mechanical calculator

This picture shows clockwise from top left: An Arithmometer, a Comptometer, a Dalton adding machine, a Sundstrand, and an Odhner Arithmometer In 1642, Blaise Pascal invented the first operational mechanical calculator with better tens-carry. Concerned about his father's exhausting work as tax collector in Rouen, Pascal designed the Pascaline to help with the large amount of tedious arithmetic required. In 1672, Gottfried Leibniz started designing an entirely new machine called the Stepped Reckoner. It used a stepped drum, built by and named after him, the Leibniz wheel, was the first two-motion design, the first to use cursors (creating a memory of the first operand) and the first to have a movable carriage. Leibniz built two Stepped Reckoners, one in 1694 and one in 1706. The Leibniz wheel was used in many calculating machines for 200 years, and into the 1970s with the Curta hand calculator, until the advent of the electronic calculator in the mid-1970s. Leibniz was also the first to promote the idea of a pinwheel calculator. During the 18th century, several inventors in Europe were working on mechanical calculators for all four species. Philipp Matthäus Hahn, Johann Helfreich Müller and others constructed machines that worked flawlessly, but due to the enormous amount of manual work and high precision needed for these machines they remained singletons and stayed mostly in cabinets of curiosity of their respective rulers. Only Müller's 1783 machine was put to use tabulating lumber prices; it later came into possession of the landgrave in Darmstadt. Thomas' arithmometer, the first commercially successful machine, was manufactured in 1851; it was the first mechanical calculator strong enough and reliable enough to be used daily in an office environment. For forty years the arithmometer was the only type of mechanical calculator available for sale until the industrial production of the more successful Odhner Arithmometer in 1890. The comptometer, introduced in 1887, was the first machine to use a keyboard that consisted of columns of nine keys (from 1 to 9) for each digit. The Dalton adding machine, manufactured in 1902, was the first to have a 10 key keyboard. Electric motors were used on some mechanical calculators from 1901. In 1961, a comptometer type machine, the Anita Mk VII from Sumlock, became the first desktop mechanical calculator to receive an all-electronic calculator engine, creating the link in between these two industries and marking the beginning of its decline. The production of mechanical calculators came to a stop in the middle of the 1970s closing an industry that had lasted for 120 years. Charles Babbage designed two kinds of mechanical calculators, which were too sophisticated to be built in his lifetime, and the dimensions of which required a steam engine to power them. The first was an automatic mechanical calculator, his difference engine, which could automatically compute and print mathematical tables. In 1855, Georg Scheutz became the first of a handful of designers to succeed at building a smaller and simpler model of his difference engine. The second one was a programmable mechanical calculator, his analytical engine, which Babbage started to design in 1834; "in less than two years he had sketched out many of the salient features of the modern computer. A crucial step was the adoption of a punched card system derived from the Jacquard loom" making it infinitely programmable. In 1937, Howard Aiken convinced IBM to design and build the ASCC/Mark I, the first machine of its kind, based on the architecture of the analytical engine; when the machine was finished some hailed it as "Babbage's dream come true".

Howard Aiken, Proposed automatic calculating machine, presented to IBM in 1937 • Illustration — A Chinese Suanpan (the number represented in the picture is 6,302,715,408) A short list of other precursors to the mechanical calculator must include a group of mechanical analog computers which, once set, are only modified by the continuous and repeated action of their actuators (crank handle, weight, wheel, water...). Before the common era, there are odometers and the Antikythera mechanism, a seemingly out of place, unique, geared astronomical clock, followed more than a millennium later by early mechanical clocks, geared astrolabes and followed in the 15th century by pedometers. These machines were all made of toothed gears linked by some sort of carry mechanisms. These machines always produce identical results for identical initial settings unlike a mechanical calculator where all the wheels are independent but are also linked together by the rules of arithmetic.

