ON LIFE CONTINGENCIES. 173 



In the Equitable table, 5000 persons are supposed, 

 each aged 10 years; this I have altered to 6460, to 

 make the two tables agree at their outset. 



The successive quinquennial decrements of the Car. 

 lisle table from the age of 20 are 211, 237, 280, 287, 

 348, 330, 324, 430, &c. If these deaths be supposed 

 to take place at equal or nearly equal intervals during 

 the five years, if, in fact, we may suppose each of the 

 individuals who die .in a period to enjoy, one with 

 another, half that period of existence, we may ascertain 

 the law of mortality from the table of mean durations 

 in the following manner. 



RULE. To the mean duration at the end of the 

 period add the term elapsed and subtract the mean 

 duration at the beginning; divide by the smaller 

 duration increased by half the term, and the quotient 

 is the fraction which expresses the proportion dying 

 during the term. For example : the mean durations of 

 life at 25 and 30 in the Carlisle table are 37'9 and 

 34-3; and 34-3 + 5 37'9 is 1-4; which, divided by 

 34-3 + 2-5 or 36'8, gives ^ or ^ T ; so that of 184 

 persons aged 25, 7 die before attaining 30 years. In 

 the table, we have -/-/^ while -^ is about -g-gfo. 



If we were to take any table now existing on English 

 lives, and ask, (as in p. 92-), what is the probability 

 that a large number of lives, say 1000, should drop 

 nearly in the same manner as those from which the 

 table was formed, we should find the resulting chance 

 not strong enough to make it prudent to risk much 

 money in such contingencies. Nevertheless, the appli- 

 cation of this theory to pecuniary risks has always been 

 in a more forward state than the physical theory of 

 human life. The reasons will be explained when we 

 come to treat on the grounds of the confidence to which 

 a contingency office is entitled. In the mean while, 

 supposing a table to represent perfectly the average of 

 a large number of the lives of the class to which an in- 

 dividual belongs, I proceed to show the method of using 

 such a table 



