Pascal's calculator

A Pascaline, signed by Pascal in 1652

Blaise Pascal invented the mechanical calculator in 1642.^[1][2] He conceived it while trying to help his father who had been assigned the task of reorganizing the tax revenues of the French province of Haute-Normandie ; first called Arithmetic Machine, Pascal's Calculator and later Pascaline, it could add and subtract directly and multiply and divide by repetition.

Pascal went through 50 prototypes before presenting his first machine to the public in 1645. He dedicated it to Pierre Séguier, the chancellor of France at the time.^[3] He built around twenty more machines during the next decade, often improving on his original design. Nine machines have survived the centuries,^[4] most of them being on display in European museums. In 1649 a royal privilege, signed by Louis XIV of France,^[5] gave him the exclusivity of the design and manufacturing of calculating machines in France.

Its introduction launched the development of mechanical calculators in Europe first and then all over the world, development which culminated, three centuries later, by the invention of the microprocessor developed for a Busicom calculator in 1971.

The mechanical calculator industry owes a lot of its key machines and inventions to the pascaline. First Gottfried Leibniz invented his Leibniz wheels after 1671 while trying to add an automatic multiplication and division feature to the pascaline,^[6] then Thomas de Colmar drew his inspiration from Pascal and Leibniz when he designed his arithmometer in 1820, and finally Dorr E. Felt substituted the input wheels of the pascaline by columns of keys to invent his comptometer around 1887. The pascaline was also constantly improved upon, especially with the machines of Dr. Roth around 1840, and then with some portable machines until the creation of the first electronic calculators.

History

Four Pascalines and a clone from Lépine on display at the CNAM museum in Paris

Precursors

From antiquity to the renaissance

An odometer drawn by Léonard de Vinci (before 1519)

A short list of precursors to the mechanical calculator must include the Antikythera mechanism from around 100 BC, early mechanical clocks and geared astrolabes ; they were all made of toothed gears linked by some sort of carry mechanisms.

Some measuring instruments and automatons were also precursors to the calculating machine.

An odometer, instrument for measuring distances, was first described around 25 BC by the roman engineer Vitruvius in the tenth volume of his De architectura. It was made of a set of toothed gears linked by a carry mechanism ; the first one was driven by one of the chariot wheels and the last one dropped a small pebble in a bag for each Roman mile traveled.^[7]

A Chinese text of the third century AD described a chariot equipped with a geared mechanism that operated two wooden figures. One would strike a drum for every Chinese Li traveled, the other one would strike a gong for every ten Li traveled.^[8]

Han dynasty odometer cart.

Around the end of the tenth century, the French monk Gerbert d'Aurillac, whose abacus taught the Hindu-Arabic numeral system to the Europeans,^[9] brought back from Spain the drawings of a machine invented by the Moors that answered Yes or No to the questions it was asked (binary arithmetic) ; but its existence is contested.^[10]

Again in the thirteenth century, the monks Albertus Magnus and Roger Bacon built talking androids without any further development (Albertus Magnus complained that he had wasted forty years of his life when Thomas Aquinas, terrified by his machine, destroyed it^[11]).

The Italian polymath Leonardo da Vinci drew an odometer before 1519.

In 1525, the French craftsman Jean Fernel built the first pedometer. It was made in the shape of a watch and had 4 dials (units, tens, hundreds, thousands) linked by a carry mechanism.^[12]

Pascal versus Schickard

From the introduction of the Pascaline and for more than three centuries Pascal was known as the inventor of the mechanical calculator, but then, in 1957, two letters written by Wilhelm Schickard (in 1623 and 1624) to his friend Johannes Kepler were discovered each one showing a drawing of a hybrid device with the top half consisting of a set of Napier's bones for multiplications and divisions and the bottom half had a calculator for additions and subtractions. This machine had stayed unknown for three centuries because it was destroyed in a fire in 1624 (as it was being built) and Schickard decided not to build another one.^[13]

Even though Schickard designed his machine twenty years earlier, Pascal is still the inventor of the mechanical calculator because, for an invention to be certified, a working prototype has to be produced and checked by an independent, knowledgeable witness,^[2] and this was not the case for Schickard's machine. Furthermore Schickard's calculating clock had no influence whatsoever on the mechanical calculator industry.^[14]

Just as the Wright brothers were credited for the first flight and therefore the invention of the airplane while Clément Ader flew 10 years before them, and Thomas Edison was credited with the invention of the incandescent light bulb while ten people had already worked on it before, Blaise Pascal is credited as the inventor of the mechanical calculator because he was the first person to present a machine that had all the parts required for its use, that had adequate solutions to all its challenges, a primitive machine, complete and ready to evolve.

