com. 



28 Mr. T. R. Edmonds on Vital Force according 



or negative. In the construction of the English Life Table it 

 has been assumed that the errors of any two consecutive quin- 

 quennial rates observed are in opposite directions and balance 

 one another. This is the most favourable mode of estimating 

 the amount of error existing — one observed rate being supposed 

 to be 9 per cent, above the true rate, and the next observed rate 

 being supposed to be 9 per cent, below the true rate. The least 

 favourable mode of estimating the amount of error existing is 

 by supposing that the errors in two consecutive quinquennial 

 rates are not in opposite directions, and that the errors in 

 such observed rates are united or concentrated on one only of 

 the two observed rates, so that the proportional errors are al- 

 ternately 18 per cent, and nothing. 



In observations of rates of mortality according to age, no 

 lower estimate than 5 per cent, can be admitted as the probable 

 amount of errors of observation. This amount or rate of error 

 of observation is fifty times as great as the rate of error of obser- 

 vation made on the force of steam according to temperature. 

 The formula for steam-force according to temperature is the 

 same as the formula for surviving population according to age, 

 with difference of sign only. Either formula is 



.^,.±'-={.-(1^)"}. 



In the case of steam-force, the formula gives results which seldom 

 differ from the results of observation so much as one in a thou- 

 sand at any temperature from 30° to 230° C, or from 86° to 

 446° F. The observations on steam-force alluded to are those 

 of M. Hegnault, published in 1847, and contained in the twenty- 

 first volume of the Memoir es de VAcade'mie de Vlnstitut de 

 France^ p. 624. This insignificant amount of error of observa- 

 tion is applicable not only to the quantity P representing pres- 

 sure in pounds to the square foot, but also to the rate of incre- 



AP 

 ment -jj- for any degree of temperature throughout the above 



range of 200° C. The comparison between the observed rates 

 and the theoretical rates for steam-force may be seen at pages 

 185 & 186 of the Philosophical Magazine for March 1865. 



In Table VI. (hereunto annexed) is presented a comparison of 

 the results of the two principal observations which have been made 

 in England on the mortality according to age of children below 12 

 years of age, with the results at the same intervals of age as indi- 

 cated by two different theoretical Tables. It wall be seen that, with 

 exception of the first month from birth, the Carlisle Table of Heys- 

 ham and Milne is in close agreement with my Table of " Village 

 Mortality" (and with the empirical formula of 1832 on which it 

 is founded) at each of nine intervals of age comprehended between 

 birth and 12 years of age. Also it will be seen that, with a 



