90 KEl'OKT— 1873. 



from 10,000 to 100,000, with differences and all the proportional parts on the 

 page. The change of figure in the line is denoted by a bar placed over the 

 fourth figures of all the logarithms affected. S and T (see § 3, art. 13) are 

 given at the bottom of the page, as also are the numbers of degrees, minutes, 

 and seconds corresponding to every tenth number in the number-column of 

 the table. At the end of this table is a table containing the first hundred 

 multi])les of the modulus -434 . . . and its reciprocal 2-302 ... to 7 places. 



T. II. Log sines and tangents from 0° to 5° to every second, to seven 

 places : no differences. At the end of this table is given a page of circular 

 arcs, containing the circular measure of 1°, 2°, . . . 180°; 1', 2', . . . 60'; 1", 

 2 ', . . . 60" to seven places. 



T. III. Log sines and tangents for every ten seconds of the quadrant, to 

 seven places, with differences : proportional parts are added after 5°. 



T. III. is followed by a page containing tables for the conversion of arc 

 into time : the other tables are astronomical. On p. 547 are a few con- 

 stants. The tables are stereotyped. 



An edition with an English Introduction, edited by Prof. W. L. F. 

 Fischer, was published in 1857 (title in § 5) ; the contents are the same as 

 in the above work, the tables being printed from the same plates. 



Bruhns, 1870. T. I. Seven-figure logarithms of numbers to 1000, and 

 from 10,000 to 100,000, with differences, and all the proportional parts. 

 The all is printed in italics, because in Eabbage, Callet, &c. only every other 

 table of proportional parts near the beginning of the table is given, for want 

 of space. 



In this work there is no inconvenient crowding, as even where the side-tables 

 are very numerous, the type, though small, is still very clear. The constants 

 y and T, for the calculation of sines and tangents (§ 3, art. 13), are added, 

 and placed at the bottom of the page, as also are the numbers of degrees, 

 minutes, and seconds in every tenth number of the number-column (regarded 

 as that number of seconds), and the same for each of these numbers multi- 

 pHed by 10. 



T. II. Log sines, cosines, tangents, and cotangents to every second from 

 0° to 6°, to seven places, with differences throughout, and. proportional parity, 

 except in the portion of the table from 10' to 1° 20', where the size of the 

 page would not admit of their insertion. 



T. III. Log sines, cosines, tangents, and cotangents from 6° to 45° to 

 every ten seconds, to seven places, with differences and proportional parts. 

 Of course room could not be found for the proportional parts of all the dif- 

 ferences ; but throughout all the table on no page are there less than six 

 proportional-part tables. 



On p. 186 tlie first hundred multiples of the modulus and its reciprocal 

 are given, to ten places ; and at the end of the book are tables of circular arcs, 

 viz. the circular measure of 1°, 2°, . . . 180°, 1', 2', . . . 60', 1", 2", . . . 60", 

 to ten places, a page for the conversion of arc into time, and some constants. 

 In T. I. the change in the line is denoted by a bar placed over the fourth 

 figure of all the logarithms affected, the similar change when the third figure 

 ie decreased being denoted in the other tables by an asterisk; a final 5 in- 

 creased has a bar superscript. It is incorrectly stated in the preface that the 

 practice of marking all the last figures that have been increased was intro- 

 duced by ScHEON ; for this innovation was due to Babbage (see his preface, 

 p. x). Dr. Bruhns may, however, merely mean that the mark (viz. a bar sub- 

 script) introduced by Schron (1860) fatigues the eye and is of next to no 

 use ; and if so, we entirely agree with him. In Babbage the increase is 



