# Hillerin de Boistissandeau

Imitation is not just the sincerest form of flattery – it’s the sincerest form of learning.
George Bernard Shaw

In 1735 was published the first book of six volume set of Jean Gaffin Gallon—Machines et inventions approuvées par l’Academie Royale des Sciences, depuis son établissment jusqu’a présent; avec leur description, in which are described several calculating machines. In one of the books (Tome 4) was described the machine arithmetique of the French mathematician and inventor Hillerin de Boistissandeau, sent for approval to the Academie in 1730.

The machine of Hillerin is quite similar to the earlier Lépine’s machine (a solid, but simple adding device, with limited practical usefulness), so obviously Boistissandeau was strongly influenced by Lépine. Actually in the publication (see desciption of Hillerin’s machines) there are three separate articles, which described three different machines, but the second and the third are essentially improvements of the first one.

It seems at least one copy of the device was manufactured, preserved now in the collection of CNAM, Paris. The dimensions of the device are: height: 6.00 cm, width: 17.00 cm, length: 30.50 cm. The weight is 3.250 kg. Materials used are: wood, leather, iron, brass, and textile.

The machine of Boistissandeau has six digital positions, appropriate to the french monetary system in the 17th century. The rightmost position is for deniers, that’s why its wheel is divided into 12 parts, the next is for sols (the wheel is divided into 20 parts), remaining wheels are decimal (wheels are divided into 10 parts).

Entering and resetting the numbers is done by means of a stylus with two edges—short and long, which can be stuck into openings of the input wheels. When the short edge of the stylus is used, then will be rotated only the upper (input) disk and it can be set to 0. When the long edge of the stylus is stuck, then will be rotated not only the upper (input) disk, but also the lower disk of the calculating mechanism, and the number will be entered into it. The small wheels, which are placed over the big wheels are working as revolution counters and are used during a division operation. In these wheels is stored the quotient of the division, while below in the main mechanism is stored the remainder.

The five wheels (marked with w in the upper figure), which are placed between the six small wheels-revolution-counters, can be rotated by means of a special rod. These wheels are not connected to the calculating mechanism and are used as temporary storage for intermediate results.

Bellow, each input wheel is placed a small window, in which can be seen digits, inscribed on the wheel below. Here can be seen the result of the calculations. Over the digital wheel actually are inscribed two rows of digits. The first row is used during adding and multiplication, and the second—during subtraction and division. Which row of digits can be seen is determined by the rods (marked with B-B on the figure), which are moving a plate, covering one of the rows. Over the input wheels are placed small axles, which are stopping the styles during the rotation of the input wheels, and actually are determining which digit will be entered.

Below the digital disk, which digits can be seen in the windows below the input disk, are mounted on the same axes 3 disks. The first disk is a pinion-wheel, which can have 10, or 12 (according to the digital position of the wheel) teeth. This wheel takes the carry from the neighboring position (this is the reason that the rightmost position doesn’t have such a wheel). After this wheel is placed one-tooth wheel, which during each revolution will be engaged with the wheel of the higher position and will rotate it to 1/10 (or 1/12) revolution. The carrying is not direct but by means of an intermediate pinion-wheel, which is placed in the same plane, as the one-tooth wheel of the previous digital position and with pinion-wheel of the next digital position.

The lowest wheel actually is a ratch-wheel, and together with a rod and spring forms a system, destined for fixing the position of the digital positions mechanism.

The small wheels-revolution-counters also have openings, by means of which can be rotated, thus resetting the wheels. Bellow these wheels are placed ratch-wheels, which are fixed by means of rod and spring. The transfer of rotation from the main counter-wheels to these wheels is done by means of a special tooth on the big wheels, which once during a full revolution pulls a rod, which rotates to one tooth the ratch-wheel of the appropriate revolution-counter. Their digits are seen in the windows over each wheel.

