ON MATHEMATICAL TABLES. 143 



T. TX. Tlcciprocals (to 7 places) of numbers from 1 to 1010. 



T. XVII. List of primes to 10B3. 



T. XXI. gives some constants. 



The other tables are chemical &c. 



This is one of the most complete five-figure tables we have seen. Tlio 

 change in the leading figures, -where it occurs in the midrlle of a line, is 

 throughout denoted by an asterisk prefixed to the third figure of all the 

 logarithms afl'ected. It may be remarked that though the introduction &c. is 

 in Swedish, the headings of the tables are in Latin. 



. A list of four errata in the tables is given by Prof. Wackerbarth himself 

 in the ' Monthly Notices of the Iloyal Astronomical Society,' t. xxxi. No. 9 

 (Supplementary Number, 1871). 



Wallace, 1815. [T. I.] Six-figure logarithms to 100, and from 1000 to 

 10,000, "with differences. 



[T. II.] Log sines, tangents, and secants to every minute of the quadrant, 

 to places, with differences. 



[T. III.J Natural sines to every minute of the quadrant, to 5 places. This 

 is followed by a traverse table. 



The tables are preceded by 148 pp. of trigonometry &c. 



^VaI•nstorff*s Schumacher, 1845. Out of 221 pages, only 21 

 (pp. 116-120 and 206-221) come within the scope of this Report. 



[T. I.] For the conversion of arc into time, and vice versa. 



[T. II.] The circular measure of ]°, 2=, 90°, 95° 120°, 130° 



360°, of 1', 2' ... . 60', and of 1", 2", .... 60", to 7 places, 



[T. III.] Four-figure logarithms to 1009. 



[T. IV.] Log sines, cosines, tangents, and cotangents at intervals of 4' 

 to 10°, and thence to 45° at intervals of 10', to 4 places. 



[T. v.] Gaussian logarithms; B and C are given for argument A from A = 

 •00 to 1-80 at intervals of -01, and thence to 4-0 at intervals of -1, to 4 places, 

 with differences. 



The other tables are astronomical. 



"Willich, 1853. T. XX. Seven-figure logarithms to 1200, followed by a 

 few constants, &c, 



T. XXI. Squares, cubes, square and cube roots (to 7 places), and reci- 

 procals (to 9 places) of numbers to 343, followed by some constants. 



T. A. Hyperbolic logarithms of numbers from 1 to 1200, to 7 places. 



T. B. Natural and log sines, tangents, secants, and versed sines, for every 

 half degree, to 7 places. 



T. C. Circumferences and areas of circles for a given diameter, viz. -nd 



(to 5 places) and -j- (to 2 jjlaces) for d^l, 2, . . . .9, and from d=l to 



100 at intervals of -25. 



T. D. Circular measure of 1°, 2°, 1 80°, to 7 places. 



The other tables in the work are of a very varied character. 



We have also seen the second edition (1852), which does not contain the 

 tables A to D ; and we nave seen a review of the seventh edition, edited by 

 M. Marriott, 1871. 



§ 5. List ofworhs containing Tables that are described in this Report, with refer^ 

 cnees to the section and article in which the description of their contents is 

 to he found. 

 [Thoso works to which an asterisk is prefixed have not come under tho 



inspection of the reporter ; and the description of their contents is therefore 



