The difference engine, a mechanical calculator based on Sir Isaac Newton's method of divided differences and designed to tabulate polynomial functions, consisted of columns (1 to n) that each stored one decimal number. A crank on the side of the engine caused the gears to move and add the value of column n + 1 to column n to produce the new value of column n. Further, column n could store only a constant, while column 1 displayed the value of the calculation. Despite this limited ability, both logarithmic and trigonometric functions could be calculated through the use of polynomials and, consequently, added more functions to even the limited nature of the original difference engine. Before its execution, the mechanism had to be programmed, with initial values set to the columns.

When Charles Babbage wrote a paper for the Royal Astronomical Society proposing the design and construction of a calculating machine, the government was impressed enough with the idea to award him limited funding in 1823. The failure of the original project, however, caused the withdrawal of support even though Babbage greatly improved the design of the original engine in his plans for his analytical engine and its successive versions. Babbage requested funding several times, but the lack of observable progress made his patron leery of investing in his designs. It was only the intense curiosity of curators at London's Science Museum and Babbage scholars that led to the construction and testing of Babbage's designs for the difference engine and the analytical engine. Although Babbage did not live to see the vindication of his theories, his faith in the promise of his calculators inspired many generations of later mathematicians to perfect his mechanisms.

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