5,2 UEPORT — 1873. 



unite to 100000 London, printed by George Miller, 1G31" (full titles arc 



given in § 5). 



Speaking of Briggs's ' Arithmetiea Logarithmiea' of 1G24, De Morgan, in 

 his article on Tables in the ' English Cyclopedia,' says : — " After his [Briggs's] 

 death, in 1(331, a reprint was, it is said, made by one George Miller ; the 

 Latin title and explanatory parts were replaced by English ones — •' Logarith- 

 micall Arithmctike ' &c. We much doubt the reprint of the tables, and think 

 that they were Briggs's own tables, with an English explanation prefixed in 

 place of the Latin one. Wilson (in his ' History of Navigation,' prefixed to 

 the third edition of llobertson) says that some copies of Vlacq, of 1628, were 

 purchased by our booksellers, and published at London with an English ex- 

 planation lu'cmised, dated 1031 . Mr. Babbage (to whose large and rare col- 

 lection of tables we were much indebted in the original article) has one of 

 these copies ; and the English explanation and title is the same as that which 

 was in the same 3'ear attached to the asserted reprint of Briggs. We have no 

 doubt that Briggs and Vlacq were served exactly in tlie same manner." On 

 referring to Robertson (fourth edition, p. xvi), there is found to be no further 

 information than that contained in the above extract. That De Morgan's 

 suggestion is quite correct, and that Miller's and Vlacq 's tables are both 

 printed from the same types, we have assured ourselves by a most careful 

 comparison, which leaves no doubt whatever that the two works are printed 

 from the same type throughout. We are thus enabled to state that the 

 same errata-list suffices for both ; and this is important, as Vlacq (1G28, 

 or 1031) is still the most convenient and most used ten-figure table in ex- 

 istence. Briggs's friends were annoyed at Vlacq's publication ; but it must 

 be borne in mind that their objections have reference, not so much to the table 

 (which is the only thing of practical importance now) as to the prefixed tri- 

 gonometry, which Vlacq curtailed in his '•' second edition." George Miller also 

 published some copies of the original 'Arithmetica' of 1624, with the same title- 

 page and introduction as were prefixed to the copies of Vlacq of 1628 ; and this 

 was distinctly wrong, as the titlepage does not in this case describe the con- 

 tents correctly. 



It thus appears that Briggs's table was published in 1624, and Vlacu's in 

 1628 — that copies of the tabular portions of both these works were obtained by 

 George Miller, and published by him in 1631, with the same (English) title- 

 page and introduction, Avhich, though correctly describing the contents of 

 Vlacq, is quite inaj^propriate for Briggs. This has led to a verj^ great amoinit 

 of confusion, which has been greatly increased by the fact that on the title- 

 pages Briggs's and Neper's names occur, and that Vlacq only called his work 

 a second edition. It is in consequence exceedingly common to see Vlacq's 

 work assigned to Briggs or Neper ; and it is almost invariably ascribed to one 

 or other of the latter in the catalogues of libraries. 



Vlacq's 'Aritlimetica' of 1628 was also published with the same date, with 

 a French title (" Arithmetique Logarithmctique " &c.) and introduction. 

 Vlacq modestly describes his share of the calculation in the words : — " La 

 description est traduit du Latin en Francois, la premiere Table augmentee, 

 et la secoude composee par Adriaen Vlacq." Miller's (1631) copies of Vlacq 

 are not so rare as the extract from De Morgan might imply. We have seen 

 five of them, and only three or four of the original (1628) works (including 

 both Latin and French). 



In 1031 Vlacq published his ' Trigonometria Artificialis' (§4). This 

 work contains, among other tables, the logarithms of the numbers from unity 

 to 20,000, printed also (with the exception of the last sheet, referred to fur- 

 ther on) from the same type. 



