296 Mr. J. W L. Glaisher on some new Facts in 



with Decker^s first Table. A comparison of any two corre- 

 sponding pages is enough to estabhsh this; but the best proof 

 is afforded by the g of Logarithm! (which is Italic instead of 

 Roman) at the top of the page the first number on which is 

 7801. The second Table is not the same as the second in the 

 TelJwnstf but gives logarithmic sines, tangents, and secants^] 

 further, it is not printed in the fine bold type which charac- 

 terizes Decker^s work (and the other Tables printed by Ram- 

 maseyn), as well as many of the subsequent small Tables printed 

 at Amsterdam, 1681, Frankfort and Leipzig, 1757, &c., and 

 known by the name of Vlacq. The reason for the change in this 

 Table is evident, as Decker merely reprinted Gunter''s Table. 

 But in 1628 appeared Vlacq's Arithmeiica (containing loga- 

 rithmic sines &c, to every minute), and in 1633 his Trigono- 

 metria Artificialis (giving the same for every ten seconds), in 

 both of which the results were carried to more decimals than by 

 Gunter, and consequently very many (chiefly last figure) errors 

 of his detected, so that by 1635 Gunter's calculation had already 

 been superseded. It will be noticed that the title-page to the 

 Tables in the Sciographia only applies to the first (or otherwise 

 the date could not be 1626, as there given); and I have no 

 doubt that the second Table has no connexion with the first, 

 having been probably printed in England. Sherwin^s words in 

 the preface (1705) to his well-known Tables are, "The Tables of 

 Logarithmic Sines, Tangents and Secants were examined by a 

 Table of the said Vlacq, in large octavo, printed at Gouda, 1626/^ 

 That there must be some error here is quite clear, as, by Vlacq^s 

 own statement, he only became acquainted with Briggs^s Arith- 

 metica in that year. It seems to me quite clear (for reasons that 

 will be stated further on) that Sherwin did not refer to Decker^s 

 work; and the only explanation (and, I have little doubt, the true 

 one) of his statement is that he made use of a copy of the Scio- 

 graphia having a title-page to the Tables. Imagining, as De 

 Morgan did afterwards, that the two Tables and the title-page 

 had formed a separate work, and knowing "no one else in the 

 least likely to have published logarithms at Gouda in 1626,^^ he 

 assigned the work to Vlacq. The reason why the two Tables 

 could not have appeared together in 1626 is that the second one 

 contains Briggs^s or Vlacq^s logarithmic sines &c., first published 

 in 1628, while in 1626 only Gunter'sf had appeared: the dif- 



* The six columns in the (semiquadrantally arranged) Table are headed 

 Sinus, Sinus CompL, Tang., Tangens CompL, Ar. Compl. Sinus, Ar. Com, 

 Sin. Com. 



t There is a copy of Gunter*s Canon Triangulorum (1820), which is 

 extremely scarce, in the British Museum. De Morgan, who had never 

 seen a copy, says it contains,besides the trigonometrical functions, logarithms 

 of numbers from 1 to 1000 to 8 decimals ; but the British-Museum copy 



