ON MATHEMATICAL TABLES. 91 



denoted by a point subscript, which the reader scarcely notices ; but in 

 Schron the bar catches the eye at once and is confusing. The cases also 

 in which it is necessary to know whether the last figure (unless a 5) has been 

 increased are excessively rare ; and in fact any one who wants such accuracy 

 should use a ten-figure table. 



On the whole, this is one of the most convenient and complete (considering 

 the number of proportional-part tables) logarithmic tables for the general com- 

 puter that we have met with ; the figures have heads and tails ; and the pages 

 are light and clear. Purther, we believe it is published at a low price. 



Byrne, 1849 (Practical . . . method of calculating &c.). [T. I.] Primes 

 to 5000, pp. xiii and xiv. 



[T. II.] A very small table to convert degrees &c. into circular measure, 

 p. XV. 



[T. III.] List of constants (69 in number), chiefly relating to tt (which 

 Mr. Byrne denotes by jj), such as 2 n-, 36 tt, y^g- tt, tt^S, V"", &c. (pp. xviii 

 to xxiii) : the value of n is inaccurate ; see § 3, art. 24. 



[T. IV.] Logarithms of numbers from unity to 222, to 50 places (pp. 77-82). 

 Callet, 1853. [T. I.] Seven-figure logarithms to 1200, and from 10,200 

 to 108,000 (the last 8000 being to 8 places). Differences and proportional 

 parts are added ; but near the beginniug of the table, where the differences 

 change very rapidly, only the proportional parts of alternate differences are 

 given, through want of room on the page (this is also done by Babe age and 

 others). The constants S and T (see § 3, art. 13) for calculating the log 

 sines and tangents of angles less than 3°, as also Y the variation for 10", 

 are given in a line at the top of the page (see p. 113 of the Introduction). 

 To the left of each number in the number-column are placed not only the 

 degrees, minutes, &c. corresponding to that number of seconds, but also, in 

 another column, those corresponding to ten times that number. When the 

 change of figure occurs in the middle of the block of figures the line is broken 

 — the best theoretical way of overcoming the difficulty. De Morgan and 

 others, however, have expressed a strong dislike to it ; and we agree with 

 them. 



[T. II.] I. Common and hyperbolic logarithms of numbers from 1 to 1200 

 to 20 places, the former being on the left and the latter on the right-hand 

 pages. II. Common and hyperbolic logarithms of numbers from 101,000 to 

 101,179 to 20 places, with first, second, and third differences, the hyper- 

 bolic logarithms being on the right-hand pages. (Note. AU the common 

 ■logarithms from 101,143 to 101,179, with one exception, contain errors.) 

 III. Common and hyperbolic antilogarithms from -OOOOl to -00179 at 

 intervals of -00001, and from -000001 to -000179 at intervals of -000001, 

 respectively, to 20 places, with first, second, and third differences. 



[T. III.] I. Common logarithms (to 61 places) and hyperbolic logarithms 

 (to 48 places) of all numbers to 100, and of primes from 100 to 1097; and 

 (II.) from 999,980 to 1,000,021 : the hj'-perbolic logarithms occupy the right- 

 hand pages as before. 



[T. IV.] The first hundred multiples to 24 places, and the first ten mul- 

 tiples to 70 places, of the modulus -434 . . . and its reciprocal 2-302 . . . 



[T. v.] Ratios of the lengths of degree &c. (ancient and modern) to the 

 radius as unit, viz. the circular measure of 1°, 2°, . . . 100°, 1', 2', . . . 60', 

 1", 2", . . . 60", and of the corresponding quantities in the centesimal divi- 

 sion of the right angle (1» . , . 100" ; 1^ . . 100' ; 1". . .100") to 25 places. 



[T. VI.] Log sines and tangents for minutes (centesimal) throughout the 

 quadrant (to seven places), viz. from 0" to oO", at intervals of V, with differences. 



