to Age, and the "English Life Table." 2 1 



formly increases during childhood, as well as the true law ac- 

 cording- to which the vital force uniformly decreases during 

 manhood, were first communicated to the public through the 

 Philosophical Magazine of January 1866, in a paper written by 

 me. I had previously, in the year 1832, given to the public a 

 triple series of "Life Tables/'' all founded upon an empirical law 

 which yields results nearly coincident with the results of the true 

 law published in 1866. For practical purposes, in the construction 

 of Tables of mortality, it is not easy to determine whether the 

 true law of 1866 ought to be preferred to the empirical law of 

 1832. In either case the law of variation of vital force from 

 birth to the end of life is expressible in very simple terms, the 

 result in either case being a differential of the logarithm of the 

 living (d . log e P) of great simplicity. But when the two differ- 

 entials are integrated, the resulting formula for the living (or 

 survivors) at any specified age t or a-\-t is found to be more 

 simple when the empirical law is adopted than when the true 

 law is adopted as the basis of calculation. 



In the Philosophical Magazine for January 1866 (No. 206, 

 page 9), it has been shown, according to the true law, that the 

 force of mortality at any age, either in the period of childhood 

 or in the period of manhood, is known when the force of mor- 

 tality at any other age in the same period is known, from the for- 

 mula following, 



wherein t is the difference of age ; a is a constant representing 

 distance (in time or age) from a fixed point, which is one of the 

 tw r o zeros of life ; ct is a given or observed force of mortality at 

 a known absolute age a ; a t is the force of mortality to be de- 

 termined for any other absolute age (a + t); and wherein y is 



the hyperbolic logarithm of 10, and equal to 2*302585. 



There are two zeros of vital force — one belonging to the period 

 of childhood, and the other to the period of manhood. The zero 

 of childhood is at the age 2-j- years before birth, or at the age lj 

 year before conception. The zero of the period of manhood is 

 at the age 102 years after birth-time. The length of the period of 

 childhood (which terminates at 9 years after birth-time) is 

 2J + 9 = 11 J years. The length of the period of manhood is 

 102—12 = 90 years. The length of the period of manhood is 

 just eight times the length of the period of childhood. The in- 

 crease of vital force during each year in childhood is just eight 

 times as great as the decrease of vital force during each year in 

 the period of manhood. There is an intermediate period, from 



