The machines of Doctor Roth (1800-1885)


I) Chronological Nomenclature / Théodore Olivier

*Transcribed from the Bulletin de la Société d'Encouragement pour l'Industrie Nationale, 1843, by Valéry Monnier, September 2008;
English translation by Brian Stone, October 2008*

'We shall separate calculating instruments into two series:

The first series will contain those instruments which shorten or assist calculations, but require some human attention and intelligence;

The second series will contain those instruments which function even without the aid of man's intelligence, and which we shall call automatic machines (1)

A) First series

1) In 1624, Edmond Gunther had the happy idea of putting the logarithms of numbers on to a linear scale, by means of which it would be possible, through once setting a compass [dividers], to find the result of a multiplication or division (2)

2) In 1668, Gaspard Schott was the first to stick the rulers [transform the "bones"] of Napier on to multiple faceted cylinders, which could rotate around their long axis, and enclose these in a box. Several people did similar things in that period, notably M. Hélie (Meeting of Paris Academy of Sciences, 28 October 1839). The invention of Mr. Schott was a modification of Napier's "Rhabdology". (See Organum mathematicum a P. Gasparo Schotto e societate Jesu; Herbipoli, 1668, page 134)

3) In 1673, Grillet made public in Paris a new calculating instrument. (See Curiosités mathématiques du Sieur Grillet, horlogeur du roi. Chez l'auteur, au cloître Saint-Jean-de-Latran). In this booklet we certainly find the external description of the machine, but the reader is left in complete ignorance about its internal construction. According to Journal des sçavans, 1678, page 162, Grillet marked Pythagoras' tables on to small cylinders which functioned as did Napier's bones.

4) In 1678, M. Petit made an arithmetic cylinder, known as Petit's drum, around which he fitted strips of card carrying Pythagoras' tables which could be slid parallel to the cylinder axis by means of a knob on each strip. So it is correct to describe this machine as simply the rods of Napier's Rhabdology, structured differently. (See Journal des Sçavans, 1678, page 162).

5) In 1696, Biler gave Gunther's calculating rule a semi-circular form, and called it Instrumentum mathematicum universale.

6) In 1727, Leupold put Petit's drum into a decagonal form, replacing the cylindrical form given to it by its original maker (See Theatrum arithmetico-geometricum, 1727, page 25).

7) M. Clairaut invented a trigonometric instrument in the form of a small board, intended to replace tables of logarithms and to solve triangles without [longhand] calculation (See Machines de l'académie des sciences de Paris, vol. 5, page 3).

8) In 1728, Michael Poetius, in his Introduction à l'arithmétique ??(allemande)??, page 495, described a mensula pythagorica, which was nothing but a new application and modified form of Napier's Rhabdology, the instrument [this time] composed of movable concentric circles.

9) In 1731, M. de Méan set out Pythagoras' table so as to suit multiple calculations. To use it, the [various] cases are taken in different directions (See Machines de l'académie des sciences de Paris, vol. 5, page 165).

10) In 1750 (3), Ch. Leadbetter described the slide rule, an invention wrongly attributed since then to M. Jones. (See Bulletin de la Société d'encouragement pour l'industrie nationale, August 1815). (4)

11) In 1789, M. Prahl made public an instrument which he called the arithmetica portatilis, and which was the same as the mensula pythagorica of Poetius, except only that the movable circles were much larger and carried the numerals 1 to 100, so that with the aid of that instrument numbers could be added and subtracted up to 100.

12) In 1792, M.J.-P. Gruson published a booklet entitled Machine à calcul inventée par M. Gruson, Magdebourg, 1790 (This brochure appeared in a second edition in 1795). The machine consisted of a cardboard disk with an index [pointer?] at the centre, and consequently was a version of the mensula pythagorica of Poetius.

13) In 1797, Jordans published a booklet with the following title: Description de plusieurs machines à calcul inventées par Jordans, Stuttgard, 1798. This booklet contained only a simple modification of the promptuarium of Napier.

14) In 1798, Gattey modified Gunther's linear scale, by putting it into cirular form. (See Bulletin de la Société d'encouragement, annual volume 15, page 49. (4)

15) In 1828, M. Lagrous presented to the Société d'encouragement an adding machine composed of several concentric circles. This is described and illustrated on page 394 of the Bulletin de la Société, annual volume 27 (1828).

