TAill.K. 





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tiirrocted the faults in most copies with his own hand. 1 1 

 nch a table, acoordiiiK to Wallis, anil Dr. 1V1I t..|,l Wallw that Warner 

 had finished the table, ami tint it was in the hand* of Dr. Busby, 

 master of Watminiiter School. It was never published, an 1 

 bably Kwt. AH our efforts to trace it, by help of published letters, ie., 

 lead to the conclusion that, if existing, it must be among Lord Maccles- 

 field's unexamined manuscripts at Shireburn Castle : this U by no means 

 improbable. 



171'J. (iardiner, 'Tables of Logarithms,' London. Numbers 1 

 100100, aines, Ac., (1") 72' (10") 45, all to seven places, with logistic 

 logarithms, and logarithms 0(1)1143 and 101000(1)101139, and 

 numbers to logarithms -00001 (-00001) -00139, to twenty decimal 

 place*. Rare, and much esteemed for accuracy : the author * corrected 

 the faults with his own hand. Few copies were printed. 



1742. Anonymous, printed by J. F. Gleditschen, ' Des vollstiiixli^'ii 

 Mathematiachen Lexici zweyter Theil,' Leipzig. Here we have squares 

 and cubes 0(1)10,000; seven-deoim.il logarithms of sines, tangents, 

 and secants 0(1')46; logarithms of numbers 0(1)20000; sines, 

 tangents, and secanto 0(1')45 to seven decimals; factors of odd 

 numbers not ending with 5, to 10,000. 



1743. Hivard, ' Tables des Sinus, At-.,' Paris, with the official "appro- 

 bation " of Clairaut. Seven-decimal logarithms of sines, tangents, and 

 secants (!') 45 ; sines and tangents to five decimals ; secants in a 

 separate table; logarithms of numbers 0(1)20000 : all with character- 

 istics and no decimal points. 



1747. James Dodson, 'The Calculator .... adapted to Science, 

 Business, and Pleasure,' London. A large collection of small tables, 

 with sufficient, though not the most convenient, seven-figure loga- 

 rithms. If a person of varied mathematical pursuits wanted a book, 

 say for travelling, he would not easily find one which would answer 

 more purpose^ at a pinch than the one we now speak of. The contents 

 are too varied for enumeration. 



1757. In the original articles there was a gap from 1712 to 177". 

 which shows that there was a lull in the publication of pure mathe- 

 matical tables. The period was one in which the mathematicians were 

 very much absorbed in physical investigation. When this is the case, 

 tables of pure mathematics find their way into works of physics and 

 astronomy under headings of application. Should any one ever enlarge 

 upon our plan, he must search astronomical and other works for such 

 tables as the following : Thomas Barker, ' Account of cornets .... with 

 new tables,' London, 4to., 1757. The tables give, for focal distance 

 unity, and for angles of anomaly (5') 180, the distance of a point 

 from the focus of a parabola, and the area of the sector on the snppnsi. 

 tion that at 90 the sector is 100. Halley had given a table of the 

 same kind on a much smaller scale : and Euler, in the ' Theoria 

 Motuum Planetirutn,' in 1744, had given the area of the parabola for 

 each degree of anomaly. Professor Schumacher (September 3, 1846), 

 wrote to us as follows : " Professor Knorre has sent me this (Barker's) 

 table, calculated from to 180 of anomaly, from 10" to In" (like 

 Callet's sines), to see if I can get it printed. It ia a work of immense 

 labour, executed by Mr. Rupertus in Russia, The booksellers, oi 

 course, will not undertake it." We have heard nothing more of this 

 table. More tables than we think it desirable to describe here, on the 

 ellipse, parabola, and hyperbola, as orbits of a comet, are given in 

 ' Methods of computing the Orbit of a Comet or Planet/ being the 

 appendix to the third volume of Bowditch's translation of the ' Me'- 

 canique Celeste,' Boston (U.S.), 1834, 4to. 



(1760). Lacaille and Lalande first published a small table : Marie 

 reprinted it in 1768 : there were editions in (1781, 1791, 1799). So 

 far Lalande, in his preface of 1805 (see that year) : none of these works 

 have come to our hand-. 



