the early History of Logarithmic Tables, 301 



is given up to Brig-gs. That Briggs's friends were annoyed at 

 Vlaeq's publication of 1628 is undoubted"^* ; and it is to be re- 

 gretted that the former was not tirst consulted. The feeling, 

 however, does not appear (in spite of Norwood's assertion, 

 quoted in the note) to have been shared by Briggs to any great 

 extent, if we may judge from the fact of his having asked Vlacq 

 to print the Trigonometria Britannica; and this is satisfactory, 

 as, seeing that Briggs died before the completion of the last- 

 named work, it is clear that, in point of fact, as matters turned 

 out, Vlacq did not at all check the completion of Briggs's Arith- 

 metica. The intention of the latter was to calculate the inter- 

 vening 70,000 logarithms to 14 decimals; and as no one has 

 since been willing to perform this work, it is possible that some 

 years might have elapsed, bnt for Vlacq, before the gap was filled 

 up even to 10 places. The French manuscript Tables only ex- 

 tend to 12 places (the twelfth figure being uncertain) ; so that 

 even if they were published, Briggs's original scheme would not 

 be completely carried out. 



Briggs perceived the advantage of a centesimal division of the 

 right angles, and made a step in this direction in the Britannicay 

 where he divided the degrees, not into minutes, but into hun- 

 dredths. In the Artificialis Vlacq expresses his entire approval 

 of this change, but proceeds to add that, as those who were accus- 

 tomed to the old system would not take kindly to the new, he was 

 induced to calculate his Tables, in which the old sexagesimal divi- 

 sion is retained (the intervals being 10"). Hutton has made the 

 remark that, had it not been for Vlaeq's publication, a partial refor- 

 mation of the sexagesimal system might have taken place then. 

 This seems very true ; and on consideration it appears that the 

 only time when the change could have been conveniently effected 

 was when the use of the natural was replaced by that of the 

 logarithmic trigonometrical canon. It is thus not a little 

 curious that Vlacq, while expressing his approbation of the 

 change introduced by Briggs, should have done the very thing 



* The only objection I have seen is that made by Norwood in his TrigO' 

 nometrie, 1631 (quoted by Hutton, p. 38 of the History prefixed to his 

 Tables) . The statement that Ylacq's work was "nothing like his [Briggs's], 

 not worthy his name " is certainly untrue. The assertion, however, that 

 Vlaeq's Latin edition was " against Briggs's mind and liking " is more to 

 the point. It should be added that it is not at all clear that Vlacq was in 

 any way accessory to the publication of Miller's copies (about which Briggs 

 certainly had some right to complain) as this may have been done by the 

 bookseller on his own account. I may remark that of two editions of Nor- 

 wood (second, 1641, and seventh, 1678) now before me, the passage in 

 question appears only in the latter. It there forms part of "the Epilogue 

 or Conclusion," which ought to be at the end of the trigonometry and 

 before the Tables ; but through a mistake of the printer the pages are out 

 of order, 



