ON MATHEMATICAL TABLES, 109 



tunate, as they form a most valuable collection, and are supplemental to 

 Callex. Wc have seen advertised a second edition (1849) ; and Zkch's tables 

 (see Zech, 1849, § 3, art. 19) are extracted from it. The last-figure error 

 noticed above is the only one of the hereditary Vlacq's errors that appears 

 in the table of tlie logarithms of numbers ; so that but for this curious 

 blunder the present work would have been, we believe, the first to 

 be free from errors of this class (see ' Monthly Notices of the Roy. Ast. 

 Soc' March, 1873). Some remarks by Gauss on T. XII. appear in t. iii. 

 pp. 255-257 of his ' Werke.' 



Hutton, 1781 (products and powers of numbers). [T. I.] Products to 

 1000 X 100 (pp. 51). 



[T. II.] Squares and cubes of numbers from 1 to 10,000 (pp. 54-78). 



[T. III.] Squares of numbers from 10,000 to 25,400 (pp. 78-100). 



[T. IV.] Table of the first ten powers of numbers from 1 to 100. Two 

 eiTors (viz. the last three figures of 81' should be 401, not 101, and the last 

 three of 98^ should be 672, not 662) are pointed out by the reporter in the 

 Philosophical Transactions, 1870, p. 370. 



The remaining three pages of the book are devoted to weights and mea- 

 sures &c. The table is closely printed; and some of the pages contain a great 

 many figures, as there are a hundred lines to the page. De Morgan states 

 that the table has not the reputation of correctness ; and the charge is no 

 doubt true, as, besides the two errors noted above (both of which we found 

 on the only page we have used), it is to be inferred from Barlow's intro- 

 duction to his tables that he found errors ; he did not, however, publish any 

 account of them. 



Hutton, 1858. T. I. Seven-figure logarithms to 1000, and from 10,000 

 to 108,000, with proportional parts for all the differences. The change in the 

 line is denoted by a bar placed over the fourth figure of all the logarithms 

 affected. 



T. II. Logarithms to 1000, and thence for odd numbers to 1199, to 20 

 places. 



T. III. Logarithms from 101,000 to 101,149, to 20 places, with first, 

 second, and third differences. 



T. IV. Antilogarithms, viz. numbers to logarithms from -00000 to 

 •00149 at intervals of -00001, to 20 places, with first, second, and third 

 differences. 



T. V. Hyperbolic logarithms from 1-01 to 10-00 at intervals of -01, and 

 for 10^. . . .10', to seven places. 



T. VI. Hyperbolic logarithms to 1200, to seven places. 



T. VII. Logistic logarithms, viz. log 3600" -log .r, from x=l" to .r= 

 5280" (=88') at intervals of 1", to four places, the arguments being ex- 

 pressed in minutes and seconds. 



T. VIII. Log sines and tangents to every second of the first two degrees, 

 to seven places ; no differences. 



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

 minute of the quadrant, with differences, to seven places, semiquadrautally 

 arranged. The natural functions occupy the left-hand pages, and the loga- 

 rithmic the right-band. In both these last two tables the logarithms are all 

 written at full length. 



T. XI. Circular arcs, viz. circular measure of 1°, 2°, . . . .180°, of 1', 2' 

 00', of 1" 60", and of 1'" to 60'", to seven places. 



T. XII. Proportional parts to hundredths of 2-302 , the reciprocal of 



the modulus. 