16) The machine patented by M. Briet on 8 December 1829, which he called an adder, was somewhat similar to the preceding machine. It is described and pictured on page 336, vol. 29 of the Décription des brevets dont la durée est expirée.

17) In 1834, M. Nuisement invented two calculating instruments: one depended on the principle of the balance, and the other on that of similar triangles. (See Recueil de la Société d'agriculture, sciences et arts du département de l'Eure, 1834, and Archives des inventions et découvertes, 1835, page 200).

18) In 1839, M. Bardach, in Vienna, placed on sale two calculation tables, of which one was just a copy of Perrault's abacus for addition and subtraction, lacking its mechanical transmission of tens, which was left to the care of the operator; the other, for multiplication and division, was again only a modification of Napier's multiplicationis et divisionis promptuarium.

19) On 2 September 1839, M. Léon Lalanne presented to the Paris Academy of Sciences an arithmetical balance, and on the following 16 December, an instrument for facilitating calculations, which he designated an arithmoplanimeter. (See Archives des découvertes, 1839, page 166).

20) In 1840, M. Lapeyre patented an instrument which was none other than an abacus; in it the iron wires were replaced by slots in which slid small rods marked with numerals.

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B) Second Series : automatic machines

1) In 1642, Blaise Pascal was the first to enter this field. (See Grande encyclopédie de Diderot, Vol. 1, page 681, Recueil des machines de l'académie des sciences de Paris, Vol. 3, page 137, and the Oeuvres complètes de Pascal, published by la Haye, 1779, Vol. 4, page 34). This machine could carry out addition and subtraction (5)

2) In 1673, Leibnitz submitted to the Royal Society, London the design of an automatic machine to execute the four rules of arithmetic. Some while later, he presented it before the Académie des sciences de Paris; it could never be operated [demonstrated?], despite the large amounts spent by the designer (6). Leibnitz expended 100000 francs on his trials (See Ludovici, Essai historique sur la philosophie de Leibnitz, printed in German, vol. 1, pages 237-238).
This machine is illustrated in Miscellanea Berolinensia, 1710, vol. 1, page 319. Its internal mechanism has never been known.

3) In 1666, Samuel Morland published, in London, a small volume with the title: Description and use of two arithmetic instruments (7).

4) In 1700, Mr Perrault presented before the Académie des sciences de Paris an arithmetic machine made up of small rules [linear sliders], each containing two series of figures placed one following the other and forming a single column; the first series was in the order 0 to 9, and the second in reverse order, 9 to 0. One used it by sliding the rules in the grooves which held them. When one rule reached the end of its travel, a pawl housed within the thickness of the rule passed through an opening which allowed it to engage a notch on the adjacent rule, and advance the latter rule one step to represent ten units of the first rule (8). See the drawing and description of this machine in the first volume of Machines de l'Académie des sciences de Paris, page 55)

5) In 1709, Jean Poleni attempted to build an arithmetic machine; its description and illustration are to be found in his Miscellanea; Venetiis, 1709, page 27. It was a large machine made of wood, very awkward to use, in which springs were replaced by weights. According to all reports this invention was notably inferior to that of Pascal.

6) In 1725, M. Lépine invented a machine which was the same as Pascal's, simplified in construction (9) (See Machines de l'Académie des sciences de Paris, vol. 4, page 103.

7) In 1730, the machine of M. Lépine suggested to M. Hillerin de Boistissandeau the idea of a new machine of the same kind; but friction was so great that it was unusable: he made two attempts to modify it, hoping to reduce friction and do away with the flywheel, but was unsuccessful (See Machines de l'Académie des sciences de Paris, vol. 5, pages 103, 117 and 121).

8) Jacques Leupold, in his work entitled Theatrum arithmetico-geometricum (Leipzig, 1727, page 38) published some words about a calculating machine of his own invention, promising to provide later all necessary details on the subject; but he died before being able to put his plan into practice and without communicating clearly and precisely his [proposed] machine.

