There is thus a virtual use of decimal fractions preceding the formal one. The same thing happens in the tables of Richard Witt, presently mentioned, which we believe to be the first English tables of compound interest, and the first English work (except a translation of the Disine' of Stevinus) in which decimals were used: the use of them being something more than the virtual use by Stevinus in the Practique The next English writer who gave tables of compound interest, Reber Butler, in his Scale of Interest,' London, 1633, makes a rather mor decided use of these fractions than Witt, and uses the phrase claim fractions, which had then hardly found its way into books. It shoul be noted that both Witt and Butler give real half-yearly and quarterl tables, as well as yearly ones.
Tables of interest began to be published at the beginning of the lit] century. The earliest we have met with is Richard Witt, Arithrne ticall Questions,' London, 1613, which, before the introduction of th notation of decimal fractions, gives tables, or brericcts, containing th significant figures, with rules equivalent to the management of th decimal point ; and Clay's Briefe, &c., Tables,' London, 1624. In th first half of that century we find in catalogues the works of Fisher Butler, Webster, and others, with anonymous writers, all containing tables of interest, annuities, or leases. For the tables known by th name of Xeroid, see MORTALITY. The tables of leases, Cambridge 1656, had the approbation of Newton, as Lucasian professor, and hay, since been often reprinted and styled Newton's.
Mr. Pocock, in his Bibliography of Annuities, &c. (' Familiar Expla nation .... of Assurances upon Lives,' London, 1842), gives the follow ing works, which we do not remember to have seen Tables o Lease% and Interest... ,' London (1628), 12mo.; and William Purser ' Compound Interest and Annuities, containing the Art of Deeima Arithmetic,' London (1634), Svo.
In Newton's Scale of Interest,' mentioned in the list of logarithms is a set of tables for six per cent., then the maximum legal rate There is here what we never met with elsewhere-a common almanac with months, dominical letters, and fixed saints' days ; having, in liet of astronomical information, simple and compound interest and die count tables, telling for each day the amount of une pound from the beginning of the year, or the present value for the end.
The first edition of Smart's tables, the original of all our large table: of compound interest, is Tables of Simple Interest and Discount, at 3 4, 5, 6, 7, 8, 9, and 101. per cent. per Ann.; also Tables of Compounc Interest at the same rates, whereby,' &c. By John Smart, at the Towr Clerk's Office, London : London, 1707, 4to (duodecimo size). The second edition, of 1726, is as large, compared with the first, as it ii possible its author, "John Smart of Guildhall, Gent.," may have become, compared with the subordinate at the town clerk's office It adds 2i, 3i, and 4I per cent. The results are interpolated for hall years, which give the tables the appearance of being calculated for interest payable half-yearly ; but the fact is that yearly payments are supposed. A second edition of this work, enlarged, by C. Brand London, 1780, has the reputation of containing many errors. The first edition (which we did not know of when we first wrote, and we find all • modern writers knew as little), besides a smaller range of rates, has not the half-years, and has only six decimal places. The tables of simple interest are also of very little extent. This set of tables was incorporated (with acknowledgment) in the article Interest' in the second volume of Harris's Lexicon Technicum; London, 1710. There was an abridged edition, with somo of the rates and of the half.years left out, but still to eight figures, Tables of Interest, &e., abridged for the use of Schools, in order to instruct young gentle men in the use of Decimal Fractions,' by John Smart, &c., London, 1736, quarto (octavo size).
Mr. Baily's 'Doctrine of Interest and Annuities,' London, 1808, is as extensive as Smart's for whole years, and as correct; and the Tables of Leases,' London, 1807, by the same author, contain the simple cases which the name implies, tabulated by themselves. The Doctrine of Interest,' by Francis Corbaux, London, 1825, contains the real dis tinction of yearly, half-yearly, and quarterly interest: these tables are repeated in the same author's work on ' Population,' Loudon, 1833. Mr. Hardy's 'Doctrine of Simple and Compound Interest,' London, 1839, contains rates of interest increasing by I per cent. from up to 5 per cent., with succeeding integer rates. All the standard works on life annuities contain tables of compound interest.