In a Postscript to the introductory matter of the Assurance and Annuity Tables, compiled and published by Messrs. Smith, Orchard, and myself in April, 1851 (and which Postscript was written by me), it is stated that I had “devised a new table, which, while answering all, and more than all, the purposes of Tables V. and VI. [which show the single and annual premiums for a survivorship assurance of £1 for every combination of two ages], by means of a single value for each pair of ages, and thus occupying little more space than one of them, would also be very much less laborious in its construction than the former of those tables. The new tables would, in fact, consist of series of columns supplementary to Mr. Jones's Commutation Tables for Two Lives, and possessing all the properties, mutatis mutandis, with respect to the formation of temporary and deferred, as well as present, whole life benefits and payments, that give to tables of the form of those mentioned their great value.”