1001 



TABLE. 



TABLE. 



1002 



' Tables Portatives,' &c., Paris. Two volumes. This second edition, 

 stereotyped by Finnin Didot, is one of the most correct and convenient 

 as well as extensive works in existence : many persons prefer it to any 

 other. Jt contains the usual seven-figure logarithms from 1 to 108000 

 common and hyperbolic logarithms, each to 20 decimals, up to 

 1200 logarithms, common and hyperbolic, to 18 decimals, with first, 

 second, and third differences, from 101000 to 101179 numbers to 

 logarithms, common and hyperbolic (to 20 figures), from '00001 to 

 00179, with the same differences; common logarithms* to 61 

 decimals, and hyperbolic to 48, to all numbers from 1 to 100 and all 

 primes to 1097 ; the same for numbers from 999980 to 1000021 mul- 

 tiples of 2-30258 . . . and "43429 .... to 100 times arcs to 25 

 decimals, for both sexagesimal and centesimal division seven-figure 

 logarithmic sines, &c. for each minute of the centesimal division sines 

 (15 decimals) and their logarithms (the remaining places up to 14, the 

 first seven being in the last table) for centesimal degrees and tenths 

 proportional parts sexagesimal seven-figure logarithms of sines and 

 tangents (1") 5 (10") 45 logistic logarithms. Those tables are 

 tolerably, but, we believe, not extremely, correct in all parts, except in 

 the latest tirage. The tirage of 1827, on yellow paper, was taken to 

 accompany Mr. Babbage's logarithms. 



1784. M Robert, curate of St. Genevieve a Toul, sent Lalande 

 (' Ency. Meth.' Tables.) a manuscript volume containing sines to every 

 second, t'> hmv many places he does not say ; shortly afterwards he sent 

 the tangents. Lalande gives a hint that the approaching publication of 

 Taylor's logarithms prevented any steps being taken to print these. He 

 also states that there was in the library of the Academy of Sciences a 

 manuscript of Mouton, giving the logarithmic sines and tangents of 

 ( 1 ") 4 to eleven figures ; we suppose he means to ten places of deci- 

 mals (gee 1770). M. Robert's manuscript came into Delambre's posses- 

 xion, and was bought at the sale of his books by Mr. Babbage, in whose 

 possession it now is. It is in two large folio volumes, the figures (to 

 even decimals) being written in printed skeleton columns. Some cor- 

 rections of Callet, discovered by means of this manuscript, were printed 

 in one of the nautical almanacs. 



1785. Button, ' Mathematical Tables,' London. Many editions, 

 the second in 1794; one in 1849. A very correct set, with sines, 

 tangents, &c., and versed sines, complete, both natural and logarithmic. 

 Fur thoee who want seven places, and can have but one book, there is 

 none better. The additional matters, especially the historical introduc- 

 tion, arc well-known. 



1789. William Oarrard ' Copious Trigonometrical Tables.' This is 

 one of the largest of what are called in navigation traverse tables. For 

 every integer hypothenitse from 1 to 300 are given, to two decimals, 

 the value of the base and altitude, for every angle (10') 90. 



17'.'2. Michael Taylor, 'Tables of Logarithms,' London. In the 

 trigonometrical part the sines and tangents are to ererij semnd. The 

 errata of this work have been published in various nautical almanacs. 

 ThU widely used work, the first to which O'(l") 90 applies, was 

 by a most industrious computer, attached to the staff of the ' Nautical 

 Almanac.' He died just before the last half sheet was printed ; and 

 l>r. Maskelyne supplied the introductory matter. This book, like 

 others published by the Admiralty, was not sufficiently advertised. It 

 sold as a second-hand book, neither sellers nor buyers knowing that 

 Mr. Murray had plenty on hand. For ought we know, the same thing 

 may still go on. 



17!M807. Maseres, 'Scriptpres Logarithmic!,' London. The first 

 volume contains a reprint of Kepler's Logarithms, the sixth and last 

 of Xapicr'a work of 1614, and John Sperdell's logarithms of 

 numbers. 



