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XXI. "Supplement to Two Papers published in the Philo- 

 sophical Transactions (1820 and 1825) on the Science con- 

 nected with Human Mortality." By BENJAMIN GOMPERTZ, 

 Esq., F.R.S. Received June 19, 1861. 

 (Abstract.) 



The first of the two Papers referred to is entitled "A Sketch of 

 an Analysis and Notation applicable to the estimation of the value of 

 Life Contingencies." It is especially devoted to the explanation of 

 a new notation and a new mode of analysis applicable to the subject. 

 The second Paper, entitled "On the Nature of the Function ex- 

 pressive of the Law of Human Mortality, and on a new mode of 

 determining Life Contingencies," treats, in its first part, of the equa- 

 tion L. r =6?.#| *, in which L# denotes the number of persons who 

 would be living at the age #, out of the number of persons who may 

 have been living at some given common previous age, in which d, g, q 

 maybe considered constant quantities through a long series of years, 

 and the equations to give the real rate of mortality during that 

 period within a very satisfactory approach to coincidence, say, for 

 instance, from the age ten to the age sixty ; a theorem from whence 

 the number living at an assigned age may be derived, by what the 

 author calls the vital rule of three, from the number living, for in- 

 stance, at the age twenty, forty, and sixty, given in a table of mor- 

 tality. But the author observes that though the above formula with 

 suitably determined constant values of d, g, q appears within a great 

 approach of the observed result, to agree with the tabular data 

 through so long a period, still that actually d, g, q are not constant 

 quantities, as every different selection from the table of the living 

 to which the formula is applied, for the purpose of determining the 

 three constants contained in it, even if that table throughout were 

 an accurate representation of the law of mortality, which no table 

 based on obtainable data can be expected to be, would give different 

 values of d, g, q, as they are not really absolutely constant, but 

 slightly variable throughout, because the formula ~L x =d *g\ qX does 

 not represent perfectly the law of mortality, if d, g, q are perfectly 

 constant ; and the author complains of its misinterpretation in this 

 respect by a subsequent writer, who lays claim to discovery on this 

 subject. 



