68 JtEPORt — 1873. 



NoRiE, 1836, T. XXIII. ; Shoetrede (Tables), 184^ T. V. ; Doxif, 1789, 

 T. II. (sines and cosecants only). 



(To 6 places) Eiddle, 1824, T. lY. ; Galbraith, 1827, T. lY. ; J. Taylor, 

 1833, T. XYII. ; Trotter, 1841 [T. II.] ; Griffin, 1843, T. 16 ; J. Taylor, 

 1843, T. 3; Coleman, 1846, T. XIX.; Domke, 1852, T. XXXTL; IIaper, 

 18.57, T. 65. 



(To 5 places) Adams, 1796 [T. III.] ; Bowditch, 1802, T. XYI. ; Moore, 

 1814, T. III. 



Log. I elapsed time, mid time, and rising. — (To 5 places) ,Donn, 1789, 

 T. lY. ; Maskelyne (Requisite Tables), 1802, T. XYI. ; Bowbitch, 1802, 

 T. XIII. 



The tbree Tables are separated in the following : — (To 5 places) Mackay, 

 T. XLYIII.-L. ; Moore, 1814, T. XXIII. ; Norie, 1836, T. XXYII.- 

 XXIX. ; DoMEE, 1852, T. XXXYII.-XXXIX. 



We have thought it worth while to collect into one list below all the tables, 

 giving log sines &c. to every second. It must be particularly noticed, how- 

 ever, that in the great majority of cases only the functions for the first few 

 degrees of the quadrant are given to every second in the tables z'eferred to, 

 which should in all cases be sought in § 4. 



Tables of logarithmic trigonometrical functions to seconds. — Gardiner, 

 1742 [T. il. I, and (Avignon) 1770 [T. II.] ; Schulze, 1778 [T. III.] ; 

 Taylor, 1792, T. III. (for the whole quadrant) ; Yega, 1794, T. II. ; Yega, 

 1797, T. II. ; Yega, 1800, T. II.; Ducom, 1820, T. IX. ; Xerigan, 1821, 

 T. Yllt. ; [Schumacher, 1822?] T. VI.; *Salomon, 1827, T. IX.; Bagay, 

 1829, Appendix (for the whole quadrant) ; Hassler, 1830 [T. II.] ; Jahn, 

 1837, Yol. II. ; [De Morgan] 1839 [T. lY.] ; HUlsse's Yega, 1840, T. U. ; 

 Muller, 1844 [T. lY.] ; Shortrede (Tables), 1844, T. III. and 1849, 

 Yol. II. (for the whole quadrant); Rarer, 1846, T. II.; Kohler, 1848 

 [T. lY.] ; DoMKE, 1852, T. XXXIY. ; Bremiker, 1852, T. II. ; Callet, 1853 

 [T. IX.]; Bremiker's Yega, 1857, T. II. ; Raper, 1857, T. 66; Hutton, 

 1858, T. YIII. ; Wackerbarth, 1867, T. III. ; Dupuis, 1868, T. YI. and 

 YII. ; Bruhns, 1870, T. II. ; Inman, 1871 [T. III.] and [T. YIII]. 



We have formed the following lists of tables in § 4, which (not only in tho 

 same work, but side by side in the same table) give both natural and 

 logarithmic functions : — 



Tables containing both natural and logarithmic functions (^in the same table). 

 —(To 15 places) Callet, 1853 [T. YII.] (centesimal). 



(To 7 places) Sir J. Moore, 1681 [T. III.] ; Ylacq, 1681 [T. I.] ; 

 OzANAM, 1685 ; SherwixN, 1741 [T. lY.] and [T. Y.] ; Hentschen (YLAca), 

 1757 [T. I.] ; Schulze, 1778 [T. Y.] ; Donn, 1789, T. III. ; Lambert, 1798, 

 T. XXYI. ; HoBERT and Ideler, 1799 [T. I.] (centesimal) ; Willich, 1853, 

 T. B ; Hutton, 1858, T. IX. 



(To 6 places) Oughtred, 1657 [T. I.]; Ursinus, 1827 [T. Y.]. 



(To 5 places) HoiJEL, 1858, T. II. 



(To 4 places) Donn, 1789, T. Y. 

 (Mixed) Bates, 1781 [T. II.]. 



Natural and log versed sines (in the same table). — (To 7 places) Sir J. Moore, 

 1681 [T. lY.] ; [Sir J. Moore, 1681, versed sines] ; Sherwin, 1741 [T. Y.] ; 

 Douglas, 1809, T. lY. 



Art. 16. Tables of Hyperbolic Logarithms (viz. logarithms to base 2-71828. . .), 



The logarithms invented by Napier, and explained in the ' Descriptio ' 



(1614) and ' Coustruetio ' (1619) (see § 3, art. 17), were uot the same as 



