Napiers Bones
   
  
 
Napier's Bones is a calculating device invented in the 1600s by Scottish Aristocrat John Napier.  It is a remarkably simple device, yet is capable of calculating up into the millions!
 
 
 
 
 
Click on this link for an interactive Napier's Bones simulation:
 
http://www.cee.hw.ac.uk/~greg/calculators/napier/simulation.html
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
How to make your own Napier's Bones from paper:
 
 Draw the bones from table 2 (above 'game of rods) onto a sheet of paper. Units are in the lower triangle, tens in the upper.  Cut out each column to make strips. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
How to use Napier's Bones to multiply:
 
Let us suppose we want to multiply 46785399 * 7
 
Simply place the strips down so that the number 46785399 appears in the top row.
 
Look at what is now row 7.  Add the diagonals together in this row to calculate the answer, which is 327497793
 
 
 
 
 
 
  
 

 

 
 
 
 
                                                                                                          
 
 
 
 

Napier's Bones(1)

This calculating device can be made of bones (hence the name), wood, or paper.

    

  

 
  Table 2. Construction diagram for Napier's bones(2)
 
 
 

Table 3. Simple multiplication using Napier's bones(2)

 

References

(1)Maxfield & Montrose Interactive Inc., (1997) John Napier and Napier's Bones <http://www.maxmon.com/1600ad.htm>

(2)Wikipedia (2004) <http://en.wikipedia.org/wiki/Napier's_bones>