On the Construction and Use of Commutation Tables for Calculating the Values of Benefits depending on Life Contingencies

Abstract

It is to a Mr. George Barrett, of whom nothing besides is publicly known, that we are indebted for the principle of the Commutation Tables, and for the method of computing, by means of them, the values of benefits depending on the contingencies of human life. The method was first introduced to public notice, after it had been refused a place in the Transactions of the Royal Society , by Mr. Baily, in an Appendix to the second edition of his Doctrine of Life Annuities , published in 1813. Mr. Griffith Davies, in a work on life contingencies, published in 1825, by certain additions to the tables, and alterations in their structure, according to Professor De Morgan, “increased the utility and extended the power of the method to an extent of which the inventor had not the least idea.” Mr. Barrett's method was also briefly noticed in the Appendix to Mr. Babbage's Treatise on Life Assurance. The method, as improved by Mr. Davies, has since been treated, and a very large collection of tables adapted to it, for both one and two lives, has been given, by Mr. Jones, in his work on annuities, in the Library of Useful Knowledge . But by far the most valuable papers on the subject are two in the Companion to the Almanack , for 1840 and 1842, by Professor De Morgan, which contain the materials of many thousand formulae, applicable to almost every case that can occur. There is also some notice of the method in the article “Reversions,” in the Penny Cyclopaedia , which article likewise is the production, we believe, of Professor De Morgan.