[ 837 ] 
XXXIV. On the Construction of Life-Tables, illustrated by a New Life-Table of the 
Healthy Districts of Lkgland. By W. Fare, Esg., M.D., F.B.S. 
Eeceived March 17, —Bead April 7, 1859. 
CoNTEKTS : — 
Introduction 
I. GENEEAL DESCEIPTION OE A LIFE-TABLE (Table C.) 
{a)Age(x) 
(b) Two primary series representing (1) the surviving (Z^) at each year of age, and (2) the 
first differences of the same, representing the dying (<Z^) in annual intervals of age 
Plate XLII. figs. 1 and 2, representing by lines the series Ij, and 
Page 
838 
839—841 
839 
839— 840 
840— 841 
II. PEIXCIPLES OF CONSTETJCTION 
841—849 
( 1 ) 
( 2 ) 
(3) 
Hypothesis of an invariable annual number of births, equalling the deaths, has never 
been observed in any city or country ; and consequently Tables on the plan of Halley’s 
are often exceedingly erroneous, as in the case of the old Northampton Table 841 
The direct method of construction from the ascertained rates of mortality (ot«) in 
several periods of life g4X 342 
(«) By Demolvee’s hypothesis, the series Ig is an arithmetical progression 842 
(5) The series h on the hypothesis that the cause of death is of equal intensity at aU ages. 842—843 
(c) The hypothesis that the values form geometrical progressions ; rate of mor- 
tality explained 843 — 844 
(d) Application of this hypothesis to the construction of Life-Tables by Mr. Gompeetz 
and by Mr. Edmonds. Investigation of the formula. The limits to the applica- 
tion of the hypothesis 844 848 
(e) The determination of difference of and {1—p^). Comparison of derived 
(/) 
from the formulae (\ — and w=10^'''' . . 
The determination of the values of^^ at the earlier ages 
848 
848—849 
III. INTEEPOLATION OF THE LOGAEITHMS (X^.,) BY THE METHOD OF FI- 
NITE DIFFEEENCES 849—854 
(a) Formulae when the intervals are (1) equal and (2) unequal 850 — 854 
(b) The series XZ, constructed by series of four orders of differences, of which the first is Xp^. 850 — 854 
(c) Table of first differences 854 
(<Z) Introduction of the factor 854 
(e) In this form the series XZj can be calculated and printed by Schetjtz’s new machine ... 854 
IV. CONSTEHCTION OF THE COLUMNS d„ h, L„ P„ Q,, T„ and notices of some of 
their practical applications ; mean lifetime ; illustrations by Plate XLII 855 — 860 
(a) Nature and uses of the new column 3 mean ages of the population ; mean ages at death 857 
(b) The determination of the value of sums of money dependent on the continuance of life ; 
probabilities of life 5 probable lifetime 858 — 860 
MDCCCLIX. 5 S 
