180 ESSAY ON PROBABILITIES. 



would be indicated by a correct table of mortality. 

 The burials at the younger of two ages would therefore 

 occur in too large a proportion to those at the older. 

 Suppose, for instance, that 350 deaths take place at 

 the age of 4041, and 1200 at the age of 56; 

 we are not therefore to conclude, that out of 10,000 

 individuals born, the deaths at 40 and 5 would be as 

 350 to 1200 : for since the population doubles itself 

 in 35 years, those who now die aged 5, are part of 

 twice as great a number of such lives as were of the 

 same age 35 years ago : consequently, of the set from 

 whom 350 died at the age of 40, 600 died at the age 

 of 5. If, then, a table were constructed from burials 

 alone, without paying any attention to the rate of 

 increase of the population, the older lives would appear 

 too good of their kind ; that is, relatively to the younger 

 ones of the same society. This, as already observed, is 

 the case in the Northampton table; whereas, in the 

 formation of the Carlisle table, proper attention was 

 paid to the variation in question. The difference is 

 very perceptible in comparing each of these tables with 

 that of the insurance office which it most resembles. 

 At 25 years of age, the mean duration of the North- 

 ampton table is 30*9? and that of the Amicable 34*1. 

 If the proportions of the mean durations remained 

 nearly the same, (as generally happens,) then the 

 Amicable table at 6*0 giving 12*5, the Northampton 

 table should give 11-4 ; instead of which it gives 13 2. 

 The preceding supposes, that while the population 

 changes, the law of mortality remains stationary. It is 

 very unlikely that such should be the case ; and observ- 

 ation, so far as it goes, tends to confirm the a priori 

 suspicion. When provisions are cheap, or wages high, 

 when, in fact, it is easy to maintain a family, marriages 

 are more frequent, and are contracted at earlier ages. The 

 same abundance of nourishment which tends to production, 

 also tends to preservation, both of parents and children ; 

 the consequence of which is, that a rapid increase of 

 population is often accompanied by a diminution of the 



