46 REPORT — 1873. 



cosines of all angles from. 1° to 45° at intervals of 10' to two places. The table 

 occupies 442 closely printed pages. 



T. II. gives the first 109 multiples of the sine of all angles from 0° to 15° 

 at intervals of 1' to two places. 



The above is the mathematical description of these tables ; but in the 

 book, which is intended for surveyors &c., the multiples correspond to differ- 

 ent lengths (1.0,1.1,.. ..50.0 Eutheu) of the hypothenuse ; and the sine 

 and cosine columns arc headed Rohe and Grundlinie, and are given in 

 lluthen. As the arguments are at intervals of a Fuss (= jL of a lluthe) 

 the table exhibits the results apparently to 3 places. The arrangement in 

 T. I. is different from that in T. II., as while in the former the lluthen and 

 Fiisse run down the column, and the minutes along the top line (so that aU 

 the multiples of the same sine or cosine are given consecutively), in T. II. the 

 minutes run down the column, and the Fiisse along the top line (so that the 

 same multiples of different angles are given consecutively). In this table also 

 the results are given to 3 places, if the method of statement used in the book 

 be followed. As it has been assumed that a Ruthe = 10 Puss, while fre- 

 quently it = 12 Fuss, T. III. is given to convert decimals into duo- 

 decimals, or, more strictly, lluthen Decimalmaass into Werkmaass and 

 Bergmaass. 



T. I. and II. are of course simple traverse tables. 



Junge, 18(34. Natural sines and cosines for every ten seconds of the 

 quadrant to G places. The table is one of the clearest we have seen, the 

 figures being distinct, and plenty of space being left between the columns 

 &c., so as to give a light appearance to the page, though its large size is 

 rather a disadvantage. The tabular results were interpolated for by Thomas's 

 calculating machine from the natural sines in Ht/lsse's tables ; and the last 

 figure may bo in error by rather more than half a unit. The connexion 

 between the tables and Thomas's machine, referred to in the title and in the 

 preface, merely amounts, we suppose, to this — that Avhilo' computers in 

 general use log sines, those who possess Thomas's machine will find it 

 easier to dispense with logarithms and use natural sines and ordinary 

 arithmetic. 



*Clouth. Natural sines and cosines (to G places) and their first nine 

 multiples (to 4 places) for every centesimcil minute of the quadrant, arranged 

 seraiquadrantaUy, the sines and their multiples occupying the left-hand pages, 

 and the cosines the right ; the arguments axe also expressed in sexagesimal 

 minutes and seconds, the intervals being then 32"-4. We have not seen the 

 work itself, but only a prospectus, containing 2 pp. (108 and 109) as specimens. 

 Judging from this, the book would contain 208 pp. In the copy of the pro- 

 spectus before us, the words " Mayen (chcz I'auteur) " are covered by a piece 

 of paper on which is printed "Halle, Louis Nebert, Libraire-Editeur." 

 There is no date; but we should judge the table to have been only recently 

 published. 



We have also seen advertised ' Tafcln zur Bercchnung goniometrischer 

 Co-ordinaten,' by F. M. Clouth — no doubt a German edition of the same 

 work. 



The following is a classified list of trigonometrical tables described in 



iSines, iangents, secants, and versed sines. — (To 7 places) HAKiscni,, 1827j 

 T. V. ; WiLLicH, 1853, 1.B; IIutton, 1858, T. IX. 

 (To 6 places) Galbraith, 1827, T. VL 

 ^'mes, tanrjents, awl secants. — (To 7 places) Sir J. Mooee, 1G81 [T. III.] ; 



