ON MATHEMATICAL TABLES. 131 



The editions ^ye have Been are 1705 and 1706, 1717, 1726; the third 

 edition 1741 and 1742, the fourth 1761, and the fifth 1771 and 1772. It 

 thus appears that it was uot at all an uncommon thing (probably as the 

 impression was being made up from time to time) to advance the date by one 

 year. The first four dates we may distribute among the first two editions as 

 we please ; most likely 1705, 1706, and 1717 for the first, and 1726 for the 

 second. 



Hogg (p. 401) gives the editions as 1706, 1742, 1763, and 1771 ; but else- 

 where (p. 262) he speaks of the fifth as of 1785, which must be incorrect. 



De Haan (' lets over Logarithmentafels,' p. 57) gives the dates of the 

 editions as 1706, 1717, 1726, second 1742, 1751, 1763, fifth 1771. The 

 subject of the dates of the editions of Sherwin is discussed at some length in 

 the ' Monthly Notices of the Eoyal Astronomical Society ' for March and 

 May 1873 (vol. xxxiii. pp. 344, 454, 455, 457). Mr. Lewis, in his letter 

 to the reporter, printed in the second of these papers, mentions 1717, 1742, 

 1761, and 1771 as the dates of the editions he had seen, agreeing perfectly 

 with those mentioned by De Morgan, Lalande (' Eibliog. Astron.'), and the 

 results of our own observation. He remarks that Barlow gives 1704 and 

 Callet 1724 as dates of editions, of which the former may bo dismissed at 

 once as an obvious blunder. The editions therefore tliat we have not seen, 

 but which mai/ exist, are those of 1724, 1751, and 1763. About any of 

 these or any others we should be glad to receive information. 



Eogg mentions that Skerwin has often been confounded with Gardinee, 

 even by Kiistner and Bugge. 



With regard to the accuracy of the tables, Httttoit writes (we quote from 

 p. 40 of the Introduction to his tables, 3rd edit. 1801) : — " The first edition 

 was in 1706 ; but the third edition, in 1742, which was revised by Gardiner, 

 is esteemed the most correct of any, though containing many thousands of 

 errors in the final figures : as to the last or fifth edition, in 1771, it is so erro- 

 neously printed that no dependence can be placed in it, being the most in- 

 accurate book of tables I ever knew ; I have a list of several thousand errors 

 which I have corrected in it, as well as ia Gardiner's octavo edition." 



De Haan ('lets' &c., p. 20), speaking of the 1742 edition, says that it 

 contains the logarithms of the numbers from 999,980 to 1,000,020 to 61 

 places ; but on examination we find that the above descrii^tion of [T, II.] is 

 correct. The advertisement to the book itself is no doubt the source of the 

 error ; for it is there said to contain the logarithms of the 41 numbers from 

 999,980 to 1,000,020, whereas it rcaUy contains the logarithms of the 35- 

 numbers from 999,981 to 1,000,015. 



Sherwin's tables are of historical interest as forming part of the main line 

 of descent from Briggs ; and the different editions cover the greater part of 

 the last century. The chief succession (considering only logarithms of num- 

 bers) is Briggs, Yiacq, Eoe, Joitn Newton, Skerwin, Gardiner ; and then: 

 there are two branches, viz. Hutton founded on Sherwin, and Callet on 

 Gardiner, the editions of Vega forming an offshoot. 



Shortrede (Compendious logarithmic tables), 1844. Small tables of 

 common logarithms with sexagesimal arguments, logarithms to 12,600, anti- 

 logarithms from to -999, log sines and tangents to 5', also from 0° to S\ 

 and from 3° to 5° for every two minutes ; aU to five or six places. The 

 tract only contains 10 pp. 



Shortrede (Tables), 1844. T. I. Seven-figure logarithms to 10,800 with 

 characteristics, but without difterenccs, and from 10,800 to 120,000, with 

 differences, and their first nine multiples at the bottom of the page : the uum- 



k2 



