ON MATHEMATICAL TAULKS. 101 



ply that Mr. Filipowski's table was the result of an independent calculation ; or 

 at all events they ought not to have been ■written unless such had been the case. 

 It is, however, nowhere stated in the preface that the table was calculated 

 anew ; and we may therefore assume that it was copied from Dodwn, after 

 examination (which would not have been difficult, as a mere verification by 

 differences would have sufficed). In a letter by Mr. Peter Gray, in the 

 ' Insurance Record ' for Juue 9, 1871, there are given two errors in Dodson 

 which also occur in Filipowski, affording additional evidence that the tables of 

 the latter were not calculated independently ; and, this being so, Dodson 

 has not been treated fairly, as Mr. Pilipowski should have acknowledged the 

 obligations he was under to his table. In the same letter Mr. Gray 

 gives three other errors in FUipowski (1st edit.) ; and it is to be in- 

 ferred from other passages in the letter that a second and a third edition, 

 *' corrected," have been published. Mr. Gray proceeds : — " but he [Fili- 

 powski] has never, so far as I know, given a list of the errors contained in the 

 first and second, and corrected in the third," an omission on which he strongly 

 (and most justly) animadverts. See Shortrede (1849). 



De Morgan has stated that no antilogarithmic table was published from 

 Dodson (1742) till 1849 ; but this is only true if Shortrede's tables of 1844 

 be ignored ; for which there is no sufficient reason, as thej' were published 

 and sold in that year, and copies of the 1844 edition are contained in all good 

 libraries. 



Galbraith, 1827. T. II. Six-figure logarithms of numbers to 10,000, 

 with proportional parts on the left-hand side of the page. This table is 

 headed " Logarithms of numbers to 100,000." 



T. IV. Log sines, tangents, and secants to every quarter point, to 6 places. 



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

 (arguments expressed also in time, the intervals being 4^), with differences, 

 to 6 places. 



T. VI. N'atural sines, tangents, secants, and versed sines to every degree 

 of the quadrant, to 6 places. 



T. IX. Diurnal logarithms : proportional logarithms for every minute 

 to 24'' (viz. log 1440— log a;) from x—1 to .r=1440 (expressed in hours and 

 minutes), to 5 places. 



T. X. Proportional logarithms for every second to 3°, to 5 places. Same 

 as T. 74 of Paper, except that 5 instead of 4 places are given. 



T. LXIII. A few constants. The other tables are nautical. 



There are a few small tables in the introduction that may be noticed, viz. : — 

 T. XI. and XII. (p. 113), to express hours as decimals of a day, convert 

 lime into arc, &c. ; T. XV. (p. 141), of the areas of circular segments 

 (same as in T. XIII. of Hantscul, but to hundredths only, and to 5 places) ; 

 and T. XVI., table of polygons (as far as a dodecagon), giving area, and radius 

 of circumscribing circle for side=unity, and factors for sides, viz. length of side 

 for radius = unity ; there are also one or two small tables for the mensuration 

 of solids. 



Galbraith and Haughton, 1860. [T. I.] Five-figure logarithms to 

 1000, arranged in columns. This is followed by a small table to convert 

 common into hyperbolic logarithms, and vice versa. 



[T. II.] Five-figure logarithms from 1000 to 10,000, M'ith proportional 

 parts. 



[T. III.] Log sines and tangents to every minute of the quadrant, to 5 

 places, with differences. 



[T. IV.] Gaussian logarithms. B and C arc given for argument A, from 



