242 ESSAY ON PROBABILITIES, 



7 that he will outlive this term. We have now to 

 ask, What are the principles which should guide the 

 office in the determination of its premiums, it being 

 remembered that there is an absolute security required, 

 and that the remote chance of bankruptcy, which is 

 almost essential to the ordinary run of commercial affairs, 

 is not to be encountered ? 



The basis of the tables is the observation of the lives 

 of a comparatively small number of individuals; it being 

 well known that the value of life varies considerably in 

 passing from one class of society to another. Now, we 

 have seen (page 91-). ^ at we cannot depend upon a 

 law of probability, derived from a limited number of 

 instances, with the same degree of confidence, as upon 

 one which we know to exist a priori, if we were sure 

 beforehand that the great average of life in England 

 was according to the Northampton, or any other table, 

 we might rely upon such a document as being extremely 

 likely to exhibit, with small fluctuations, the future 

 course of the lives of the two thousand or ten thousand 

 persons insured in any given office. Let such a table 

 be assumed, and let the premiums be so calculated, that 

 it shall be a thousand to one against any ruinous amount 

 of fluctuation, taking the law of the tables as that which 

 will certainly prevail in the long run. Then return 

 from the hypothesis to the truth, and, taking the num- 

 ber of lives from which the table was actually formed, 

 say 5000, suppose another 5000 persons to have com- 

 menced an insurance office. The degree of fluctuation 

 within which it was 1000 to 1 that the future re- 

 sults should be contained, is now larger than before, 

 in the proportion of the square root of 2 to 1, or 

 in that of 14 to 10, nearly. Larger premiums would 

 then be required to make ruinous fluctuation as unlikely 

 as upon the preceding supposition. These considerations, 

 which may easily be reduced to calculation by the rules 

 in chapters IV. and V., will serve to show that there 

 may be danger in the assumption of any table formed 

 from experience ; and they ought to operate powerfully 