The 17th century marked the beginning of the history of mechanical calculators, as it saw the invention of its first machines, including Pascal's calculator, in 1642. Blaise Pascal had invented a machine which he presented as being able to perform computations that were previously thought to be only humanly possible. The 17th century also saw the invention of some very powerful tools to aid arithmetic calculations like Napier's bones, logarithmic tables and the slide rule which, for their ease of use by scientists in multiplying and dividing, ruled over and impeded the use and development of mechanical calculators until the production release of the arithmometer in the mid 19th century. • Illustration — Four of Pascal's calculators and one machine built by Lépine in 1725, Musée des Arts et Métiers

In 1623 and 1624 Wilhelm Schickard, in two letters that he sent to Johannes Kepler, reported his design and construction of what he referred to as an “arithmeticum organum” (“arithmetical instrument”), which would later be described as a Rechenuhr (calculating clock). The machine was designed to assist in all the four basic functions of arithmetic (addition, subtraction, multiplication and division). Amongst its uses, Schickard suggested it would help in the laborious task of calculating astronomical tables. The machine could add and subtract six-digit numbers, and indicated an overflow of this capacity by ringing a bell. The adding machine in the base was primarily provided to assist in the difficult task of adding or multiplying two multi-digit numbers. To this end an ingenious arrangement of rotatable Napier's bones were mounted on it. It even had an additional "memory register" to record intermediate calculations. Whilst Schickard noted that the adding machine was working, his letters mention that he had asked a professional, a clockmaker named Johann Pfister, to build a finished machine. Regrettably it was destroyed in a fire either whilst still incomplete, or in any case before delivery. Schickard abandoned his project soon after. He and his entire family were wiped out in 1635 by bubonic plague during the Thirty Years' War. • Illustration — Replica of Schickard´s calculator Schickard's machine used clock wheels which were made stronger and were therefore heavier, to prevent them from being damaged by the force of an operator input. Each digit used a display wheel, an input wheel and an intermediate wheel. During a carry transfer all these wheels meshed with the wheels of the digit receiving the carry. Blaise Pascal invented a mechanical calculator with a sophisticated carry mechanism in 1642. After three years of effort and 50 prototypes he introduced his calculator to the public. He built twenty of these machines in the following ten years. This machine could add and subtract two numbers directly and multiply and divide by repetition. Since, unlike Schickard's machine, the Pascaline dials could only rotate in one direction zeroing it after each calculation required the operator to dial in all 9s and then (method of re-zeroing) propagate a carry right through the machine. This suggests that the carry mechanism would have proved itself in practice many times over. This is a testament to the quality of the Pascaline because none of the 17th and 18th century criticisms of the machine mentioned a problem with the carry mechanism and yet it was fully tested on all the machines, by their resets, all the time. • Illustration — In the position shown, the counting wheel meshes with three of the nine teeth of the Leibniz wheel. In 1672, Gottfried Leibniz started working on adding direct multiplication to what he understood was the working of Pascal's calculator. However, it is doubtful that he had ever fully seen the mechanism and the method could not have worked because of the lack of reversible rotation in the mechanism. Accordingly, he eventually designed an entirely new machine called the Stepped Reckoner; it used his Leibniz wheels, was the first two-motion calculator, the first to use cursors (creating a memory of the first operand) and the first to have a movable carriage. Leibniz built two Stepped Reckoners, one in 1694 and one in 1706. Only the machine built in 1694 is known to exist; it was rediscovered at the end of the 19th century having been forgotten in an attic in the University of Göttingen. In 1893, the German calculating machine inventor Arthur Burkhardt was asked to put Leibniz's machine in operating condition if possible. His report was favorable except for the sequence in the carry. Leibniz had invented his namesake wheel and the principle of a two-motion calculator, but after forty years of development he wasn't able to produce a machine that was fully operational; this makes Pascal's calculator the only working mechanical calculator in the 17th century. Leibniz was also the first person to describe a pinwheel calculator. He once said "It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used."

