138 iiEPOKT~1873. 



by a page giving the siucs of 3°, 6°, 9°, . . . . 87° accurately (/. e. expressed as 

 radicals). 



[T. IV.] Longitudes of chords, viz. lengths of chords subtending given 

 angles (the arguments) at the centre. The arguments proceed from 0° to 

 108°, at intervals often minutes, and thence to 180° at intervals of 1°; and 

 the tabular results are given to 3 i^laces. 



[T. v.] Abacus irlyonometrlcus, viz. natural sines, tangents, and secants, 

 and log sines and tangents from 0° to 90° (quadrantally arranged), to 

 every ten minutes, to 6 places. Then follow a few formiila; and con- 

 stants. 



Vega (Thesaurus, fol. 1794). T. I. (Magnus Canon logarithmorum 

 vulgarium). Logarithms of numbers from 1 to 1000, without differences, and 

 from 10,000 to 100,999, with diiferenccs, to 10 places, arranged like an 

 ordinary seven-figure table. Proportional parts are also given, but only for 

 the first two or three figures of the difference. The table can thus be used 

 as an ordinary seven-figure table. A change in the fourth figure in the 

 middle of the line is denoted by an asterisk prefixed to all the logarithms 

 affected. T. I. occupies pp. 1-310. The last page and a half arc devoted to 

 multiples of the modulus, a few constants, and a tabic to convert degrees (1° 

 to 360°) and minutes (1' to 60') into seconds. 



T. II. (Magnus Canon logarithmorum vulgarium trigonometricus). Log 

 sines, cosines, tangents, and cotangents, from 0° to 2° at intervals of one 

 second, to 10 places, without differences, and for the rest of the quadrant at 

 intervals of ten seconds, also to 10 places, with differences. All this occupies 

 pp. 311-629, and is followed by 3 pp. containing natural sines for angles less 

 than twelve minutes, to every second, to 12 places. 



The appendix occupies pp. 633-685 : p. 633 contains formulte ; and pp. 634 

 and 635 are occupied with tables of the longitudes of circular arcs &c. Of these 

 the first gives the circular measure of 1°, 2°, 3°, . . . . 360°, the second of 1', 2', 



3', 60', the third of 1", 2", 3", 60", aU to U places ; the fourth is a 



small table to express minutes and seconds as fractions of a degree. Pp. 636- 

 640 are occupied with formuhc for the solution of triangles ; and on pp. 641- 

 684 [T. III.] we have Wolfram's great table of hyperbolic logarithms (see 

 ScHTJLZE, § 4). The six omittcil in ScmjLZE are given ; and it is stated in the 

 preface that several errors have been corrected. The error pointed out by Mr. 

 Gray (see Scuulze [T. II.]) is reproduced. An error in log^ 1099 is pointed 

 out by Prof. Wackerbarth in the ' Monthly Notices of the Iloyal Astronomical 

 Society' for April 1867. 



Some of the errata found in Ylacq are indicated in the preface. These are, 

 as a rule, corrected in the book ; others, given in a list at the end of the in- 

 troduction, were found after the printing, and must be corrected in manu- 

 script before use. There is a third list at the end of the work (p. 685) ; but 

 it is identical with that at the end of the introduction. 



In some copies the list at the end of the introduction is much more com- 

 plete than in others, the errors in Vlacq being marked by an asterisk, and the 

 errata being also given in Latin and German. It is probable that additional 

 errata were found before the edition was all made up, and that the original 

 list was suppressed and the new one substituted. In all copies the titlepage 

 is the same. See ' Monthly Notices of the Eoy. Ast. Soc.,' June 1872, and 

 May 1873 (p. 454). 



There is a great difference in the appearance of different copies of the work. 

 In some the tables are beautifully printed on thick white paper, with wide 

 margin, so that the book forms one of the hand'jomgst collections of tables we 



