ON MATHEMATICAL TABLES. 5" 



and trigonometrical functions, -whicli form the basis of, and are the means 

 by -which all other calculations are made, llegarded from this point of view, 

 tliis division may be said to contain auxifiary or subsidiary tables, viz. such 

 as are not per se of any very great intrinsic interest (multiplication tables 

 are a good instance), but which are nevertheless of such paramount import- 

 ance that, without their aid, the calculation of other tables would be too 

 laborious to be practicable. As before remarked, one reason why these tables 

 may well form a division by themselves is, that, being intended for calcula- 

 tions of all kinds, they arc usually published separately, and have not to be 

 sought among the transactions of societies and other periodicals. The num- 

 ber of tables in this class is of course many times greater than are all the 

 other classes put together ; but then, on the other hand, they admit of more 

 brief description, as scarcely any explanation is needed of the functions 

 tabulated, or of the purposes for which the calculation or publication was 

 undertaken. In the present Eeport not above five or six tables printed in 

 periodical publications are noticed ; while it is probable that in the Reports 

 on the other classes there will not be a much greater number that will have 

 appeared as separate and independent books. 



Art. 2. The object of the lleport is to enable any one by means of it to 

 find out with ease what tables have been computed on any of the twenty- 

 five subjects (see § 3) to which it relates, and where they are to be found ; 

 and the desire to form a catalogue that shall give a systematic and practical 

 account of the numerical tables in existence that bear upon each of the 

 subjects included has been steadily kept in view ; in fact little else has been 

 aimed at. Still, as in the search for and examination of so many books of 

 tables (the Repoi-t contains an account of more than 230) a good many works 

 of considerable historical or bibliographical interest came to light, it was ]iot 

 thought desirable to suppress all notice of them. The majority of seven- 

 teenth-century works included are described, on account either of their rarity 

 or because they serve to illustrate the history and progress of the subject. 

 Of this kind are Napier's ' Canon Mirificus ' (1614), containing the first an- 

 nouncement of logarithms, Ltidolf's 'Tetragonometria' (1 690), (fee. ; and when 

 such works have been included, their full titles have been given in § 5, with 

 suitable bibliographical accuracy. It would be a mistake, however, to suppose 

 that all the tables of the seventeenth century have been superseded ; VLAca's 

 ' Arithmetica,' 1028, is the most convenient ten-figure table of logarithms 

 that exists (it has only been reprinted once, and not in so useful a form) ; and 

 no natural canon published subsequently can bear comparison with Pitiscus, 

 1613. In performing mathematical calculations, we have had repeated occa- 

 sion to use both Vlacq and Pitiscus. Uksinus's 'Napierian Canon' (1624) 

 is the largest in existence. The points in which the Keport is least complete 

 are the descriptions of common tables of the eighteenth century, and of com- 

 paratively modern Italian, Spanish, &c. tables of logarithms. Tlie former 

 class we have purposely omitted, though avo have examined many, as they 

 are neither of value intrinsically nor historically ; a good many are biiefly 

 noticed by De Morgan ; and the latter we have not been able to see : several 

 titles Avill be found in the Babbage Catalogue. 



Art. 3. The most valuable detailed list of tables hitherto published is the 

 article Tables written by De Morgan for Knight's ' English Cyclopasdia ' 

 (1861). This article first appeared in the ' Penny Cyclopaedia' (1842), but 

 it was carefully revised and largely augmented by its author before its re- 

 printing in the ' English Cyclopedia.' In this article arc contained notices 

 of 457 tables, many of which, however, are outside the scope of this lleport. 



