ON MATHEMATICAL TABLES. 121 



the m is loft out, -where it is thought the context prcveuts risk of mistake ; 



and instead of — n o jn there is sometimes written n om, and the lieading 



" cologarithm." The^Last page of the hook, headed (wrongly) Tahlc XXXIII., 

 contains a very imperfect list of the abbreviations used. 



It is to be inferred from the Preface &c., that the book was set up and 

 electrotyped by the author himself, Avho states that " it is probable that there 

 is not now a single error in the whole table." The reward of a copj' of the book 

 is also offered to the first finder of any important error under certain condi- 

 tions. Parts of the book, in the cojiy before us, are very badly printed, so 

 badly in fact that one or two images are wholly illegible ; and the tables are so 

 crowded that we should think no one would use them who could procure any 

 others that could be made to do as well. In fact the author's object seems to 

 have been to crowd the greatest possible amount of tabular matter into the 

 smallest space, without any regard to clearness. It is stated in the work that 

 in the course of the printing, incomplete copies (some containing proofs almost 

 illegible) were distributed to the author's friends ; and an advertisement on the 

 cover states that copies containing proofs rejected in the printing may be had 

 at different prices according to their completeness and the order of the tables. 

 The book is printed phonetically ; and this adds to the awkwardness of the 

 most confused, ba3ly printed, and ill-explained series of tables we have met 

 with in the preparation of this Report. By issuing his tables in the form 

 and manner he has adopted, the author has not done justice to himself, as 

 several are the results of original calculation and are not to be met with 

 elscAvhere. 



Pasquich, 1817. T. I. Five-figure logarithms to 10,000 (arranged 

 consecutively in columns), without diff'erences. 



T. II. Log sines, cosines, tangents, and cotangents, from 0' to 56' at in- 

 tervals of 10", thence to 1° at intervals of 20", and thence to 45° at intervals 

 of l',.witli difterences for 1". Also squares of natural sines, cosines, tangents, 

 and cotangents from 1° to 45° at intervals of 1', all to 5 places. De Morgan 

 says, "This trigonometrical canon in squares is, we suppose, almost unique." 



T. III. Gaussian logarithms. B and C (same notation as in Gauss), to 5 

 places, with differences, for argument A, from A = -000 to A = 2-000 at 

 intervals of -001, from A = 2-00 to A = 3-40 at intervals of -01, and from 

 A = 3-4 to A = 5 at intervals of •!. This table is the same as that originally 

 given by Gauss, 1812 (§ 3, art. 19). 



A iv\Y constants &c. are added in an Appendix. 



A lengthy review of this Avork by Gauss appeared in the ' Gottiugische 

 gclehrte Anzeigen' for Oct. 4, 1817. It is reprinted on pp. 246-250 of 

 t. iii. of his ' Werke.' 



Pearson, 1824. Yol. I. contains 296 large quarto pages of tables ; but 

 only three pages come within the range of this lieport, viz.: — [T. I.], p. 109, 

 a one-page table to convert space into time, and vice versa. [T. II.], p. 261, 

 w^hich expresses 1°, 2°, 3° 360°, and 1', 2' 60' as decimals of the cir- 

 cumference of the circle to 4 and 5 places respectively ; and [T. III.], p. 262, 

 which gives the circular measure of 1°, 2°. . . .180°, of 1', 2'. . . .60' and of 

 1", 2".. ..60", to 8 places. 



The other tables are nautical, astronomical &c. 



Peters, 1871. [T. I.] pp. 16, 17. Himdredths, thousandths, ten-thou- 

 sandths, hundred-thousandths and millionths of a day expressed in minutes 

 and seconds. 



[T. II.] pp. 18, 19. For the conversion of arc into time, and vice versa. 



