Napier's
Bones These numbered rods
were created by Scottish mathematician John
Napier to aid
multiplication and division of long numbers.
Each face of the rod is marked at the top with
one of the ten counting digits and below are
listed each of its multiples. The rods are laid
alongside each other so that the multidigit
number to be multiplied appears in the topmost
row. Any multiple of this number can then be read
off right to left along the row of the required
multiple. The trick of the bones is in the layout
of the numbers. The units and tens are separated
by a diagonal, and in a given row the tens digit
from a column on the right shares a parallelogram
with the units digit in the column immediately
left. By reading from right to left and mentally
adding pairs of numbers in each parallelogram on
the same row, answers can be read off directly
and written down.
In the picture at left, the number to be
multiplied is 272,968. To multiply that number by
4, run down the lefthand index to "4"
and read that row from right to left adding
number pairs, resulting in the answer 1,091,872.
Division of numbers was assisted by using the
bones to perform trial multiplications. Separate
sets of bones were devised to calculate square
and cube roots.
Napier's ingenious device got its nowpopular
name from the fact that more expensive versions
of it were made from bone, horn or ivory.
Cossons, Neil. Making of the Modern
World, Milestones of Science and Technology.
London: John Murray (Publishers) Ltd., 1992
John Napier
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