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HISTORY OF

TRACT 20 .

Gardiner also printed at London, in 1742, a quarto volumeof “ Tables of Logarithms, for all numbers from 1 to 102100,and for the sines and tangents to every ten seconds of eachdegree in the quadrant; as also, for the sines of the first 72minutes to every single second: with other useful and neces-sary tables;” namely a table of Logistical Logarithms, andthree smaller tables to be used for finding the logarithms ofnumbers to twenty places of figures. Of these tables ofGardiner, only a small number was printed, and that by sub-scription; and they have always been held in great estimationfor their accuracy and usefulness.

An edition of Gardiner’s collection was. also elegantlyprinted at Avignon in France, in 1770, with some additions,namely, the sines and tangents for every single second in thefirst four degrees, and a small table of hyperbolic logarithms,copied from a treatise on Fluxions by the late ingenious Mr.Thomas Simpson : but this is not quite so correct as Gardi-ner’s own edition. The tables in all these books are to sevenplaces of figures.

Lastly, my own Mathematical Tables, being the most ac-curate and best arranged set of logarithmic tables ever beforegiven; preceded also by a large and critical history of Tri-gonometry and Logarithms, and terminating with a copiouslist of the errors discovered in the principal other tables ofthis kind.

There have also lately appeared the following accurate andelegant books of logarithms; viz. 1. “ Logarithmic Tables,”by the late Mr. Michael Taylor, a pupil of mine, and authorof “ The Sexagesimal Table.” His work consists of threetables ; 1st, The Logarithms of Common Numbers from 1 to1260, each to 8 places of figures; 2dly, The Logarithms ofall Numbers from 1 to 101000, each to 7 places; 3dly, TheLogarithmic Sines aud Tangents to every Second of theQua-drant, also to 7 places of figures: a work that must provehighly ur.eful to such persons as may be employed in very niceand accurate calculations, such as astronomical tables, &c.The author dying when the tables were nearly all printed off,