ON MATHEMATICAL TABLES. 89 



tangents in this work : the result was the detection of a great number of 

 last-place errors, which are given on pp. 117-119 (see p. 114, Preface de 

 I'cditeur). There are other errata given on p. 116. 



De Morgan remarks that Delambre is wrong in saying that Hobeet and 

 Idelee's tables, 1799 (§ 4), subdivided the quadrant as minutely as those 

 which he and Borda had published ; but this is not the case, as the latter 

 are as stated above. The mistake is one into which any one accustomed 

 to describing tables would naturally fall, as the mode of arrangement gives 

 the impression that the portion of [T. VI.] to 3" is to every second, and that 

 that from 3" to 40^ is to every ten seconds : at first sight it is not easy to see 

 why this was not the form of table adopted ; but the reason for the arrange- 

 ment being as it is was no doubt that the sine and cosecant, tangent and co- 

 tangent might be placed exactly on the same footing, as the proportional 

 parts are the same for each pair. [Mr. Lewis, of Mount Vernon, Ohio, men- 

 tions that Bremiker has fallen into the same mistake as De Morgan did, thus 

 giving additional proof of how misleading is the arrangement of the table to 

 those who have not had occasion to use it : see ' Monthly Notices of the 

 Eoyal Astronomical Society,' May 1873, vol. xxxiii, pp. 455-458.] 



Bowditch, 1802. T. XII. For the conversion of arc into time. 



T. XIII. Log I elapsed time, mid time, and rising ; same as T. XVI. of 

 Maskelyxe, 1802. It is stated in the preface that this table was first 

 jmblished by Mr. Douwes, of Amsterdam, about 1740, and that he re- 

 ceived £50 for it from the Commissioners of Longitude in England. 

 1024 (small) errors contained in this table in the second edition of Eequisite 

 Tables are said to be here corrected. 



T. XIV. Natui'al sines for every minute to 5 places. 



T. XV. Proportional logarithms for every minute to 3° ; same as T. 74 of 

 RirER. 



T. XVI. Log sines, tangents, and secants for every quarter point to 5 

 places, and five-figure logarithms to 10,000. 



T. XVII. Log sines, tangents, and secants for every minute of the qua- 

 drant to 5 places : arguments also in time (90°=twelve hours), and the com- 

 plement to 1 2"^ given also. The other tables are nautical. 



On the titlepage it is stated that the tables are "corrected from many 

 thousand errors of former publications ; " most of them doubtless only affect- 

 ing the last figure by a unit. 



Bremiker, 1852. T. I. Six-figure logarithms to 1000, and from 10,000 

 to 100,010, with proportional parts ; with degrees, minutes, and seconds 

 corresponding to every tenth number of seconds, and ten times each such 

 number; the change in the line is denoted by a bar over the 3rd figure 

 in all the logarithms affected. The table is followed by the first hundred 

 multiples of the modulus •434 . . . and its reciprocal to 7 places. 



T. II. Log sines (left-hand pages) and tangents (right-hand pages) for 

 every second to 5° to 6 places, and log sines and tangents for every ten 

 seconds of the quadrant to 6 places, with differences, and proportional parts 

 beyond 5°. This is followed by small tables giving the circular measure of 

 1°, 2° . . . 180°, 1', 2', . . . , 60', 1", 2". . . 60" to 6 places; and for the 

 conversion of arc into time &c. The last page contains a few constants. 



There is an introduction of 82 pp., containing, among other things, an in- 

 vestigation " De erroribus, quibus computationes logarithmicae afficiuntur." 



Nine errors in this work are pointed out by Prof. Wackerbarth in the 

 ' Monthly Notices of the lloyal Astronomical Society " for April 1867. 



Bremiker's Vega, 1857. T. I. Seven-figure logarithms to 1000, and 



