ON MATHEMATICAL TABLES. 47 



Vlacq, 1G81 [T. I.J ; Ozanam, 1G85 ; Sheravin, 1741 [T. IV.] ; Hent- 

 RCHBN (Vlacq), 1757 [T. I.] ; ScncLZE, 1778 [T. V.] ; Lambert, 1793, T. 

 XXVI. ; Douglas, 1S09 [T. III.]. 



(To 6 places) Oughtred, 1657 [T. I.] (centesimal division of the degree) ; 

 Ursinus, 1827 [T. V.] ; Eeardmore, 1862, T. 38. 



(To 5 places) Houel, 1858, T. II. ; Peters, 1871 [T. V.]. 



^ines and taivjents (only). — (To 7 places) Uates, 1781 [T. II.] ; Vega, 

 1797, T. III. ; Hobert and Ideleu, 1799 [T. I.J (centesimal) and B (cen- 

 tesimal) ; (?) *Salomon, 1827, T. XII. ; Turkish Logaruhms f 1834J ; 

 HtJLSSE's Vega, 1840, T. III. 



(To 6 places) Trotter, 1841 [T. IV.]. 



(To 5 places) Schmidt, 1821 [T. III.] ; Eankine, 1866, T. G ; Wacker- 

 BARTH, 1867, T. VIII. 



(To less than 5 places) Parkhurst, 1871, T. XXX. and XXXI. 



TancjenU and secants (only). — Donn, 1789, T. V. (4 j)laees) ; [Sheep- 

 shanks, 1844] [T. IV.] (4 places). 



Sines (alone). — (To 15 places) Callet, 1853 [T. VII.] (centesimal). 



(To 7 places) Donn, 1789, T. Ill ; Hassler, 1830 [T. V.]. 



(To 6 places) Maskelyne (Eequisite Tables, Appendix), 1802, T. I.; Ducom, 

 1820, T. XIX. ; KERiG.iiT, 1821, T. IX. ; J. Taylor, 1833, T. XX. ; Norie, 

 1836, T. XXVI.; Griefin, 1843, T. 19; J, Taylor, 1843, T. 32; Domke, 

 1852, T. XXXVI. 



(To 5 places) Lambert, 1798, T. XXV. ; Maskelyne (Requisite Tables), 

 1802, T. XVII. ; BowDiTCH, 1802, T. XIV. ; Moore, 1814, T. XXIV. ; 

 Wallace, 1815 [T. III.] ; Gregory, &c., 1843, T. X. 



Midtiples o/ suies.— Schulze, 1778 [T. VI.] ; Lambert, 1798, T. XXV. 



Versed sines (alone).— (To 7 jjlaces) Sir J. Moore, 1681 [T. IV.] ; [Sir 

 J. Moore, 1681, Versed sines'] ; Dodson, 1747, T. XXVI. ; Douglas, 1809, 

 [T. IV.] ; Farley, 1856 [T. I.]. 



(To 6 places) Maskelyne (Requisite Tables, Appendix), 1802, T. II. ; 

 Mackay, 1810, T. XLI. ; Lax, 1821, T. XVII. (and coversed &c. sines) ; 

 Riddle, 1824, T. XXVIIL ; IS'orie, 1836, T. XXXVI.; Rumker, 1844, 

 T. III. ; Inman, 1871 [T. VIIL] and [T. IX.]. 



Sines &c. expressed in radicals.- — Lambert, 1798, T. XIX. ; Ursinus, 

 1827 [T. III.] ; Vega, 1797, Appendix. 



Miscellaneous. — Sin" -U, Andrew, 1805, T. XIII ; sin" x and tan- x, 



Pasuuich, 1817, T. II. ; suversed, coversed, sucoversed sines, Lax, 1821, T. 

 XVII. ; I sin .r, Stanseury, 1822, T. Y; sexagesimal cosecants and cotan- 

 gents, Beverley (1833 ?), T. VI. (pp. 232 &c.) ; sexagesimal sines. Id. T, 



XV.; sin lHt;LSSE'sVEGAT.IV.1840;sin^~, [Sheepshanks, 1844] [T. VL] ; 



I sin X expressed sexagesimally, Gordon, 1849, T. XVIII. ; see also Schlo- 

 milch [1865 ?]. 



Note. — A list of tables in which both natural and logai-ithmic functions are 

 given side by side in the same table is added at the end of § 3, art. 15. 



Art. 11. Lengtlis of Circular Arcs. 



Tables of the lengths (or longitudes) of circular arcs are very frequently 

 given in collections of logarithmic and other tables ; but we have seen none 

 of sufficient extent to be published separately. Angles are measured either 

 by degrees, minutes, &c., or by the ratio which the corresponding arc bears 