1770. J. H. Lambert, ' Zusatze zu den Logarithmischen imd Trigo- 

 nometrischen Tabellen.' This is a miscellaneous collection of tables 

 and formula;, containing Primes, at least divisors of all odd numbers 

 which do not divide by 3 or 5, up to 102,000; three-digit terminations 

 of odd squares : first ten multiples of all prime numbers up to 313; 

 primes alone up to 102,000; powers of 2 as far as the 70th, and of 

 8 and 5 as far as the 50th ; hyperbolic logarithms, seven decimals, 

 0(1)100, and 1('01)10, and 1(1)10 to 25 places; numbers whieh 

 divide by 2, 3, 5, or 7 only, or their powers or products (except those 



instances. Bat In the ' Misc. Sclent. Cur.,' of which Green and Wales were 

 co-editors, be felt that the conjunction of his luminaries demanded n ^iriMir- 

 tide, and he accordingly wrote the following eccentricity of genius in private 

 life on the fly-leaf of his copy, now before us, and left it to posterity : 

 " MUcellne Scientiflca Curimia, or a Buldcirtash Miscellany of ilamn'.l 

 Bafgamnffin, McthodUtlcal Nonsense and Spuabllity. By two of the most 

 tupiil and most dirty of all possible Fools, Ro f < mdrels ; viz'., 



John Or. in, A.M., l.te Tub-thumper, now Soul-driver in Hell ; and William 

 Wale, brusher at Christ's Hospital, not only the dirtiest Scoundrel that God 

 er made, but the dirtiest raMal that he possibly could make. Amen." 

 There are other note* in the book about thee persons and others as well ; but 

 this U enough. The reader will excu-c the production of such coaix 

 consideration of the expediency of fixing the value of extract* made, or to be 

 made, from Burrow's diary. 



The work had a imall Hit of very influential subscribers. Of about 130 

 names of persons and institutions in the lift, one in three i the name of u 

 person now known bjr name to any amatterer in scientific and literal j 

 Few subscription list* would (rive uch a result after a century of existence. 

 Th work ttm recommended makes an epoch In the history of tables. 



Hviduby 2 or 3 only), up t . 



pies expressed qundratically : i.-al ratio ; 



0(1) 100 (20) 120 (30) UoO, and for minutes u* 

 decimal sines and nine multiples 0(1") 90 ; seven-it 

 genta, and secants, and logarithms of sines and tangent 

 tables for facilitating cubic equations ; sines and cosines of li<i 

 triginiomrlry, the only table of the kind we have met with; .- 

 and cubes 0(1)1000; figiiratr numbers to the Uth onli-r, :!n oi 

 eight-decimal powers of fractions 0('01)1 to thellth power; seven- 

 decimal square roots 0(1) 100 ; with smaller matters and man 

 braical formula: of development. There is said to be another edition 

 of this useful miscellany, Lisbon (1798). 



1770. Reprint of Gardiner at Avignon, by Pezenas, Duma 

 Blanchard, with the first four degrees to single seconds, from a manu- 

 script which Mouton had bequeathed to the Academy < 

 The three industrious editors, all of them priests, who found time 

 to complete this useful undertaking, modestly withheld their i 

 but Lalande, who as in communication with them, and who -. 

 old pupil of Dumas, has recorded them. There was a repi 

 sort at Florence, in (1782), and we have been informed of a third 

 Italian edition, so-called, Florence (1810), badly printed, and contain- 

 ing also logarithms of prime numbers up to 6607, to twenty figi . 



(1772). Oherli's 'Logarithms,' Modena. Very much the same as 

 Button's in their contents. 



1775. Donwes ' Tafellen behelzende de Sinussen . . . . alg mede de 

 Logarithmen,' &c., Amsterdam. A complete minute-canon to 

 decimal places ; followed by logarithms to seven places ; versed sines 

 and logarithms on the same scale to 90 degrees; logarithms of nu 

 from 1 to 101000 ; and traverse tables. 