Achievements

Pascaline made for French currency. The least significant denominations, sols and deniers, are on the right.

View through back of calculator above showing wheels.

This machine once belonged to Louis Perrier, Pascal's nephew

Besides being the first calculating machine made public during its time, the pascaline is also:

• the first calculator to be used in an office (his father's to compute taxes)
• the first calculator commercialized (with around twenty machines built)^[4]
• the first calculator to be patented (royal privilege of 1649)^[15]
• the first calculator to be described in an encyclopaedia (Diderot & d'Alembert, 1751):

  "...The first arithmetic machine presented to the public was from Blaise Pascal, born in Clermont, Auvergne on June 19, 1623 ; he invented it at the age of 19. Other machines have been designed since which, in the judgement of Mr of the Academy of Sciences, seem to have more practical advantages ; but Pascal's machine is the oldest one ; it could have served as model to all the others ; this is why we preferred it."^[16]

• the first calculator sold by a distributor:

  "Mr de Roberval ... located in the college Maitres Gervais ... every morning until 8..."^[17]

• the first calculator to be cloned (a clockmaker from Rouen before 1645)^[17]
• the first calculator to have a controlled carry mechanism which allowed for an effective propagation of multiple carries^[18]

Development

Pascal began to work on his calculator in 1642, when he was only 19 years old. He had been assisting his father, who worked as a tax commissioner, and sought to produce a device which could reduce some of his workload. Pascal received a Royal Privilege in 1649 that granted him exclusive rights to make and sell calculating machines in France. By 1654 Pascal had sold about twenty machines, but the cost and complexity of the Pascaline—combined with the fact that it could only add and subtract, and the latter with difficulty—was a barrier to further sales, and production ceased in that year. By that time Pascal had moved on to other pursuits, initially the study of atmospheric pressure, and later philosophy.

Fields of application

Pascalines came in both decimal and non-decimal varieties, both of which exist in museums today. They were designed to be used by scientists, accountants and surveyors. The simplest Pascaline had five dials ; later production variants had up to ten dials.

The contemporary French currency system used livres, sols and deniers with 20 sols to a livre and 12 deniers to a sol. Length was measured in toises, pieds, pouces and lignes with 6 pieds to a toise, 12 pouces to a pied and 12 lignes to a pouce. Therefore the pascaline needed wheels in base 6, 10, 12 and 20. Non decimal wheels were always located before the decimal part.

In an accounting machine (..10,10,20,12), the decimal part counted the number of livres (20 sols), sols (12 deniers) and deniers. In a surveyor's machine (..10,10,6,12,12), the decimal part counted the number of toises (6 pieds), pieds (12 pouces), pouces (12 lignes) and lignes. Scientific machines just had decimal wheels.

The metric system was adopted in France on December 10, 1799 by which time Pascal's basic design had inspired other craftsmen, although with a similar lack of commercial success. Child prodigy Gottfried Wilhelm Leibniz devised a competing design, the Stepped Reckoner, in 1671 which could perform addition, subtraction, multiplication and division; Leibniz struggled for forty years to perfect his design and produce sufficiently reliable machines.

Calculating machines did not become commercially viable until the early 19th century, when Charles Xavier Thomas de Colmar's Arithmometer, itself using the key break through of Leibniz's design, was commercially successful.^[19]

Known machines

Most of the machines that have survived the centuries are of the accounting type. Seven of them are in European museums, one belongs to the IBM corporation and one is in private hands.

