ox MATHEMATICAL TABLES. 105 



versed sines are the arguments ; and the table proceeds from '001 to -500 (of 

 the diameter). The table may therefore be described as giving ^(2^— sin 2d) 

 from ^(1— cos 0) = -001 to -500 at intervals of -001. 



A few constants are then given to a great many places ; and the last page 

 (T. XIV.) is for the calculation of logarithms to 20 places. 



The work is clearly printed. 



Hartig, 1829. The tables are of so commercial a kind that only one or 

 two deserve notice here. 



The first (T. I.) is for computing the contents of planks &c., the thickness and 

 breadth being given in Zolle and the length in Fusse, and may be described 

 as a sort of duodecimal table, as the Kubik-ZoU =; J^ Kubik-Fuss, and the 

 Kubik-Linie = J^ Kubik-ZoU. Thus for arguments 3 Zoll, 13 ZoU, and 

 5Fusswehave 1 F. 4 Z. 3 L. as result; ioT j\x\-lx5=\^^=l + -Jj + j^^. 

 The arguments are : — (thickness) 1 ZoU to 9 Zoll at intervals of i Zoll ; 

 (breadth) 1 Zoll to 18 Zoll at intervals of 1 Zoll; (length) 1 Fuss to 60 

 Fuss at intervals of 1 Fuss. 



Another table (T. II.) is of the same kind, only intended for blocks &c. ; 

 BO that the thickness is greater, and the result is only given in fractions of 

 a Kubik-Fuss. 



T. III. contains volumes of cylinders for diameter (or circumference) of 

 seciion and length as arguments ; expressed as in T. I. and II. The money- 

 tables can have no mathematical value, as the Thaler = 30, 24, or 90 

 Groschen, &c. 



T. X. is for the calculation of interest. The simple-interest tables (T. A) 

 are too meagre to be worth description. T. B and C may be described as 

 giving the compound interest and present value of £1 for any number of 

 years up to 100 at 3, 4, 5, and 6 per cent, per annum, viz. 



(i + mj -* (i + m)' 



to 6 decimal places. 



Other tables of this kind that we met with have not been noticed ; the 

 title of one such is given under Jahn, 1837. 



Hassler, 1830. [T. I.] Seven-figure logarithms of numbers from 10,000 

 to 100,000, with proportional parts. The line is broken for the change in 

 the third figiire, as in Callet. 



[T. II.] Log sines and tangents for every second of the first degree, to 7 

 places. 



[T. III.] Log cosines and cotangents for every 30" of the first degree, to 

 7 places,, with differences. 



[T. IV.] Log sines, cosines, tangents, and cotangents, from 1° to 3°, at 

 intervals of 10", with difierences, and from 3° to 45°, at intervals of 30", with 

 differences for 1 0", to 7 places. 



[T. v.] Natural sines for every 30" of the quadrant, with differences for 

 10", to 7 places. 



Copies of this book were published with Latin, English, French, German, 

 and Spanish introductions and titlepages (the titles will be found in the list 

 at the end of the Eeport). The tables are the same in all ; and the special 

 titlepages for each table have the headings in the five languages. The 

 Eoyal Society's library contains the Latin copy perfect, and the introduc- 

 tions in the four modern languages boimd together in another volume, pre- 

 sented to the Society by the author. At the end of the latter volume is 

 pasted-in a specimen page of the table, set up with the usual even figures ; 