9) In 1735, M. Gersten submitted for judging by the Royal Society, London an arithmetic machine for addition and subtraction; it was composed of a set of jacks, each one moved by a toothed wheel [lit. star]; each jack, in moving up or down, pushed the following toothed wheel one tenth [of a revolution]. The author consider[ed] that [beyond] a certain number of jacks and toothed wheels very considerable force would be required (See the drawing and description of this machine in Philosophical Transactions, vol. 39, page 124) (10)

10) In 1750, M.Pereire brought before the Académie royale des sciences de Paris a new arithmetic machine, consisting of small wheels of boxwood and very short cylinders, sharing the same spindle[s]. The circumference of each wheel was divided into equal parts. On the perimeter of each wheel figures were marked, in the following manner: three times in succession the figures 1-0 were inscribed; then three times in succession the figures 0-1. All the wheels were enclosed in a case, whose top was open in as many slots as there were wheels, each slot having a length of one third the diameter of the corresponding wheel; and, by means of a pin passed through the slot, the wheel could be rotated. (See Journal des sçavants, 1751, page 508).

11) In 1776, Lord Mahon, Count Stanhope, invented two calculating machines; one for addition and subtraction, the other for multiplication and division. The mechanism of these machines is unknown.

12) In 1777, Matthieu Hahn, pastor of Kornwestheim, near Ludwigsburg, after many years of work and great expense, demonstrated a machine which aroused general astonishment, but its faulty construction rendered it inexact; its external description is to be found in the Mercure allemand de Wieland, May 1779, page 137. Its internal structure has never been known.

13) In the Mercure allemand for May 1784, page 269, is an announcement of a new machine, invented by the captain of industry J.-H. Müller, which showed none of the inconveniences of that of Hahn. The inventor described the external form of his machine and indicated the manner in which it was to be used, in a booklet entitled Description d'une nouvelle machine; Frankfurt, 1786 (in German). There ensued a discussion between Hahn et Müller, during which each one made known the faults of his adversary's machine. (See the Mercure allemand for June 1785). History has made its judgement of both machines; they have been forgotten. The internal mechanism of Müller's machine is not known.

14) In 1814, M. Abraham Stern, of Warsaw, submitted for examination, by a commission nominated by the Royal Society of the Sciences of Warsaw, a new machine. This commission, composed of Messrs. Gutkovsky, chief engineer, Dabrowsky, professor of mathematics, and Bystazcky, made a report which was extremely complimentary to the designer (See the Leipzig Literary Gazette, February 1814, and Archives des inventions nouvelles, vol. VIII, page 264).

15) In 1821, Mr. Babbage, of London, was charged by the British government to construct a machine which would be able to calculate mathematical and astronomical tables. Part of this machine was finished in 1833; but suddenly Mr. Babbage ceased work on it. (See the note which he inserted into the ninth Bridgewater treatise; London; 1838, 2nd edition, page 186.)(11)
On the subject of Mr. Babbage's machine, Dr. Roth expressed himself as follows in his memoir:
"During my stay in London, in the month of August 1841, Mr. Babbage explained to me with the utmost goodwill the mechanism of his machine. It gives [calculates] the successive terms of a series which proceeds by [is defined by] its differences; but it has been completed only as far as three columns.
"In the first column, at the left, is entered the second difference, which, in this case, must be a constant; in the second column the first difference appears, and in the third column each term of the series.
"For each new term of the progression, the lever which operates the machine must be given two half-turns, until the small barrel of the middle column displays 'circulating complete'.
"But the excessively slow movement of the machine, the sum of 17,000 pounds sterling which it has already cost, and the still more considerable spending which would be necessary to complete it on a large scale will doubtless cause it never to be finished.
"Since the month of October 1834, Mr. Babbage has been occupied ceaselessly with perfecting the plans for his machine and making it capable of carrying out all the operations of differential and integral calculus. Last year I saw the thirtieth design by this engineer: if it were to be constructed one day, which is unlikely, considering that at least 20,000 pounds sterling would have to be spent to achieve it, it would be a marvel of human conception.
"I can not go further into detail on this subject, since I am not at all authorised to do so by Mr. Babbage."
/ Roth (12)

16) In 1822, M. Thomas, de Colmar, presented before the Société d'Encouragement pour l'industrie nationale a calculating machine. (See Bulletin de la Société d'encouragement; Paris, 21st annual volume, pages 353 and 354.)

17) In September 1838, Mr Scheutz, of Stockholm, announced in a note addressed to the Academy of Sciences in Paris, that he had invented a machine for the formation of series: a machine which, according to him, would be greatly superior to that of Mr. Babbage. For lack of funds this machine has not been constructed, and the designer has not made its mechanism known.

