16
Some Other Contributors to Early Logarithmic Tables
Vlacq and De Decker were not the only Dutchmen who have been actively
involved in logarithmic tables. Christiaen Huygens, one of the inventors of the
pendulum clock, has published in 1661 a method for fast calculation of logarithms
by approximation, based on "squaring an equilateral hyperbola", see [25]. It is not
known if this method has ever been used. Some Dutchmen in the 17th century
have published existing Vlacq tables in new books, like Dirk Rembrants van Nierop
(1671), Claas Jansz Vooght (1685), Johannes van Keulen (1698) and Christiaan
Wolff Nicolaas Epkema (many editions between 1711 and 1780). Also the well-
known handbooks for navigation at sea by Abraham de Graef (Z?e Seven Boecken
van de Grote ZeeVaert, 1657) and Klaes Hendriksz Gietermaker ('f Vergulde Licht
der Zee-vaert, ofte Konst der Stuur/uyden, 1671) contained Vlacq's tables
of logarithms amongst the many other navigational and astronomical tables,
see [14].
During the 17th and 18th century more than a hundred logarithmic tables
have been published, see [19], which were derived - completely or partially -
from the Briggs/De Decker/Vlacq computations. Many of those even had the print
image of the "small" Vlacq tables, but later editions were provided with improved
and more "user-friendly" table lay-outs. No extensive new calculations have been
done since the 1620's, until Georg von Vega in Austria and Gaspard de Prony in
France recalculated logarithms in the 1780's.
Other scientists on the continent were closely involved with trigonometries
and table construction, but have not contributed directly to Briggian tables. For
example, Willebrord Snellius calculated a new non-logarithmic trigonometric table
(another Canon Triangulorum) around 1626, just before he died, but apparently
he was not acquainted with logarithms. Kepler on the other hand, was keenly
aware of Napier's publications, and he published limited logarithmic tables, e.g. in
his Rudo/phine Tables (1627), but these were still Neperian, not Briggian.
Precision of Logarithmic Tables
Under Table 1, the precision of input and output of logarithmic tables, in number
of decimals, was already mentioned. Generally speaking, the mathematicians had
a tendency to increase the output precision from Briggs' original 14 decimals, for
example to 28 decimals (of numbers 1 to 10,000) by E. Sang near the end of the
19th century, or even higher. But for practical use of a logarithmic table as a
calculating instrument, a lower precision was allowable, and even advisable to
keep the books within manageable size.
Vlacq already started that trend by decreasing output precision first
from Briggs' 14 to 10 decimals, and later in his "small" table to 7 decimals,
while reducing the input precision to 4 decimals (1 to 10,000). As a further
example, Jrme de La Lande has produced in 1827 a table of 4 by 5 decimals
precision, with even smaller size and weight than the 1972 electronic scientific
calculator HP 35 (the "terminator" of logarithmic tables and slide rules alike).
