78 REPORT— 1873. 



The addition table occupies 45 pp., the subtraction table 156 pp. The 

 whole is a reprint from Hulsse's Yega of 1849, the paging being unaltered, 

 and running from 636 to 836. The second edition is identical with the first, 

 except that the 3 pp. of introduction are omitted. 



■Wittstein, 1866. A fine table of Gaussian logarithms in a modified 

 form. H (=log (1 +.v)) is given to seven places for the argument A ( =log a) 

 for values of the argument from 3'0 to 4'0 at intervals of -l, from 4-00 to 

 600 at intervals of -01, from 6-000 to 8-000 at intervals of -001, from 

 8-0000 to 10-0000 at intervals of -0001, and also from -0000 to 4-0000 at the 

 same intervals. Differences and proportional parts (or rather multiples) are 

 given, except on one page (p. 5), where they are given for alternate 

 differences as there is not sufficient space. 



The arrangement is similar to that of a seven-figure logarithmic table. 

 The figures have heads and tails, and are very clear. 



On p. 127 there is given a recapitulation to three places, and to hundredths, 

 of part of the table and the formulaj. A complete explanation is given in 

 the introduction to the work'. 



Gaussian logarithms are very useful in the solution of triangles in such 



formulae as cot „ — _ t tan (A — B), in which Weidenbach's table would 



also be useful. 



The following is a list of tables of Gaussian logarithms contained in 

 works noticed in § 4. 



Tables of Gaussian hgaritJims. — Pasquicit, 1817, T. III. (5 places) ; 

 [Encke, 1828] [T. III.] (4 places) ; Xohlee, 1832 [T. III.] ; Hulsse's Vega, 

 1840, T. XII. ; Mt-LLER, 1844 [T. II.] ; [Sheepshanks," 1844] [T. V.] ; 

 KoHLEH, 1848 [T. II.] ; Shortrede, 1849, T. VII. ; Filipowski, 1849, T. II. ; 

 HouEL, 1858, T. III. ; Galbraith and Haughton, 1860 [T. IV.] ; Oppolzer, 

 1866. 



Art. 20. Tallies to convert Bri(/c/ian into Hyperholic Logarithms, and vice versa. 



Tables for the conversion of Briggian into hyperbolic logarithms, and vice 

 versa, are given in nearly all collections of logarithmic tables. Such a table 

 merely consists of the first hundred (sometimes only the first ten) multiples 

 of the modulus -43429 44819 03251 82765 11289. . . ., and its reciprocal 



2-30258 50929 94045 68401 79914 , to five, six, eight, and ten or even 



more places. A list of such tables, contained in works described in § 4, is 

 given below ; tables of this kind, however, rarely exceed a page in extent, 

 and are very easy to construct. It is not unlikely that the list is far from 

 perfect, for in some cases it was not thought worth Avbilc noticing such 

 tables when of small extent and to few places. "We mention Degen (§ 4) as 

 containing one of the largest. 



The following is a list of tables contained in works noticed in § 4. 



To convert Briggian into hiiperholic logarithms and vice versa. — (To more 

 than 10 places) Schtjlze, 1778 [T. I.] ; "Degen, 1824, T. II. ; Sjiorxrede, 

 1849, T. VII. ; Callet. 1853 [T. IV.] ; Paskhxjrst, 1871, T. V. 



(To 10 places) Schron, 1860, T. I. ; Bruhns, 1870. 



(To 8 places) Shortrede (Tables), 1844, T. XXXIX. ; Kohler, 1848, 

 [T. I.] ; HotJEL, 1858, T. III. 



(To 7 places) Bremiker, 1852, T. I. ; Beejiiker's Vega, 1857, T. I. ; 

 Dupuis, 1868, T, V. 



(To 6 places) Dodson, 1747, T. XXXVII. 



