Making the Arithmometer Count
Stephen Johnston
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Fig.1 The arithnuvneter as sh,m,n in an 18o5 instructhm manual
fnote 47).
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Fig.2
51).
Introduction
The anthm,m~--ter of Charles Xavier Thomas
de Colmar ( 178%1870) has a firmly established
place in the history of computing. While the
lure's share of recent scholarly attention has
been lavished ~m Charles Babb'age's difference
and anah'tical engines, historians examining
calculat,~n in the 19th century, have nevertheless repeatedly affirmed the unportance of
Thomas's device. Typical charactensations are
remarkabh, uniform: 'the first multiplication
machine tO be made commercially for general
sale', 'the firstcommeroalh" successful calculator' and 'the first commercia[ calculating
machine'.
The anthm(~neter was not howe'ver the first
machine to accomplish the four basic anthmetical operati(ms of addition, subtracti~m, multiplication and division; earlier machines such
as t h ~ e of Hahn and MUller had achieved this
level of ~nctioualitv m the 18th century. 2 But
the implied virtues of the anthmometer are
clear. [.ackmg the mathematical ambition
driving the work of 8abbage and his followers,
the machine was solid, dependable and
successful, an industrial product manufactured m quanti~'.
Yet despite this apparent con.sensus there are
stnking problems with standard accounts of
the arithmometer. Rather than a smooth
pas.,,age to success, ! will suggest that the
machine's earl,,' decades witnessed a different
and more troubled trag-,ctory, in which the
mechanical and public character of the
anthmometer was repeatedly transformed.
This pn~'ess of development took place over
an e x t r a o r d i n a r i l y p r o t r a c t e d period.
Although first made public m 1820, a lengthy
reJxwt of 1878 remarked that the anthm(maeter
had still not taken its 'rightful' place in
industo,. ~ Perhaps this perception of failure
should be attributed to the overoptimistic
expectations of a sympathetic advocate. But
the widespread acceptance of the arithmometer cannot be dated much before the late
187lh. Only then was the machine deemed
sutficientlv successful to be worth copying,
12
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view of the
when arithm(mleter 'clones' were first manufactured in Germany by Burkhardt and,
slightly later, in Bntain.4
In this paper l focus on the perk~ 04 more
than ~ years between the invention of the
machine and its establishment as an accepted
instrument 04 calculation. I examine three
aspects of the arithm(m~eter's early history:
its development as a mechanism, the means
used to publicly pron~e it and the concrete
ways in which it was adopted by an
expanding circle of users. This multiple
approach seeks to reveal the technical,promotional and pers~mal investment required before
the anthmon~eter could be 'counted on', n~
just in the straightforward arithmetical sense
but also counted on as a reliableresource for a
whole range of potential users.
Design and Development
Examples of the arithmometer survive in
many public and private collections. Yet
despite its easily recognisable outward appearance, we should be wary. of di~u~ing the
arithmometer, as if the machine existed in a
single unchanging form. A few of the
machine's basic principles did remain constant, but almost every feature of their
implementation was altered by Thomas. Moreover, the long list of internal and external
changes does nc,t represent simply a uniform
sequence of improvement. In some of the most
iml:X~rtant instances of redesign Thomas did
r~t just rectify, or add to an existing model;
rather, he attempted to redefine the character
and the ambitions of the machine, and thus its
I~sible market.
The familiar features of the mature version 04
the anthmometer provide a convenient standpoint from which to survev its changing form
and operaticm. The machine presents two
principal parts, a fixed setting plate with a
series of sliders for inputting numbers (Fig.l:
A), and a movable carriage where results
appear (Fig.l: M). A number set with the
sliders is mechanically transferred to the result
dials on the carriage (Fig.l: C) by turning the
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arithmometer in 1862. From Reuleaux (note
handle (Fig.I: N). This transferopera,m, basic
to all the arithmometer's workings , is accomplis!x~ using the celebrated stepped cylinders
first intn~uced by Leibniz.
Each cylinder carries 9 teeth whose length
increases stepwise (Fig.2: A). The cylinder's
teeth engage a pinion (Fig.2: B) whose position
is controlled by the setting slider (Fig.2: C).
The higher the number set by the slider, the
larger the number 04 teeth on the cylinder
engaging the pinion. When the handle is
turned the cylinder rtRates and as a result the
pinion's square arbor (Fig.2: F) is turned
through an arc proportional to the value set
on the slider. It is this rotation which is
communicated to the result dial (Fig.2: K) via
a bevel wheel (Fig.2: G). One turn 04 the
handle adds the value set on the sliders to the
result dials and, since multiplication is simply
repeated additi(m, turning the handle, say, 5
times multiplies the given number by 5. To
multiply by 25 it is not nece~sary to turn the
handle 25 times. Rather, after turning it 5 times
the carriage is moved tree step to the right and
the handle then turned two times.
