On November 27th 2013, the renowned Breker auction house hammered off a Thomas de Colmar arithmometer at the sum of €233.814,- auction costs included [1]. This constitutes an unprecedented record. One cannot help but to observe that the machine in question has plenty of features to seduce – marquetry box by Boulle, dedication by the inventor, a real little jewel (Fig.1). And then also the date, 1835!, which would apparently make it one of the oldest arithmometers known. In terms of price, only the prototype constructed by Piolane in 1848 has come close, having been sold for £166 000 at Christie’s in 1997 [2], which no doubt has served as a reference point. (Fig.2).

Figure 1 / Arithmometer Sn541	Figure 2 / Arithmometer T1848

Is the arithmometer sold at Breker’s really exceptional ?

In order to be able to judge, one should learn more about this machine

At first we will discuss the various criteria which permit to date an arithmometer. The serial number, the shape of the stamp and the structure of the carry mechansism are good indicators. Other criteria such as the shape of the direction switch or the absence of a revolution counter may lead to confusion. A stamp carrying the serial number (Sn) 541 confirms that one is not dealing with an absolute rarity. Therefore, an error in the dating will be exposed.

Note: This date has been changed on the site of the auction house there a few weeks. (A little late? Too late? Really too late?)

Later we will look in the magnificent box. Its beauty is undisputable; however, its connection to the machine poses problems. The box was not made for this model of arithmometer, because it is too small. A certain number of adjustments were necessary. By means of a comparative analysisone concludes that the machine has been cut at the lower edge of the top plate. The problem is now to establish when this « forced marriage » between the box and the machine has taken place, and this leads to several possible hypotheses.

Finally, we will try to find out who Mlle. Renaud was. Genealogival sources shed a certain amount of light on the subject, without leading to absolutely certain conclusions.

I) Methods of dating

1. Serial numbers

The year 1850 marks a turning point in the history of the arithmometer. Thomas had become a rich man, his insurance companies [3] were prospering. Europe was industrialising! The machine became reliable! In short, all the elements were present to favour commercialisation.

Between 1850 and 1854, the production ran at a relatively modest pace. The reverend Moigno, editor of the well known science journal « Cosmos», indicates [4] that during this period, approximately 200 machines with 10 positions and 50 machines with 16 positions left the workshop.

The first machines of the type T1850 were not numbered (Fig.3), and it wasn’t until 1852 that Thomas started to add a serial number to the top plate of the machines (Fig.4).

Figure 3 / Arithmometer T1850	Figure 4 / Arithmometer T1852 - Sn 45

Each type of model had its own numbering. This system persisted for around a decade and has been the source of serious errors in dating. An arithmometer T1860 can for example be found with the serial number (Sn) 14, and a T1852 that was for sale in year 1854 has the serial number 105 (Fig.5 et 6).

Figure 5 / Arithmometer T1860 - Sn14	Figure 6 / Arithmometer T1852 - Sn105

This problem no longer exists as soon as the numbering becomes continuous. Thomas de Colmar chose to start this continuous numbering from serial number 500. This may seem like a strange choice, as no known arithmometer has a serial number in the 200, 300 or even 400 range. So why this large leap ?

In fact, the reason is simple, and related to the model-specific numbering. Since no particular model had been made in large quantities, a succession of small serial numbers is found. Only the 10-digit models (T1850A et T1852A) have approached 200 manufactured units.

To commence the new numbering scheme, our inventor simply added up the total of all the arithmometers made, and obtained a value « close to » 500. We will not question the real number of machines constructed. It is possible Thomas inflated the numbers a bit.

Mlle Renaud’s machine is the 41st machine of this model to have benefited from this new numbering scheme. (Fig.7). The number 541 is engraved in the stamp on the top plate. Let’s notice that the first contingent of serial numbers (500-550) has been allocated to the same type of machine. At least ten of these machines survived. They must have been not very popular as the most 50 of them were made. Not much further on, with Sn 581, we already find an arithmometer of the next generation, the T1865 [5] (Fig.8).

Figure 7 / Arithmometer Sn 541	Figure 8 / Arithmometer T1865 – Sn 581

Sn 581 is the oldest T1865 known. It is currently preserved at the Technische Universität in Chemnitz, Germany. It is reasonable to date it to 1865, but one could just as well subtract an extra year, knowing that the optimisation of the model had to take place before the deposition of the patent. What is certain is that not more than 40 machines separate it from Mlle Renaud’s Sn 541. That is not much in terms of production. If the one machine has a production date of 1864-1865, the other one is not going to be much earlier …

The press of the period provides very valuable information on the subject. Numerous publications[6-7], from 1863-64, mention a « small model » with 10 digits available from the works at the sum of 150 francs. Models with 12 and 16 digits are sold at 300 and 400 francs respectively. The latter ones are equipped with revolution counters.

