The ternary calculating machine of Thomas Fowler
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Thomas Fowler

Balanced ternary arithmetic

Fowler's binary and ternary tables

DeMorgan's description

The reconstruction

About the machine
Carry mechanism
Instructions for use
Video demonstration

Photo gallery

References and links



Fowler's ternary calculating machine - an overview

Thomas Fowler, fearful that his ideas would be stolen by others, designed and built his wooden calculating machine entirely on his own in the workshop behind his printing business. To compensate for the limited precision that he could achieve in wood, the machine was very large: six feet wide by three feet deep and one foot high (180 x 90 x 30 cm.). The model Fowler built has not survived, and almost all other evidence of the machine has disappeared. The descriptions of the machine that follow are based on our interpretation of how Fowler’s machine might have worked, based on the limited information available.

Fowler had developed a technique that used balanced ternary to simplify complex monetary calculations for the Poor Law Union, publishing his methods in his book, Tables for Facilitating Arithmetical Calculations. His calculating machine was built several years later, giving mechanical form to the techniques outlined in the book. The choice of balanced ternary allowed the mechanisms to be very simple. Of course, it also required all the numerical values to be converted to balanced ternary, and then converted back to decimal at the end of the calculation. Clearly, this machine was not practical for simple addition or subtraction problems. Where the machine became really useful was for complex problems that required a great number of intermediate calculations in between the conversions to and from ternary. The calculations that Fowler faced at the Poor Law Union were exactly that sort of problem (see An Example of Calculating With Fowler’s Ternary Tables).

In the context of a multiplication problem, Fowler’s machine consists of four distinct sections:

- the multiplicand
- the multiplier
- the product
- the carry mechanism

The machine can also be used for division, but in reverse – the product becomes the dividend, the multiplier becomes the divisor, and the multiplicand becomes the quotient. For the purposes of the descriptions that follow, it is easiest to limit the discussion to problems of multiplication.