ON .AlAXHJiMATlCAL TVBLISS. 55 



make any use of it, that we have received from Professor Bicrcns do Haan a 

 copy of a very valuable tract, ' Jets over Logarithmentafels,' extracted from, 

 the ' Yerslagcii en Mededeelingen der Kouinklijke Akademie van Weten- 

 schappen, Afdeeling Natuurkuudc,' Deel xiv. Amsterdam, 1862, 8vo (pp. SO), 

 which contains by far the most complete list of authors or editors of loga- 

 rithmic tables of all kinds, with the dates and places of publication (from 1014 

 to 1862), that we have seen, and must be nearly perfect. Some remarks arc 

 made on those of them that de Haan has examined himself ; and there is ap- 

 pended a valuable index of reference to papers on logarithms that have ap- 

 peared in any Journal or Society's Proceedings. 



We may also refer to the paper of Gernerth's noticed under Rheticus, 

 1596 (§ 3, art. 10), Avhich contains a number of last-figure errors in logarith- 

 mic ancl other tables. Gernerth was desirous of ascertaining the care bestowed 

 on the editing of mathematical tables, and considering that it was best 

 measured by the accuracy of the last figure, he confined himself to the exa- 

 mination of this point alone (except in the cases of Rheticus and Pitiscus, 

 where tlie first seven or eight figures were included) , and detected very many 

 errors. He altogetlicr examined tables by eighteen authors ; but generally, 

 where the errors were numerous, he has given only five per cent, of those that 

 he found. 



Also, as this sheet is passing through the press, we add references to two 

 papers in the ' Monthly Notices of the Royal Astronomical Society ' for 

 April and May, 1873, " On the Progress to accuracy of Logarithmic Tables," 

 and " On Logarithmic Tables ;" in the former of which the number of Vlacq's 

 original errors that were reproduced in succeeding works is discussed, while 

 the latter contains remarks on logarithmic tables both of numbers and trigo- 

 nometrical fanctions. An abstract of the first appears also in the ' Journal 

 of the Institute of Actuaries,' vol. xvii. pp. 352-354. 



Briggs, 1617. Logarithms of numbers from unity to 1000 to 14 places 

 of decimals. This was the first table of Rriggian logarithms calculated or 

 published. Neither author's name nor date nor place appears on the title- 

 page of the work, which is a mere tract of 16 pp. (at all events in the Brit. 

 Mus. copy) ; but that it was published by Briggs in 1617 is beyond doubt 

 (see ' Phil. Mag.' he. cit. below). 



The preface concludes with the motto "In tenui; sed non tenuis fructusve 

 laborve." On the work see the introductory remarks to tliis Article, aud 

 also 'Phil. Mag.' December (Supplementary No.) 1872. It is stated by 

 Hutton and all the other writers to be an 8-place table ; but it really is as 

 described above. One reason for the universal error is that copies are so 

 extremely rare that we have only been able to see one *, viz. that in the British 

 Museum, in the catalogue of which it is entered under Logarithms, and 

 marked as of [1695 ?]. The book is not in the printed Bodleian Catalogue. It 

 is peculiarly interesting as being the first publication of decimal logarithms. 

 Nearly all the descriptions and bibliographies will be found very erroneous, 

 several confounding it with "Wright's translation of Napier's ' Canon ' (see 

 § 3, art. 17). 



Briggs, 1624. Logarithms of numbers from 1 to 20,000, and from 90,000 

 to 100,000, to 14 places, with interscript differences. The characteristics to 

 the logarithms are given ; aud this has led to the table being sometimes erro- 

 neously described as being to 15 places. The table occupies 300 pages. 



* We think we remember to have met with another among the Birch lilSS. in tho 

 British Miisewm. 