Thomas de Colmar arithmometers always carry the stamps of their inventor. Because of this, the stamps are also very valuable indicators of the chronology of the machines. There are sufficiently many machines known to establish trustworthy correlations between machine types and their stamps. In certain cases, they can even help to date precisely a type of machine  little referenced in the literature.

The table below (Fig. 9) shows the different stamps being used on the « Thomas » arithmometers between 1850 and 1887.

Figure 9 / Stamps from 1850 to 1887

The stamp on arithmometer Sn 541 is identical to the one found on the very first models T1865 (here Sn 840), which links them chronologically. Notice that this stamp was used until well after the death of Thomas de Colmar, up to the year 1875, the time when the son, Thomas de Bojano, moved the workshop to 16 rue de la Tour des Dames, in Paris. This probably coincides with the hiring of Louis Payen, the genius construction engineer who helped the arithmometer reach its true potential [8].

Figure 10 / Inclined plane on T1850	Figure 11 / T1850 lever

In order to fix this problem, Thomas adopted small hooks on the T1852 models, serving to keep the carriage in place during the carrying operation (Fig. 12). This worked very well indeed, except that, if for any reason the machine came to be blocked during the operation, it became simply impossible to lift the carriage and remedy the problem. The only solution would be to lift the machine from its box, and, with considerable difficulty, fix the problem from below. There was thus a certain urgency to fix this new problem. In order to avoid the carriage from lifting, Thomas made the pressure to be effected on the lever no longer vertical, but instead horizontal. The lever rocks horizontally and thus moves a tooth to mesh it with the gear of the higher decade. From 1860 on, the process is improved by adding a third part, named the « équerre de retenue » (Fig.13). Each « équerre » is precision-machined so that the actuator on the result dial can push it horizontally in its rotation, and then move by without blocking. Around 1865, the assembly is made even more accurate by employing double springs that effect the precise and rapid positioning of the tooth in the gear, and its return into the neutral position at the end of the cycle.

Figure 12 / Hook on T1852	Figure 13 / Right angle bracket + lever on T1860

The carry mechanism on arithmometer Sn 541 is identical to the one found on T1860 and can under no circumstances be confused with an older type, due to the mechanical construction of the assembly. The fact that it does not contain the double springs dates the model prior to 1865.

The various criteria mentioned lead us to believe that this type of arithmometer dates from 1863. We will thus denominate it, until demonstrated otherwise, as T1863.


II) The possible confusions

The direction switch was not introduced on the Thomas arithmometer until approximately 1848. This ingenious system permits the result digits to turn right or left [9] whereas the stepped drums themselves always turn in the same sense. In order to effect this, on the axle of each cylinder, a double set of pinions is mounted, each of which can mesh with the crown gear of the result wheel. (Fig.14). In the Addition/Multiplication mode (AM), it is the front pinion which meshes with the totaliser, whereas in Subtraction/Division mode (SD), it is the rear pinion.

Figure 14 / Principle of the direction reversal

A metal link, fixed to the barrel of each double pinion, permits them to be moved front to back. This link is operated via the direction switch, the shape of which is unique between the different models. This permits to identify a particular type of machine (Fig.15).

Figure 15 / Evolution of the switches

At this point, confusion can set in, since the arithmometer Sn 541 possesses a horizontal direction switch, nearly identical to those in the 1852 model. It is thus tempting to date it to the same period. Certain details however, permit to recognise the differences between the models. On the one hand, the position of the direction switch on the top plate is different, one being placed much higher. On the other hand, the shape of the cutout, which permits the button to move horizontally, is not the same. In Sn 541, it is cut into two upwards triangles at both outside edges of the slot.

In 1855, at the Universal Expo in Paris, Thomas the Colmar pulls out all the stops! He presents a giant arithmometer in the shape of a buffet piano¹[10] (Fig.16). The scientific community has reason to be enthousiastic! The reverend Moigno writes a beautiful article on the subject, in July 1855 :

« What we find most remarkable in the appearance of the giant arithmometer of the universal exposition is that whereas it seems very difficult to make it display all the obvious advantages of the much smaller and easier to construct machines, M. Thomas de Colmar has attempted to introduce new refinements. As an example, the number of revolutions is indicated in special windows (Fig.17), and as these numbers are always smaller than 9, they show themselves as they are produced in the successive partial multiplications or divisions, in such a way that once the multiplication is complete, this row of numbers becomes solely through its presence an authentic witness and irrefutable proof of the truth and the correctness of the operation ; whereas, the division being completed, it gives the quotient, without the need to write down the intermediate results as they are being obtained.».[11]

