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### Napier's Bones

```
Date: 01/20/97 at 11:14:12
From: Crystal
Subject: Napier's Bones

How do I solve the problem 364 x 27 on the bone rods?  Can you explain
how to figure this out?

Thanks
```

```
Date: 01/20/97 at 12:28:49
From: Doctor Ken
Subject: Re: Napier's Bones

Hi there -

Here's some information I found by searching the math-history mailing
list on our site.  You can search the Math Forum site too by going to:

http://mathforum.org/grepform.html

and using the keyword Napier:

On Mon, 12 Feb 1996, Emmanuel CE Middle wrote:

Hello! Our names are Mark Atkins and Richard Pinel aged 12 of Emmanuel
C of E aided school and we are wondering if anyone knows anything
about John Napier or his "bones".

John Napier was Baron Napier of Merchistoun, Scotland, and lived in
Merchistoun Castle.  The thing he's really famous for is his discovery
of logarithms: his book on them was published in 1609.

Napier's "bones" are a collection of little sticks, each one bearing
the multiples of some particular digit: for instance the "8-bone"
would look like:

___
|0 /|
|_/8|
|1 /|
|_/6|
|2 /|
|_/4|
|3 /|
|_/2|
|.. |
..

(actually those slanting lines should be diagonals of the squares they
are in).

These were used in multiplying:  to multiply by 8314 for instance,
you'd put an 8-bone, a 3-bone, a 1-bone and a 4-bone side-by-side, and
then you'd find it easy to read of the first 9 multiples of 8314.
[The digits above the slanting lines "carry over" to the preceding
place.]

I suggest you make a set of such "bones" out of paper, place them
side-by-side like this, and see how easy they make these
multiplications.  If you have any difficulty in following this, please
write again.

It's probably much better to try to make them yourself and work out
how to use them, rather than to just read about them in a book.

John Conway

----------------------------------------------------------------------

You can also check out the previous answer in Dr. Math's archives
about just how the bones work:

http://mathforum.org/dr.math/problems/powers10.11.html

As a cautionary note, you may find that different people have
different ideas of what exactly Napier's Bones are.  Some people use
the term as a funny name for a slide rule, and others mean the actual
objects that John Napier used to do multiplication, which were the
forerunners of the slide rule. So if you see conflicting information
out there, that may be where it came from.

-Doctor Ken,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication