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The Blaise Pascal calculator (the pascaline)

The history of the birth of the Blaise Pascal calculator (the pascaline) is reported in several web sites and written documents. I will just briefly recall this history hereafter.

écusson de Blaise Oascal

Blaise Pascal was born in 1623 in Clermont Ferrand and lost his mother at the age of three. His father Etienne Pascal was a tax collector, in 1626 after the death of his wife he will settle in Paris. In 1639, after a revolt in normandie region, he is sent to Rouen to collect the taxes. In order to facilitate the calculations his father had to do, Blaise Pascal conceives a calculator.
In 1642, after several tries, the conception of his calculator called the pascaline is finalized. He asks to a watchmaker in Rouen to construct the machine, but the calculator does not work. Pascal then decides to supervise the construction and directs the workers all along the work (it seems he worked himself on different parts of the calculators). He succeeds in presenting in 1645 a working model of the pascaline. Several pascaline were constructed and was marketed by Messire Roberval (Pofesssor at the "collège de France"). The price of the calculator was expensive. Different models of calculators were constructed, depending of the application they was for : decimal (for arithmetical calculations), for accountants (with the french money units of the 17th century), for surveyors (with the french lenght units).

Today 9 Blaise Pascal calculators are known.

The capacity of these pascalines goes from 5 (for accountants in the Lecoq museum) to 10 columns (for accountants in Dresde). The calculators are more or less finished (no wood framing on the top of some calculators, no engraving of the input wheels, ...). Some improvements have been done during the production years :

The user's manual of the pascaline :

Several explanations on how to do calculations with the Blaise Pascal calculator can be found on the Web or in various articles. These explanations arose from the examination of the known pascalines and/or are deduced from various articles.

These "user's manual" that have been written 300 years after the pascaline birth can not obviously take account of the cultural context and of the knowledge of the customers to which these calculators was sold. If the explanations given in these manuals allow to add, subtract, multiply and divide with a pascaline, there content is, with no doubt, very different with the one that would have been written in the 17th century. It would be educational to read a user's manual written by Blaise Pascal himself. Unfortunately, if we trust the "Avis nécessaire à ceux qui auront la curiosité de voir la machine arithmétique et de s'en servir" ( advice to those which will have curiosity to see the arithmetical machine and use it ), such a manual doesn't exist.

Meanwhile, to promote his invention, he sent an exemplary to the queen Christine of Sweden necessarily accompanied with some written explanation because nobody in Sweden was able to explain the operation of the calculator. One can read in a letter he sent to the confidant of the queen that this written explanation exists ( he calls it a "discours" ) and says about it : "j'y ai touché en peu de mots toute l'histoire de cet ouvrage, [...] et les règles de son usage" ( I wrote in few words the history of this work, [...] and how to use it )

Unfortunately this "discours" has not been recovered.
In 1982, a manuscript from the 18th century has been bought by the CIBP (Blaise Pascal International Center) in Clermont Ferrand. This paper is titled Usage de la machine (usage of the machine). The first part of this document is a manual for an accountant pascaline and describes how to perform the addition, the subtraction, the multiplication and the division.

The explanations which I give on the way of doing calculations are those described in the manuscript.

Movies carried out on a reproduction belonging to the Lecoq museum of Clermont-Ferrand illustrate the four operations (+ - / x ) according to the method indicated in the manuscript "Usage de la machine".

What we learn from the manuscript and the examination of the pascalines (personal point of view).

The Blaise Pascal calculator is the first known calculator built in several exemplaries which was used. With the calculator of Schickard, it is the first real mechanical implementation of a mental process.

Today only 9 pascalines are retrieved. These calculators have either 5, 6, 8 or 10 dials for entering the numbers. Some people have examined them and have deduced the manner to perform calculations. The explanations they give were wrongly taken by some people to be the truth.

For example

The pascaline must be on a perfect horizontal position in order to work
( see the heading "I disagree" )

The clearance of the calculator requests a mental calculation. The complement to 9 must be entered for each dial ( complement to 19 and 11 for the "sols" and the "deniers" money units )
In fact, no mental calculation is necessary as attested by the 18th century manuscript. The only thing to do was to put a stylus in between the marked spokes of the dials and to turn them until they stop (as shown in the vidéo). Marked spokes are on all the known pascaline.

For the subtraction, the complement to 9 of each digit of the number to subtract must be entered on the dials.
I suppose that this assertion comes from the double numeration of the numeral drums. Two digits whose the sum is 9 can be seen in the display for each angular position of the drums. With the complement to 9 method, each digit of the number to subtract is replaced by its complement and added to the content of the accumulator, at the end, a one is added in order to abtain the result (this technic is used on the Felt & Tarrant comptometer).
To make a subtraction with the pascaline, you firstly put the cover slide in the subtract position. Then you put the first number visible in the display ( you just have to set the marked spokes in front of the digit you want on the engraved circle). Finaly you enter the number you want to subtract in the same way as for to add. The result appears in the display windows (see the video relative to the subtraction).

The multiplication is complex and the pascaline is not useful for this calculation
With the aid of a paper strip and a multiplication table, this operation is not so complicated (see the video).

The division was too hard to be practicable on the pascaline.
With a paper strip, although not easy to conduct from our point of view in the 21th century, the division is not so difficult to achieve (see the video). Is a user who needs the multiplication table to make calculations able to make a division without the pascaline ?

The commercial failure of the pascaline.

One reason could be that this calculator was too expensive, 100 french pounds (reference : Les collections du musée Henri Lecoq - Volume V "Les Machines Arithmétiques De Blaise Pascal").
As an indication, the daily average wage was equal to 1 pound (20 sols), 10 sols for 12 eggs and 6 sols for 500g of butter (reference Banque de France).

Some persons say that it was mechanically unreliable (due to the carry mechanism). May be is it true, but what is known of it ? To verify this, it would be necessary to make calculation on an original pascaline of the 17th century (and not a modern replica).

About the robustness, a calculator travelled by horse-drawn carriage on long distance on the paths of the time. I don't know if this test was done for all the pascalines.

Some books :

Guy Mourlevat - "Les machines arithmétiques de Blaise Pascal" - Clermont-Ferrand, La Française d'Edition et d'Imprimerie (1988)

Les collections du musée Henri Lecoq - Volume V "Les Machines Arithmétiques De Blaise Pascal"

Courrier du centre international Blaise Pascal - n°8 - Clermont-Ferrand (1986)

Jean Marguin - "Histoire des instruments et machines à calculer, trois siècles de mécanique pensante 1642-1942" - Hermann (1994) ISBN 2 7056 6166 3

René Taton - "Le calcul mécanique" - Que sais-je ? n° 367 - Presses universitaires de France (1949)