Figure 16 / The « Piano arithmometer from 1855	Figure 17 / Revolution counter

One could ask oneself the question why Thomas did not think of this earlier ! Earlier models certainly possessed revolution counters, but only of one digit (Fig.18). In the case of a multiplication, the operator had to check the advancement of the operation for every number of the multiplicator. For a division, every number of the quotient had to be written down carefully in order to get to the final result. Not so simple…

It wasn’t really until 1858 [12] (Fig.19) that the revolution counters were being integrated as standard on the arithmometers. Technically, this was not so easy to do, because the carriage was already quite stuffed with wheels and springs ! In order to fit in all the necessary gimzos without increasing the size of the machine, Thomas had to increase the thickness of the top plate of the carriage, and work in several layers. In that way, the parts could partially overlap without being hindered in their respective functions.

Figure 18 / Multiplier index on T1850	Figure 19 /Multiplication counter (1858)

The absence of a revolution counter is thus another source of possible confusion on machine Sn 541.

III) The boxes (chests)

Figure 20 / A few distinguished boxes

In order to promote his machine, Thomas offered beautiful machines with richly decorated boxes (Fig. 20) to the influantial persons: crowned heads of Europe, pope as well as to other important persons. In return, he received many honorable distinctions: diamond Nicham (rank of commander) from his Highness Le Bey of Tunis, a gold snuffbox from the prince president (future Napoléon III), title of Commander in the order of Saint Gregory the Great by his Holiness the pope Pius IX. The list is long – the king of Greece, the Archduke of Tuscany, the King of Sardinia, the king of Portugal, the King of the two Sicilies, would reward him as well.

Thomas did not skimp on the quality of his boxes. He wanted them sumptuous, at the level of their future proprietors. They were fabricated in the purest spirit of Boulle, and their quality had nothing to envy with regard to the boxes of the great woodworker Tahan: ebony box, tortoiseshell, bronze handles, exquisite arabesques …

At present, 6 boxes of this type are known. 5 of these received arithmometers of the types T1850 and T1852, which, in itself, is nothing strange, because this was just the period when Thomas was offering these machines to the leaders of society. Seeing the number of distinctions received, we can estimate that around 15 of these boxes have been made during this short period.

Finally, the only box which appears somewhat anachronistic is the box of Mlle Renaud, which contains, as we have demonstrated above, an arithmometer of later vintage. What can be the explanation? Did Thomas have other luxury boxes made in the 1860’s ? Or did he use an older leftover box to spruce up his gift?

Visually, the boxes are similar – the arabesques are identical, and both sides present the same patterns (Fig.21).

Figure 21 / Similarity of the boxes

The table below gives the respective dimensions of the 10 digit machines and the normal wooden boxes as fabricated by Thomas de Colmar

The first thing that we notice is that the length of the machines is identical, and has not evolved over the course of time. On the other hand, the width is different. T1863 is 6mm wider, which is significant. This would logically mean that the width of the box is also influenced, and it is indeed larger in the T1863 [13].

If we start from the hypothesis that the box of Mlle Renaud was made to receive arithmometer Sn 541 (T1863), its width must be larger than that of the boxes T1850-1852, because the machine would otherwise not fit. We find however, that it has the exact same dimensions as the other Boulle boxes.

How does one fit a larger machine in a smaller box ?

There are two possibilities :

•Either the necessary amount is trimmed from the inside of the box in order to increase the available space
•Or the machine is trimmed in order to make it fit into the box.

Comparative analysis teaches us that the box is unmodified. On the other hand, we remark that the main crank handle is situated very closely to the edge of the top plate, which is not normal. No other arithmometer displays this arrangement. There is always 5 to 7 mm space from the crank handle to the edge of the top plate, in order to prevent the transmission shaft [14] from touching the inside of the box and thus harm the operation of the machine.

From the available evidence it is clear that the top plate has been cut.

There are two additional elements pointing to this.

It is observed that a circular cutout has been made in the inside edge of the cover [15](Fig.22). Without this modification, the box would be unable to close, due to the fact that the base of the crank handle surpasses the edge of the top plate. The box had to be cut (Fig.23).

Figure 22 / Circular indentation on the box to accomadate crank handle	Figure 23 / The crank handle exceeds base dimension

All of the arthmometer boxes possess an opening on the right hand side (Fig.24-25). It permits the operator to move the totaliser carriage [16], which is mobile. For example, in case of a multiplication where the multiplier has several digits, the carriage must be moved one digit at a time to the right for every digit of the multiplier. It works the same as if one would make the same multiplication on paper.