Components

Top view and overview of the entire mechanism

Detail of the carry mechanism and of the sautoir

Œuvres de Pascal in 5 volumes, La Haye, 1779

User interface

Overview

The calculator had spoked metal wheel dials, with the digit 0 through 9 displayed around the circumference of each wheel. To input a digit, the user placed a stylus in the corresponding space between the spokes, and turned the dial until a metal stop at the bottom was reached, similar to the way a rotary telephone dial is used. This would display the number in the boxes at the top of the calculator. Then, one would simply redial the second number to be added, causing the sum of both numbers to appear in boxes at the top. Since the gears of the calculator only rotated in one direction, negative numbers could not be directly summed. To subtract one number from another, the method of nines' complements was used. To help the user, when a number was entered, its nines' complement appeared in a box above the box containing the original value entered.

Input wheel

Input wheel

For a 10 digit wheel (N), the fixed outside wheel is numbered from 0 to 9 (N-1). The numbers are inscribed in a decreasing manner clockwise going from the bottom left to the bottom right of the stopping lever. To add a 5, one must insert a stylus in between the spokes that surround the number 5 and rotate the wheel clockwise all the way to the stopping lever. The number displayed on the corresponding display register will be increased by 5 and, if a carry transfer takes place, the display register to the left of it will be increased by 1. To add fifty, use the tens input wheel (second dial from the right on a decimal machine), to add 500, use the hundreds input wheel, etc...

Quick re-zeroing

On all the wheels of all the machines,^[22] two consecutive spokes are marked, but the marks differ from machine to machine^[23] (There are two dots on two consecutive spokes on the wheel pictured on the right). These marks are used to set the corresponding cylinder to its maximum number, ready to be re-zeroed (the operator has to insert the stylus in between these two spokes and turn the wheel all the way to the stopping lever to do so). This works because each wheel is directly linked to its corresponding display cylinder (it automatically turns by one during a carry operation) ; To mark the spokes during manufacturing, one can move the cylinder so that its highest number is displayed and then mark the spoke under the stopping lever and the one to the right of it.

The Sautoir

Principle

The sautoir

The sautoir is the center piece of the pascaline's carry mechanism. In his "Avis nécessaire...", Pascal wrote:

... as for the ease of use of this ... movement ... moving one thousand even ten thousand wheels if they were there, each one performing their motion perfectly, is as easy as moving only one (I don't know if, after the principle that I perfected to design this device, there is another one left to be found in nature)...^[24]

A machine with 10,000 wheels would work as well as a machine with two wheels because each wheel is independent from the other. When it is time to propagate a carry, the sautoir, on the sole influence of gravity,^[25] is thrown toward the next wheel without any contact between the wheels. During its free fall the sautoir behaves like an acrobat jumping from one trapeze to the next without the trapezes touching each other (sautoir comes from the french verb sauter which means to jump). All the wheels (including gears and sautoir) have therefore the same size and weight independently of the capacity of the machine.

Pascal used gravity to arm the sautoirs. One must turn the wheel five steps from 4 to 9 in order to fully arm a sautoir, but the carry transfer will only move the next wheel one step. Therefore there is a lot of extra energy built up during the arming of a sautoir.

All the sautoirs are armed by either an operator input or a carry forward. To re-zero a 10,000 wheel machine, if it existed, the operator would have to set every wheel to its maximum and then add a 1 to the "unit" wheel. The carry would turn every input wheel one by one in a very rapid Domino effect fashion and all the display registers would be reset.

The three phases of a carry transmission

The three phases of a carry transfer operation

The animation on the right shows the three phases of a carry transmission.

1. The first phase happens when the display register goes from 4 to 9. The two carry pins (one after the other) lift the sautoir pushing on its protruding part marked (3,4,5). At the same time the pawl (1) is pulled up, using a pin on the next wheel as guidance, but without effect on this wheel because of the ratchet (C).
2. The second phase starts when the display register goes from 9 to 0. The pawl passes its guiding pin and its spring (z,u) positions it above this pin ready to push on it. The sautoir keeps on moving up and suddenly the second carry pin drops it. The sautoir is falling of its own weight.
3. The pawl (1) pushes the pin on the next wheel and starts turning it. The ratchet (C) is moved to the next space. The operation stops when the protruding part (T) hits the buffer stop (R).

See also

• Adding machine

Notes

Sources

External links

• Website explaining the operation of a Pascaline.