ON MATHEMATICAL TABLES. 67 



T. XIX. ; NoRiE, 1836, T. XXV. ; Jahn, 1837, Vol. II. ; Parley, 1840 

 [T. II.] ; J. Taylor, 1843, T. 5 ; Kumker, 1844 ; Domke, 1852, T. XXXIV. ; 

 Bremiker, 1852, T. II. 



(To 5 places) Bates, 1781 [T. II.] ; Lalande, 1805, T. II, ; De Prasse, 

 1814 [T. II.] ; Pasquich, 1817, T. II. ; Reynaud, 1818 [T. II.] ; Schmidt, 

 1821 [T. II.] ; KoHLER, 1832 [T. II.] ; [Db Morgan], 1839 [T. III.] ; 

 Galbraith and Haughton, 1860 [T. III.] ; Wackerbarth, 1867, T. III. 



(To 4 places) [Encke, 1828] T. II.; Beverley (1833?), T. XVII. ; 

 MuLLER, 1844 [T. IV.]; [Sheepshanks, 1844] [T. III.]; Warnstorff's 

 Schumacher, 1845 [T. IV.J ; Thomson, 1852, T. XVI.; Oppolzer, 1866; 

 Parkhurst, 1871, T. XXX. and XXXI. 



(Miscell.) Shortrede (Comp. Log. Tab.) 1844. 



Log sines and secants (only). — (To 5 places) Stansbury, 1822, T. H. 



Lo(j sines (alone*) (for small arcs, sines = tangents). — (To 7 places) 

 Gardiner, 1742 [T. II.], and (Avignon) 1770 [T. II.] ; Hulsse's Vega, 1840, 

 T. II. ; KiiHLER, 1848 [T. IV.]. 



(To 6 places) Mackay, 1810, T. XLVI. ; Kerigan, 1821, T. VIII. ; 

 Hanxschl, 1827, T. II. ; Farley, 1840 [T. III.] ; Rapbr, 1846, T. III. ; 

 Raper, 1857, T. 66 and 67 ; Beardmore,'1862, T. 37 ; Inman, 1871 [T. III.]. 



(To 5 places) [Schumacher, 1822?] T. VI.; [De Morgan] 1839 [T. IV.] ; 

 Raper, 1846, T. II. ; Thomson, 1852, T. XII. 



(To 4 places) [Sheepshanks, 1844] [T.II.]; Parkhurst, 1871, T. XXXVIII. 



(Expressed otherwise) Acad:6mie de Prusse, 1776 [T. I.] ; Callet, 1853 

 [T. VII.] (centesimal) (15 places). 



Lot/ tangents (alone*) (for small arcs, sines = tangents). — (To 7 places) 

 Gardiner (Avignon), 1770 [T. II.]. 



(To 6 places) Mackay, 1810, T. XLVII. ; Hantschl, 1827, T. III. 



Log versed sines (alone). — (To 7 places) Sir J. Moore, 1681 [T. IV.] ; 

 [Sir J. Moore, 1681, versed sines] ; Douglas, 1809 [T. IV.] ; Parley, 1856 

 [T. 11.]. 



(To 6 places) Rumkeb, 1844, T. IV. 



(To 5 places) Kerigan, 1821, T. XI.; J. Taylor, 1833, T. XXI., and 

 1843, T. 30. 



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



JS^ote. — Log rising (in nautical tables) =log versed sine. See next page. 



Log secants (alone). — (To 5 places) Thomson, 1852, T. XI. 



Miscellaneous.— IjOg sec x, \ log sec x, and | log sin x, Croswell, 1791, 

 T. I. ; log difF. sin., Borda and Delambre, 1800 or 1801 [T. V.] (centesimal) ; 

 log I (1 + cos x), log I (1 ± sin .r) &c., Rios, 1809, T. XVI. ; log tan 



*|, Stansbury, 1822, T. Z»; log i (1 - cos x) &e., Stansbury, 1822, T. R. ; 



log 1 (1— cos x), NoRiE, 1836, T. XXXI. ; log h (1— cos x), Coleman, 1846, 

 T. XXL; log I (1-cos x\ Gordon, 1849, T.'XVIII. ; log! (1-cos x), 

 Thomson, 1852, T. XIII. ; log cosec .r-r54000, Thomson, 1852"; T. XV. ; log 



sin "^^ Thomson, 1852, T. XXIII.; log \ (1-cos x), Raper, 1857, T. 69; 



\ log \ (1 — cos x) and log \ (1— cos x), Inman, 1871, T. V. and VI. 

 The following arc tables generally met Avith in nautical collections : — 

 Log sines, tangents, and secants to everg quarter-point. — (To 7 places) 



* Tables of sines and tangents are not unfreqiiently printed with the sines on the versos 

 and the tangents on the rectos of tlie leaves, or vice versa, so that practically they arc sepa- 

 rated ; hxit in such cases the table has usually been regarded merely as one of sines and 

 tangents. 



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