102 REroiiT — 1873. 



A = -OpO to A=2-000 at intervals of -001, thence to 3-40 at intervals of -01 

 and to' 5 at intervals of -l to 5 places, with differences. This table is followed 

 by a page of constants. 



Gardiner, 1742. [T. I.] Seven-figure logarithms to 1000, and from 

 10,000 to 100,100, with proportional parts ; the change of the fourth figure 

 in the line is not marked ; the first three figures of the logarithm are sepa- 

 rated from the block of figures bj' a point, which is very clear. 



[T. II.] Log sines to every second to 1' 12", to 7 places, without diflTer- 

 enees; and log sines and tangents throughout the quadrant at intervals of 10", 

 to 7 places, with differences. 



[T. III.] Four-figure logistic logarithms, viz. log. 3600"— log x from .t'=0 

 to .r=4800" (=80') at intervals of 1". 



[T. IV.] Twenty-figure logarithms to 1000, thence of odd numbers to 

 1069, and of primes &c. to 1143. 



[T. v.] Twenty-figure logarithms of numbers from 101,000 to 101,139, 

 with first, second, and third differences. 



[T. VI.] Anti-logarithms, viz. numbers to logarithms from -00000 to 

 •00139 at intervals of -00001, to 20 places, with first, second, and third dif- 

 ferences. 



A list of errata is given in the Prench reprint described below ; and 69 

 errors are pointed out by Hution on p. 342 of the edition of 1794 (and 

 no doubt in other editions) of his mathematical tables. The list given in the 

 edition of 1822 (the last published in Hutton'e lifetime) is much fuller. De 

 Morgan speaks of Gardiner as "rare, and much esteemed for accuracy;" and 

 its rarity in 1770 is the reason assigned by the French editors for the neces- 

 isity of reprinting it. 



Gardiner (Avignon Eepriut, 1770). The reprint is so similar to the ori- 

 ginal edition that it is only necessary to point out the differences. 



[T. I.] is the same ; but in [T. II.] the log sines are given at intervals of 

 1" as far as 4°, and a similar table of log tangents is added ; they were taken 

 from a manuscript calculated by ilouton, bequeathed by him to the Academy 

 of Sciences, and lent to the editors by Lalande. Also in the original edition, 

 in the second portion of this table, viz. that giving the functions at intervals 

 of 10", the parts common to both are repeated ; but this is not done in the 

 reprint, in which therefore there is a table of log cosines and cotangents only, 

 from 0° to 4°, at intervals of 10", the sines and tangents being given in the 

 previous portion. 



[T. III., v., and VI.] are unaltered ; but [T. IV.] proceeds by odd numbers 

 to 1161. One fresh table is added, viz. [T. VII.], giving hyperbolic loga- 

 rithms from 1-00 to 10-00 at intervals of -01, to 7places, and also log^ 10", . . . 10'. 

 Mouton's manuscript also gave log cotangents and cosines to every second 

 of the first four degrees ; but the former are so easUy deducible from the tan- 

 gents, and the latter vary so slowly, that their publication in e.vtenso seemed uu- 

 ueccssarj\ A page of errata at the end of the book contains errors in Vlacq 

 (1628), in Gardiner (1742), and in the French reprint itself (1770), the last 

 having been published in the ' Connaissance des Temps ' for 1775. As the 

 ' Connaissance des Temps' could not have been published as much as five 

 years in advance, it is clear either that some copies of the French reprint were 

 published subsequently to 1770, although retaining that date on the titlcpage, 

 or that this page was circulated separately and bound up afterwards with the 

 work. We have examined two copies, in one only of which this errata-pago 

 appears. 



No editors' names aj»pcar ia the work i but Lalande (Bibliog.Astron. p. 516) 



