376 Mr. J. W. L. Glaisher on Early Logarithmic 



tions (pages 305-326), and the Index (pages 327-332, not 

 paged). 



Of this work there exists a second, enlarged edition, in 4to, 

 printed at Rotterdam, 1659. 



This first edition being printed in 1631 by Vlack himself, 

 the author residing then at Rotterdam, refutes, I think, the idea 

 of Vlack and de Decker having quarrelled ; neither is the as- 

 sumption of a quarrel, as I think I have shown, necessary to 

 explain the non-appearance of the " Groote werck," or the 

 fact that Vlack does not mention de Decker, as the parts of the 

 two volumes of the Nieuwe Telkonst that were translated from 

 Neper, were Vlack's own work and not de Decker's. 



Leyden, March 3, 1873. 



XLVIII. On Early Logarithmic Tables, and their Calculators. 

 By J. W. L. Glaisher, B.A., Fellow of Trinity College, Cam- 

 bridge *. 



THERE are a few remarks in connexion with Prof, de Haan's 

 paper (which he was kind enough to submit to me pre- 

 viously to publication) that it will be convenient to make in im- 

 mediate juxtaposition with it. And, first, in reference to the 

 paper itself I may recall to mind the circumstances that gave 

 rise to it. My former communications, October and December 

 (Supplement) 1872, contained descriptions of two works which 

 had apparently dropped completely out of notice in regard to 

 the history of logarithms, viz. De Decker's Nieuwe Telkonst and 

 Eerste Deel van de nieuwe Telkonst (full titles given above) 

 published at Gouda in 1626. The former of these contains loga- 

 rithms ; and in the prefaces of both are acknowledgments of the 

 services rendered by Vlacq in their preparation. The most curious 

 point, however, was, that in both there are allusions to a much 

 larger work on logarithms, for which the reader was directed to 

 wait patiently, using the Nieuwe Telkonst merely as a make- 

 shift till its appearance. Now the only book to which these 

 promises (supposing them to have been fulfilled) could apply 

 was the Arithmetica Logarithmica of 1628, which, as is well 

 known, was published by Vlacq alone, and contains not the 

 slightest allusion to De Decker, or to any previous publication of 

 logarithms at Gouda. The difficulty, therefore, is to account 

 for Vlacq* s total silence with regard to a work in the preparation 

 of which he had had a share, and which contained an announce- 

 ment either of the Arithmetica itself, or of some abandoned project 

 which had been superseded by it. In either case the omission 



* Communicated by the Author. 



