ON MATHliMATlCAL TABLES. 137 



T. XXV. Natural versed sines for every minute to 120°, to 6 places, with 

 proportional parts for seconds. 



The other tables are nautical &c. 



Trotter, 1841. [T. I.] Six-figure logarithms of numbers to 10,000, 

 with differences. This is followed by a small table to convert Briggian into 

 hyperbolic logarithms drc. 



[T. II.] Log sines, tangents, and secants to every quarter point, to 6 

 places. 



[T. III.] Log sines and tangents for every fifth minute of tlic quadrant, 

 to 6 places. 



[T. lY.] Natural sines and tangents for every fifth minute of the quadrant, 

 to 6 places. 



[T. v.] Areas of circular segments, to 6 places ; same as T. XIII. of 

 Hantschl. 



[T. VI.] Squares, cubes, square and cube roots (to 6 places) for numbers 

 from 1 to 1000. 



[T. VII.] Circular measure of 1°, 2°, . . . . 180°, of 1', ... . 60', of 1", ... . 60", 

 and of 1'", 60'", to 7 places. 



[T. VIII.] lleciprocals of numbers from 1 to 500, to 9 places. 



[T. IX.] Logarithms of ntimbers from 1000 to 1100, to 7 places. 



[T. X.] Lengths of sides of inscribed and circumscribed polj'gons (up to a 

 20-sided figure), the diameter of the circle being unity, to 7 places. 



[T. XL] Hyperbolic logarithms of numbers from 1 to 100, to 8 places, 



[T. XII.] For finding the areas of oblong and oblate spheroids. A few 

 constants are given. The other tables are astronomical, meteorological, &c. 

 Some trigonometry &c. is prefixed at the beginning (i^p. 102). 



Turkish Logarithms &c. [1834]. The book commences on the ]a.st 

 page ; and the first table gives seven-figure logarithms of numbers from unity 

 to 10,080, arranged consecutively in columns, there being three columns of 

 arguments and tabular results to the page. The tables begin at the last page, 

 as before remarked, the extreme right-hand column being the first column of 

 arguments ; to the left of it is the corresponding column of tabular results, 

 then to the left of that the second column of arguments, and so on. The 

 table occupies 84 pp. (up to p. 85). Then " ^Uows " a table of log sines and 

 tano-ents for every minute of the quadrant (semiquadrantally aiTanged), the 

 sines and cosines being side by side, and separated by some " white " from 

 the tangents and cotangents. This table occupies 90 pp., and is followed by 

 a similar table of natural sines and tangents (to 7 places), which also occupies 

 90 pp. Except that the table runs in the wrong dii-ection, it only differs from 

 an ordinary table in the ten digits being denoted by different marks from 

 those to which we are accustomed. A few minutes' practice, however, is quite 

 sufficient to get used to the new numerals ; and then the table could be used 

 as well as any other. There is no introductory or explanatory matter. The 

 book is in the British Museum ; and the place and date in § 5 are taken from 

 the Catalogue of the Library. 



Ursinus, 1827. [T. I.] Six-figure logarithms to 1000, and from 10,000 

 to 100,000, without differences ; the values of S and T for finding log sines 

 and tangents of angles below 2° 46' 40" (see § 3, art. 13) are given at the top 

 of the page. 



[T. II.] Log sines and tangents for every 10 seconds throughout the 

 quadrant, with differences, to 6 places. 



[T. III.] Longitudes of circular arcs, viz. circular measure of 1°, 2°, 3°, . . . . 

 360°, of 1', 2', 60', and of 1", 2", 60", to 7 places. These are followed 



