98 REPORT— 1873. 



T. III. Hyperbolic logarithms to 1000, to 7 places. 



T. IV. & V. First hiuiidred multiples of the modulus and its reciprocal, to 

 7 places. 



T. YI. & VII. Log sines and tangents for every second to 5°, to 7 places, 

 ■with negative characteristics (viz. 10 not added). 



T. VIII. Log sines, tangents, cotangents, and cosines (arranged in this 

 order) from 0° to 45° at intervals of 10", with negative characteristics, 

 to 7 places ; with diiferences and proportional parts, as before, to tenths. 



T. IX. Circular measure of 1°, 2°, . . . , 180°, 1' . . . . 60', 1" . . . . 60", to 7 

 places. 



T. X. (reduction des parties de I'equateur en temps) ; hours and minutes 



(or minutes and seconds) of time in 1°, 2°, 360° (or 1'. .. . 300'), and 



seconds of time in 1", 2", .... 60", to 7 places ; then foUows an explanation 

 of the use of the tables. 



This is the only work we can call to mind in which negative characteristics 

 (with the — sign printed over the figure) are given throughout ; and to the 

 mathematical computer such are preferable to the ordinary characteristics 

 inei-eased by 10. Also the edges of the pages of T. VI.-VIII. are red (the 

 rest being grey), which facilitates the use of the tables. It is curious that 

 it never should have occurred to any editor or publisher of a collection of tables 

 to colour the edges of the pages of the separate tables difi"erently, and print 

 thereon also their titles, as is done with the different businesses &c. in the 

 Loudon Post-OfRce Directory. 



Dupuis was also the editor of the 1862 edition of Callet ; and the titles of 

 several small tables of logarithms that we have not seen are advertised in 

 this work, viz, : — (1) an edition of Lalande's five-figure tables, with Gaussian 

 logarithms added, &c. ; (2) an 18mo book of four-figure tables ; and (3) 

 logarithmic and antilogarithmic tables to 4 places, for the use of physicists, 

 giving log (1 -f at) for the calculation of dilatations &c. 



[Encke, 1828.] [T. I.] Four-figure logarithms to 100 (with characteris- 

 tics and differences), and from 100 to 1009. 



[T. II.] Log sines, tangents, cotangents, and cosines for every 4' from 

 0° to 10°, and thence to 45° at intervals of 10', to 4 places, with dif- 

 ferences. 



[T. III.] Gaussian logarithms ; B and C are to 4 places, for argument 

 A, from A=-00 to 1-80 at intervals of -01, and thence to 4-0 at intervals of -1, 

 with differences. 



Encke's name is written on the Royal Society's copy of these tables ; and 

 they are also spoken of as Encke's by De Morgan. They are reprinted in 



'WAENSTOEFi-'s ScHUMACHEE, 1845 (§ 4). 



Everett [1866]. Two cards (one of which, unfolded, is equal in size to three 

 folio pages, the other, which is equal in size to one, being perforated), in a cover. 



This very frequently gives rise to errors, as the computer who is accustomed to tlu-ee 

 leading figures common to the block of figures is liable to fail to notice that in this part 

 of the table there are four ; and on this account a figure (the fourth) is sometimes 

 omitted in taking out the logarithm. It is therefore often desirable to ignore the con- 

 tinuation of the table and only use the portion below 100,000. The extra logarithms 

 are thus not always an advantage ; and it is on the face of it inconvenient that some of the 

 tabular results should be given to 7 and others to 8 places. When tables of logarithms 

 are placed in the hands of common computers, it is as a rule better to forbid the use of 

 the portion beyond 100,000 ; and it may have been some considerations of this nature 

 that induced M. Dupuis to take this number as his limit. But there is no objection that 

 we can see against giving the logarithms beyond 100,000 to 7 places (as in Sano, 1871) ; 

 aad whenever this is done, the continuation is found very useful. 



