132 REPORT— 1873. 



ber of degrees, minutes, and seconds corresponding to the numbers in the 

 number-column multiplied by 10 is given throughout ; and at the top of every 

 page are printed, to seven places, the logarithms of certain constants, viz. 

 of 360°, 180°, 90°, 1°, 2i\ 12^ 3\ 1^, and radius (all expressed in seconds) 

 of arc 1", TT and M the modulus. The change of figure in the line is 

 denoted by a " nokta," the same as that employed subsequently by Mr. Sang 

 (see Sang, § 3, art. 13) ; and its use is open to the same objections here as 

 there. 



T. II. Antilogarithms, viz, numbers to logarithms from "00000 to 1*00000 

 at intervals of -00001, to 7 places, with diiferences and multiples at the 

 bottom of the page. The same logarithms of constants are given on the top 

 of the page as in T. I. ; and the change in the line is denoted in the same 

 way. At the end of this table (p. 1 95), under the head " Useful Numbers," 

 the logarithms of some constants are given. 



T. III. (pp. 59S). Log sines and tangents to every second of the circnni' 

 ference, to 7 places (semiquadrantally arranged), the arguments throughout 

 being also given in time. The use of the word circumference instead of 

 quadrant in this description is justified by the fact that the signs are given 

 for the diiferent quadrants at the top and bottom of the page : thus we have on 

 the first page, at the top, 0° Sin +, 90° Cos—, 180° Sin — , 270° Cos +, and 

 at the bottom 89° Cos +, 179° Sin +, 269° Cos -, 359° Cos -, and the same 

 for the tangent and cotangent, the arguments being also expressed in 

 time. Complete proportional parts are given throughout for tenths of a 

 second of space, and for the first six hundredths of a second of time, both 

 for the sine and tangent ; but near the beginning of the tables coefficients of 

 correction for first and (sometimes) second differences are added instead. The 

 arguments, as before stated, are given also in time ; so that corresponding to 

 1", 2'', 3", &c. we have -06% -13', -20', &c. This table is the most complete of 

 the kind we know of, and is unique ; the figures are clear ; and the objection 

 to the "nokta" docs not apply here; in one column (p. 142) there are tivo 

 changes on the page. 



T. V. Seven-place log sines, tangents, and secants to every point and 

 quarter point of the compass. 



T. XXXVIII. Lengths of circular arcs, viz. circular measure of 1° 2°, 3° 

 .... 180°, of r, 2', . . . . 60', of 1", 2", .... 60", and of 1'", 2'", .... 60'", to 7 

 places. 



T. XXXIX. Proportional parts to hundredths of the reciprocal of the 

 modulus, viz. 2-302 . . ., to 8 places. 



There are thirty-nine tables in the book (T. XLI. is the last ; but XXXV. 

 and XXXVI. are accidentally omitted), the others being astronomical or me- 

 teorological &c. 



The paging recommences with T. III. and proceeds to p. 634. See Shoet 

 HEDE, 1849 (next below). 



Shortrede, 1849. This is a second edition of the work of 1844, and is 

 in 2 vols. There is a preface of xxv pages to vol. i. T. I. and II. are the 

 same as T. I. and II. in the 1844 edition; T. III. is a small ten- 

 place table of the lengths of circular arcs. T. IV. and V. are for finding 

 logarithms and antilogarithms to many places ; viz. colog (1 + -Oln) 

 ,. .colog (1 + -01' w), &c. are given for n = 1, 2,.. .100, to 16 places, and 

 colog (1 + -01 n).. .colog (1 + -Ol'^n) for n = 1, 2,. ..10, to 25 places 

 (initial ciphers being omitted). There are added small auxiliary tables 

 for facilitating the resolution of numbers into convenient factors. T. 

 VI. The first hundred multiples of the modulus and its reciprocal to 32 



