342 



P radical Comparison of different Tables 0/ Mortality. In 

 a Letter to Sir Edward Hyde East, Bart., M.P.,F.R.S. 



(By a Correspondent.) 

 My Dear Sir, 



I had the honour of addressing to you, a few years since, 

 an investigation of the value of human life, which was published in 

 the Philosophical Transactions for 1 826 : and I had then occasion 

 to employ a formula for expressing the annual decrements of life at 

 all ages, in such a manner, as to serve sufficiently well for the in- 

 tended purpose, of harmonizing the mean standard table, of which 

 I had obtained the basis from a comparison of various documents. 

 This formula would have been much too complicated for any thing 

 like a direct introduction into the detail of calculation : but I have 

 lately had the good fortune to discover some simpler expressions, 

 which are capable of being extensively applied, with great con- 

 venience, to different cases occurring in the practice of Insurance, 

 and which may also be readily adapted to a variety of tables of 

 mortality, so as to afford a far nearer approach to the results belong- 

 ing to each, than could be obtained from calculations derived from 

 any other tables ; and will frequently indeed be more likely to 

 represent the true law of nature at each place of observation, than 

 the actual records of a limited experience for each particular year 

 throughout life. 



2. The great computer Demoivre employed, on different occa- 

 sions, two different hypotheses respecting the mean value of life : 

 and each of these has its advantages in particular cases. The first 

 was the arithmetical hypothesis, supposing, for instance, that out of 

 100 or of 86 persons born together, 1 shall die annually till the whole 

 number be exhausted. The second was the geometrical hypothesis, 

 as, supposing that 1 in 50, or in 100, of the living at any age shall 

 die within a year : a law which seems somewhat to approach to 

 that of nature in extreme old age. 



3. I have lately added to these, from examining a report of the 

 experience of the Equitable Assurance Office, a third hypothesis, 

 which may be called the exponential; the proportional mortality ap- 