Figure 24 / Opening on the right	Figure 25 / Carriage movement

The left sideways opening has a completely different function (fig.26). It serves for the rezeroing mechanism of the totaliser. The principle is the following : a rack simultaneously turns, in a right-to-left movement (and back), all the display wheels of the totaliser. Under each of the display wheels is a cog of which one tooth has been removed. At the precise moment where the display wheel turns to zero, the rack does no longer engage, and the display wheel remains stationary. During this process, the rack exits at the side, which supposes a cutout would be provided in the box in order not to prevent its movement.

Figure 26 / Opening on the left on T1852 =  Shaft output on the left	Figure 27 / Right opening on Sn548 = Shaft outpout on right

During the years, modfications have been made to this mechanism. In T1863, the zeroing button has changed sides, and is now on the right (Fig.27). The movement of the rack is thus also situated on the right hand side, rendering the presence of an opening on the left side  useless. For this reason, it is omitted in the regular boxes. (Fig.28)

Figure  28  / Absence of the opening/depression on the left side of the box on Sn 547 (same model as Sn 541)

The presence of an opening on the left hand side in Mlle Renaud’s box thus indicates it is older (fig.29).

Figure 29 / Vertical opening on the left side of Sn541

IV) The gift to Mlle Renaud

Who was Mlle E. Renaud ?

If we retain the exact spelling of the name, no information can be found. Genealogical research done by Michel Arnold [17] has revealed a name bearing a resemblance. It concerns Emilie Charlotte Marguerite Reynaud de Barbarin (1816-1906). She seems to be connected to the fourth son of Thomas de Colmar, Louis François Charles Thomas (1816-1881). In 1864, he encounters Irma Carabin, dancer at the opera. Lovestruck, he makes up a will, dated May 28 1864, in which he leaves his entire fortune to her. Next, he encounters Jeanne Suzanne Dumas, with whom he wil have a daughter, Charlotte Jeanne. On the 1st of April 1871, in a second will, he declares his daughter the lawful beneficiary of all his goods and properties, and names her mother, Jeanne Dumas, as her guardian. In 1872, he is placed under protection for acts of prodigality. One year later, he entrusts his little girl to Mlle E. Renaud.  Then he marries Mlle Gabrielle de Gama, aged only 22.

After this, there are several consecutive wills. First he makes a donation to his daughter of an important package of shares in the companies « le Soleil » and « l’Aigle », then he makes his wife his heir. In another testament, he leaves his wife the guardianship to his daughter Charlotte, to finally determine, in an umpteenth will (1 month before his death) that his daughter be entrusted to the care and watch, without restriction, of Mademoiselle E. Renaud!

«A somewhat erratic course, let’s call it …».

This mademoiselle E. Renaud, who received as a present this beautiful arithmometer (Fig.30), is she Emilie Charlotte Marguerite Reynaud de Barbarin, of which the tomb is situated right next to the one of Louis François Charles Thomas? It is difficult to be entirely sure.

Figure  30  / Inventor’s dedication to Mlle E. Renaud

It would have been desirable, at a prestigious auction, to stress the lack of biographical information, rather than to launch into doubtful statements [18]. To state that the arithmometer Sn 541 comes straight from the Thomas family is not correct [19]. It originates from a private collection.

Another question also remains – has the machine been offered by Thomas de Colmar himself, and thus prior to 1870, or by his son, Louis François Charles Thomas, in thanks for the care extended to his daughter Charlotte?  A simple answer is we do not know, we have no certainty, only a number of hypotheses.

V) Hypotheses

© Valéry Monnier 2014

Acknowledgments

I thank  all of the passionate collectors who help and encourage me in my research. Thank you to  Walter Szrek, Serge Roube, Cris Vande Velde, Edmond Kern, and Michel Bardel, Bruno Nicole and Benoît Martin  for the proofreading. Thanks again to Cris Vande Velde for the English version of this article, and to Edmond Kern for the German version. Thanks Giovanni Breda for sending me a series of photographs in a record time. Finally, thanks to the museums in the entire world for the precious documents which they delivered. The list is long – I am certain to have forgotten some!

Notes

Photo credits
Fig.1,7,22,24,29,30 (Auction Team Breker, Cologne,  2013) - Fig.6 (Bibliothèque de l’Observatoire de Paris) - Fig.2 (Christie’s sale, South Kensington, 1997) – Fig.8 (Technische Universität, Chemnitz, Germany) – Fig.16,17 (IBM collection, USA) – Fig.27 (Giovanni Breda) – Fig.28 (Serge Roube) - Fig.3,4,5,6,9,10,11,12,13,14,15,18,19,20,21,23,25,26 (www.arithmometre.org)

Bibliography
The entire bibliography can be consulted online on the website www.arithmometre.org, under the heading « Bibliothèque ».