70 REPORT— 1873. 



Rees's Cyclopaedia, 1819 (Art. " Hyperbolic Logarithms," vol. xviii.). 

 Hyperbolic logarithms (to 8 places) of all numbers from 1 to 10,000, arranged 

 in groups of five. 



The table was calculated by Bablow, and appears also in hia mathema- 

 tical tables (1814). 



Dase, 1850 (Hyperbolic Logarithms). Hyperbolic logarithms, from 

 1 to 1000, at intervals of unity, and from 1000-0 to 10.500-0 at intervals 

 of 0-1 to seven places, with differences and proportional parts, arranged 

 as in an ordinary seven-figure table. The change of figure in the line is de- 

 noted by an asterisk prefixed to all the niimbers affected. The table is a 

 complete seven-place table, as by adding log 10 to the results the range 

 -is from 10,000 to 105,000 at intervals of unity. The table appeared in the 

 34th part (new series, t, xiv.) of the ' Annals of the Vienna Observatory' 

 (1851); but separate copies were printed, in the preface to which Dasegavc 

 six errata. This portion of the preface is reproduced in the introduction by 

 Littrow to the above volume of ' Annals.' The table was calciilated to ten 

 places, and three rejected. It was the author of this table who also com- 

 puted the factorial tables (§ 3, art. 8), and calculated the value of n cor- 

 rectly to 200 decimal places (Crelle's Journal, t. xxvii. p. 198). 



Filipowski, 1857. Hyperbolic logarithms, from 1 to 1201, to 7 places, 

 are appended to Mr. Filipowski's English edition of Napier's ' Canon 

 Mirificus.' 



The folloAving is a list of references to § 4 : — 



Hyperholic logarithms of numhers. — (To 48 places) Schulze, 1778 [T. II.] ; 

 Vega, 1 794 [T. III.l ; Callet, 1853 [T. III.], I., and II. 



(To 25 places) Lambert, 1798, T. XVI. 



(To 20 places) Callet, 1853 [T. II.], I. and II. 



(To 11 places) Borda and Delambre, 1800 or 1801 [T. IV.]. 



(To 10 places) *Salomon, 1827, T. VIII. 



(To 8 places) Vega, 1797, Vol. II. T. II. ; Barlow, 1814, T. VI. ; Hant- 

 echl, 1827, T. VI. ; HtLssE's Vega, 1840, T. VI. ; Trotter, 1841 [T. XI.] ; 

 KoHLER, 1848, T. I. 



(To 7 places) Gardiner (Avignon), 1770 [T. VII.]; L.uibert, 1798, 

 T. XIII.-XVI. ; WiLLicH, 1853, T. A ; Hutton, 1858, T. V. and VI. ; 

 Duruis, 1868, T. III. 



(To 5 places) Uankine, 1866, T. 3 ; Wackerbarth, 1867, T. V. 

 • See also *Schlomilch [1865 ?]. 



Art. 17. Napiei-ian Loganthms (not to base 2-71828. . . . ). 

 The invention of logarithms has been accorded to Napier of Merchiston 

 with a unanimity not often met with in reference to scientific discoveries. 

 The only possible rival is Justus Byrgius, who seems to have constructed a 

 rude kind of logarithmic table ; but there is every reason to believe that 

 Napier's system was conceived and perfected before Byrge's in point of time ; 

 and in date of publication Napier has the advantage by six years. Further, 

 Byrge's system is greatly inferior to Napier's ; and to the latter alone is the 

 whole world indebted for the knowledge of logarithms, as (with the exception 

 of Kepler, one of the most enthusiastic of the contemporary admirers of 

 Napier and his system, who does allude to Byrge) no one ever suggested 

 any one else as having been the author whence they had drawn their 

 information, or as having anticipated Napier at all, tiU the end of the last 

 century, when Byrge's claim was first raised, though his warmest advocates 

 always assigned far the greater part of the credit of the invention to Napier. 



