to Age, and the " English Life Table" 23 



In the case both of surviving population and of steam force, 

 ^log e P is of the same form though of different signs, whether P 

 represents population or pressure per square foot of steam of 

 maximum density. The differential of log e P represents decre- 

 ment in one case and increment in the other case. Surviving 

 population is always diminishiDg as age increases ; whilst steam 

 force is always increasing as temperature increases. 



dY 



In the case of population, d . log), P, or ^- represents rate of 



decrement of life or force of mortality at the absolute age a + 1. 

 In the case of steam force, d . log e P stands for rate of incre- 

 ment of force, to which no specific name is attached We 



con- 



re- 



know,, however, something of the chief factor ( 1 -\ — ) 



tained in the expression d . log e P applicable to the pressure 

 of steam of maximum density; for if steam were a perfectly 

 elastic gas and did not increase in density according as the 

 temperature of the subjacent water increased, in that case the 

 increment per degree of the expansive force of such steam at any 



temperature a + 1 would be represented by a (l + - j , if a 



presented the increase of expansive force per degree at the tem- 

 perature a. That is to say, the factor which represents incre- 

 ment of force per degree in the two cases is the same, with this 

 difference, however, that the exponent of the factor in one case 



is unity and in the other case - — 2*302585. The law just 



mentioned as expressing the increment per degree of expansive 

 force of a perfect gas according to temperature, was discovered 

 eighty years ago, by Dalton in England, and by Gay-Lussac in 

 Prance. The quantity a measuring degrees from the zero of 

 heat is the same in the ease of air as in the case of steam of 

 maximum density. The value of a is 276° C, being the dis- 

 tance of the zero of heat below the temperature of melting ice. 



Recurring to the formula for the force of mortality already 

 given, we have, in the period of childhood, for the force of mor- 

 tality at any age t measured from birth-time, where a is given 

 by observation and a = 2*25 years, 



^{M^K^f^ a 



t) 



That is, the force of mortality at any age t varies inversely as 



Rfc, if R be taken equal to (a-\-t) and be made to represent dis- 

 tance in time or age from a fixed point which is the zero of 



