22 Mr. T. It. Edmonds on Vital Force according 



the age of 9 to the age of 12 years, during which the rate of 

 mortality is constant and at a minimum. It may be well to ob- 

 serve that the zero of life in the period of childhood may be real 

 and mark the commencement of animal organization. Also it 

 may be useful to observe that, if the law of mortality is conti- 

 nuous above and below 84 years of age as well as above and 

 below birth-time, it will ensue that the rate of mortality at the 

 age 90 years is equal to the rate of mortality immediately after 

 the time of conception, and the rate of mortality at the age 96 

 years is equal to the rate of extinction of germs existing at the 

 age of 9 months, measured from the day of commencement of 

 organization. 



The differential of the hyperbolic logarithm of the living or 

 surviving at any age a + 1 is known when the force of mortality 

 a at the absolute age a measured from one of the two zeros of 



vital force is known, and is of the form following : — 



i 



dt. 



«Uog e P, = «(l+^)~ £ 



The above equation yields on integration (after assuming P 

 to be equal to unity when ^ = 0) the following equation, corre- 

 sponding to anv absolute age a-\-t, 



^Wp.-^{i-(i + ,jn. 



wherein n= - — 1 = 1*302585, and wherein a is the decrement 



in a unit of time on a unit of life, at the absolute age a whence 

 / is measured, the infinitesimal rate of decrement for the same 

 precise age being adt. 



The above formula for the surviving population from a given 

 age a to any other age a-{-t is similar to the formula which re- 

 presents the ratio of increase of the expansive force of ivater 

 (with its steam envelope) from a given temperature a to any 

 other temperature a-\-t, measured from the zero of heat, which 

 is at 276° C. (or 496°-8 F.) below the temperature of melting 

 ice. That is to say, the law of surviving population accord- 

 ing to age is the same as the law of expansive force of water 

 according to temperature. Both laws are expressed by similar 

 functions of the variables, whether in time or in temperature. 

 The expansion by heat of the force of water (or of steam in- 

 cumbent on water) is the chief instrument employed by man 

 in producing motion for mechanical purposes. In interest and 

 importance to man, the law of vital force is at least equal to 

 the law of steam force. The knowledge of either of these two 

 laws is as valuable as the knowledge of any other law which 

 corcerns mankind, 



