Müller, an engineer in the Hessian army, devised and built an adding machine and described the basic principles of a difference machine in a book published in 1786 (the first written reference to a difference machine is dated to 1784), but he was unable to obtain funding to progress with the idea. ===Charles Babbage's difference engines=== Charles Babbage began to construct a small difference engine in c.

Müller, an engineer in the Hessian army, devised and built an adding machine and described the basic principles of a difference machine in a book published in 1786 (the first written reference to a difference machine is dated to 1784), but he was unable to obtain funding to progress with the idea. ===Charles Babbage's difference engines=== Charles Babbage began to construct a small difference engine in c.

A difference engine, a calculating machine designed in the 1820s, was first created by Charles Babbage.

1819 and had completed it by 1822 (Difference Engine 0).

He announced his invention on 14 June 1822, in a paper to the Royal Astronomical Society, entitled "Note on the application of machinery to the computation of astronomical and mathematical tables".

The British government was interested, since producing tables was time-consuming and expensive and they hoped the difference engine would make the task more economical. In 1823, the British government gave Babbage £1700 to start work on the project.

In 1832, Babbage and Joseph Clement produced a small working model (one-seventh of the calculating section of Difference Engine No.

Lady Byron described seeing the working prototype in 1833: "We both went to see the thinking machine (or so it seems) last Monday.

to the 2nd and 3rd powers, and extracted the root of a Quadratic equation." Work on the larger engine was suspended in 1833. By the time the government abandoned the project in 1842, Babbage had received and spent over £17,000 on development, which still fell short of achieving a working engine.

Babbage was able to take advantage of ideas developed for the analytical engine to make the new difference engine calculate more quickly while using fewer parts. === Scheutzian calculation engine === Inspired by Babbage's difference engine in 1834, Per Georg Scheutz built several experimental models.

In 1837 his son Edward proposed to construct a working model in metal, and in 1840 finished the calculating part, capable of calculating series with 5-digit numbers and first-order differences, which was later extended to third-order (1842).

In 1837 his son Edward proposed to construct a working model in metal, and in 1840 finished the calculating part, capable of calculating series with 5-digit numbers and first-order differences, which was later extended to third-order (1842).

to the 2nd and 3rd powers, and extracted the root of a Quadratic equation." Work on the larger engine was suspended in 1833. By the time the government abandoned the project in 1842, Babbage had received and spent over £17,000 on development, which still fell short of achieving a working engine.

In 1843, after adding the printing part, the model was completed. In 1851, funded by the government, construction of the larger and improved (15-digit numbers and fourth-order differences) machine began, and finished in 1853.

2" design (31-digit numbers and seventh-order differences), between 1846 and 1849.

2" design (31-digit numbers and seventh-order differences), between 1846 and 1849.

In 1843, after adding the printing part, the model was completed. In 1851, funded by the government, construction of the larger and improved (15-digit numbers and fourth-order differences) machine began, and finished in 1853.

In 1843, after adding the printing part, the model was completed. In 1851, funded by the government, construction of the larger and improved (15-digit numbers and fourth-order differences) machine began, and finished in 1853.

The machine was demonstrated at the World's Fair in Paris, 1855 and then sold in 1856 to the Dudley Observatory in Albany, New York.

The machine was demonstrated at the World's Fair in Paris, 1855 and then sold in 1856 to the Dudley Observatory in Albany, New York.

Purchased by the Dudley Observatory's first director, Benjamin Apthorp Gould, in 1856.

Delivered in 1857, it was the first printing calculator sold.

In 1857 the British government ordered the next Scheutz's difference machine, which was built in 1859.

In 1857 the British government ordered the next Scheutz's difference machine, which was built in 1859.

1859, his machine has the same capacity as Scheutz's - 15-digit and fourth-order) but used his device only for producing and publishing printed tables (interest tables in 1860, and logarithmic tables in 1875). Alfred Deacon of London in c.

1 was put on display to the public at the 1862 International Exhibition in South Kensington, London. Babbage went on to design his much more general analytical engine, but later produced an improved "Difference Engine No.

Grant started working on his calculating machine in 1869, unaware of the works of Babbage and Scheutz (Schentz).

One year later (1870) he learned about difference engines and proceed to design one himself, describing his construction in 1871.

In 1874 the Boston Thursday Club raised a subscription for the construction of a large-scale model, which was built in 1876.

1859, his machine has the same capacity as Scheutz's - 15-digit and fourth-order) but used his device only for producing and publishing printed tables (interest tables in 1860, and logarithmic tables in 1875). Alfred Deacon of London in c.

In 1874 the Boston Thursday Club raised a subscription for the construction of a large-scale model, which was built in 1876.

It could be expanded to enhance precision and weighed about . Christel Hamann built one machine (16-digit numbers and second-order differences) in 1909 for the "Tables of Bauschinger and Peters" ("Logarithmic-Trigonometrical Tables with eight decimal places"), which was first published in Leipzig in 1910.

It could be expanded to enhance precision and weighed about . Christel Hamann built one machine (16-digit numbers and second-order differences) in 1909 for the "Tables of Bauschinger and Peters" ("Logarithmic-Trigonometrical Tables with eight decimal places"), which was first published in Leipzig in 1910.

It weighed about . Burroughs Corporation in about 1912 built a machine for the Nautical Almanac Office which was used as a difference engine of second-order.

It was later replaced in 1929 by a Burroughs Class 11 (13-digit numbers and second-order differences, or 11-digit numbers and [at least up to] fifth-order differences). Alexander John Thompson about 1927 built integrating and differencing machine (13-digit numbers and fifth-order differences) for his table of logarithms "Logarithmetica britannica".

This machine was composed of four modified Triumphator calculators. Leslie Comrie in 1928 described how to use the Brunsviga-Dupla calculating machine as a difference engine of second-order (15-digit numbers).

It was later replaced in 1929 by a Burroughs Class 11 (13-digit numbers and second-order differences, or 11-digit numbers and [at least up to] fifth-order differences). Alexander John Thompson about 1927 built integrating and differencing machine (13-digit numbers and fifth-order differences) for his table of logarithms "Logarithmetica britannica".

He also noted in 1931 that National Accounting Machine Class 3000 could be used as a difference engine of sixth-order. ===Construction of two working No.

2 difference engines=== During the 1980s, Allan G.

2 from 1985 to 1991, under Doron Swade, the then Curator of Computing.

2 from 1985 to 1991, under Doron Swade, the then Curator of Computing.

This was to celebrate the 200th anniversary of Babbage's birth in 1991.

2, finally built in 1991, can hold 8 numbers of 31 decimal digits each and can thus tabulate 7th degree polynomials to that precision.

In 2002, the printer which Babbage originally designed for the difference engine was also completed.

2, which was on exhibit at the Computer History Museum in Mountain View, California from 10 May 2008 until 31 January 2016. It has since been transferred to Intellectual Ventures in Seattle where it is on display just outside the main lobby. == Operation == The difference engine consists of a number of columns, numbered from 1 to N.

2, which was on exhibit at the Computer History Museum in Mountain View, California from 10 May 2008 until 31 January 2016. It has since been transferred to Intellectual Ventures in Seattle where it is on display just outside the main lobby. == Operation == The difference engine consists of a number of columns, numbered from 1 to N.

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