The construction of the wonderful canon of logarithms

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;
Appendix, 163
man mathematicians, as he mentions in his Preface, not being satisfied
with Napier's demonstration based on Arithmetical and Geometrical
motion. The two parts together with the Table are reprinted in
'Scriptores Logarithmici,' vol. I. p. i. At the beginning of the same
volume is reprinted the Introduction to Hutton's Mathematical Tables,
on p. Hii of which will be found a "brief translation of both parts,
omitting only the demonstrations of the propositions, and some rather
long illustrations of them."
The logarithms in the Table are of the same kind as Napier's, but
they are not affected by the mistake in the computation of the Canon
of 1614.
The Tables of Kepler and Napier are differently arranged, and the
numbers for which the logarithms are given are also different. In
Napier's Canon the numbers in column "Sinus" are the values of
sines of equidifFerent arcs, while in this table the numbers or sines are
equidififerent. For specimen page of the Table see preceding page.
The arrangement is as follows :
Column 2 contains looo equidififerent numbers, 10,000, 20,000,
30,000, . . . 9,980,000, 9,990,000, 10,000,000. It also has at the beginning
the 36 numbers i, 2, 3, to 9; 10, 20, 30 to 90; 100, 200 to
900 ; and 1000, 2000 to 9000.
Column 4 contains the logarithms of the numbers in column 2, with
interscript differences.
The 2nd and 4th are the only columns containing entries for the first
36 numbers.
It will be observed that a point marks oflf the last two figures of the
values in these two columns, but if it be left out of account the numbers
and logarithms agree with those of the Canon of 16 14, in being referred
to a radius of 10,000,000. So that the values really represented are
the ratios of the numbers there given to 10,000,000.
Taking as an example the first entry in the specimen page, the number
in column 2 which is 4,850,000 represents the ratio 4,850,000 to
part of radius. Similarly column
I o, 000, 000 or a j^ggg ^^th = a yM**
I gives the arc, in degrees, minutes, and seconds, corresponding to a
sine equal to the j-^th part of the radius, with interscript differences
Column 3 gives in hours, minutes, and seconds the
day of 24 hours ; and finally
xMf^h part of a
X 2 Column