ON THE NATURE OF INSURANCE. 253 



certainty of ruin which is thus known to exist, if they 

 play upon equality of chance, by allowing for the first 

 two of the three preceding considerations. There must 

 still remain more risk than it is safe to face of insolvency, 

 either temporary or permanent. And though, in con- 

 sequence of the smallness of the portion which the office 

 risks upon one hazard, a very small mathematical ad- 

 vantage might he sufficient, yet, so long as the necessity 

 for such an advantage exists, and its absolute amount is 

 unknown, so long must an office guard itself by requiring, 

 in the first instance, a sensible addition to the real 

 premiums. 



With regard to the old lives, there is an additional 

 ground of insecurity. Not only are the probable errors 

 of the tables exceedingly large with respect to them, 

 but, from the smallness of the number which will 

 enter an office, there will be a liability to great fluc- 

 tuations in the results of transactions with them. The 

 first circumstance would prevent the second from be- 

 coming ruinous, but at a risk of loss to the capital 

 invested by younger lives : it is usual, therefore, to 

 exclude all lives above a certain age from entering the 

 office, upon the principle that no risks are to be taken 

 of which the numerical amount is not well understood, 

 and of which the number is not large enough to secure 

 an average. But, since the tables of old lives are only 

 a very unsatisfactory approximation, and since the pre- 

 miums payable by young lives depend in part on the 

 chances of those lives becoming very old, how does it 

 happen that the insecurity of the latter part of the 

 tables does not affect the premiums throughout? It 

 does affect them, but not sensibly, for the following 

 reason. If, assuming the Northampton table, we sup- 

 pose a person aged 40 to insure his life, we see that 

 the portion of the present value of his insurance which 

 depends upon his dying in his 85th year is very small, 

 on two accounts : firstly, because the chance of his 

 living to the age of 84 is very small; and, secondly, 

 because the present value of a sum to be received 



