ON MATHJiMATIOAL TABLES. 93 



remarks in §3, art. 13), and also Hutxon's tables (editions 1783-1822), 

 Gernerth remarks (p. 25) that errors pointed out by Hutton in 1822 still re- 

 mained uncorrected in the tirage of 1846. We may also refer to a paper by 

 Herrmann, entitled " Verbesserung der II. Callet'schen Tafel der gemeinen 

 Logarithmen mit 20 Decimalen, nebst Vorschliigen fiir die weitere Porde- 

 rung dieses Zweckes," printed in the ' Sitzungsberichte der Kaiserlichen 

 Akademie der Wissensdhaftcn,' Vienna, 1848, part ii. pp. 175-190. 



On p. liii of their work, Hobert and Ideler (1799) remark that they 

 found that in general the natural sines of Callet were calculated accurately, 

 but that in the log sines the last two figures were generally doubtful ; they 

 mention also that they found many other faults in the work, but, being un- 

 certain how far these are corrected in the stereotype edition, they only give 

 one : viz., on p. 117 of the introduction, in the eighth place in the value of f 

 there is a 2 for a 3 ; and this fault renders erroneous the multiples of /. A 

 list of 380 errors is given on pp. 348 and 349 of the book, in all of which 

 the error is + 1 in the last place, and also an error in a natural sine is given. 

 The above error in /is corrected in the tirage of 1853. 



On p. 120 of EoRDA and Delambre there are given six eiTors in the ste- 

 reotyped tables of Callet. A good many errors are also given at the end of 

 Vega's Manual (1800). 



Many other errata are noted in other books ; but it seems useless to give 

 references without at the same time examining whether the errors have been 

 subsequently corrected, and, if so, in what tirages. 



Hobert and Ideler consider that Callet obtained his log sines most pro- 

 bably by interpolation from the ' Trigonometria Artificialis ' of Vlacq. 



The number of tirages of this work has been very great : it was first 

 published in 1783, we believe; but the type from which the earlier tirages 

 were printed was subsequently reset, as the size of the page in the editions 

 published in this century is larger than that of the first, which had tlierefore 

 more right to the title " Tables portatives." The tirage we have described 

 above is that of 1853 ; and we have seen one of 1862, " revue par J. Dupuis " 

 (Dupuis was himself subsequently the editor of a set of logarithmic tables, 

 described in this section). There is also a stiU more recent edition, edited 

 by M. ISaigey. We have an impression that the Callet of 1793 was the first 

 logarithmic table stereotyped ; but we have not investigated the matter. 



Coleman, 1846. T. XIX. Log sines, tangents, and secants to every 

 quarter point, to 6 places. 



T. XX. Six-figure logarithms to 10,000, arranged in decades, with pro- 

 portional parts above 1000. 



T. XXI. Logarithms for finding the apparent time or horary angle, viz. 



1 • / , 1 — cos 07 \ „ 



log semi- versed sines f = log ^ ) ^1'°°^ ^ to 9^ at intervals of 5% to 



5 places, with proportional parts. 



T. XXIII. Log sines, tangents, and secants for every minute of the 

 quadrant, to 6 places. 



T. XXIV. Proportional logarithms for every second to 3° ; same as T. 74 

 of IIaper, only to 5 instead of 4 places. It must be observed that on the 

 first page (extending to 10') the logarithms are not given completely, the 

 last figure, two figures, or three figures being printed as ciphers. This 

 is done, we presume, because in the cases to M'hich the table is intended to 

 be applied accuracy in these places is not required. The same is done in 

 several other copies of this table occurring in other nautical collections. 

 Opposite is given 4 . 88 . . instead of — oo. The other tables are nautical. 



