to his Fifth Annual Keport, year 1843. 