1778. J. C. Schulze, ' Neuc und erweiterte Sammlung i 

 cher . . . Tafeln,' Berlin. Also, ' Recueil de tables logaritlnnii|ites 

 The titles and preliminary explanations are both in French and i ' 

 Two volumes. This is a valuable and original collection It contains 

 the usual seven-figure tables (1) 101000 ; a page of mult , 

 . . . and Us reciprocal to 48 places, and powers of 2'718 . . 

 figures; Wolfram's* hyperbolic logarithms of all nnml 

 to 2200. and from thence to 10,000 for all numbers not divisible l>y 

 any single digit, all to furl;/-/ //</</ s ; common logarithms 



to seven decimals of sines and tangents (1") 2 ; logistic 1 

 four decimals (1") 1" ; a complete canon (10") 4 (!') 45 containing 

 sines, tangents, and secants to seven decimals, common loparit i 

 sines and tangents to seven decimals, Naperian (not hyperbolic) loga- 

 rithms of sines and tangents to eight decimals ; first pies of 

 sines of every degree to five decimals; lengths of arcs 0(1).'> 

 twenty-seven decimals ; ditto (!') 1 and (1") 1'; powers of fractions 

 0(-01) 1 as far as the eleventh, to eight decimals; square* and 

 0(1)1000; square and cube roots 0(1)1000 to seven deeinnls; bino- 

 mial coefficients (-01) 1 to six factors ; a table for the fall of bodies, 

 of rational right-angled triangles with the angles, and small tal 

 specific gravities and of weights and measures. Half-a-dozen of 

 Wolfram's logarithms which were accidentally missing in consequence 

 of an illness, are supplied in the Berlin Epherneris for 1783, p. 191. 

 The .\aperian logarithms of sines and tangents are an abbreviation of 

 Ursinus, (see 1624). 



(1 783). Vega ' Logarithmische Trigonometrische und andere . . 

 Tafeln und Formeln,' Vienna. This was Vega's first work, and we 

 have never met with it. (Octavo.) 



1783. Callet, ' Tables Portative.* de Logarithmes, publi. 

 Londres par Gardiner,' &c., Paris. The first edition of Callet, as it is 

 called, was really made from Gardiner's tables "augmenteY 

 tionn(!es dans leur disposition par M. Callet." Callet added as much 

 of each kind of table as would leave no white in his last page, and. 

 from Mouton, completed the single-second t-il>|. ngents 



up to 2. Here also first occurs the broken line at the cli 

 third figure. On this edition Mutton, commonly said t.i liav 

 prejudice against French men and things, says "it is but just 

 remark the extraordinary spirit and elegance with which the 1< 

 men and the artisans of the French nation undertake and e 

 of merit :" and the compliment is well deserved by the 1 

 of the type and the general accuracy of the work. The . 

 I seven figure logarithms ,,f members (1) 102960, of sines n (1") 2, 

 I of sines and tangents (10") 45 ; logistic logarithms ; 1. > 

 I twenty decimals (1) 1000 and for primes up to 1161 ; also for 101000 

 1 (1) 101179 with three orders of differences; 20 figures 

 (to logarithms -00001 (-00001) -00179 with the same differences; 

 hyperbolic logarithms to seven decimals 1 (-01) 10 J . r >:>. 



17!. p . r > (new tirage, 1821, with many errors corrected). Callet, 



This table was the work of Lieut. Wolfram, of the Dutch artillery, nnd 

 took six years of hard labour. It is one of the most striking additions to the 



iila of the subject which has been made in modern times. l>< 

 (' Hist. Astr. Mod.,' v. i., p. 801, &c.) introduces his comparisons of Napier 

 nnd Wolfram so abruptly, and so many pages elapse before the reader can find 

 out who the latter was, that most probably many have inferred that th.- t<i 

 were contemporaries. But this is Delanilm '- \\.it. ami is often liable to confuse 

 n render who has no warning on thu subject. With a work before him from 

 which he is drawing his materials, he perhaps never mentions it till t 

 of his remarks, or perhaps casually in the middle, though until such men 

 made, all he says is very liable to be misunderstood. 



