24 Mr. T. 11. Edmonds on Vital Force according 



vital force. The chief of physical forces is that of gravity, which, 

 according' to distance from a fixed point in space, varies inversely 

 as R' 2 . That is to say, the law of variation of the force of mor- 

 tality measured from a central point, differs from the law of va- 

 riation of the force of gravity similarly measured, only in the 

 exponent of the radial distance. The exponent is two in the 



case of the force of gravity, and the exponent is y, or 2*302585 



in the case of the force of mortality. 



The empirical formula published in 1832 was founded on the 

 supposition that the mortality according to age decreases or in- 

 creases in a constant geometrical ratio in each of three definite 

 periods of human life. The com. logs, of the three constant 

 ratios are -—•17, +*0128, and -f'0333; the corresponding 

 numbers being '6761, 1-0299, and 1-0797. The first period 

 begins at birth, and ends near 9 years of age. The second 

 period begins at 12 and ends near 55 years of age. And the 

 third period begins near 55 years of age, and continues until 

 the end of life. There is probably an intermediate fourth pe- 

 riod, from the age of 9 to the age of 12 years, during which 

 the rate of mortality is constant and at a minimum. 



From the above law of geometric increase or decrease of mor- 

 tality according to age, was obtained for each of the three periods 

 the differential equation following, viz. 



d Ao% e ~? t — -~ up*dt -, 



and afterwards by integration, assuming P = l when £ = 0, 



com.logP,= ^(l-jp*) or Y t = l0x^ (1 ^ p \ 



The quantity a in the empirical formula of 1832 represents 

 the annual rate of mortality at the precise age« whence £is mea- 

 sured, that is when if = 0. The actual or infinitesimal rate of 

 mortality at the time or age when /=0 is adt. The actual or 

 infinitesimal rate at any other point of time, say t years or frac- 

 tions of years, is aphlt. The quantity a thus used to indicate 

 the rate of mortality at a particular point of age was not known 

 to the public until the year 1832. In my book of " Life Tables," 

 published in that year, the above quantity was first described and 

 made the subject of a special Table, of which the following is the 

 title: — "Table A 27, showing at quinquennial intervals of age the 

 force of mortality, or the number of deaths which would occur 

 in one year, upon 100 constantly living." Without the quantity 

 a, as first described by me, any formula similar to that of 



com. log V t = - — (1 — p f ) is of no use except for the interpola- 



Kp 



