130 REPORT— 1873. 



to 101,000, with proportional parts. The proportional parts near the begin- 

 ning of the table, being too voluminous for insertion on the page, are printed 

 on a fl}'- sheet, and bound up facing the introductory page of the table. 



[T. IV.] Natural and log sines, tangents, and secants for every minute, to 

 seven places. Differences for the logarithmic functions are added, but not 

 for the natural ones. 



[T. v.] Natural and log versed sines from 0° to 90° at intervals of a 

 minute, to seven places. Part of a page at the end of [T. V.] is occupied by 

 a small table to convert sexagesimals into decimals, &c., and vice versa. 



The remaining table (of difference of latitude and departure) is not in- 

 cluded in this llcport (see § 2, art. 12). 



Sherwin went through five editions ; but as none were stereotyped, some of 

 the later are less accurate than the earher. De Morgan remarks, " Second 

 edition, 1717; third revised by Gardiner, and the best, 1742; fifth and last, 

 1771, very erroneous — the most inaccurate table Hutton ever met with." 

 In speaking of the third edition we at first thought that De Morgan should 

 probably have written 1741 instead of 1742, as the edition we have described 

 bears the former date, but we have since seen a copy of 1742. 



Wo possess an edition (1726) which contains a list of " Errata for the 

 second edition of Sherwin's Mathematical Tables " by Gardiner. In this edi- 

 tion, in place of [T. I.] and [T. II.] there are given two pages (pp. 28 and 29) 

 headed " M. Brigg's {sic) Logarithms for all Numbers, from 1 to 100, and for 

 all Ffime Numbers from 100 to 200, calculated by that Ingenious Gentleman 

 and Indefatigable Mathematician, Mr. Abr. Sharp, at Little Horton, near 

 Bradford in Yorkshire." The logarithms are given to from 50 to 60 places 

 (not all to the same extent). 



We have also before us an edition of 1706 ; and the dedication, which is 

 the same in aU the editions we have seen, is dated July 12, 1705. The table 

 on pp. 27 and 28 is the same as in the edition of 1726 ; but at the end of the 

 introduction is a table of errata, which are corrected in this latter edition. 

 The titlepage of the editions of 1705, 1706, and 1726, and perhaps other 

 dates, runs, " Mathematical Tables. . . .with their Construction and Use by 

 Mr. Briggs, Mr. Wallis, Mr. Halley, Savilian Professors of Geometry in the 

 University of Oxford, Mr. Abr. Sharp" (the names of the authors being 

 placed one under the other); and in the edition of 1700 is added, "The 

 whole being more correct and comjjlete than any Tables extant." Sherwin's 

 name docs not, therefore, occur on the titlepage at aU ; but the preface is 

 signed and the tables were prepared by him, so that the work is universally 

 known as " Sherwin's Tables." In library catalogues, however, it wDl gene- 

 rally be found entered under the name of Briggs, Wallis, Halley, or Sharp. 



In the edition of 1741, the names of Briggs, Wallis, Halley, and Sharp do 

 not appear on the titlepage, but we have "The third edition, carefully 

 re^^scd and corrected by William Gardiner " instead. 



It will be seen that there is some confusion in the editions, as, if De 

 Morgan is correct in saying that the second edition was published in 1717, 

 the edition of 1726 would be the third, and that of 1741 the fourth. 



The Royal Society's Library contains a copy with "1705" on the title- 

 page, while the edition of 1706 (which is in the library of Trinity College, 

 Cambridge) has the date printed in Eoman characters, MDCCVI. 



We have seen (in the Graves Library) the fourth edition, 1761; and the 

 British Museum contains, besides the editions of 1717 and 1742, the fifth 

 edition, " revised and improved by S. Clark " (1772), while the Cambridge 

 University Library has the same edition with the date 1771. 



