ON MATHEMATICAL TABLES. 165 



their successors, and are only of historical interest, a table forms a piece of 

 work done, and, if done correctly, is done for all time. Thus Briggs, 1624, 

 or Vlacq, 1628, when procured, are as useful now as if the tables had been 

 calculated and published recently, subject to the one drawback, that it needs 

 a bibliographical research to determine how far their accuracy is to be relied 

 upon. A table is calculated for a special purpose, which purpose in process 

 of time ceases to be an object of practical interest, and the table is forgotten ; 

 but, for all that, it is the expression of a certain amount of abstract truth, 

 and as such is always of value, and is liable at any moment to be utilized 

 again for some other purpose. Thus one of the most useful objects of the 

 Report is to give in an accessible form accounts of old tables that have passed 

 out of notice, as even the most special table is never so obsolete that some 

 fresh use may not be found for it in the future ; and it is of little value to 

 describe an old and unimportant work without such additional explanation as 

 may lead to its easy identification, with references to the works that contain 

 information of importance to its user. 



Art. 3. But, apart from the necessity of giving bibliographical information 

 with regard to some works in order to render the descriptions useful, it is to 

 be noticed that mathematical history is practically nothing but mathematical 

 bibliography, as the number of letters and other manuscript documents bear- 

 ing upon the subject is very small. This being so, it seemed a pity when the 

 examination of any work showed it to possess some interest, even though of 

 a purely historical kind, to ignore it entirely merely because the table it 

 contained was clearly destitute of practical value*. The whole additional 

 space thus devoted to bibliography does not altogether amount to more than 

 a very few pages ; and the chief concession that has been made to it is in the 

 list of titles in § 5, where in several cases the full titlepage has been tran- 

 scribed. This, with one or two exceptions, has only been done in the case 

 of the tables of logarithms immediately following their invention in 1614. 

 An examination of a great number of works of reference in regard to this 

 matter has shown us how inaccurate, not only in details but even in pro- 

 minent facts, are the accounts usually given. With the exception of 

 Delambre, Lalande (in his ' Bibliographic Astronomique '), and De Morgan, 

 it is not too mvich to say that not a single writer on the subject is to be 

 trusted. Those only who have had occasion to investigate any historical 

 point, like that of the invention of logarithms, can appreciate the slight value 

 that was set on accuracy previously to the dawning of a more careful age at 

 the beginning of the present century. It is necessary to give this caution, as 

 any one who took the trouble to compare certain statements made in this 

 Heport with those given in such works as Thomson's ' History of the Eoyal 

 Society,' or even Hallam's ' Literature of Europe ' (founded on earlier works), 

 might imagine that our account involved matters of opinion and was liable 

 to be disputed ; whereas we cannot find that any previous writer ever did 

 (or perhaps could in the then state of Kbraries) examine or even see all the 

 works relating to this period. It is also worthy of remark that the early 

 logarithmic tables form a most remarkable bibliographical tangle. For some 

 years it was customary to always place the name of J!fapier on the titlepages 



* " It would be something towards a complete collection of mathematical bibliography, 

 if those who have occasion to examine old works, and take a pleasure in doing it, 

 would add each his quotum, in the shape of description of such works as he has actually 

 seen, without any attempt to appear more learned than his opportunities hare made 

 him." — De Morgan, 'Arithmetical Books,' p. x. See also 'Companion to the Almanac,' 

 1851, p. 5. 



