the early History of Logarithmic Tables, 297 



ference between the two is readily seen by comparing the first 

 half dozen sines, three of which differ in the last figure. Sher- 

 win would therefore have gained nothing by examining his 

 Tables by any of the real copies of 1626, with all their inaccu- 

 racies. A sufficiently good reason against his having seen the 

 edition with Decker^s name on it is that, if so, he would not have 

 attributed it to Vlacq. It is remarkable that De Morgan should 

 not have noticed the above anachronism ; his words need not 

 imply that he ever saw a copy of the Tables separate from the 

 Sciographia (except the one with the Dutch title and preface*). 

 The (real) edition of 1626, with the French title-page, must either 

 have contained logarithms of numbers alone — or if there was a 

 logarithmic canon, it must have been Gunter^s. 



I have met with (in the Cambridge University Library) a se- 

 parate copy in which the two Tables appear exactly as in the 

 Sciographia, with the same title-page, which also has the snip 

 halfway up. It would be easy to frame theories to explain this; 

 but it is enough to merely notice the fact that the title-page and 

 date only are true with regard to the first Table, and that the 

 second could not have been printed before 1628. Decker's words 

 ende van ons yets by te voeghen may refer to the filling up of the 

 gap in Briggs's Table from 20,000 to 90,000; but it is not un- 

 likely that only improvements in the introductory matter were 

 meant. Decker's work leaves no doubt that to him must be 

 assigned the credit of having been the first foreigner who pub- 

 lished Briggian logarithms, an honour that has always been 

 hitherto assigned to Ylacq, but one which the latter can well 

 spare from his list of great services in the calculation and diffu- 

 sion of logarithms. 



I take this opportunity of alluding to the very meagre collec- 

 tion of facts that is generally supposed to constitute all that is 

 known with regard to the life of Vlacq, and of giving a fuller 

 account. The splendid invention of logarithms by Napier, the 

 grand improvement made by Briggs in the introduction of the 

 base 10, his great labours in the calculation of Tables, and 

 the rapidity and industry with which Vlacq completed the work 

 so well begun, form a unique episode in the history of arith- 

 metic; and, considering the great attention paid to logarithms 

 for years afterwards both by mathematicians and calculators, 



(which is bound up with Briggs's Logarithmorum Chilias prima, hut seems 

 perfect) contains no logarithms of numbers. 



* This can only refer to Decker's book. If De Morgan had seen it for 

 more than a moment it is impossible he could have failed to notice Decker's 

 name. The fact also that the difference between the second Table and 

 that in the Sciographia escaped his notice confirms the supposition that 

 he cculd only have had a mere glance at it apart from the latter. 



