LIFE, MEAN DURATION OF. This is commonly called the expectation of life, which, properly speaking, it is not. Of a thousand lives of equal goodness, any one may expect to live as long as he has an even chance of living, that is, till 500 are extinct. This period has been denominated the probable life.
The mean duration of life, or the number of years which, one person with another, are enjoyed by individuals of a given age, is found from the tables of mortality, which give, out of a certain number born, the number who are left at every successive birthday. If the absolute average law of human life were given, and if oxdx represented the chance of an individual aged n living precisely x moments of time, then/ cpxdx, taken from x= 0 to x= the longest possible term of life, would correctly represent the average duration of life in persons aged n years. The tables, however, are so imperfect that it is not worth while to attempt the accurate application of the preceding formula, or to use more than the roughest of the processes which will be described in QUADRATURES, METHOD or. The theoretical imper fretlea of this process consists in its being necessary to suppose that the individuals who die in any one year die at uniform intervals throughout that year: bo that, one with another, they enjoy half of their year of death. The mean duration of life in then constructed as
follows: Let a be the number living at the age in question, of whom let A, c,d,kc., be left at the end of successive years. Then a —b die In the first year, enjoying among them years of life, while b (who turrive) enjoy the whole year. Consequently the a persons enjoy, in the first year of the calculation, 6+ (a-6), or (a+ 6)3.cars; and similarly it may be proved that they enjoy (6 + c), i(e+d), kr,, in the second, third, &o.. years. If these be put together, the result is I s+b+erd+, lac., which, divided by a, gives for the average quantity of years enjoyed by each individual, or the rule is, add together the numbers left at every age above that given, divide by the number alive at the given age, and add half a If year.
it be judged advisable to make the preceding result a little more mathematically correct, diminish the preceding result by the 12 a-th part of a—b. [MORTALITY, Law Or; Drs 3Ioren8a Ii TTOTIIE919.1