ON MATHEMATICAL TAULES. 107 



E. Four tables to express (I,) hours, (II.) minutes, (III.) sccouds, (IV.) 

 thirds, as decimals of a day. 



F. Small table to express decimals of a day, in hours, minutes, and 

 seconds. 



G. Circular measure of "1, -2, . . . . '9, 1-0, of a right angle, to 44 places. 

 [T. III.] Logarithms of numbers to 1100, and from 999,980 to 1,000,021, 



to 36 places. 



The work concludes with two remarkable lists of errata found in the course 

 of the calculations, viz. 381 errors in the trigonometrical tables of Callet, all 

 of which, with one exception, affect only the last figure by a unit, and 138 

 similar errors in Vega's ' Thesaurus,' 1794, The errors in CaUet have, we 

 presume, been corrected in the later tirages. 



Houel, 1858. T. I. Five-figure logarithms of numbers to 10,800 with 

 the corresponding degrees, minutes and seconds, and proportional parts. 

 The constants S and T (see § 3, art. 13) arc given at the top of the page ; 

 then follows a page of small tables for the conversion of degrees, minutes, &c. 



T. II. Natural and log sines, tangents, and secants to every minute of the 

 quadrant, to 5 places, with jiroportional parts. 



T. III. Gaussian logarithms. The addition and subtraction tables are sepa- 

 rated, as in Zech (§4). In the first B is given for argument A, from A='000 

 to 1-650 at intervals of -001, thence to 3-00 at intervals of -Ol, and thence 

 to 5-0 at intervals of -1. In the second B is given for argument C, from 

 C=-3000 to -4800 at intervals of -0001, thence to 1-500 at intervals of -001, 

 thence to 3-10 at intervals of -01, and to 5-0 at intervals of 4, with pro- 

 portional parts : all to 5 places. These tables are followed by the first hun- 

 dred multiples of the modulus and its reciprocal, to 8 places. 



T. IV. Tables to calculate logarithms to 8 places &c. 



T. V. (one page). To calculate logarithms to 20 places. 



T. VI. A page of four-figure logarithms to 600, and of three-figure anti- 

 logarithms. 



T. VII. Least factors of composite numbers (not divisible by 2, 3, 5, or 11) 

 up to 10,841. 



T. VIII. A page of constants. [We have since obtained a " nouvelle 

 edition, revue et augmentee," Paris, 1871, pp. 118 and introduction xlvi.] 



Hiilsse^s Vega, 1840. T. I. Seven-figure logarithms to 1000, and from 

 10,000 to 108,000, with proportional parts ; the change in the line is denoted 

 by a small asterisk prefixed to the fourth figure of all the logarithms affected. 

 The portion from 100,000 to 108,000 is given to 8 places. One page at 

 the end is devoted to a small table to convert common into hyperbolic seven- 

 figure logarithms, and vice versa. 



T. II. Log sines, tangents, and arcs (all equal) to every tenth of a second 

 to 1' ; log sines and tangents from 0° 0' to 1° 32' to every second ; log sines, 

 cosines, tangents and cotangents for every ten seconds from 0° to 6°, and 

 for every minute to 45° : all to 7 places. AVhen the intervals arc 10" or 1', 

 differences for. a second are added: the logarithms are written at length. 

 The table is followed by a page giving the circular measure of 1°, 2°, . . . . 10°, 

 and thenco by tens to 360°, of 1', 2', . . , . 60', and of 1", 2", .... 60", to 11 

 places. 



T. III. Natural sines and tangents to every minute of the quadrant, to 7 

 places, with differences for 1". 



T. IV. Chord-table to radius 500, viz. lengths of semichords of arcs 



from 0° to 125° at intervals of 5', to 6 laces, for radius unity. 



\i.e. sm -, I 



