Vn some new Facts in the early History of Logarithmic Tables. 291 



solution of sulphate of copper arrived at the same result * — it is 

 true, by a somewhat more circuitous route (compare § 60), — 

 and Bufff, too, by a method very similar to that described. 

 Berlin, July 1, 18/1. 



XXXIV. Notice respecting some new Facts in the early History of 

 Logarithmic Tables. By J. W. L. Glaisher, B.A.j F.R.A.S., 

 Fellow of Trinity College^ Cambridge %. 



THE main facts with regard to the original calculation of 

 logarithms are briefly as follows : — In 1614 Napier pub- 

 lished his Mirifici Logarithmorum Canonis Description in w^hich 

 Napierian logarithms were introduced. Briggs perceived the 

 advantages of the base 10, and in 1624 published the Arithme- 

 tica Logarithmica, containing the (Briggian) logarithms of the 

 natural numbers from unity to 20,000 and from 90,000 to 

 100,000, to 14 places of decmials. There was thus left a gap of 

 70,000, which was filled in by Vlacq, who published in 1628, at 

 Gouda, his Arithmetica Logarithmica (which he called a second 

 edition of Briggs's work of the same name), containing the loga- 

 rithms of all numbers from 1 to 100,000, to 10 places. This 

 Table is that from which every Table of logarithms that has 

 subsequently appeared has been copied. It contains, of course, 

 many errors, which have gradually been discovered and corrected 

 in the course of the 244 years that have elapsed ; but no fresh 

 calculation has ever been made and published §, so that the 

 results of the work performed by Briggs and Vlacq are those 

 that still appear in our Tables. The first logarithmic trigono- 

 metrical canon was published oy Gunter in 1620; it contains 

 logarithmic sines and tangents for every minute to seven decimals. 



Vlacq^s work of 1628 was not the first Table of Briggian 

 logarithms that was published on the Continent; for in 1625 

 appeared, at Paris, Wingate's Arithmeiique Logarithmique, giving 

 seven-figure logarithms of numbers to lOOO, and logarithmic 

 sines and tangents from Gunter. Of the next book that ap- 

 peared on the Continent, I extract the following account from 

 De Morgan^s well-known catalogue of Tables in the "^English 

 Cyclopedia ^ (1861):— 



*' 1626. ' Tables des Logarithmes pour les nombres d\in a 

 10000 composes par Henry Brigge. A Goude. Par Pierre Bam- 



'^ Pogg. Ann. vol. xcvii. pp. 402 & 597 (1856). 



t Jahresbericht von Liebig und Kopp/wr 1856, p. 241. 



X Communicated by the Author. 



§ The only exception is Mv. Sang's Table, that has lately appeared, })firt 

 of which was the result of an original calculation. The Tables du Cadastre 

 have, as is well known, never heen published ; but they have been compared 

 with Vlacq, and some errors found in the latter by means of them. 



U2 