1794 or 1795. (an III., a Port-Malo, chez L. H. Hovius, fils) Tables 

 de* logarithmes des nombres, depuis 1 jus quTi 10700 .... dressees 

 4 1'unage de la* navigation .... Six figure logarithms of the common 

 type, in all respects but one, and that one curious and perhaps unique. 

 A rectangle which o/rners with the upper right of the page, has an 

 extent of 30' with the usual semi-quadrantal arrangement of trigono- 

 metrical logarithms. In the remaining gnomon comes a part of the 

 table of logarithms of numbers. At ninety of these to a page, the 

 logarithms of numbers come so near in the book to the corresponding 

 figures in the sines and tangents, up to 45, that a person who wants 

 the natural sine or tangent has very little turning of pages to do. .But 

 this is no help to the second half of the sines, or the first half of the 

 cosines. When the half-quadrant is finished, the remaining logarithms 

 nl numbers ran on in the usual way. Had the author made a full 

 quadrantal arrangement, and checked the speed of his logarithms of 

 numbers a little, by additional lead or otherwise, as he went on, he 

 might have made something which would possibly have been judged 

 worthy of imitation, in tables specially intended for astronomers and 

 other trigonometers. 



1795. The Abbe 1 Borne, a Frenchman, gave a table of logarithms of 

 numbers of a peculiar kind at the end of his ' Principle ragionati de 

 Aritmetica,' I'eiaro, 8vo. All numbers which end with 1, 3, 7, 9, are 

 found by double entry ; thus 6973 is in column headed 69, and row 

 fronted 73. If this were a prime number, seven decimals of logarithm 

 would have been entered : as it is, the lowest divisor, 19, is entered. 

 Thus, in 20 pages there is a potential table (1) 10,000. But the 



The last 51 places are given, the first ten being accessible in a former table. 



Abbe' did not see that the same space would have contained the loga- 

 rithms of all odd numbers not ending with 5 : and these, with the 

 logarithms of 2 and 5 printed at the head of every 'page, would have 

 done better service than the factors. Authors often t'orget that they 

 do not save either space or cost of printing by what appear abbrevia- 

 tions or omissions in the manuscript : the saving is but so much of 

 what the printer calls white, which is done by types ; and white is 

 black, both in the room it takes and in the printer's bill. 



1794. George Vega, ' Thesaurus Logarithmorum completus,' 

 Leipzig, folio. Vega's edition of Vlacq. See Vlacq of 1628 and 1633. 

 A very correct work ? a ducat was offered for every error detected. 

 There is also a German title-page, and the explanations are both in 

 German and Latin. This is, no doubt, up to this time, t/ie table 

 of logarithms; the one of all others to which ultimate reference 

 should be made in questions of accuracy. Its contents are, a tin- 

 decimal table of common logarithms 1 (1) 101000 distributed in the 

 common manner, a decad in each line of the double page, with the 

 differences arranged in the same way, and tables of proportional parts 

 for the first three figures of the differences. Logarithmic sines and 

 tangents to 10 decimals, (1") 2 (10") 45. Sines (1") 12' to ten 

 decimals. Lengths of arcs to 1 1 decimals. Wolfram's hyperbolic loga- 

 rithms (see 1778) above described, reprinted from Schulze. 



1794. J. J. Girtanner, ' Logarithmische Tafeln zur Abkurzung 

 kaufmannischer Rechnungeu,' commercial logarithms. The plan is to 

 have logarithmic tables for integers and different sorts of fractious, 

 among which eighths, tenths, sixteenths, and sixtieths are conspicuous. 

 But it will not do : Mohammed must go to the mountain. When 

 coinage, weights, and measures, are decimalised, the use of logarithms 

 will follow as a matter of course. It is useless trying to bring loga- 

 rithms to ordinary fractions. 



