Counting Rods

There is a lot of confusion about who invented such counting devices, the Chinese or Napier. It wasn't until about 50 years after the publication of Napier's account of his rods (1617) that a similar device was described by the Chinese. 'These Chinese computing rods are thought by some to be of Chinese invention, dating from perhaps the thirteenth century. Other investigators believe that knowledge of Napiers rods was taken to China by Jesuit missionaries and that these rods are an adaptation of Napier's idea' (Sanford, 1958, p 340). Whose idea they were originally is still unknown, but for the time they were made they made multiplication a lot easier.

In China they were originally made from bamboo sticks about 1/10 of an inch (3mm) in diameter and 6 inches (150mm) long. Today they are primarily made from wood or paper. As can be seen in diagram 14, the set comprised of a rod for the numbers 1-9 and unlike Napiers also included a zero, square and cube rod. They are divided into 9 cells, with a space for both tens and units. These 9 cells allow for the first 9 multiples of the digit.

Diagram 14. The Chinese set of counting rods.

In multiplying two numbers, the multiplicand was laid out by placing the rods of this number evenly in order, each with its smallest number on the right hand side (look at diagram 15). The number in the far column gave the product of the number one. The number in the second right column gave the product of number two and so on.

Diagram 15. The multiplicand 3312.

In finding these products a number below a number on another rod were added together, starting from the bottom up. Using diagram 15, lets multiply 3312 by 679. For example the product number for the 9 is as below:

The partial products are 19872, 23 184 and 29808. They then would be written down as

NOTE: They are lined up according to which number they correspond to in the multiplier.

Thus the rods made it possible to multiply mechanically without memorising any tables what so ever.