110 REPORT~1873. 



Some constants are given in T. XX. ; the other tables consist of a traverse 

 table, formulae, &c. 



The edition described above is one of those edited by Olintlius Gregory, 

 and is the last we have met with. The first edition was published in 1785, 

 the second in 1794, the third in 1801, the fifth in 1811, and the sixth, the 

 last published in Hutton's lifetime (he died 1823), in 1822. 



We have compared the first, second, and sixth editions, and that of 1858 

 described above. The first two are nearly identical, so that we need only 

 notice the diff'erences between the tables of 1785^ 1822, and 1858. In both 

 the two former of these editions T. I. only extends to 100,000 ; and while in 

 that of 1785 the change of figure in the line is not marked at all, in that of 

 1822 the fourth figure in the first logarithm aflfected only is marked. T. II. is 

 the same in the 1822 edition, but it ends at 1161 instead of 1199 in that of 

 1785. T. III. in 1785 ended at 101,139, and is extended to 101,149 in both 

 the other editions, as also did T. IV. originally end at '00139. In the edi- 

 tions of 1785 and 1822 occur two tables that were left out by Gregory in 

 1830 and in succeeding editions, viz. T. 5, giving logarithms of all numbers 

 to 100, and of primes from 100 to 1100, to 61 places, and T. 6, giving the 

 logarithms of the numbers from 999,980 to 1,000,020, to 61 places, with first, 

 second, third, and fourth differences. T. VI., of hyperbolic logarithms, ap- 

 pears in the edition of 1822, but not in that of 1785. T. VII. extended only 

 to 80' in 1785. 



To all the first six editions is prefixed Hutton's introduction, containing a 

 history of logarithms, the difi"erent ways in which they may be constructed, 

 &:c. This very valuable essay was omitted by Gregory in the seventh (1830) 

 and subsequent editions (on account of its being rather out of place in a col- 

 lection of tables), and with some reason. In the 1785 edition it occupied 

 180 pp., 55 pp. of which are the " Description and Use of the Tables." This 

 portion Gi'egory retained ; and in the 1858 edition it occupied 68 pp. 



The whole work was reset in the later editions, published in Hutton's 

 lifetime, the chief additions, as we infer from the preface, having been made 

 in the fifth (1811) edition. On the last page of the 1822 edition are some 

 errata found in Callet (1783, 1795, and 1801), and also in Taylor (1792); 

 the lists of errors in GARDrNER (London and Avignon) are also more complete 

 than in the earlier editions. Hutton's tables were the legitimate successors 

 of Sheewin's, and bring down to the present time one of the main lines of 

 descent from Vlacq (see Sherwin, § 4). 



Inman, 1871. [T. I.] Logistic logarithms, viz. log 3000'— log a* from .v 

 = 2 to A' =3600^ (=60™) at intervals of 2% to 5 places. Arguments expressed 

 in minutes and seconds. 



[T. II.] Proportional logarithms, viz. log 10800"— log .r to every second 

 to 3° (same as T. 74 of Raper, only to 5 places instead of 4), preceded by a 

 jjage giving the same for every tenth of a second to 1'. 



[T. III.] Log sines at intervals of 1" to 50', to 6 places. 



[T. IV.] Log sines, tangents, and secants at intervals of 1^ to S^ (argu- 

 ments also given in arc, the intervals being 15"), to 6 places : the table is 

 followed by a page of proportional parts for use with it. 



[T. v.] g log liaversines, viz. g log semi- versed sines = log sin '-, from 



a=0° to 15° at intervals of 15", thence to 60° at intervals of 30", and 

 thence to 180° at intervals of 1', to 6 places (arguments also in time). 

 Nole. — In several instances in this table ' is misprinted for ". 



[T. VI.] Log havenines, Same as previous table, except that 2 log sin 



