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Published online by Cambridge University Press: 18 August 2016
The following letter from M. Réboul will serve to introduce the several subjects upon which he has addressed the Institute:—
“Gentlemen,—The Institute of Actuaries being the most competent tribunal in matters of assurance, it is to you, as to my natural judges, that I have conceived it proper to submit my first essays in that science.
“ The manuscript, which I have the honour to present to you, contains:—
“ 1st. Five new tables of life annuities.
“ 2nd. The introduction and plan of a work upon assurance.
“ 3rd. Note upon a new formula for calculating the assurance of a capital sum to the survivor nominated.
The annuity tables accompanying M. Réboul's communication are sufficiently described by that gentleman himself. The rate of mortality, and the rates of interest upon which they are based, will, no doubt, be considered by our readers as circumstances affording sufficient reason for not reproducing them here.
page 10 note *
The quantity in question represents, in fact, the value of A's share of the premium paid annually for assurance of £I at decease of the survivor of A and B, supposing it to be arranged that each is to pay half the premium while both are living, and that the survivor is to pay the whole. How far its value differs in particular cases from what M. Réboul supposes it to be, will be seen in the following instances, which are based on the Three-per-cent. Northampton Table—the first column being derived from M. Réboul's expression, and the second from the 
of the tables:—
page 11 note * See page 6 of the Introduction to that Work.
page 11 note † “On the true Measure of the Probabilities of Survivorship between Two Lives (see vol. i., p. 137).
page 11 note ‡ See also Milne, vol. i., article 110.