ON MATHEMATICAL TABLES. Gl 



reversed commas. The absence of rules does not appear to us by any 

 means an unqualified advantage ; and a farther drawback is that numbers 

 and logarithms are printed in the same type. The change of figure in the 

 line is denoted by an Arabic nokta (a sign like the diamond in a pack of cards) ; 

 and this, tliough very clear for O's, leaves the other figures unchanged, and 

 is greatly inferior in all points of vievr to the simple asterisk prefixed, or the 

 small figure as used by Babbage. 



In spite of these drawbacks the table is very convenient, and has 

 advantages possessed by no other, as, in addition to the greater ease with 

 which the interpolations can be performed, greater accuracy is obtained — the 

 last figure being often inaccurate by one or tv/o units in logarithms inter- 

 l^olated from the usual seven-figure tables. We find, however, that computers 

 prefer Babbaoe, except for numbers beginning with 1. 



The logarithms of the numbers between 100,000 and 200,000 were calcu- 

 lated de novo by Mr. Sang, as if logarithms had never been computed before ; 

 and a very full account of the method and manner in whicli the calcula- 

 tions were performed is given by him in the * Edinbm-gh Transactions,' 

 vol. xxvi. pt. iii. (1871). Tliis is the only calculation of common logarithms of 

 numbers since the days of Vlacq, 1628 (except the French manuscript tables). 



Two errors in the book (which is stereotyped) were pointed out in the 

 * Athenajum' for Juno 8 and 15, 1872, viz. the last figures of log 389G2 and 

 52943 should be 2 and 5 instead of 3 and 6 respectively. 



Mr. Peter Gray has kindly communicated to us the following six im- 

 portant eiTors which have been discovered and communicated to Mr. Sang 

 (or found on revision) and circulated by him in certain later copies of his 

 tables : — 



Page 203, log 118530, /or 9503 read 8503 



„ 354, for number 19540 read 19440. 



The following is a classified list of the tables of logarithms contained in 

 works that are described in § 4 : — ■ 



Tables of Lor/arithns of Numbers (to more than 20 places). — Sharp, 

 1717 [T. IV.] (61 places) ; SmmwiN, 1741 [T. I.] and [T. II.] (61 places) ; 

 HoBEitT and Ideler, 1799 [T. III.] (36 places); Byrne, 1849 [T. IV.] 

 (50 places) ; Callet, 1853 [T. III.], I. and II. (61 places) ; Huttox, 1858, 

 T. 5 and 6 (61 places, early editions onlv) ; Parkhurst, 1871, T. II., III., 

 and IX. (102 places), and T. XVIII. (Ol'places). 



(To 20 places) Gardiner, 1742, and (Avignon) 1770 [T. IV.] and [T. V.]; 

 Paekhttrst, 1871, T. XIII. and XIV. 



(To 15 places) Douglas, 18i)9, T. IV., Supplement. 



(To 11 places) Boeda and Delambrk, 1800 or 1801 [T. II.] ; Kohlee, 

 1848 [T. III.] ; Callet, 1853 [T. II.], I. and II ; Hovel, 1858, T. V. 

 (table to calculate logarithms) ; IIxiTXOjr, 1858, T. II. and III. 



(To 10 places) De Decker, 1626 [T.I.]; Henrion, 1626 LT.I.]; Vlacq, 1628 

 and 1631 [T. I.] ; Vlacq, 1633 [T. II.] ; Vega, 1794 [T. I.] ; Hantschl, 

 1827, T. IV. ; *-Saloiion, 1827, T. VIII. ; Parkhurst, 1871, T. XII. 



(To 8 places) John Newton, 1658 [T. I.] ; Houel, 1858, T, IV. (table to 

 calculate logarithms) ; PAEKnuRST, 1871, T. XXXVII. 



(To 7 places) Faulhaber (Logarithmi), 1631 ; Norwood, 1631 ; Roe, 1633, 