18) Finally, in 1840, 1841 and 1842, several patents were awarded in France for machines to calculate, to add, and to cut short the four rules [basic operations] of arithmetic'.

Théodore Olivier

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(1) A third series is formed by table-based machines. The results of completed calculations have been published, and brought together in works commonly called tables. These tables have not only been printed in books, but stuck on to cylinders and disks, where, with the aid of a pointer, the [required] result, already calculated, may be looked up. There are innumerable devices of this sort, which do not deserve any attention in scientific respects.

(2) Description d'une machine arithmétique jusqu'ici inconnue, et donnée au public par Louis Lanoge, à Lyon, 1661, in-8e.[8vo.]

(3) The slide rule was invented by Milburne, 1650, and perfected by S. Partridge, 1657

(4) Anveisung zum Gebrauche der Rechenmaschiene, von Joh. Peter Schürmann Mechanikus und Geometer in Herz. Geldern bey Bontemps im Selbstverlage des Verf. 29 octavs. 1 kupfer, 1782

(5) This machine consists of a large box topped by a brass plate and pierced by several round apertures, and by small windows through which the numerals are visible. The circular openings contain movable toothed wheels. The internal mechanism connected to these wheels is such, that each complete rotation of the last wheel at the right advances the second wheel on the left by one tooth. The shaft of [each of these] movable wheels is vertical and carries a second flat horizontal wheel. The latter engages with a pinwheel, which in turn has on its shaft a second pinwheel for the ratchet which prevents backward rotation, and a third one engaging with a pinion attached to a small barrel. This barrel carries two series of figures which are in opposite order to each other, from 0-9 and from 9-0. These figures are visible through the small window. The box contains as many similar gear mechanisms as there are circular apertures, and for that number of digits. The carrying of tens employs pawls which, at each complete turn of a wheel, are lifted by two pins, and advance the following digit mechanism by one step.

The inconvenient aspects of this machine are : (a) its large volume makes it very awkward; (b) it is very susceptible to deterioration because of the complexity of its mechanism; (c) the imperfection of the mechanism and the inertia of the moving parts can cause the latter to keep turning after being moved abruptly; (d) as transfer is made from each digit mechanism to the next directly and simultaneously, it can happen that all the gears engage at once, as in the case where one wishes to add one unit to a large sum like 9999999: in this case the machine invariably fails; (e) to begin operations, the machine must necessarily be reset to zero, which is slow and tedious. / Roth

(6) Specimen machinae arithmeticae a me adolescente inventae quam exhibeo jam anno 1673, societati Regia Londinensis Ostendi. Paulo provectiorem eam vidit academia Regia Parisina. Et tune quidem Dominus Mathion, mathematicus eruditus lutetiae in edita a se tabula aeri incisa, qua orgyam in mille partes acquales dividebatn cique operationes in usum vulgarem recomadabat notavit machina mea adhibita (quam viderat) calculos a puerulo peragi posse. Mentionem quoque eius fecit celeberrimus Tschirhusnius in medicina menis novissima. Miscell. berol. 1 . 317.

(7) Samuel Morelands, Description and use of two arithmetick instruments together with a short treatise explaining and demonstrating the ordinary operation of arithmetick [...], London, 1666, in-12e.

(8) If the rule which had just come up below [in the less significant decade] did not show a numeral in the lower window, the user raised it until the pin which was driving it reached the top of the groove; then the lower window would be displaying the single digits to go with the ten that the ratchet had made active./ Roth

(9) The machine of Lépine possesses all the defects of that of Pascal; the mechanism offers less probability of safe transmission [carrying] of the units into the tens, the tens into the hundreds, etc. In it the small barrels of Pascal are not used. The figures are engraved on wheels which are placed horizontally; on the lower surface of each wheel small round iron pins are fixed perpendicularly along a concentric line, at equal distances from one another. In the space between the two wheels there are movable pieces [wheels?] equipped with springs, by means of which the transmission is achieved; additionally each wheel has a ratchet lever. When the first wheel is turned from left to right, nine pins pass below the lever without touching it; only the tenth, longer than the others, necessarily pushes the movable piece and advances it by one tenth.

(10) The description and use of an arithmetical machine invented by Christian Ludovicus Gertsen, F.R.-S., professor of mathematicks in the university of Glessen, inscribed by Sir Hanns Sloanne, Philosophic. transactions, 1735, vol. 39, page 79.

