ON MATHEMATICAL TABLES. 129 



riglit circular cones, tlie segment being contained by the base of the cone (a 

 segment of a circle), a hyperbolic section perpendicular to the base, and the 

 curved surface. The use of the table (which contains 500 values of the 

 argument and occupies 5 pp.) is explained on pp. 24—26 of the work. 



[T. lY.] Briggian logarithms of numbers from 1 to 100, and of primes 

 from 100 to 1100, to 61 places; also of numbers from 999,990 to 1,000,010, 

 to 63 places, these last having first, second. . . .tenth differences added. The 

 logarithms in this table were copied into the later editions of Shekwin and 

 other works. 



The portion of the work which contains the tables is followed by a 

 " Concise treatise of Polyedra, or solid bodies of many bases " (pp. 32). 



The work is universally attributed to Abraham Sharp, and no doubt exists 

 as to his having been tlie author. 



[Sheepshanks, 1844.] [T. I.] Four-figure logarithms from 100 to 

 lOOO, arranged as in seven-figure tables, with proportional parts. 



[T. II.] Log sines and cosines (the arguments being expressed in time) to 

 24"' at intervals of 1™, to four places, with proportional parts for multiples of 

 10' (to 60'). Also log sines to l"" for every 10^, with differences for l^ 



[T. III.] Log sines, cosines, tangents, and secants from 0° to 6° at 

 intervals of 1', thence to 84° at intervals of 10', and then at intervals of 1' to 

 90°, to four places. In the parts of the table where the intervals are 10', 

 differences for 1' are given. 



[T. IV.] Natural secants and tangents from 0° to 80"^ at intervals of 10', 

 with differences for 1', and then to 86° at intervals of 1', with difterences for 

 10", to four places. 



[T. v.] Mochfied Gaussian logarithms. There are two tables. The first 



(-.^) 



gives log I 1 + - 1 as tabular result for argument log .r, the range of log 



,^' 



being from "000 to -909 at intervals of "001, from -90 to 2-00 at intervals of 



•01, and thence to 4-0 at intervals of -1. The second table gives log I 1 — - | 



as tabular result, corresponding to the argument log .v, the range being from 

 •000 to 1-000 at intervals of -001, from 1-00 to 3-00 at intervals of -01, and 

 from 3*0 to 6-0 at intervals of •! : both tables to four places, with propor- 

 tional parts. 



[T. VI.] Log sin" (^ hour angle) from 0'' to 9*^ at intervals of 1'", to four 

 places, with proportional parts for multiples of 10' (from IlirER). 



[T. VII.] Autilogarithms, for logarithms from -000 to 1*000 at intervals 

 of '001, to four places, with proportional parts. 



There are also two or three astronomical tables, 



De Morgan states that the work was issued under the title given in § .5 in 

 1840, and tAVO years previously without name or titlepage. It is from one of 

 these earlier copies that the above description has been written ; we have 

 seen no copy bearing either author's name or date. 



Sherwin, 1741. [T. I.] (which follows p. 35 of the introduction) gives 

 Briggian logarithms to 61 places of all numbers to 99, and the logarithms of 

 primes from 100 to 1097, calculated by Abraham Sharp (see Suarp, 1717, 

 [T. IV.]). 



[T. II.] Briggian logarithms of thirty-five other numbers (viz. 99.9,981 

 — 1,000,015), to Gl places, with first, second, third, and fourth differences, 

 to 30 places (Sharp [T. IV.]). 



[T. III.] Seven-figure logarithms of numbers to 1000, and from 10,000 

 1873. K 



