Jacob-Rodrigues Pereire

In the July 1751 issue of the earliest scientific journal in Europe—the french Le Journal des Sçavans, was published a description of Machine Arithmétique of Jacob-Rodrigues Pereire. The device was initially made as an aid for deaf and mute people (Pereire is known as the first teacher of deaf-mutes in France), but the inventor mentioned that it is very useful not only for mute children, but for all those wishing to learn the science of numbers.

The Arithmetical Machine of Pereire is a simple adding device with a mechanism quite similar and inspired by Abaque Rhabdologique of Claude Perrault, but was more complex. The device is enclosed in a small box approximately three inches long, its constriction consists of coaxial wheels, and it was built in a very modular way, with no auxiliary wheels and no gears. At least one example has been manufactured, and Pereire donated it to a friend—the famous french statesman Baron Jacques Necker (1732—1804), who used it for personal calculations. Unfortunately, the device didn’t survive to the present day, so we have to limit our research to the elaborate description in the journal. Here it is (Excerpt from the register of the Royal Academy of Sciences, 5 May 1751, translated by Cris Stenella):

We have examined on the orders of the Academy an Arithmetical machine, presented by Mr. Pereire, of whom the Company has already approved the method of teaching speech to mutes.

Mr. Pereire cites in the paper he read to the Academy on the 16th of last December, everything currently known about machines of this kind, among which those by Mrs. Pascal, Perrault, Lépine, and Boistissandeau are the best-known. The first and two last take up a somewhat embarrassing volume and consist of many wheels, springs, ratchets, and other parts which make them costly, subject to repair, and inconvenient in use.

The rabdological abacus of Mr. Perrault is much simpler, and it is this instrument that the machine of Mr. Pereire resembles most. The abacus is composed of small rulers, each containing two columns of numbers, one on top of the other, separated by an empty space. The numbers in the first column are along the order 0, 1, 2, 3, etc. until 9 and those in the second column are in the reverse order, 9, 8, 7, etc. until 0, and the operation is by shifting the rulers in the grooves that contain them. Once they arrive at the bottom end of their travel, a ratchet that is built into the body of the ruler finds an opening for engaging in a groove in the neighboring ruler, making it advance by one step to mark tens of units for the first ruler, and if the ruler arrives at the bottom of its travel and thus indicates no number in the bottom window, one makes the ruler move up until the pointer that is moving it stops at the top of its groove—thus one finds at the bottom window the units that accompany the ten that the ratchet has been made to indicate, as will be explained more thoroughly in describing the use of this instrument.

Instead of putting the two columns on top of each other on each slide, Mr. Perrault could have put them side by side, in putting one slightly higher than the other, and placing the indicator windows in which the numbers appear conveniently accordingly. In this way, the abacus would have no more need for such a substantial length.

The machine of Mr. Pereire adopts this idea but is more ingenious.

Instead of rulers, it uses small wooden wheels or very short cylinders, like trictrac stones, all put on a common axle. The cylindrical surfaces of these stones or wheels thus become rods without end: he has divided the circumference of each of the wheels into thirty equal parts where he has written two series of numbers: the first contains three times the numbers 1 2 3 4 5 6 7 8 9 0, the second one three times the numbers 0 9 8 7 6 5 4 3 2 1. Of these wheels, there is one for the “Deniers”, one for the “Sols”, one for the simplest fractions like 1/2, 1/3, 1/4, 1/6, etc. and seven for the whole numbers, units, tens, hundreds, thousands, etc. until millions: and all these wheels together form but one cylinder three inches long to 18 eights in diameter, enclosed in a small trunk-shaped box.

There are on top of this box as many grooves as there are wheels, each occupying one-third of the circumference of the cylinder, by which one makes the wheels turn with the tip of a stylus, in the same way, one makes Mr. Perrault’s abacus’ rods move, taking the number one wants from 1 to 9 and 0, with this advantage that here the columns of numbers follow each other without interruption, one is never obliged to make the wheels turn back to make the number which results from the operation one makes, appear, as Perrault´s abacus often requires.

Mr. Pereire has divided the circumference of the wheel into thirty parts as opposed to twenty, so that the slits which are on top of the box would occupy only one-third of the circumference of the circle, instead of half, which would not have been as convenient. He could have divided them into forty or fifty parts as well, and then the slits would have taken only 1/4th or 1/5th part of the circle circumference, but this larger number of divisions would have necessitated making the wheels larger.