Schickard, Pascal and Leibniz were inevitably inspired by the role of clockwork which was highly celebrated in the seventeenth century. However, simple-minded application of interlinked gears was insufficient for any of their purposes. Schickard introduced the use of a single toothed "mutilated gear" to enable the carry to take place. Pascal improved on that with his famous weighted sautoir. Leibniz went even further in relation to the ability to use a moveable carriage to perform multiplication more efficiently, albeit at the expense of a fully working carry mechanism. The principle of the clock (input wheels and display wheels added to a clock-like mechanism) for a direct-entry calculating machine couldn't be implemented to create a fully effective calculating machine without additional innovation with the technological capabilities of the 17th century, because their gears would jam when a carry had to be moved several places along the accumulator. The only 17th-century calculating clocks that have survived to this day do not have a machine-wide carry mechanism and therefore cannot be called fully effective mechanical calculators. A much more successful calculating clock was built by the Italian Giovanni Poleni in the 18th century and was a two-motion calculating clock (the numbers are inscribed first and then they are processed). • In 1623, Wilhelm Schickard, a German professor of Hebrew and Astronomy, designed a calculating clock which he drew on two letters that he wrote to Johannes Kepler. The first machine to be built by a professional was destroyed during its construction and Schickard abandoned his project in 1624. These drawings had appeared in various publications over the centuries, starting in 1718 with a book of Kepler's letters by Michael Hansch, but in 1957 it was presented for the first time as a long-lost mechanical calculator by Dr. Franz Hammer. The building of the first replica in the 1960s showed that Schickard's machine had an unfinished design and therefore wheels and springs were added to make it work. The use of these replicas showed that the single-tooth wheel, when used within a calculating clock, was an inadequate carry mechanism. (see Pascal versus Schickard). This did not mean that such a machine could not be used in practice, but the operator when faced with the mechanism resisting rotation, in the unusual circumstances of a carry being required beyond (say) 3 dials, would need to "help" the subsequent carry to propagate. • Around 1643, a French clockmaker from Rouen, after hearing of Pascal's work, built what he claimed to be a calculating clock of his own design. Pascal fired all his employees and stopped developing his calculator as soon as he heard of the news. It is only after being assured that his invention would be protected by a royal privilege that he restarted his activity. A careful examination of this calculating clock showed that it didn't work properly and Pascal called it an avorton (aborted fetus). • In 1659, the Italian Tito Livio Burattini built a machine with nine independent wheels, each one of these wheels was paired with a smaller carry wheel. At the end of an operation the user had to either manually add each carry to the next digit or mentally add these numbers to create the final result. • In 1666, Samuel Morland invented a machine designed to add sums of money, but it was not a true adding machine since the carry was added to a small carry wheel situated above each digit and not directly to the next digit. It was very similar to Burattini's machine. Morland created also a multiplying machines with interchangeable disks based on Napier's bones. Taken together these two machines provided a capacity similar to that of the invention of Schickard, although it is doubtful that Morland ever encountered Schickard's calculating clock. • In 1673, the French clockmaker René Grillet described in Curiositez mathématiques de l'invention du Sr Grillet, horlogeur à Paris a calculating machine that would be more compact than Pascal's calculator and reversible for subtraction. The only two Grillet machines known have no carry mechanism, displaying three lines of nine independent dials they also have nine rotating napier's rod for multiplication and division. Contrary to Grillet's claim, it was not a mechanical calculator after all.

• Illustration — Detail of a replica of an 18th-century calculating machine, designed and built by German Johann-Helfrich Müller.

The 18th century saw the first mechanical calculator that could perform a multiplication automatically; designed and built by Giovanni Poleni in 1709 and made of wood, it was the first successful calculating clock. For all the machines built in this century, division still required the operator to decide when to stop a repeated subtraction at each index, and therefore these machines were only providing a help in dividing, like an abacus. Both pinwheel calculators and Leibniz wheel calculators were built with a few unsuccessful attempts at their commercialization.