The major fault of the first machine of Boistissandeau is its tens carry mechanism. The friction is huge and if it is necessary to propagate several consecutive carrying operations, then must be applied a vast effort and the mechanism can be blocked or even broken. That’s the reason in the second variant of the machine (see the nearby figure), Boistissandeau changed the tens carry mechanism.

Here the tens carry mechanism is made by partial pinion-wheels (actually a rod with an attached sector with several teeth on the edge). These rods are moved by means of a spring, which is connected to the mechanism of the junior position. This system already has the advantages of the tens carry mechanism of the Pascaline, and allows the carrying to be done without any effort. A similar mechanism is used for the wheels-revolution-counters. Another new element is the possibility to add mechanisms of new digital positions to the machine and to change the mechanisms of the digital positions, which allows the machine to be used for counting in the different numeral systems (monetary systems, weights, lengths, etc.)

Boistissandeau proposed also a third variant of his arithmetical machine (see the nearby figure), which again has improved the tens carry mechanism by lengthening the rod, which is stretching the spring, and decreasing the diameter of the pinion-wheel, which takes the carry, so it is required smaller effort during the carry.

#### Biography of Hillerin de Boistissandeau

The French mathematician and inventor Jean-Baptiste-Laurent de Hillerin, Seigneur de Boistissandeau and Seigneur de Jumaville, was born on 24 (baptized on 26) July 1704, in Paris, the first child in the noble family of Jean-Baptiste de Hillerin de Boistissandeau (13 Nov 1664-14 May 1732), conseiller au Parlement de Bretagne et du Roi, and Marie-Catherine Moreau de Villiers (born 7 Dec 1679). The family had also a daughter—Marie Catherine Armande (6 July 1709-23 Sep 1742).

The young Hillerin de Boistissandeau was energetic and passionate about the study of science. Abbé Robert, a former parish priest of Bourges, was his tutor. Growing up in the family Château du Boistissandeau (Castle of Boistissandeau) from the late 16th century (see the lower image), in the vicinity of the town Les Herbiers, western France, he made many developments around the castle and in particular construction of large raised orangeries with attics, granaries, and rooms to house servants. He was interested in physics and mathematics, and later in instrument making. Besides his calculating machine, de Boistissandeau was known as an inventor of various instruments, including a regulateur de parquet (a clock, used as a reference to other clocks, so that everyone is at the same time) in 1732, a surveyor and odometer in 1744, a portable barometer in 1758, etc.

Hillerin de Boistissandeau was a Counselor of the Parliament of Bretagne and was appointed adviser to the Board of Auditors of Paris by 1744. Chevalier Hillerin de Boistissandeau was also a Gentilhomme ordianire de la chambre du Roi and from 1744 membre correspondant de l’Académie Royale des Sciences (section of physics and mathematics) in Paris. He was a friend of the prominent french scientist René Antoine Ferchault de Réaumur, who made frequent visits to the Castle of Boistissandeau and even had a reserved room on the first floor of the castle, equipped as a small laboratory.

Hillerin de Boistissandeau married on 17 August 1735, in Paris, to Marie Agathe Bouret de Beuvron (24 Jan 1711-31 January 1794), daughter of Guillaume Bouret de Beuvron and Mathilde le Camus. The pair had eight children—six daughters and two sons (Marie Catherine (1736-1794), Antoinette Henriette (1737-1794), Louis François (1738-1799), Marie Agathe (1740-1794), Catherine (1742-1774), Julie (1744-1790), Louise Adélaïde (1750-1790), and Armande (1752-1820).

Seigneur de Boistissandeau died on 15 February 1779, in the Castle of Boistissandeau, happy to live not long enough to see the French Revolution. During the massacres of War in the Vendée, in 1793 his castle was looted and partly destroyed by the Republican army. Moreover, on 31 January 1794, a group of hussars-republicans raided the castle and killed his widow, the 83 years old paralyzed Marie Agathe, together with her daughters Antoinette Henriette and Marie Agathe.