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XXXIII. A Supplement to Two Papers published in the Transactions of the Boyal Society, 
“ On the Science connected with Human Mortality f the one published in 1820, and 
the other in 1825. By Benjamin Gompeetz, F.B.S., F.B.A.S. Ac. 
Eeceived June 19, — Bead June 20, 1861*. 
In offering to the Eoyal Society the ensuing Supplement to my two former papers on the 
Law of Mortality, with subsequent remarks on mvalidism, I am anxious to acknowledge 
that I have derived great advantage from the encouragement and persuasion of my 
esteemed brother-in-law. Sir Moses Montefioee, Bart., given me to endeavour to com- 
pile and publish some of my later observations on the subject; knowing that, though I 
felt flattered by the attention originally shown by scientific gentlemen to these papers, 
they appeared to me capable of advantageous illustrations. Therefore I may venture to 
hope that if this Supplement merit the attention of those interested in this branch of 
science, I may consider that he has added a mite further to entitle him to the good 
wishes of those who applaud him for his constant endeavours to promote the general 
interest of mankind — endeavours which he has shown to extend through Europe and 
Asia in the cause of humanity, and to be exercised at home in various ways, among 
which I notice his attention to the practice of Life, Eire, and Marine Assurance ; he 
being the President of the Alliance British and Foreign Life and Fire Assurance Com- 
pany ; of which I was the founding Actuary, and in which Institution, though retired 
from it, I feel greatly interested; it having been established about the year 1824 by the 
late N. M. de Eothschild, Esq., the late John Ieving, Esq., the late Samuel Gueney, 
Esq., and Eeancis Baeing, Esq., and himself conjointly with other gentlemen, and he 
being also President of the Alliance Marine Assurance Society, founded at the same time 
by them with him. 
Art. 1. In the year 1820 the Eoyal Society did me the honour to publish in their 
Transactions a paper of mine on the Analysis and Notation applicable to the valuation 
of Life Contingencies, in which I introduced a new and general notation, which appeared 
to me far more extensively useful, and more explanatory of its object, than any other 
notation I had met with ; and in that paper I think I introduced a new manner of deal- 
ing with the subject, by offering an analysis, with examples of the extensive use of it, 
applicable to some of the most intricate questions which had up to that period met with 
anything like a proper solution; and showed, by selections from the treatise of Life 
Annuities of my late learned and much-respected friend, Eeancis Bailt, Esq., a mode 
of solution of all the problems in chapter 8 of that work, depending on a particular 
* Subsequently revised by tbe author, with the insertion of some additional matter. 
MDCCCLXII. 4 A 
