A difference engine is an automatic, mechanical calculator

Mechanical calculator

A mechanical calculator is a device used to perform the basic operations of arithmetic. Mechanical calculators are comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator....

 designed to tabulate polynomial functions

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

. Both logarithm

Logarithm

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

ic and trigonometric function

Trigonometric function

In mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle...

s can be approximated

Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....

 by polynomials, so a difference engine can compute many useful sets of numbers.
J. H. Müller, an engineer in the Hessian army conceived the idea in a book published in 1786, but failed to find funding to progress this further.

In 1822, Charles Babbage

Charles Babbage

Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer...

 proposed the use of such a machine in a paper to the Royal Astronomical Society

Royal Astronomical Society

The Royal Astronomical Society is a learned society that began as the Astronomical Society of London in 1820 to support astronomical research . It became the Royal Astronomical Society in 1831 on receiving its Royal Charter from William IV...

 on 14 June entitled "Note on the application of machinery to the computation of astronomical and mathematical tables".