The construction of the wonderful canon of logarithms

46 Construction of the Canon.
Outline of the Construction, in another
form,
of a Logarithmic Table.
60. OINCE the logarithms found by 54 sometimes differ
^ from those found 4y 58 {for example, the logarithm
of the sine 378064 is 32752756 by the former, while by
the latter it is 32752741), it would seem, that the table of
sines is in some places faulty. Wherefore I advise the
learned, who perchance may have plenty ofpupils and computers,
to publish a table of sines m,ore reliable and with
larger num,bers, in which radius is made 1 00000000, that
is with eight cyphers after the unit instead of seven only.
Then, let the First table, like ours, contain a hundred
numbers progressing in the proportion of the new radius
to the sine less than it by unity, namely of 1 00000000 to
99999999.
Let the Second table also contain a hundred numbers in
the proportion of this new radius to the number less than
it by a hundred, namely of 100000000 to 99999900.
Let the Third table, cilso called the Radical table, contain
thirty-five columns with a hundred numbers in each
column, and let the hundred numbers in each column progress
in the proportion of ten thousand to the number less
than it by unity, namely of 1 00000000 to 99990000.
Let the thirty-five proportionals standing first in all the
columns, or occupying the second, third, or other rank, progress
among themselves in the proportion of 100 to 99, or
of the new radius 1 00000000 to 99000000.
In continuing these proportionals and finding their logarithms,
let the other rules we have laid down be observed.
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