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### Napier's Rods

```
Date: 03/05/99 at 11:38:48
From: phyllis rodin
Subject: Napier's Rods

I have been asked to do a math workshop on Napier's rods and  I need a
picture of them and some basic information.

```

```
Date: 03/05/99 at 11:56:04
From: Doctor Peterson
Subject: Re: Napier's Rods

There is a nice site about Napier's rods at

http://www.cee.hw.ac.uk/~greg/calculators/napier/

Here is an explanation from our Dr. Math archives:

http://mathforum.org/dr.math/problems/crystal1.20.97.html

The basic idea is that each "bone" represents a column of the
multiplication table, like this (the 8 bone):

+--+
|0/|
|/8| 8*1 = 8
+--+
|1/|
|/6| 8*2 = 16
+--+
|2/|
|/4| 8*3 = 24
+--+
|3/|
|/2| 8*4 = 32
+--+
|4/|
|/0| 8*5 = 40
+--+
|4/|
|/8| 8*6 = 48
+--+
|5/|
|/6| 8*7 = 56
+--+
|6/|
|/4| 8*8 = 64
+--+
|7/|
|/2| 8*9 = 72
+--+

To multiply a number by a single digit, you put together the bones for
its digits, then add along the diagonals in the row for the digit you
are multiplying by. For example, if I line up the bones for 287, row 6
will be

2  8  7
|  |  |  |
+--+--+--+
|1/|4/|4/|
6 |/2|/8|/2|
+--+--+--+
|  |  |  |

+--+--+--+
|1/|4/|4/|
/|/2|/8|/2|
/ +--+--+--+
/  /  /  /
1  6 12  2 (carry the one)
------------
1  7  2  2

so 287 * 6 = 1722.

To multiply by a multiple-digit number, you would use the bones to get
each row of the normal multiplication method:

287
* 26
----
1722 <-- what we did above
574  <-- the same, using row 2 instead of 6
----
7462

As you can see, Napier's bones mostly just save you from having to
memorize the multiplication table; you have to do all the rest of the
work yourself. They are little more than a mechanization of the
"lattice method" for multiplication, which is not limited to single-
digit multipliers. (You can look that up in our archives, if you are
not familiar with it.) Oddly, Napier also invented the logarithm, which
was the basis of the slide rule, a much more effective tool for
multiplication; but his bones, which have nothing to do with
logarithms, were as popular in his day as the slide rule was in mine.

I think that should get you started.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 09/15/2001 at 21:30:42
From: Doctor Jodi
Subject: Re: Math history

There's a great page on various methods of multiplication, including
Napier's Bones, at

Napier's rods, abacus and slide rule - Gerold Beckers
http://www.geo.tudelft.nl/mgp/people/gerold/indnap.htm

For some historical information, see

1600 AD  John Napier and Napier's Bones - A History of Computers

For instructions on making Napier's bones, see

Napier's Bones - Rokeby High School, Rokeby, Tasmania
http://www.tased.edu.au/schools/rokebyh/curric/infotech/stage1/assign2/napier.htm

This last page is part of a great site about pre-20th century computing.

- Doctor Jodi, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication

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