ON MATHEMATICAL TABLES. 7 



We may also mentiou Do Morgan's ' Arithmetical Books from the inveutiou 

 of printing to the ^jresent day,' London, 1847, 8vo, the introduction of which 

 contains useful bibliographical information about the description of books, 

 and Peacock's " History of Arithmetic " in the ' Eueyclopffidia Metropolitana.' 

 There is one bibliographical work, viz. Scheibel's ' Einleitung zur mathe- 

 matischen Biicherkenntuiss.' Neue Auflage. 3 vols. Svo, Breslau, 1781 

 (as given in the Babbage Catalogue), which is continually referred to by 

 Murhard, Rogg, &c., though we have never been able to see a copy in any 

 library to which we have had access, or procure one otherwise. _ De Morgan 

 says, "Scheibel (additions) may be considered as partly repetition, partly 

 extension, of Heilbronner. He is one of those bibliographers who collect 

 from various sources the names and dates of more editions than those who 

 know catalogues wiU readily believe in." 



It is imnecessary here to mention works on general bibliography, such as 

 Hain, Ebert, Watt, &c., Avhich are well known; we maj', however, parti- 

 cularly notice 'Tresor de livres rares et precieux ou Nouveau dictionnaire 

 bibliographique,' par Jean George Theodore Graesse, Dresde [also Geneva, 

 London, and Paris], 1859-1867 (7 vols, including supplement), which might 

 be of use, though we have found the mathematical works it contains very 

 inaccurately described ; but this is a fault common to all works of general 

 bibliography. 



Montucla, ' Histoire des Mathematiques,' we have not found valuable ; but 

 we may call attention to the accurate information given by Delambre in his 

 ' Histoire de I'Astronomie Moderne,' t. i. Paris, 1821 ; and also in his other 

 histories. 



Reuss's ' Eepertorium Commentationum a.societatibus litterariis editarum,' 

 GottingEB, 1801-1821, 16 vols. 4to, is a work very similar in its plan to 

 the Royal Society's Catalogue of Scientific Papers, except that it is an iiidea; 

 rerum instead of an ijidex auctorum. The mathematics is contained in vol. 

 vii., the arithmetic occupying pp. 2-31 of that volume. On p. 30 are refer- 

 ences to descriptions of calculating and other arithmetical machines. 



We have found Nos. XIX. and XX. (on trigonometrical and logarithmic 

 tables) of Hutton's ' Mathematical Tracts,' London, 3 vols. Svo, 1812, very 

 useful. 



Art. 4. The mode of arrangement of this Report (which properly occu- 

 pies § 3, § 4, and § 5), and the reasons that have led to its adoption, are as 

 follows : — If every table were published separately and formed a work by 

 itself, the obvious course would be to divide them into a certain number of 

 classes according to their contents, to prefix to each class a brief intro- 

 duction and explanation, and then to give a detailed description, in chrono- 

 logical order, of the tables included under it. This is, in fact, the course 

 that has been pursued with regard to separate tables (i. e. works containing 

 either a single table or only tables that come under the same class) ; § 3 is 

 divided into 25 articles, each article being devoted to one subject: — art. 1, 

 multiplication tables ; art. 2, tables of proportional parts, *fec. (for the con- 

 tents of all the articles, see the commencement of § 3). Each article begins 

 with a general account, partly historical, of the subject included in it; and 

 then follow the' descriptions of the separate tables ou that subject. But the 

 majority of works noticed are collections, and iuclude tables that are com- 

 prised under several articles ; thus Hutton's tables contain Biiggian and 

 hyperbolic logarithms of numbers, a natural and logarithmic canon, &c. &c., 

 each of which belongs to a different article. Two courses were therefore 

 open for the treatment of such works : — (1) to describe them under the article 