(11) The ninth Bridgewater treatise. A fragment by Charles Babbage esq. London 1838, second ed., page 189.

(12) This is how a wheel is advanced by any single division when the one preceding it should show ten. On one of the flat sides of each wheel are thirty notches. The other flat surface is reserved for a small rocking lever, with a hook at one of its extremities and a ramp at the other. Whenever some of the characters [numerals] dividing up the circumference of this wheel are rotated, the ramp on the lever meets a lug fixed on the plate of white iron [tin-plate] which is between the two wheels. This lug forces the rocking lever to sink down at that end into the thickness of the wheel. The hook at the other end rises, crosses through the white iron plate via an opening machined there, engages one of the thirty notches on the surface of the adjacent wheel, and moves it one step. At the completion of this step, the ramp has moved beyond the lug and is returned to its rest position by a spring, [while] the hooked end stays within the thickness of the wheel, and leaves the adjacent wheel, having moved it by one notch. / R.

(13)-On the 27th of May 1841, M. J.-S. Henry (rue Chabrol, 63) took out a patent on a calculating device which he named the prompt calculateur.
-On the 12th of September 1842, MM. Bonnes and Foch, at Toulouse, took out a patent on a mathematical machine, which they named an additionneuse.
-On the 31st of December 1842, M. Maurel (Place du Palais-Royal, 229) took out a patent on a calculating machine.
-On the 27th of January 1841, Mr. Marston, at Ashton, took out an English patent for a machine suitable for doing calculations.
-On the 22nd of July 1843, M. Marescha took out a patent for a new machine suitable for addition and subtraction.

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II) A short history of calculation / Dr Roth

** Transcribed from the first addendum to Roth's manuscript patent **

'Since the most ancient times people in the East have made use, to facilitate calculations, of an instrument which is also employed in Russia and which consists of a frame fitted with several iron wires positioned parallel to one another and horizontally.
These iron wires are fastened at both ends to the upper and lower faces of the frame, in such a manner that they are otherwise unrestricted over their full length.
On each one ten small balls of wood or metal are threaded. The first wire at the left represents the units; the second to its right the tens; the third the hundreds; the fourth the thousands, and so on.
To calculate with this machine, one moves all the balls to the upper end of the frame.
To add, for example, 236 + 266 + 179, one moves down six balls on the units wire, three on the tens wire and two on the hundreds wire. Then returning to the units wire and attending to the second number given, which again presents the digit 6 whereas only 4 balls remain in the upper part of the frame, one brings down these four remaining balls, giving one ten which is transported to the tens by bringing down the fourth on that wire, then returning the ten balls of the units wire to the top of the frame, and bringing down two of them to complete the digit 6. Going now to the wire for the tens and the digit 6 which represents them in the given number, one brings down the 6 remaining balls, which makes one hundred which is transferred to the hundreds. The ten balls which were at the bottom of the tens wire are returned to the upper part of the frame. One continues thus as in ordinary addition carried out with pen and paper.
The Romans used a similar instrument which they called the Abacus and of which there is a description in [P. Claude du Molinck ?] :  Cabinet de la bibliothèque de Ste Geneviève, in fol. Paris 1692, page 23.
In it is a drawing of a frame with nine parallel slots through which rivets at the rear fasten copper balls [which] can be slid along by the user.
Until the 16th century, in Europe, use was generally made of counters which were placed on small tablets marked with numerous lines of which the intervals represented the units, the tens, the hundreds, etc ...
Country people in certain parts of Germany still make use of these today.
These three systems are nothing more than the material representation of figures by figures, balls, buttons, or counters. Like pen and paper, they require use of the intelligence in doing arithmetic, without offering any increased speed of calculation.

2) The following is a system of a different kind.
One uses two small rods of wood or brass, each divided into 10 equal parts on which  are engraved the figures from 0 to 100 in their natural order. If one wishes for example to add 17 and 23, one places one of these rods alongside the other so that the 0 of the first is aligned with the figure 17 on the other. The sum 40 is given by the figure which, on the second rod, corresponds with the figure 23 on the first.
If, on the other hand, we want to subtract 13 from 30, we so place the rods that the figure 13 on the first is aligned with the figure 30 on the second, and the difference 17 is given by the number on the second rod, which is aligned with 0 on the first.
Many kinds of apparatus are based on this system but they, too, all demand that one's intelligence be used, since the person doing the calculation must transfer to the tens the overflow from the units, to the hundreds that from the tens, etc ...

