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XVII. ^ Sketch of an Analysis and Notation applicable to the 
estimation of the value of Life Contingencies • By Benjamin 
Gompertz, Esq. F. R. S. 
Read June 29, 1820. 
The estimation of the value of property, connected with 
life contingencies, has for many years occupied the attention 
of the philosophers, as well as the monied and landed interest 
of this country. The many institutions now existing in Eng- 
land, for the purpose of granting annuities and assurances on 
lives, are a sufficient evidence that they are conceived to yield 
advantages to the community : — advantages which seem to 
present themselves in two points of view ; the one, the gain 
accruing to the parties granting the assurance or other ob- 
ject ; the other, the benefit to he received by persons pur- 
chasing those grants. In a political point of view, it appears 
a question of great importance to decide, what ought to be 
the demands of those companies, so that the public may reap 
the greatest benefit from them ? And the only means of 
answering this question, is the possession of the mathemati- 
cal and philosophical principles, by which those institutions 
ought to be guided. In the present improved state of the 
science of life assurances, it is not sufficient for a proper re- 
gulation to follow old customs, and calculations, drawn from 
a less perfect experience than we have now the means of 
obtaining ; but every company, to reap the advantage of the 
progressive state of the science, should not only possess 