• Illustration — A mechanical calculator from Anton Braun, dated 1727 • In 1709, Italian Giovanni Poleni was the first to build a calculator that could multiply automatically. It used a pinwheel design, was the first operational calculating clock and was made of wood; he destroyed it after hearing that Antonius Braun had received 10,000 Guldens for dedicating a pinwheel machine of his own design to the Holy Roman Emperor Charles VI in Vienna. • In 1725, the French Academy of Sciences certified a calculating machine derived from Pascal's calculator designed by Lépine, a French craftsman. The machine was a bridge in between Pascal's calculator and a calculating clock. The carry transmissions were performed simultaneously, like in a calculating clock, and therefore "the machine must have jammed beyond a few simultaneous carry transmissions". • In 1727, German Anton Braun presented the first fully functional four-operation machine to Emperor Charles VI in Vienna. It was cylindrical in shape and was made of steel, silver and brass; it was finely decorated and looked like a renaissance table clock. His dedication to the emperor engraved on the top of the machine also reads "...to make easy to ignorant people, addition, subtraction, multiplication and even division". • In 1730, the French Academy of Sciences certified three machines designed by Hillerin de Boistissandeau. The first one used a single-tooth carry mechanism which, according to Boistissandeau, wouldn't work properly if a carry had to be moved more than two places; the two other machines used springs that were gradually armed until they released their energy when a carry had to be moved forward. It was similar to Pascal's calculator but instead of using the energy of gravity Boistissandeau used the energy stored into the springs. • In 1770, Philipp Matthäus Hahn, a German pastor, built two circular calculating machines based on Leibniz' cylinders. J. C. Schuster, Hahn's brother-in-law, built a few machines of Hahn's design into the early 19th century. • In 1775, Lord Stanhope of the United Kingdom designed a pinwheel machine. It was set in a rectangular box with a handle on the side. He also designed a machine using Leibniz wheels in 1777. "In 1777 Stanhope produced the Logic Demonstrator, a machine designed to solve problems in formal logic. This device marked the beginning of a new approach to the solution of logical problems by mechanical methods." • In 1784, German Johann-Helfrich Müller built a machine very similar to Hahn's machine.

Luigi Torchi invented the first direct multiplication machine in 1834. This was also the second key-driven machine in the world, following that of James White (1822). The mechanical calculator industry started in 1851 Thomas de Colmar released his simplified Arithmomètre, which was the first machine that could be used daily in an office environment. For 40 years, the arithmometer was the only mechanical calculator available for sale and was sold all over the world. By 1890, about 2,500 arithmometers had been sold plus a few hundreds more from two licensed arithmometer clone makers (Burkhardt, Germany, 1878 and Layton, UK, 1883). Felt and Tarrant, the only other competitor in true commercial production, had sold 100 comptometers in three years. The 19th century also saw the designs of Charles Babbage calculating machines, first with his difference engine, started in 1822, which was the first automatic calculator since it continuously used the results of the previous operation for the next one, and second with his analytical engine, which was the first programmable calculator, using Jacquard's cards to read program and data, that he started in 1834, and which gave the blueprint of the mainframe computers built in the middle of the 20th century. • Illustration — Desktop Mechanical Calculators in production during the 19th century

