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ESSAY ON PROBABILITIES. 



distributed through the period. This supposition is 

 not actually true, though for a long course of ages the 

 amount of mortality does not vary much from year to 

 year. The main feature of De Moivre's hypothesis, 

 equal decrements, appears in some measure at the adult 

 and middle ages of life in all tables. I do not, however, 

 know of any observations in which the numbers dying 

 at every age are large enough to produce much confidence 

 in the details of the tables of decrements, though the 

 fluctuations may compensate each other in the deter- 

 mination of the mean durations of life. Tables which 

 agree in the latter point may differ materially as to the 

 former. As an instance, I give the following com- 

 parison of the Carlisle and Equitable tables, which 

 agree more closely than any others in their mean 

 durations. The first column shows the common age of 

 10,000 persons, the second and third the number who 

 die in the following year in the Carlisle (C.) and 

 Equitable (E.) tables. 



According to the Carlisle table, of 10,000 persons 

 aged 30, 101 die before attaining the next birthday ; 

 while one fifth less die in the Equitable table. And 

 yet, one with another, the average lives of two sets of 

 10,000 do not differ by more than their 170th part. 

 I now compare the actual tables of decrements, writing 

 opposite to each age the survivors of 10,000 births who 

 attain that age. (A, age ; C, Carlisle; E, Equitable.) 



