516 Mr. Gompertz on the nature of the function 
deferred, should be deemed incorrect, though indeed for im- 
mediate annuities, where the probability of death is very 
great, the limit of the table would not be of so much con- 
sequence, for the present value of the first payment would 
be nearly the value of the annuity. 
Such a law of mortality would indeed make it appear that 
there was no positive limit to a person's age ; but it would 
be easy, even in the case of the hypothesis, to show that a 
very limited age might be assumed to which it would be 
extremely improbable that any one should have been known 
to attain. 
For if the mortality were, from the age of 92, such that ^ 
of the persons living at the commencement of each year 
were to die during that year, which I have observed is nearly 
the mortality given in the Carlisle tables between the ages 
92 and 99 * it would be above one million to one that out of 
three millions of persons, whom history might name to have 
reached the age of 92, not one would have attained to the 
age of 192, notwithstanding the value of life annuities of all 
ages above 92 would be of the same value. And though the 
limit to the possible duration of life is a subject not likely 
ever to be determined, even should it exist, still it appears 
interesting to dwell on a consequence which would follow, 
should the mortality of old age be as above described. For, 
it would follow that the non-appearance on the page of 
history of a single circumstance of a person having arrived 
* If from the Northampton tables we take the numbers of living at the age of 
88 to be 83, and diminish continually by | for the living, at each successive age, we 
should have at the ages 88, 89, 90, 91, 92, the number of living 83; 61.3 ; 45.9; 
34.4; 25.8 ; almost the same as in the Northampton table. 
