166 REPORT — 1873. 



of works on logarithms, as being their inTentor, and, if the logarithms were 

 decimal, that of Briggs (and perhaps also that of Ylacq) in addition. Thus 

 the ' Arithmetica ' of 1628 will be found in bibliographies and library cata- 

 logues usually under the name of Napier or Briggs, and very rarely under 

 that of its author Vlacq. If to this confusion be added the additional com- 

 plication produced by the varieties of ways in which the names of the three 

 leading logarithmic calculators were spelt, it may easily be inferred how 

 incorrect and confused is all the infonnation to be obtained from bibliogra- 

 phical sources, whether general or mathematical*. It is on this account 

 that we have thought it desirable to give the titles of these works in full in 

 § 5. Perhaps it would not have been possible to sec so many of them 

 in any one other country except this ; and the value of a number of such 

 titles collectively in the same list is much greater than the sum of their 

 separate values when scattered in different works. 



Art. 4. While on the subject of bibliography, it is proper to remark that, 

 in the cases where the full titles have been given in § 5, there is a certain 

 slight want of uniformity in the way in which they have been transcribed, 

 viz. in the use of capitals, the writing at fuU length of words abbreviated, 

 and the modernizing the language by the substitution of u for v or i for j, 

 and vice versa. Titlepages are printed partly in capital and partly in Roman 

 and italic characters ; and when they are transcribed whoDy in Eoman letters, 

 there arise several uncertainties. Thus it is usual in the portion printed in 

 capitals to replace U by V and J by I, and very often not to use a larger 

 letter after a full stop or for a proper name ; and in copying the whole in 

 Roman letters it is doubtful whether to write these as they are, or to recon- 

 vert them. We are inclined to think that the best plan (except when capitals 

 are reprinted as capitals &c., in which case no difficulty occurs) is to make an 

 exact copy, and not even introduce a capital letter after a full stop, although 

 the author would no doubt have done so himself had he printed his title- 

 page in Roman characters throughout. Exception must, however, be made 

 in the case of proper names. These rules have not been followed out com- 

 pletely in one or two of the earliest titles that we copied, before experience 

 hsd taught us that in bibliographical matters the greatest attainable accu- 

 racy should be invariably striven after ; also one or two abbreviations have 

 been replaced by the words at length (such as e.g. " serenis™'-' by " sere- 

 nissimi " or " atq ;" by " atque"). Whejiever, of course, any difference from 

 ordinary spelling is observed, it may be taken for granted that the title is so 

 printed in the book ; the utmost change that has been made being that some 

 words in a few of the titles are modernized. 



The foregoing remarks apply to the titles that are transcribed at length ; 

 but a few words must also be said with regard to those in which only 

 enough is given to identify the books described without possibility of mis- 

 take. Wherever words are left out from the title, the omission is marked 



* Even Babbage makes a bibliographical error on the first page of the preface to his 

 tables, where he says that " the first 20,000 were read with those in the Trigonoinetria 

 Artificialis of Briggs." The 'Trigonometria Artificialis' was calculated by Vlacq, and 

 published by him two years after Briggs's death, though the 20,000 logarithms ap- 

 pended were of course originally computed by Briggs. Any one who will look at the 

 title of the ' Trigonometria Artificialis ' in § 5 will see how easily a mistake of this kind can 

 be made ; and in fact an inspection of the titles of the other works of this period will show 

 that it would be difficult for any one who had not bestowed some attention on the history 

 of logarithms to assign them to their true authors. Part of the confusion that exists is 

 due to Vlacq's excessive modesty, which led him on the titlepages of his works to give 

 quite a subordinate position to his own name compared with those of Napier and Briggs. 