• Illustration — Front panel of a Thomas Arithmometer with its movable result carriage extended • In 1851, Thomas de Colmar simplified his arithmometer by removing the one-digit multiplier/divider. This made it a simple adding machine, but thanks to its moving carriage used as an indexed accumulator, it still allowed for easy multiplication and division under operator control. The arithmometer was now adapted to the manufacturing capabilities of the time; Thomas could therefore manufacture consistently a sturdy and reliable machine. Manuals were printed and each machine was given a serial number. Its commercialization launched the mechanical calculator industry. Banks, insurance companies, government offices started to use the arithmometer in their day-to-day operations, slowly bringing mechanical desktop calculators into the office. • In 1878 Burkhardt, of Germany, was the first to manufacture a clone of Thomas' arithmometer. Until then Thomas de Colmar had been the only manufacturer of desktop mechanical calculators in the world and he had manufactured about 1,500 machines. Eventually twenty European companies will manufacture clones of Thomas' arithmometer until WWII. • Dorr E. Felt, in the U.S., patented the Comptometer in 1886. It was the first successful key-driven adding and calculating machine. Key-drivenrefers to the fact that just pressing the keys causes the result to be calculated, no separate lever or crank has to be operated. Other machines are sometimes called "key-set".] In 1887, he joined with Robert Tarrant to form the Felt & Tarrant Manufacturing Company. The comptometer-type calculator was the first machine to receive an all-electronic calculator engine in 1961 (the ANITA mark VII released by Sumlock comptometer of the UK). • In 1890 W. T. Odhner got the rights to manufacture his calculator back from Königsberger & C, which had held them since it was first patented in 1878, but had not really produced anything. Odhner used his Saint Petersburg workshop to manufacture his calculator and he built and sold 500 machines in 1890. This manufacturing operation shut down definitively in 1918 with 23,000 machines produced. The Odhner Arithmometer was a redesigned version of the Arithmometer of Thomas de Colmar with a pinwheel engine, which made it cheaper to manufacture and gave it a smaller footprint while keeping the advantage of having the same user interface. • In 1892 Odhner sold the Berlin branch of his factory, which he had opened a year earlier, to Grimme, Natalis & Co. They moved the factory to Braunschweig and sold their machines under the brand name of Brunsviga (Brunsviga is the Latin name of the town of Braunschweig). This was the first of many companies which would sell and manufacture clones of Odhner's machine all over the world; eventually millions were sold well into the 1970s. • In 1892, William S. Burroughs began commercial manufacture of his printing adding calculator. Burroughs Corporation became one of the leading companies in the accounting machine and computer businesses. • The "Millionaire" calculator was introduced in 1893. It allowed direct multiplication by any digit – "one turn of the crank for each figure in the multiplier". It contained a mechanical product lookup table, providing units and tens digits by differing lengths of posts. Another direct multiplier was part of the Moon-Hopkins billing machine; that company was acquired by Burroughs in the early 20th century. * • Illustration — 19th century Comptometer in a wooden case — • Illustration — 19th and early 20th centuries calculating machines, Musée des Arts et Métiers — • Illustration — Odhner's arithmometer

• Illustration — The London Science Museum's working difference engine, built a century and a half after Charles Babbage's design. • In 1822, Charles Babbage presented a small cogwheel assembly that demonstrated the operation of his difference engine, a mechanical calculator which would be capable of holding and manipulating seven numbers of 31 decimal digits each. It was the first time that a calculating machine could work automatically using as input results from its previous operations. It was the first calculating machine to use a printer. The development of this machine, later called "Difference Engine No. 1," stopped around 1834. • In 1847, Babbage began work on an improved difference engine design—his "Difference Engine No. 2." None of these designs were completely built by Babbage. In 1991 the London Science Museum followed Babbage's plans to build a working Difference Engine No. 2 using the technology and materials available in the 19th century. • In 1855, Per Georg Scheutz completed a working difference engine based on Babbage's design. The machine was the size of a piano, and was demonstrated at the Exposition Universelle in Paris in 1855. It was used to create tables of logarithms. • In 1875, Martin Wiberg re-designed the Babbage/Scheutz difference engine and built a version that was the size of a sewing machine.