I do not know of any [such] apparatus older than that of Pérault, going back to 1700 (see Machines de l'Académie, vol. 1 [..]). After him came Pereyre (Histoire de l'académie des sciences 1750, p. 169), Gruson (1792), Gütle (1799), Sachs (1815), Briet (1829), Bardach (1839) and Lapeyre (1840); some of these adopted rods sliding in grooves; others preferred disks with concentric rings.

3) To facilitate calculation, some have also set out [arithmetic] tables on movable cylinders or disks. The usage of these is as restricted as that of ordinary tables. Among the numerous devices of this kind, we shall only mention those of M. Lorimier (1839) and Mr Delacroix (1840).

4) Lord Napier of Edinburgh thought of a fourth type of apparatus based on the logarithmic system and called rhabdological rods. The construction of these is well known, and likewise the manner of use, so that I need say no more.

In 1699, Michel Scheffer at Ulm invented the calculating scale [ruler] which he made known under the name of the "Des Mechanicus". This has been mistakenly attributed to the Englishman Gunther. In 1761, Biler [Biter] modified this instrument, giving it a semi-circular shape, and calling it the Instrumentum Mathematicum Universale. This species of machine is generally known by the name English calculating rulers. Mm. Galtey ? Roijeau ? Sargeant, Jomard, Laur, Mouzin, and Clouet did much to make it popular in France.
Father Scott was the first to apply Napier's rods on cylinders (Organum Mathematicum).
Leupold (Theatrum mathematicum) and M. Petit applied them on disks, the former on decagonal disks, and the latter, on circular disks.
There were also combinations of Napier's rods as applied on cylinders by Father Scott with the disks of the system described in paragraph 2. The first moves in this direction were made by Samuel Morland in 1673 and Samuel Grillet in 1678.
And finally, Mm. Jordans, Fitch, Roget, and Bardach, in different ways modified the rhabdological systems of Napier.

5)In 1727, Mr Clairaut senior invented a trigonometric instrument in the form of small boards to replace tables of logarithms and solve triangles without calculations.
In 1731, M. de Mean set out Pythagoras' table in such fashion that it could be used for different arithmetic operations. To do so, one takes the cases in different directions.
In 1734, Mr Nuisement devised two instruments of which one depends on the principles of the balance [?] and the other on those of similar triangles.
It is very likely that other unknown attempts will have been made to facilitate calculation. But these devices having no similarity with my machine, it is not very important that I describe them.
I shall add only that I have heard of the work of this kind by Lord Stanhope , but I have no definite information at all. As for Babbage's machine, I shall return to that in the description of my own large machine.

Chapter II

People have tried many times to invent a calculating machinewhich would function by itself, without requiring intellectual exertion on the part of the user.

1°   Pascal invented one such in..   1640
2°   Leibnitz ...............................  1673
3°   Polenius ..............................  1709
4°   Lépine .................................  1725
5°   Leupold ..............................   1727
6°   Hillerin de Boistissandeau    1730
7°   Gersten ...............................  1735
8°   Hahn ....................................  1779
9°   Muller ..................................  1786
10° Stern ...................................   1814
11° Thomas ...............................   1820
12° And myself ...........................  1840

Before describing my own I feel that, to avoid my claims being contested, I must make known in some detail the disadvantages of the others.

1) The machine of Pascal can only be used for addition and subtraction. It is extraordinarily complicated. Each [sub]system, the term we shall use for all the parts which only serve functions for one digit, is composed of 14 to 15 parts. The figures are located on the [curved] surfaces of small cylinders, which has several inconvenient consequences:

a) The machine is very awkward because of its volume
b) It is very subject to damage because of the complexity of its mechanism,
c) and very difficult to move [operate] due to the problems occasioned by that complexity.
d) It is necessary to write numbers from left to right, to the extent that one must have recourse to a pen, because with large numbers, nothing would be easier than to commit errors. That is, one could simply remember the number 63, if one had to write that in reverse, but matters would be different if the number concerned was 29172641.
Also in the drawing of the machine, the operator is represented with a pen in his hand.
e) To set the machine to 0, which must always be done in similar machines, before commencing operation, one has to search for a long time, there being no external marking of the [ ??] on the small cylinders and the layout of the machine not allowing for its indication.
f) Finally, during subtraction, it is likewise necessary to search for a long time to find the number [from?] which one wishes to subtract and which must be set initially on the machine.