1797 (2 vols. 2nd ed., or rather second work) and 1812. Vega, 

 ' Tabulae Logarithmico-Trigonometricfe,' Leipsic. Titles and introduc- 

 tion both in German and Latin. The usual logarithms of numbers, 

 (1) 101000 ; logarithms of sines (0"'l) 1', and U (l' J ) 1 30', and the 

 full canon (10") b' 3' (!') 45 divisors and primes already noticed 

 eight-figure hyperbolic logarithms from 1 to 10UO, and for all primes 

 up to 10,000 powers of 271828, aud their common logarithms (from 

 exponent '01 to lU'OO). First ten powers of numbers up to 50; 

 squares and cubes of numbers up to those of 1000, &c., logistic 

 logarithms, binomial co-efficients, and astronomical tables various. 

 There are various smaller editions from Vega, as at Leipsic (1820), and 

 (1S26). 



1799. J. P. Hobert and L. Ideler, ' Nouvelles Tables Trigonomd- 

 triques calcule'es pour la Division decimale du Quart de Cercle,' Berlin. 

 Delambre speaks highly of this table ; but he is wrong in saying it 

 subdivides the quadrant as minutely as those which himself and Borda 

 published. Meaning by 1 the hundredth of the right angle, and 1' 

 being 0'01, and so on, Hobert and Ideler's division of the quadrant is 

 (lu') 3 (l')50; but Delambre and Borda's are as below. The 

 Berlin table gives sines and tangents and their logarithms, through the 

 quadrant ; the Paris table gives logarithms only. The former has no 

 logarithms of numbers except (1) 1100 and 999980 (1) 1000021, all 

 to 36 decimals. 



1800 or 1801. (An. IX.) Delambre and Borda, ' Tables Trigouomd- 

 triques De'cimales,' Paris. These tables were corrected from the grand 

 ' Tables du Cadastre,' still unpublished.* [PRONV, in BIOG. Div.] 

 They contain, the common logarithms of numbers to seven decimals, 

 11-decimal logarithms of numbers from 1 to 1000, and from 100,000 

 to 102,000; 11-decimal logarithmic sines, cosines, tangents, and co- 

 tangents (10" centesimal) 10' aud (10') 100; 11-figure hyperbolic 

 logarithms from 1 to 1000 ; 7-decimal logarithms of sines and tangents 

 (1") 3 (10") 40 (!') 50 centesimal. 



1802. J. R. Teschemacher. ' Tables calculated for the Arbitration of 

 Exchanges, both Simple and Compound,' London. This is a book of 

 commercial loyarithvw, though the author wisely avoided frightening 

 the merchant by mentioning the word in any part of his book. There 

 is one table of logarithms for the exchange between London and each 

 other place : the tables average about a page each. With this limited 

 range, the logarithms are really effectively applied to commercial 

 purposes, and operations are very much simplified. There is no need of 

 a separate book of logarithms : all that the reader knows or needs to 

 know is that certain nameless figures are to be used in a certain easy 

 way. W r e are fully of opinion that such a work might be very useful. 



1804. De la Caille, De la Lande and Marie, ' Tables de Logarithmes,' 

 Paris. Six decimal places, which probably the preceding ones had, 

 (see 1760). The trigonometrical tables O(l') 45 as usual, with 

 differences for 1" : the numbers 0(1) 21600. La Lande has forgotten 

 to mention this edition ; or perhaps it was not published when he was 

 preparing the work next mentioned. 



1805. De la Lande, 'Tables de Logarithmes,' Paris. Stereotyped. 

 See 1760, 1831. 



1806. Thomas Whiting. 'Portable Mathematical Tables,' London. 

 Six-figure logarithms. This book is a striking proof that in the old 

 figure, the reduction of the thickness of the type very much increases 

 the legibility. This is a very easy book to read, and would exactly 

 suit those who want a large type in a small book. 



* There was once a commencement of the printing, and we have seen some 

 of the proofs. 



