856 
DE. EAEE OJf THE CONSTErCTIOX OE LITE-TAELES. 
(12.) also represents the sum of the numbers of men or women living at all ages 
over the age x, out of Qo living at all ages, as is in all cases the sum of the numbers 
Imng in each year of age, represented by the series P^. The unit is here an individual 
man. 
(13.) Thus, on referring to Plate XLIl. fig. 1, the lifetime of 100,000 childi-en 
born simultaneously may be represented by 100,000 parallel lines, drawn from AB 
horizontally in the direction of CD until they cut the cui-ved line BC. And is 
the sum of these lines expressed in the linear units of the scale on the line AC ; so 
^ ^0 — 48-99665: the mean length of those hues = the number of 
/o ”100,000 100,000 ® 
years of mean lifetime. 
It will be observed that in this Table, instead of 100,000 lines, these Ihies are thrown 
into 106 groups, each comprising the variable number of lines terminating in each of 
106 intervals numbered on the line AC, and representing years of age. And m these 
short intervals it is assumed that the mean length of the fines terminating in the 
eleventh interval (10 to 11) is represented by 10-|-, and so on. 
The relative numbers of persons living simultaneously at each interval of age wifi 
also be represented in the same Plate, fig. 1, by 106 successive vertical lines, raised 
from nearly the centre of each interval between the ordinates on the Ime AC, and 
measured in units of which the fine AB contains 100,000. The same fines hound the 
figure representing the two orders of facts ; and the numerical units expressmg the 
aggregate length of the vertical fines equal in amount the units expressing the aggre- 
gate length of the horizontal lines expressed in the horizontal units. 
(14.) I will now explain briefly the nature of the column Y^, which I have added to 
the Life-Table^. The Life-Table (column P^) exhibits a representative population, 
such as would be constituted by separating every year 100,000 births as they occuiTed. 
* See paper in Appendix to Eegistrar- General’s Sixth Annual Eeport, pp. .544-552. 
Extract from the Eegistrar- General's Sixth Annual Eeport (1845), p. 528. 
Note . — Halley’s Table (1693) contained the column P. John Smabt made 1000 “born” the basis 
of his Table (1738), and introduced the columns d and 1. Simpsox adopted Smakt’s form of Table, which 
was followed by Kersseboom (1738), Depaecietjx (1746), Pbice (1773), and Milxe (1815). The 
columns S.y, y and Ay in Dltvillaed’s ‘Loi de Mortalite (en Prance) dans I’etat naturelf,’ correspond 
with the columns L, I, d in the new Table. The S.y added by Duaullaed is our L and Baeeett’s column 
B ; Dtjtillaed’s short Table (p. 123) has the four columns d, I , P, Q for quinquennial or decennial ages, 
and the ‘expectation of life.’ Mathietj’s Table II. is an expansion of the column Q oi Dlaullabd s 
short Table, and is that column for each year of age. In a recent report on the Bengal Military Fiuid, 
Mr. Davies has a Table (1) containing columns corresponding with the d, I, E, P, Q ot the English Table, 
the ‘ Mortality per cent.,’ and the ‘ Expectation of Life’ at each ageL” 
I have in this paper employed d, I, L, instead of C, D, N, Avhich have been formerly used by me and 
others, and should still be used where the factor is introduced. 
t Influence de la Petite Verole, p. 161. 
^ See the note (A), p. 558. 
