ON MATHEMATICAL TABLES. Ill 



■- is the function tabulated; so that all the results are double those in [T. Y.], 



and that the intervals are 15" up to 135°, and then 1' to 180°. 



[T. YII.] Six-figure logarithms to 1000, and from 1000 to 10,000 in de- 

 cades, with proportional parts. 



[T. VIII.] Natural versed sines to every second (of time) to 36"", to 6 

 places. 



[T. IX.] Natural versed sines to every minute (of arc) to 180°, to 6 places, 

 witli complete proportional parts for every second up to 60". The other 

 tables are nautical. 



The paging of the book runs at the top of the pages to 216, and thence at 

 the bottom to 275 ; it then recommences at the top at p. 217. This is no 

 doubt caused by [T. Y., YI.] having been introduced in this edition only. 



\Ye have seen the original work, ' Nautical Tables designed for the use of 

 British Seamen, by James Inman, D.D. London, 1830' (400 pp. of tables), 

 but have not compared the two together : except for the " haversines," how- 

 ever, the tables seem to be nearly identical in the two editions. 



Inraan's ' Navigation and Nautical Astronomy ' (2nd edit.), Portsea, 1826, 

 contains no tables. 



Irsengarth, 1810. These are merely land tables, and the units (Ruthe, 

 Fuss, &c.) are so special that they do not appear to possess any mathema- 

 tical value. 



John, 1837. Vol. I. Six-figure logarithms to 100,000 ; the change in 

 the hne is denoted by a dagger (f) prefixed to the fourth figure of all loga- 

 rithms affected. There are no proportional parts on the page ; but they are 

 given in a separate table at the end. 



Vol. II. Logarithmic sines and tangents for every second of the first 

 degree ; log sines and tangents for every third second of the quadrant (semi- 

 quadrautally arranged) : aU to 6 places. Proportional parts are given in the 

 extreme right and left columns of the double page for every twentieth of the 

 three-second interval. 



The introductory matter is both in German and Latin. 



We rather like the paper on which the second volume is printed ; though 

 not of a good quality, it is thick and stiff, and of a brownish colour, so that 

 the book could be, we think, used for a long time at once without injury to 

 the eye : the first volume (in the copy before us) , however, is printed on 

 paper of the soft, flaccid kind common in German books. 



The author was led to publish his tables by observing that nearly all those 

 in use were either five- or seven-figure tables. 



We have seen, by the same author, 'Tafehi zur Berechnnng fiir Kubik- 

 Inhalt (Src.,' 2nd edit., Leipzig, 18-17; but the tables are commercial (argu- 

 ments expressed in ZoUe, Ellen, &c.), and do not need notice here. 



Kerigan, 1821. T. YIII. Log sines for every second to 2°, and thence, 

 at intervals of 5", to 90°, to six places ; in this latter part of the table pro- 

 portional parts for seconds are added, so that the table practically gives log 

 sines to every second ; arranged quadrantaUy. The logarithms are aU printed 

 at length. 



T. IX. Natural sines from 0° to 90° at intervals of 10", to six places ; 

 no difterences ; the sines written at length. 



T. X. Six-figure logarithms from 1000 to 10,000, with proportional parts ; 

 arranged as is usual in seven-figure tables; the change in the line is 

 marked by the ciphers after the change in the third place being filled in, 

 so as to render them black circles. 