• Illustration — Minimal but working demonstration part of the mill from the Analytical engine, finished by Babbage's son around 1906 • In 1834, Babbage started to design his analytical engine, which will become the undisputed ancestor of the modern mainframe computer with two separate input streams for data and program (a primitive Harvard architecture), printers for outputting results (three different kind), processing unit (mill), memory (store) and the first-ever set of programming instructions. In the proposal that Howard Aiken gave IBM in 1937 while requesting funding for the Harvard Mark I which became IBM's entry machine in the computer industry, we can read: "Few calculating machines have been designed strictly for application to scientific investigations, the notable exceptions being those of Charles Babbage and others who followed him. In 1812 Babbage conceived the idea of a calculating machine of a higher type than those previously constructed to be used for calculating and printing tables of mathematical functions.....After abandoning the difference engine, Babbage devoted his energy to the design and construction of an analytical engine of far higher powers than the difference engine..." • In 1843, during the translation of a French article on the analytical engine, Ada Lovelace wrote, in one of the many notes she included, an algorithm to compute the Bernoulli numbers. This is considered the first computer program. • From 1872 until 1910, Henry Babbage worked intermittently on creating the mill, the "central processing unit" of his father's machine. After a few setbacks, he gave in 1906 a successful demonstration of the mill which printed the first 44 multiples of pi with 29 places of figures.

The cash register, invented by the American saloonkeeper James Ritty in 1879, addressed the old problems of disorganization and dishonesty in business transactions. It was a pure adding machine coupled with a printer, a bell and a two-sided display that showed the paying party and the store owner, if he wanted to, the amount of money exchanged for the current transaction. The cash register was easy to use and, unlike genuine mechanical calculators, was needed and quickly adopted by a great number of businesses. "Eighty four companies sold cash registers between 1888 and 1895, only three survived for any length of time". In 1890, 6 years after John Patterson started NCR Corporation, 20,000 machines had been sold by his company alone against a total of roughly 3,500 for all genuine calculators combined. By 1900, NCR had built 200,000 cash registers and there were more companies manufacturing them, compared to the "Thomas/Payen" arithmometer company that had just sold around 3,300 and Burroughs had only sold 1,400 machines.

• Illustration — Arithmometers built from 1820 to 1851 had a one-digit multiplier/divider cursor (ivory top) is on the left. Only prototypes of these machines were built. • In 1820, Thomas de Colmar patented the Arithmometer. It was a true four operation machine with a one digit multiplier/divider (The Millionaire calculator released 70 years later had a similar user interface). He spent the next 30 years and 300,000 Francs developing his machine. This design was replaced in 1851 by the simplified arithmometer which was only an adding machine. • From 1840, Didier Roth patented and built a few calculating machines, one of which was a direct descendant of Pascal's calculator. • In 1842, Timoleon Maurel invented the Arithmaurel, based on the Arithmometer, which could multiply two numbers by simply entering their values into the machine. • In 1845, Izrael Abraham Staffel first exhibited a machine that was able to add, subtract, divide, multiply and obtain a square root. • Around 1854, Andre-Michel Guerry invented the Ordonnateur Statistique, a cylindrical device designed to aid in summarizing the relations among data on moral variables (crime, suicide, etc.) • In 1872, Frank S. Baldwin in the U.S. invented a pinwheel calculator. • In 1877 George B. Grant of Boston in the United States began producing the Grant mechanical calculating machine capable of addition, subtraction, multiplication and division. The machine measured 13x5x7 inches and contained eighty working pieces made of brass and tempered steel. It was first introduced to the public at the 1876 Centennial Exposition in Philadelphia. • In 1883, Edmondson of the United Kingdom patented a circular stepped drum calculator. * • Illustration — Detail of an early calculating machine invented by Didier Roth around 1840. This machine is a direct descendant of Pascal's calculator. — • Illustration — Grant's Barrel, 1877

History of computing hardware

Mechanical calculators continued to be sold, though in rapidly decreasing numbers, into the early 1970s, with many of the manufacturers closing down or being taken over. Comptometer type calculators were often retained for much longer to be used for adding and listing duties, especially in accounting, since a trained and skilled operator could enter all the digits of a number in one movement of the hands on a comptometer quicker than was possible serially with a 10-key electronic calculator. In fact, it was quicker to enter larger digits in two strokes using only the lower-numbered keys; for instance, a 9 would be entered as 4 followed by 5. Some key-driven calculators had keys for every column, but only 1 through 5; they were correspondingly compact. The spread of the computer rather than the simple electronic calculator put an end to the comptometer. Also, by the end of the 1970s, the slide rule had become obsolete.