Abhandlungen zur Geschichte der Mathematik.

Notes on the History of Logarithms. 35
NAPIER's logarithms". DE MORGAN carefully explains the difference between
NAPIER'S *and natural logarithms in the article "Tables" in the Englishi
Cycloaccedia, but in DE MORGAN'S Budget of Paradoxes (p. 70) GÜNTHER
has found a passage which is inaccurate. l)
Of german books, we have consulted CHRISTIAN WOLFF,12) who speaks
of NAPIER'S and BRIGGS'S logarithms, but does not mention the natural.
It is a pleasure to find that KÄSTNER presents the subject in a way free
of error. In his Gesch7ichte13) he refers to an article, which he had written,
setting forth the exact relation between the two systems. Nevertheless
the misconception became prevalent in Germany also. So wide-spread was
this error in Europe that WACKERBARTH was induced to make the following
statement:14) "Dans presque tous les ouvrages elementaires anglais, francais
et allemands, dont on fait usage dans l'enseignement des mathematiques,
il est dit que les logarithmes naturels ou hyperboliques sont identiques aux
logarithmes neperiens."
Proceeding to the question relating to the earliest publication of tables
of natural logarithms, we meet the name of JOHN SPEIDELL, who, in 1619,
brought out his New Logarithimes, only five years after NAPIER's publication
of the Descriptio. SPEIDELL'S book received little attention, either during
his life-time or since. It would seem as if the earliest publication of a
table of natural logarithms should be mentioned in histories of mathematics,
but, so far as I know, no general history by a German, French, or British
author, takes notice of SPEIDELL. The great English Dictionary of Ncational
Biogrcap7y, now being completed, does not give his name, although it mentions old writers of elementary arithmetics, such as HODDER and HUNT.
However, SPEIDELL'S Ne2v Logaritlimes has been described in at least three
special historical articles. HUTTON speaks of it in the "Introduction" to
his Tables;l5) AUGUSTUS DE MORGAN makes a careful study of his book in
the article "Tables" in the English Cyclopaedia; J. W. L. GLAISHER gives
a brief account of SPEIDELL'S work in the report on "Tables" in the
British Association Report, 1873, pp. 1-175.
I have tried for a long time to secure a copy of SPEIDELL'S work,
but have failed. Through the kindness of Dr. GARNETT of the British
Museum I have before me photographs of the title-page of the edition of
1622 and of one page of the tables. The title-page is as follows:
11) GÜNTHER, op. cit., p. 273.
12) Mathematisches Lexicon, Leipzig, 1716, article, ~'Logarithmius".
13) KÄSTNER, Gesch. d. ]Math. 3ter Band, 1799, p. 87.
14) Les Mondes, Tome XXVI, p. 626.
15) o(). cit., 1811, p. 30.
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