122 REPORT— 1873. 



o 



[T. III.] pp. 20, 21. Lengths of circular arcs, viz. 1°, 2°, 3°.... 90 



theuce to 115° at intervals of 5°, and to 360° at intervals of 10°, 1', 2' 60', 



and 1", 2". . . .60", expi-essed in circular measure, to 7 places. 



[T. IV.]. Interpolation tables. Tabic I. (p. 103) gives ''!^^^^^^^, 



xLv — l)(.v — i) , (x + lyi'lx — l)(,v—2) „ ^,„ , -, n. , 



— ^^ 7> ^- and ^ — ^_i^,- ^-y 1 from a?=-00 to ,v=l-00 at 



b 48 



intervals of -01 — the first function to 5 places (with differences), and the 

 second and third to -l places (without differences). It will be noticed that on 

 writing 1 — x for .r, the first and third functions are unaltered, while only 

 a change of sign is produced in the second. It is thus sufficient to tabulate 

 them only from to -50, and to write the arguments down the column from 0-00 

 to -SO, and ujiwards from -50 to 1*00, attending to the sign of the second func- 

 tion ; and this is accordingly the arrangement in the table. Tabic II. (pp. 1 04, 



105) contains _., _v__^ — \ -24 ' 240 " ^'"'^^ 



,v = 0-00 to ,v = 1-00 at intervals of -01, the first to 5 and the others to 4 

 places. The first two have differences added. 



[T. Y.] (pp. 106-150). Natural sines, tangents, and secants throughout 

 the quadrant to every minute, to 5 places, without differefices. 



[T. YI.] (pp. 151-169). Table of squares to 10,000, arranged as in a 

 table of logarithms, the last figures of the squares (which must be 0, 1, 4, 5, 

 6 or 9) being printed once for all at the bottom of the columns. 



The other tables are either astronomical or meteorological. There are 13 pp. 

 of formulae. 



Rankine, 1866. T. I. Squares, cubes, reciprocals (to 9 places) and five- 

 iigure logarithms of numbers from 100 to 1000. 



T. 1 A. Square and cube roots (to 7 places), and reciprocals (to 9 places) of 

 primes from 2 to 97. 



T. 2. Squares and fifth powers of numbers from 10 to 99. 



T. 2 A. Prime factors of numbers up to 256. 



T. 3. Hyperbolic logarithms of numbers to 100, to 5 places. 



T. 3 A. Ten multiples of the modulus and its reciprocal. 



T. 4. Multipliers for the conversion of circular lengths and areas, viz. a 

 few multiples of tt and its reciprocal, square roots, &c, 



T. 5. Circumferences and areas of circles, viz. ird (to 2 places), and 2' 



(to the nearest integer), from d - 101 to <? = 1000. 



T. 6. Arcs, sines, and tangents for every degree, to 5 places. 



Raper, 1846. T. I. Six-figure logarithms of numbers from 1 to 100 and 

 from 1000 to 10,000, with proportional parts at the foot of the page. 



T. II. Log sines for every second from 0"^ to 1° 30', to five places. 



T. III. Log sines for every ten seconds from 1° 30' to 4° 31', to 6 places, 

 with proportional parts. 



T. lY. Log sines, tangents, and secants for every half minute of the qua- 

 drant, to 6 places, with proportional parts. , 



T. Y. A page of constants. 



Raper, 1857. T. 21 a. Logarithms for reducinr/ daily variations, viz. log 

 -1440'^^ — log .r, from x = !■" to x = 1440" (= 24'") at intervals of a 

 minute, to 4 places, the arguments being expressed in hour's and minutes. 



T. 64. Six-figure logarithms of numbers to 100, and from 1000 to 10,000, 

 arranged as is usual in seven-figure tables, except thevt the logarithms are 



