How it Works  Principle of the Difference Engines  Difference
engines are so called because of the mathematical principle on
which they are based, namely, the method of finite differences.
In general, calculating the value of a polynomial can require
any or all of addition, subtraction, multiplication and
division.  An advantage of the method of finite differences is
that it eliminates the need for multiplication and division, and
allows the values of a polynomial to be calculated using simple
addition only. Adding two numbers using gearwheels is easier to
implement than multiplication or division and so the method
simplifies an otherwise complex mechanism.  If the first few
values of a polynomial are known, the rest may be calculated
using simple repeated addition. The method is illustrated in the
diagram above for the function F(x) = x2 + 4. The values of x
are shown in the first column incrementing by 1 each time (x =
1, 2, 3, 4 . . .). The values of the function x2 + 4 are shown
in the second column with