Additionally, on top of the box which contains the wheels, there are two rows of windows along the length of the box, one on the front, and one on the back, those here to find the sum or the product of the numbers one wishes to add or multiply, those there to dial the number from which one wants to subtract, or which one wants to divide by another. The means that Mr. Pereire has found to advance a wheel every time the preceding one passes 10 is very ingenious. For this, along one of the flat sides of each wheel, he has made thirty teeth representing more or less the teeth of a cog wheel. The other face is reserved to place a small balance, made hooked on one side, and along an inclined plane on the other. Each time ten divisions of this wheel have passed, the inclined plane meets a tooth fixed on the iron plate between the two wheels. This tooth forces the balance to move into the body of the wheel, thus pushing out the hook of which the other side consists, through the iron plate, which has an opening, especially for this purpose, hooking behind one of the thirty teeth on the flat side of the neighboring wheel, and making it advance one step. This step made, the inclined plane now being past the tooth on the iron plate, is tilted back into its place by means of a spring, the hook thus returns to the body of the wheel and retracts from the neighboring wheel after having made it move by the value of one tooth.

This entire arrangement seems well-thought-out to us, simple and convenient, and we judge it to be worthy of approval and inclusion in the array of machines approved by the academy.

This all having been said, there are only two things left that we believe would be good to draw the attention of our readers to:

1. By means of the arithmetic machine by Mr. Pereire, one can do without the help of pen and paper, the four arithmetic operations, the first two in pounds, shillings, and pences, and the seven kinds of fractions. This last peculiarity of the machine by Mr. Pereire, which is also unique about it, is all the more useful as one can add or subtract fractions of different denominators with the same ease as if operating on whole numbers: one will find for example that 1/4 1/3 3/8 5/24 makes 1 1/16 and when 5/12 is subtracted, 3/4 remain.

2. That the machine of Mr. Pereire, of which the volume is indicated above, should not be of considerable price, but nevertheless that those willing to procure the machine should advertise Mr. Pereire, as the price could even be lower as the number procured is larger. It is of little surprise that the mechanical arts will be happy to have this new machine, which by itself is very suitable for raising interest, and which is very useful not only for mute children but for all those wishing to learn the science of numbers.
*** End of excerpt from Journal des Sçavans, July 1751 ***

An attempt for the reconstruction of Pereire’s device was made by Mr. Stephan Weiss, you can find the full description on his site—www.mechrech.info. According to Mr. Weiss, the front panel of the device was something like:

Biography of Jacob-Rodrigues Pereira

Jacob-Rodrigues Pereira, better known as Pereire, was born in Berlanga, Extremadura, Spain (or in Peniche, Portugal, according to other sources) on 11 April 1715. He was a descendant of a Marrano family (Marranos were Jews living in Iberia, who converted or were forced to convert to Christianity yet continued to practice Judaism in secret).

Jacob (he was actually baptized with the name of Francisco António Rodrigues) was the seventh of nine children of Sephardi Jews—João Lopes Dias (Abraham Rodrigues) Pereira (1675-1735) and Leonor Ribea Henriques Pereira (1676-1751), native from Chacim, a village in Trás-os-Montes province of Portugal.

In April 1699, his parents with a group of new Christians from Trás-os-Montes (most of them were their relatives), decided to flee from Portugal and the Inquisition, and tried to board a ship to Livorno, Italy (on the board, besides João Lopes Dias and his pregnant wife Leonor, were his father André Rodrigues, his mother Ana Lopes, his three aunts Francisca, Beatriz and Ana, and his two daughters, Branca and Mariana, aged 2 and 3). However, the group was arrested in Cadiz at the order of the Seville Inquisition and all adults were punished with more or less harsh sentences.

On 2 June 1699, still in prison, Leonor gave birth to a boy named Paulino. After a more severe period of punishment, João Lopes Dias has been allowed to reorganize his family life, and the couple had six more children: Beatriz Maria (b. 30 Oct. 1707), Manuel (b. 23 Oct. 1710), Isabel (b. 22 Nov. 1713), Francisco António (b. 11 April 1715), André (b. 6 Oct. 1717), and Luis (b. 2 July 1720). The family lived in several places in Spain, like Berlanga and Llerena, and eventually returned to Portugal in the 1730s, where João Lopes Dias died in Moita in 1735.

