Pascaline

The Pascaline, also called the arithmetic machine or Pascal's calculator, was a mechanical calculator invented by Blaise Pascal in 1642. Pascal created this machine because his father, who worked with taxes in Rouen, France, often had very difficult math problems to solve. The Pascaline could add and subtract numbers and could also multiply and divide by repeating addition or subtraction. Users moved a stylus to do calculations on the machine.

There were three versions of Pascal's calculator: one for accounting, one for surveying, and one for science. The accounting version showed the French currency of the time, with parts for livres, sols, and deniers. Pascal’s design was special because of its carry mechanism, which moved 1 to the next part of the machine when a number changed from 9 to 0. This made each part work separately and allowed quick changes across the machine.

Pascal made the Pascaline in 1642 and showed it to the public in 1645. He built about twenty more machines over the next ten years. In 1649, King Louis XIV gave Pascal a royal privilege, which meant he had the sole right to make these calculators in France. Today, nine Pascalines still exist and are displayed in museums in Europe. Later calculators, like those invented by Gottfried Leibniz and Thomas de Colmar, were influenced by Pascal's original ideas.

History

Blaise Pascal started working on his calculator in 1642 when he was 18 years old. He wanted to help his father, who was a tax commissioner, by creating a machine that could make calculations easier. In 1649, Pascal received a Royal Privilege, giving him the right to make and sell these machines in France.

By 1654, Pascal had sold about twenty machines, but only nine of them still exist today. The machines were expensive and complicated, so he stopped making them that year and began studying religion and philosophy instead. Many years later, during World War II, people celebrated the 300th anniversary of Pascal’s invention in London, England. They praised his clever ideas and how far ahead of his time his machine was.

Operation

The Pascaline was a mechanical calculator with metal wheels showing numbers from 0 to 9. Users could input numbers by turning these wheels with a stylus, similar to using a telephone's rotary dial. This would show the added number at the top of the machine.

To subtract, a special method was used where the display bar's position and the way numbers were entered changed. Each wheel had a display window showing the current number and another showing its complement, which helped in calculations. The machine could only add directly, but subtraction was possible by using this complement method.

The machine's design included a reliable gear system adapted from large clocks, ensuring accurate and sturdy operations. A special part called the sautoir helped carry over numbers between wheels using gravity, allowing the machine to handle many digits efficiently.

Operation

The Pascaline was a machine that could add numbers directly. To subtract, it used a special method called the 9's complement, which helped change subtraction into a kind of addition.

The machine needed to be reset before each new calculation. This was done by turning all the wheels to their highest numbers and then adding one more to the rightmost wheel.

When adding, people moved a bar on the machine to show the actual numbers being added one after another.

For subtraction, the bar was moved to a different spot to show special numbers instead of the real ones. This made subtraction work like addition but with a twist in how the first number was entered.

Uses

Pascalines were special machines that could be used by scientists, accountants, and surveyors. Some of these machines used a decimal system, while others used a different system. The simplest Pascaline had five dials, but later versions had up to ten dials.

In old France, money was measured in livres, sols, and deniers. Length was measured in toises, pieds, pouces, and lignes. Because of these different units, the Pascaline needed wheels that could count in bases 6, 10, 12, and 20. Non-decimal wheels were placed before the decimal part of the machine.

Production

Most of the machines that have survived for many years are used for accounting. Seven of these old machines are kept in museums in Europe, one is owned by a big company called IBM, and one is owned by a private person.

Limits to distribution and controversies

Pascal wanted to share his invention, the Pascaline, with many people to help them do math faster. He thought it would save time for people who worked with numbers, like his father, who handled taxes. However, only 20 of these machines were ever made in the 10 years after Pascal created them.

King Louis XIV gave Pascal a special right to make and sell the Pascaline in France. Pascal was worried that others might not make the machine correctly, so he asked the king to stop anyone from making a Pascaline without his permission. This meant that workers could not change or improve the design on their own. Pascal believed that his ideas were more important than the work of the people who built the machine, which made it hard for him to find skilled workers to help. Unlike another inventor named Samuel Morland, who worked well with his team, Pascal did not always trust the workers he needed. Because of these challenges, Pascal remained the only person officially recognized for creating the Pascaline.

Achievements

The Pascaline was an important invention in the 1600s. It was the first calculating machine that people could see and use. Only about twenty of these machines were made, and they were sold to help with counting and math problems.

It was special because it could carry over numbers when adding, which made it better than other machines at the time. It was also the first calculator used in an office, where it helped compute taxes. The Pascaline was even described in a big book called an encyclopaedia many years later.

Competing designs

In 1957, it was discovered that a person named Wilhelm Schickard had made plans for a calculating machine in the 1620s, before Blaise Pascal. However, Schickard's machine was never finished because it was destroyed in a fire.

After Pascal’s work, another person named Gottfried Leibniz tried to build his own calculator. He created a design called the Stepped Reckoner, which could add, subtract, and multiply, but it had some problems with carrying numbers over. Leibniz also invented a new part called the Leibniz wheel.

Pascal’s calculator remained the best machine of its time for adding and subtracting big numbers. Other inventors tried to make similar machines, but they had problems with carrying numbers or were not truly mechanical calculators. It wasn’t until 1851 that a machine called the Arithmometer became practical for everyday office use.