ON MATHEMATICAL TABLES. 115 



headed ' and " the first refers to the argument and the second to the propor- 

 tional parts. This table occupies pp. 57-80 of the book. 



T. XVIII. yix-figurc logarithms to 15,500, with proportional parts at 

 the foot of the page to twentieths for the portion beyond 1000. The table is 

 so arranged that all the logarithms are given at full length, though this is 

 not the case with the numbers ; for example, to find the logarithm of 15184 

 we seek 15150 at the head of the column, and line 34 in the column : this 

 defect might have been partially remedied by the introduction of another, 

 column at the right-hand side of the page containing the numbers 50, 

 51 . . . 99. The other tables, 22 in number, are nautical. 



Iiynn, 1827. T. Z. (pp. 244-283). A sexagesimal proportional table, 

 exhibiting at sight, in minutes, seconds, and tenths of a second, the fourth 

 term in any proportion in which the first term is 60 minutes, the second term 

 any number of minutes under 60 minutes, and the third term any number of 

 minutes and seconds under 10 minutes. If the second term is not an exact 

 number of minutes the table can still be used, though two operations are 



ceil 

 required. The table may be described as giving ^, in minutes, seconds, &c., 



X (running down the column) being 1', 2' . . . 60', and y (running along the 

 top lines) extending to 10' at intervals of 1". 



T. E. (pp. 288, 289). Proportional logarithms for every minute to 24", 

 viz. log 1440'"— log. r, from .r=l" to a'=1860'" (=31'') at intervals of unitj% 

 tlie arguments being expressed in hours (or degrees) and minutes, to four 

 places ; the other tables are nautical. 



Mackay, 1810 (vol. ii.). T. XLI. Natural versed sines for every ten 

 seconds to 180°, to six places. 



T. XLV. Six-figure logarithms of numbers to 100, and from lOOO to 

 10,000, Avith differences; the logarithms written at length. 



T. XLVI. Log sines to every ten seconds of the quadrant, to six places. 



T. XL VII. Log tangents to every ten seconds of the quadrant, to six places. 



T. XLVIII.-L. To find the latitude hi/ doicble altitudes of the sun or stars 

 and the elapsed lime. The first and second of these tables give log cosec .^• 

 and log (2 sin x) from ,r=0'' to .r=3'' 59"^ 50' at intervals of 10' ; and the 

 third gives' log versed sines to 7'' 59'" 50' at intervals of 10', all to five places, 

 the logarithms being written at length. These tables were copied, according 

 to the author (see note, vol. ii. p. 31), from the second edition (1801) of this 

 work without acknowledgment into Norie's ' Epitome of Xavigation.' 



T. LI. Proportional logarithms to every second to 3°, to four places ; same 

 as T. 74 of Eater ; the other tables are nautical. 



The table of natural versed sines was calculated for this work, and ap-. 

 peared in the first edition (1793) ; it has since, the author states, been fre- 

 quently copied (see note, vol. ii. p. 13). 



Maseres, 1795. This is a collection of reprints of tracts, and, among 

 others, of "An Appendix to the English Translation of Ehonius's German 

 Treatise of Algebra, made by Mr. Thomas Brancker, M.A., ... At London, in 



the year 1068 " And on pp. 367-416 is given "Thomas Brancker's Table 



of lucomposit or prime Xumbers, less than 100,000," viz. least factors of all 

 numbers up to 100,000 not divisible by 2 or 5. On p. 306 is a rather long list 

 of errors in the table (we sui)posc Maseres reprinted verbatim from his copy, 

 as some of the errata are corrected and some are not), and also some errors 

 in Guldinus, Schooten, and llhonius. The table is preceded (pp. 364, 365) 

 bv ' A Tarriffa, or Table, of all Incomposit or prime numbers less than 

 V100,000, multiplied by 2, 3, 4, 5, 6, 7, 8, 9." 



i2 