It seems Pereira’s family problems with church authorities in Portugal persisted, because in 1741 to escape the charge of heresy Francisco and Leonor emigrated to France, settling initially in Bordeaux. In France, Pereira family returned openly to Judaism, as Francisco adopted the name Jacob, and his mother became Abigail Rivka Rodrigues Pereira (she died in France on 18 Nov. 1751). A lifelong devotee to the well-being of the Jews of southern France, Portugal, and Spain, he was the syndic, or lay leader, of the Sephardi Jewish community of Paris In 1753 Pereira was chosen for Agent of the Portuguese Jews of Bordeaux and in 1760 for Agent of the Portuguese Jews of Paris. In 1777, his efforts led to Portuguese Jews receiving the right to settle in France.

According to the legend, one of the sisters of Jacob-Rodrigues Pereire was deaf and dumb, and trying to communicate with her, he formulated signs for numbers and punctuation. After ten years of study of anatomy and physiology and numerous experiments on congenital deaf-mutes, Pereire received on 19 January 1747, the first testimonial for his labors from the Royal Academy of Belles-Lettres of Caen. Later on, he adapted Juan Pablo Bonet’s manual alphabet by adding 30 hand shapes each corresponding to a sound instead of to a letter.

In 1746 a wealthy French family, the d’Etavignys, hired Pereire to instruct their son. He taught the boy to speak through his method of finger-spelling, called dactylology. In 1749 he set forth his system in a memoir before the Royal Academy of Sciences in Paris. Pereire was well compensated by this family and another who hired him and dismissed Epee’s methods when it became known. His remarkable achievement was even presented to the King of France, Louis XV, who granted him 800 pounds as a mark of esteem. Pereira’s book on the subject, Observations sur les Sourds et Muets, was published by the Académie Royale des Sciences in 1778.

The memoir read before the Academy on the arithmetical machine that he had invented brought him a pension of 800 pounds annually from the King (26 October 1751), while in 1753 he received an honorable mention at a conference held by the Academy to determine the most advantageous methods of supplementing the action of the wind on large sailing vessels. In 1759 the Royal Society of London made Pereire a member, and in 1765 he was appointed royal interpreter of King Louis XV for Spanish and Portuguese.

Pereire took his method with him to the grave when he died in 1780. He is therefore seen as one of the inventors of manual language for the deaf and is credited with being the first person to teach a non-verbal deaf person to speak.

On 5 November 1766, Pereire married his kinswoman Miryam Lopes Dias, then only 19 years old. They had six children, but four died in infancy, and only two survived—Isaac (b. October 1767), and Abigail (b. 1768). Isaac Pereire became a merchant and died early, on 20 Nov. 1806, at the age of 38, but he left three children, two of whom became prominent financiers in Paris: Jacob-Emile Pereire and Isaac Pereire.

Besides his interests in mathematics and physics, Pereire had a thorough knowledge of ancient and modern languages. In 1772, he published a Tahitian vocabulary for Louis-Antoine de Bougainville’s voyage, after learning the language from Ahutoru, the first Tahitian to sail aboard a European vessel. Pereire successfully handled financial matters and discussed with Baron Necker how to restore order in the finances of France.

Jacob-Rodrigues Pereire died in Paris, on 15 September 1780, and was buried in Cimetière de la Villette (in 1876 his remains were transferred to the cemetery of Montmartre). His widow Miriam Lopes Dias moved to Bordeaux with their children, and died there in 1791, at the age of 44. In Bordeaux the street Rodrigues-Pereire was named in his honor.

Jacob’s grandsons, the Péreire brothers (see the nearby image)—Jacob Rodrigue Émile Péreire (1800-1875), and Isaac Péreire (1806-1880), were well-known French financiers and bankers during the second empire, whosе activity in the promotion and organization of railroads in Europe was extraordinary (in 1835 they built the first railway in France, that from Paris to St.-Germain). In 1852, they founded the Société Générale du Crédit Mobilier, one of the most important financial institutions in the world during the mid-19th century. Today in Paris there is Boulevard Pereire, and a metro station Pereire, named after the brothers.