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. 1. At the beginning of the same volume is reprinted the Introduction to Hutton’s Mathematical Tables, on p. liii 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 equidifferent. For specimen page of the Table see preceding page. The arrangement is as follows:—
Column 2 contains 1000 equidifferent 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 1, 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 off 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 1614, 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 10,000,000 or a 484000010000000th = a 4851000th part of radius. Similarly column 1 gives the arc, in degrees, minutes, and seconds, corresponding to a sine equal to the 4851000th part of the radius, with interscript differences;
Column 3 gives in hours, minutes, and seconds the 4851000th part of a day of 24 hours; and finally
