ON LIFE CONTINGENCIES. 177 



The quantity found in this tahle is the probability of an 

 elder life surviving the younger. The difference of ages 

 differs in the various compartments of the table ; in the 

 first it is ten years, in the second twenty years, and so 

 on. The two results accompanying each pair of ages 

 are those of the Northampton and Carlisle tables. Thus, 

 according to the Northampton table, the chance of a 

 life of sixty surviving one of thirty is *23 ; that of the 

 younger surviving the elder is therefore 1 -23 or *77- 

 According to the Carlisle table, the same chances are 

 158 and -842. 



Almost universally, the Northampton table gives a 

 greater chance of the elder life beating the younger than 

 the Carlisle. This is a consequence of that undue 

 degree of comparative goodness which the former table 

 gives to older lives, and to which I have already ad- 

 verted. 



If De Moivre's hypothesis were correct, it would be 

 sufficient to divide the mean duration of B's life by 

 twice that of A, and the result would be the chance 

 which B has of surviving A, B being the elder of the 

 two lives. This process, applied to the Northampton 

 table, will give results very near the truth, when 

 neither of the lives is very young. The same rule 

 would give comparatively but a very rough guess at the 

 result of the Carlisle table. If, however, the chance be 

 calculated which the younger life possesses of dying in 

 the average term of the elder, the result will be an 

 approximation to the probability of the elder surviving 

 the younger, when neither of the lives is very young, 

 and when their ages are not nearly equal. Thus, the 

 mean duration of a life of 50 being 21 years, and the 

 chance of a life of 30 years surviving 21 years being 

 '769, the chance of the same life not surviving 21 years 

 is -231 ; while in the table, the chance of a life of 50 

 .surviving one of 30 is *251. 



I shall, in the next chapter, consider the application 

 of the tables to pecuniary questions, and shall now 



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