106 REPORT — 1873. 



and the author has written on the back, " This sheet proves that, with 

 the usual form of figures of the same size as those used in the tables, they 

 woidd not have been distinctly legible." The figures actually used are very 

 thin, and have large heads and tails, resembling somewhat figures made in 

 writing ; and a comparison of the specimen and a page of tho tables shows 

 very clearly the superiority of the latter in point of distinctness. The words 

 in minima forma are quite justified, as we do not think it would be possible 

 to make the tables occupy less room without serious loss of clearness. All 

 that is usually given in a page of seven-figure logarithms is here contained 

 in a space about 3 in. by 5 in. ; and yet, owing to tho shape of the figures, 

 every thing is very distinct. The author says on the titlepage, " purcjaUe 

 ah erroribus prceccdeniium tabulariim ;" but the last figure of log 52943 

 is ])rinted 6 instead of 5. There is also another last-figure error. Sec 

 ' Monthly Notices of the Eoy. Ast. Soc.,' March 1873. 



A short I'eview of this work by Gauss appeared in the ' Gottingische ge- 

 lehrte Anzcigcn,' March 31, 1831 (reprinted ' Werke,' t. iii. p. 255). 



Henrion, 1026. [T. I.] Logarithms to 20,001, to 10 places, with 

 interscript differences (characteristics not separated from the mantissa)), 

 copied from Briggs, 1624, 



[T. II.] Log sines and tangents for every minute, to 7 places (charac- 

 teristics unscparated from the mantissae), taken from Guntee, 1620. Hen- 

 BION had calculated some logarithms himself when he received Beiggs's work 

 (see PhU. Mag., Supp. No. Dec. 1872). The copy of Heneion wo have 

 seen is in tho Brit. Mus. The full titlepage is given in § 5. 



Heutschen (Vlacq), 1757. [T. I.] Natural sines, tangents, and secants, 

 and log sines and tangents to eveiy minute, to 7 places (arranged on what De 

 Morgan calls the GeUibrand model) (180 pp.), and [T. II.J logarithms of 

 numbers to 10,000, to 7 places, arranged in columns (lOO pp.). 



A former edition of 1748 is spoken of in the preface ; and it is stated that 

 the tables were compared with the editions of Vlacq, Leydeu, 1051, the Hague, 

 1665, and Amsterdam, 1673. The type is very bold and clear, much easier 

 to read than in most modern tables. 



This is one of the numerous series of small tables known by the name of 

 Vlacq, and is described here because it is not mentioned by De Morgan ; 

 small editions hke the present are so difficult to meet with that it is desirable 

 to notice them whciiever any are found. 



Hobert and Ideler, 1799. [T. I.] Natural and log sines, cosines, tan- 

 gents, and cotangents for the quadrant, divided centesimally; viz. these func- 

 tions are given for arguments from -00001 to -03000 of a right angle at in- 

 tervals of -00001 of a right angle, and from -0300 to -5000 of a right angle 

 at intervals of -0001, to 7 places, with differences. Expressed in grades (cen- 

 tesimal degrees) &c., the arguments proceed to 3" at intervals of 10", and 

 thence to 50" at intervals of V. The manner of calculation of the table 

 is fully explained in the introduction ; and this adds much to the value of the 

 work. Several of the fundamenta were calculated to a great many places. 

 Two or three constants are given on p. 310. 



B. Table of natural sines and tangents for the first hundred ten-thousandths 

 (viz. for -0001, -0002 &c.) of a right angle, to 10 places. 



C. Four tables, expressing (I.) 1°, 2°, 3°,. . . .89°, (II.) 1', 2',. . . .59', 

 (111.) 1", 2",. . . .59", (IV.) V", 2'",. . . .59'", aU as decimals of 90°, to 14 

 places. 



D. Three tables to express (I.) hundredths, (II.) thousandths, (III.) ten- 

 thousandths of 90°, in degrees, minutes, and seconds (sexagesimal). 



