ae * algebraical Expression of the Values of Lives. 
sons as long as any of them remains alive; and much more 
nearly than the registers of 2 metropolis agree with those which 
have been kept in the country. It would be very easy to correct 
the expression from the average of the registers of a number of 
years ; and the formula might also be adapted with little diffi- 
culty to the mortality observed in any other situation. 
In order to find the number of persons who have died during, 
any given portion of the period of the longest human life, we 
must combine the expression for the mortality with the fluxion 
z of the age; the fluent, are tang. x + *0002005x7— 
0000014 x3, will indicate the aggregate amount of deaths at the 
given age. It has sometimes been thought sufficiently accurate to 
estimate the value of a life by the period at which half the persons 
who have attained the given age are likely to remain alive: this 
affords a true criterion of the greatest probability of the dura- 
tion of one life, but not ef the correct mean value of a number 
of lives; since tliis value can only be found by dividing the ag- 
gregate duration of all the lives in question by their number: 
now this aggregate duration is represented by the area of the 
curve having the ages and the numbers living, for its ordinates 
and abscisses ; and this area is cbtained from the fluent « — 
1» are tang. © -+ {HL (1+) ~-00006683 x? + 00000035 x4, 
Hence we may calculate the mean value of life in London, as 
shown in the following table. At birth, the most probable du- 
ration is about 27 years; the mean value more than 30, 
AGE. DEATHS, MEAN VALUE. HALLEY. 43-12, 
Registered. Calculated, (BRESLAU.) 
0 000 0000 30°29 43 
1 "1954 36°53 33°5 421 
5 385 3480 40:80 41:2 404 
10 409 “3864 58°21 40-4 38 
20 444 4492 31°80 ~ 34:2 33 
30 517 5269: 26°60 27:9 28 
40 610 “O177 21-46 22°3 23 
50 717 “7140 16:96 17:2 18 
60 813 “8080 12-90 12-4 13 
70 896 “8914 9-09 466 8 
SO 959 "9559 5°17 4'5 3 
90 994 "9935 1-64 
95 9993 
100 999°9 
The 
ieee te 
en 
