1009 



TABLE. 



TABLE. 



K10 



(something more than the virtual use by Stevinus in the ' Practique 

 The next English writer who gave tables of compound interest, Kobert 

 Butler, in his ' Scale of Interest,' London, 1633, makes a rather mor 

 decided use of these fractions than Witt, and uses the phrase decima 

 fnictiom, 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 17t 

 century. The earliest we have met with is Richard Witt, ' Arithme 

 ticall Questions,' London, 1613, which, before the introduction of th 

 notation of decimal fractions, gives tables, or treviats, 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 containin 

 tables of interest, annuities, or leases. For the tables known by th 

 name of ^Ecroid, see MORTALITY. The tables of leases, Cambridge 

 1686, had the approbation of Newton, as Lucasian professor, and hav 

 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 

 Leases and Interest . . . ,' London (1628), 12mo. ; and William Purser 

 'Compound Interest and Annuities, containing the Art of Decima 

 Arithmetic,' London (1634), 8vo. 



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 lieu 

 of astronomical information, simple and compound interest and dis 

 count tables, telling for each day the amount of one 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, 6, 6, 7, 8, 9, and 10/. per cent, per Ann.; also Tables of Compoune 

 Interest at the same rates, whereby,' &c. By John Smart, at the Town 

 Clerk's Office, London: London, 1707, 4to (duodecimo size). The 

 second edition, of 1726, is as large, compared with the first, as it is 

 possible its author, " John Smart of Guildhall, Gent.," may have 

 become, compared with the subordinate at the town clerk's office 

 It adds 24, 34, and 4} per cent. The results are interpolated for hal 

 yean, 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 * modem 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 oi 

 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 some of the rates and of the 

 half-years left out, but still to eight figures, ' Tables of Interest, &c., 

 abridged for the use of Schools, in order to instruct young gentle- 

 men in the use of Decimal Fractions,' by John Smart, Ac., 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,' London, 1833. 

 Mr. Hardy's 'Doctrine of Simple and Compound Interest,' London, 

 1889, contains rates of interest increasing by J per cent, from 4, up to 

 5 per cent., with succeeding integer rates. All the standard works on 

 life annuities contain tables of compound interest. 



There seems to have been a tendency at the beginning of the last 

 century to publish commercial tables in copper-plate, probably with a 

 Tiew to secure the advantage which stereotype has since secured in a 

 better form. Thus we have the " arithmetical! tables " of C. Bardon 

 (Boy. Soc. library) without date ; Lostau's ' Manual Mercantile,' 

 second book (first never published), London, 1733 ; Rev. G. Brown's 

 Arithmetica Infinita, London, 1717 ; the two last being multiplication 

 tables, with multiples of numbers and fractions useful in money trans- 

 actions, arranged under heads. The following may be mentioned as 

 containing hints which might even now be useful : Benjamin Webb, 

 Tables for Buying and Selling Stocks,' London, 1759; also 'The 

 Complete Annuitant, or Tables of Interest,' London, 1762; Hayes's 

 ' Moneyed Man's Guide,' a table for computing dividends, London, 

 1726 The French have a large number of tables answering to our 

 ready-reckoners, under the names of Bartme (a word of the same use 

 with them as Cocker with us), compte-faits, &c. We have seen one of 

 them of the decimal character, in which a metal plate with rectangles 

 pierced in it serves, on one rectangle being placed over the integers of 



Dr. Fair ('Rg.-Gen. Rep.,' 1844, p. 539) mentions the edition of 1726 as 

 the urond edition. 



ABTS ASD SCI. DIV. VOL. VII. 



the number given, to make another separate those of the number to be 

 found. 



Commercial tables of any real power are rendered impossible in 

 practice by the use of shillings, pence, and farthings, except by an 

 extent of matter which makes them very expensive. If, indeed, the 

 rule for decimalising the parts of a pound [COMPUTATION] were well 

 learned and properly used, some of the older tables, which have fallen 

 entirely into oblivion, would certainly be revived with effect. Two of 

 those presently mentioned will certainly be reprinted when the time 

 comes ; Brown's ' Arithmetica Infinita,' and Webb's ' Tables for Buying 

 and Selling Stocks.' The main part of the former is the first nine 

 multiples of the decimal, which expresses any number of farthings in 

 a pound. Thus, under 7s. 8Jrf. are -3854166 . . . and its multiples" up 

 to nine times. The latter has the multiples necessary to find the 

 quantity of stock which answers to any sum of money, and vice versd, 

 at different prices. These are both pocket tables, and .their places are 

 supplied at present by works of much greater bulk and less extensive 

 use. 



We now give a very condensed account of a few mercantile tables. 