It is certain that one would more easily and quickly reach the result with a pen than with Pascal's machine.

2) Leibnitz submitted in 1673 to the Academy of London, and the next year to that of Paris, the plan of a machine which received the approbation of these two learned bodies and nevertheless could never be constructed successfully. In vain he dedicated to it his whole life and a sum of almost 100,000 francs. Death overtook him before he could discover how to achieve it. This machine was to carry out the four arithmetic operations (see Ludovici : histoire de la philosophie Leibnitzienne vol. 1 page 69 and vol. 2 page 238 and 273).

3) The machine of Polenius is described in the Polenii Miscellaneas,1709, p. 27. Rough, ill-formed, powered by weights in place of springs, it offers nothing which one might be tempted to imitate.

4) Lépine was the first to use a horizontal dial. The machine is simpler than that of Pascal, but has all the inconvenient features of the latter.

5) Hillerin de Boistissandeau made three distinct attempts to construct a calculating machine. Praiseworthy though his efforts may have been, they were not crowned with any success at all. The machine only does addition and subtraction. He wanted to augment it with an indicator which would show the number of subtractions already made, hoping thus to reach the same result as by division. It serves no purpose to point out how long and boring a calculation made in that manner must be. Apart from that innovation, the machine is in no way superior to those of his precursors. To avoid one of the inconveniences (f) of Pascal's machine, he overloaded each subsystem with four series of figures, which only hinders operation and exposes it to frequent malfunctions.
In his latter two attempts, he tried to overcome another of those inconveniences (d) by means of a rack engaged with a pinion, much less efficacious and not offering all the certainty one has the right to expect of a precision machine, because of the prompt deterioration of the rack. A pile [sic] of gearing and superimposed dials renders the machine very complicated and to apply it seems impossible to me. One would hardly succeed in adding one centime to the sum 99999 francs 99 centimes, that is to say, changing all the 9's to 0 and driving the eighth subsystem which should then indicate 1. Otherwise, this machine was never built, and it is only [known] from a wooden model which the inventor attempted in order to justify himself. So it has remained in well-merited obscurity (see Machines de l'académie).

6) Leupold provided part of the plan of a machine suitable to execute the four rules, promising to go into the details later. Death prevented him from keeping that promise. I shall return to that machine on the occasion of the second addendum which I shall make to my patent in giving the design of my large machine for the four rules. I shall add only that the incomplete plan of Leupold's is to be found in the Theatrum Arithmeticum, page 102.

7) Gersten brought to the Academy of London a machine which was built [but was] equally defective. It is by a kind of jack moved by toothed wheels [lit.stars] that upward or downward motion is communicated to the following subsystem. The designer himself admitted that a certain number of subsystems would demand use of very great force. The subsystems are not in continual comunication and once the jack has been lifted, the operator must, as in the abacus of Perrault, interrupt operation to move it down again. The design of this machine may be seen in the Philosophical Transactions, vol. 39.

8) The machine of Hahn was so ill-conceived that it caused continual errors to be made. I must admit that I have not seen it myself and that what I say is according to M. Müller to whom I give all responsibility for this judgement of his which I convey (see Müller : Beschreibung einer rechenmaschine , page 32).
For me it is sufficient to know that the figures appear in it on triangles which are lifted and lowered, to affirm that it was constructed on entirely different principles from my own (see the Mercure allemand 1779).

9) The machine presented by Mr Stern of Warsaw to the academy of that city is known to me only by a note inserted in the Leipziger Litteraturzeitung, 1814.

10) That which M. Thomas de Colmar invented in 1820, was illustrated and described in the Bulletin de la Société d'Encouragement, Vol. 20. I shall speak of it on the occasion of my large machine, in order that the latter [...??]

11) [...] which was invented in 1786 and presented at the University of Göttingen par M. Müller. The internal construction has remained a secret. It is sufficient to make the observation for now that in these two machines additions do not take place instantaneously, but that after entering each series of digits, one must make use, with the first of a ribbon, and with the second, of a handle.
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Paris le 18 juin 1841
Dr Roth, docteur en médecine
Rue neuve des Mathurins, 6"



Transcription from the manuscript patent by Valéry Monnier, October 2007
Translated by Brian Stone, October 2008.
Valéry Monnier