ON MATHEMATICAL TABLES. 117 



The copy of this tract before us (which is bouiul up in a volume with 

 several otlicrs, and belongs to the Cambriclge University Library) is clearly 

 either a separate reprint or merely a table torn out from some larger 

 work. The paging runs from 262 to 351 : at the beginning there is a plate, 

 the size of the page, of a, person observing with a sextant, and the words 

 " between page 248 and 249 " below in the left hand-corner, and at the end 

 a diagram with a movable circle and pointer, headed " The fore part of the 

 Nocturnall or side held next the face in time of obser\'ation," and " between 

 page 254 and 255 " below. On examination we find the table is [T. IV.] of 

 Sir Jonas Mooee's ' Systeme of the Mathematicks,' 1681, just described. 

 The engravings do not, however, appear to be taken from cither volume 

 of this work. It is very likely that this table was merely torn out 

 from the work, and was never published separately ; still as, according to 

 De Morgan, this is the first appearance of such a table in England, it is not 

 improbable that copies may have been in request, and therefore issued 

 separately. 



J. H. Moore, 1814. T. III. Log sines, tangents, and secants to every 

 quarter-point, to 5 places. 



T. IV. Five-figure logarithms of numbers to 10,000. 



T. V. Log sines, tangents, and secants for every minute of the quadrant, to 

 5 places, 



T. XXIII. Log 2 elapsed time, mid. time, and rising (for explanation of 

 these terms see T. XVI. of Maskeltxe, § 4) for every 10' to G^, except 

 the last, Avhich is to 9^, to 5 places. The tables are separated as in Mackay. 



T. XXIV. Natural sines for every minute of the quadrant, to 5 places. 



T. XXV. Proportional logarithms for every second to 3°, to 4 places ; same 

 as. T. 74 of Eaper. 



AVe have seen the 18th edition (1810), which is identical with that above 

 described, an edition of 1793, and the 9th edition (1791) (the last two not 

 edited by Dessiou). All contain the tables described in this account (though 

 the order is diflerent), except that the tables in T. XXIII. are not separated; 

 the log rising is only given to 6'', and the intervals also 30', in the two 

 eai'lier editions. 



Three out of the four editions contain different portraits of the author. 



Mtiller, 1844. [T. I.] Five-figure logarithms of numbers from 1000 to 

 1500, and four-figure logarithms from 100 to 1000. 



[T. II.] Table of Gaussian logarithms in a somewhat modified form, 

 viz. S and U to 4 places, from A=-0000 to -0300 at intervals of -0001, 

 thence to -230 at intervals of -001, and from -20 to 2-00 at intervals of -01, 

 and thence to 4-0 at intervals of -1, with diff'ercnces ; where 



A = log X, a z=\ogfl + -\ and U = log ^ . 



.V 



[T. III.] Squares of numbers from to 1 at intervals of -0001, to 4 places, 

 and quarter squares of numbers from to 2 at the same intervals, also to 4 

 places (intended for use in the method of least squares). 



[T. IV.] Four-place log sines and tangents for every second to 10', thence at 

 intervals of 10" to 1°, thence at intervals of 1' to 4°, and to 90° at intervals 

 of 10'. 



There are given also : — the circular measure (to 12 places) of 1°, 2° . . . 

 10°, 1' . . . 10' and 1" ... 10" ; 12 constants involving n ; natural sines and 

 tangents to every half degree ; and a few three-figure logarithms. 