 We take them merely because we happen to have examined them, 

 without any selection. Such a list, meagre as it is, both in amount of 

 works and in description, may be of much use to one who is contem- 

 plating the construction of a table. He may be warned that tables 

 exist which he should consult before he settles his plan ; for those we 

 have quoted may suggest the expediency of looking out either for 

 themselves or for others resembling them ; or he may receive a hint 

 even from so brief a description as ours. There will appear, in so 

 short a list as this, sufficient evidence of the never-ceasing attempt to 

 bring decimal * fractions into tabular connection with our mixed 

 money. There has never been any lasting success with the world at 

 large ; and we must continue, in our commercial arithmetic, at per- 

 petual war with our own first principles, until we are wise enough to 

 decimalise our coinage, and ultimately our weights and measures. 



In the following list, the letters Q., O., or D., for quarto, octavo, and 

 duodecimo or under (referring to size, and not to mode of printing), 

 precede the date and begin the description of each work : 



O. 1613, London: Richard Witt, ' Arithmeticall Questions;' com- 

 pound interest. Q. 1619, Leipsic : 'Ein newes metzbar gerechnetes 

 Rechenbueh ; ' ready-reckoner, tables of multiplication of prices. D. 

 1629, London (2nd edition, many editions) : William Webster, 

 ' Webster's Tables;' small tables of simple interest. D. 1632, London: 

 John Bill, 'Accompts cast up;' ready-reckoner, simple multiplication 

 of integer numbers up to 100 times; the earliest English ready- 

 reckoner we know of. 0. 1633, London : Robert Butler, ' The Scale of 

 Interest;' tables of discount and present value. 0. 1668, London: 

 John Newton, 'The Scale of Interest' (see Logarithms, 16ti8). 0. 

 1677, London : Michael Dary, ' Interest Epitomized ; ' small tables of 

 compound interest ; a rare and remarkable book in other respects. 

 D. 1682, Amsterdam : J. Sarfatti Pina, ' De Lichtende Koopman's 

 Fackel;' multiples of money in facilitation of exchanges. D. 1686, Cam- 

 bridge [Mabbot] : ' Tables for Renewing and Purchasing of the Leases 

 of Cathedral Churches t and Colleges ; ' reprinted almost down to our 

 own time (to 1808 at least) under the name of Newton, because it has 

 Newton's certificate of approbation of the method. Mr. Edleston, who 

 bas found the name of the writer in his researches into Newton's 

 biography, says that he was manciple, a caterer, of King's College. In 

 the treasury of Trinity College, he adds, is a table and explanation, in 

 Newton's handwriting (1674-5), of the fines for renewing years lapsed 

 in a lease for 20 years. It is entitled, ' Tabula redeniptionalis ad 

 reditus Collegii SS. Trmitatis accomodata,' and gives seven years' 

 purchase for the whole lease, and one year for seven years lapsed. 

 This allows the lessee upwards of 13 per cent. This table was 



* The day after we had written this we came in contact with an extract from 

 the ' Publishers' Circular,' as follows : " An old copy of Langham's ' Nett 

 Duties and Drawbacks,' digested into an easy method, once the standard 

 authority on the subject, gives us the exact state of the ease a hundred years 

 ago, and leaves us in some astonishment that any head, native or foreign, could 

 lave mastered the complicated details then necessary for their own safely to 

 be known to importers .... Decimals, indeed, appear to have boon the delight 

 of the tariff-maker of old, for the charg on every one of the fifty-eight items 

 of paper] concludes with some such a fraction occasionally reaching the 

 delicate nicety of 92f hundredths of a penny." This merely means that com- 

 mercial arithmetic is more of a mere routine than it was, and that a hundred 

 rears ago decimal fractions were more cultivated than they are now. 



j- Later editions of this work arc accompanied by a letter on the value of 

 ihurch leases, which was one commencement of a long dispute, giving many 

 pamphlets. (See 'Notes and Queries,' 2nd series, vol. iv., p. 361.) The practice 

 3f raising the fines, which had been very much too low, had been growing for 

 ome thirty years previously to 1686 ; and the publication of these tables seems 

 o have been in justification of the rise. Hence the importance attached to obtain- 

 ng from Newton a certificate of the method, which those interested might have 

 cnied. The dispute, which never died, was very warm in 1729-31, when the 

 lergy were threatened with legislative interference, and did actually receive 

 ome implied recommendations to desist from the House of Commons. Common 

 ense, however, seems to have found out at last that the clergy, in spite of tho 

 ugmentations, were making much less of their lands than the laity ; and the 

 ext phase of this history is that of 1837, in which year the poor divines were 

 ireatened by parliament with the loss of the management of their estates, for 

 citing them too low. It is not easy lo please everybody. 



3T 