Using the reversing switch on the setting plate
(Fig.h B), the machine can be set to perform
subtraction and division. Figure 2 shows the
result of pushing the switch: M slides forward,
disengaging the bevel wheel G ~ ) m I (on the
axis of the result dial K) and bnnging H into
contact with 1. Now when a turn of the handle
causes arbor F to turn, I and thus the result
dial rotates in the opposite direction, reducing
rather than increasing the displayed value. A
turn 04 the handle thus subtracts the number
set on the sliders from a number entered on
the result dials.
As multiplication Lq repeated addition, so
division is repeated subtraction, with the
quotient appearing in the smaller set 04 dials
on the carriage (Fig.l: D). These quotient dials
are simply counters: each turn 04 the handle
increments the dial currently in contact with
the counting mechanism by one unit. The
quotient dials are aLso useful in multiplication,
since they provide a visual check on the value
Bulletin 04 the Scientific Instrument Society No. 52 (1997)
Fig.3
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General z,iew from the 1820 patent tnote 5).
[ll El I
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The oldest .~urz'/z,ms~ ar#hmometer (note 7); Smlthsonian
Institution photo no. P651074B.
Fig.4
Mechanism of the earliest arithmometer (note 7); Smithsonian
Institution photo no. P651O74A.
Fig.5
of the multiplier.Finally,when a calculation is
complete, the carriage dials can be reset to
zero: each set of dials has an independent
zeroing mechanism operated by twisting one
of the two knurled knobs at either end of the
carriage (Fig.l: O and P).
The engraving in Figure I is from an
instruction b~)klet of 1865. Some measure of
the operational transformation of the atithmometer can be gained by turning back to the
debut of the machine.
Thomas's arithmometer was first made public
in 1820 when he was gran;ed a five year patent
for his calculating machine (Fig.3)." It is clear
however that the patent represents only a
transient prototype, on which Thomas was
still actively working. By 1821, when he was
ready to submit an example to the scrutiny of
the Soci~# d'encouragement pour I'industrie
nationale, the design had already moved on
significantly. The Socibt~'s Bulletin first featured a short report on the arithmometer and
then a longer illustrated memoir.~ A machine
almost identical to the engraved design of 1821
survives m the Smithsonian's National Museum of American History (Figs 4 and 5)/The
inscription on the setting plate records not
only the machine's inventor but also apparently uniquely on a surviving Thomas
machine - who actually made it, the Parisian
m&anicien and clockmaker, Devrine.M
By comparison with Figure 1, several features
stand out in these early designs. To focus
primarily on the Smithsonian machine, it
clearly has a smaller capacity: them are only
three setting sliders. Alongside these sliders
there is a fourth slot identified as the 'multiplicateur', which is conspicuously absent from
the machine of the 1860s. The multiplicateur
was intended to abbreviate multiplicationand
division. Setting a figure on the multiplicateur
and actuating the machine caused the stepped
cylinders to rotate the desired number of
times. Thus, in multiplying by eight, for
example, a single operation was required
rather than the repetition of eight actions. ~
The carriage contains no quotient dials but
only a series of Paired result dials. Without a
switch on the setting plate to alterthese dials'
direction of rotation,subtraction and division
are accomplished by an alternative and less
direct route. Each result dial carries two
c(mcentric sequences of numbers, one increasing for addition the other decreasing for
subtractkm. In revealing one sequence the
other is hidden, so the user had to choose the
appropriate number sequence for the desired
operation. (Pascal had resorted to similar
means in his 17th-century adding machine.)
Each of these dials has to be individually reset
by twisting the knob mounted on its axis: there
is no general zeroing mechanism. Finally, it is
perhaps easy to overlook the lack of a handle.
In.stead there is a silk ribbon which is pulled
outwards to set the machine in motion.
Even dwelling only on external features makes
clear the substantial gap between the early
versions of the atithmometer and those of the
1860s. However, the devek)pment path from
one to the other was neither straightforward
nor steady. After the initial|anfare of favourable reports in the Bulletin of the Societ~
d'encnuragement, nothing further seems to
have been heard of the arithmometer for more
than 20 years. At this stage in itsdevelopment
the machine appears no different from the
many earlier arithmetical machines that had
been announced, had demonstrated their
feasibili.ty through working prototypes and
then sunk without further trace.
Later publicity material claimed that 1"h(~nnas
had worked incessantly to develop the
machine from 1820 onwards, ~° but the apparent absence of any promotional effortfor over
Bulletin of the Scientificlnstrome~t Society No. 52 (1997)
two decades warrants at leastsome scepticism
over such claims. Nor would it be surpnsing if
the anthmometer had been set aside. Thomas
was not a mechanician whose prole.~mnal
success rested on his ability to create and sell a
working commercial machine. Rather, he was
the director of an insurance company, and was
presumably pre~ccupied with this work for
most of his prok~sional lifeY
However, the anthmometer did re-emerge. A
machine of unknown design was displayed at
the 1844 French national exhibition and, by at
least 1848, a thorough redesign had been
carned out. The ribbon dnve was dLspen.,~J
with and replaced by a crank handle inserted
into the front of the ix~x. The capacity was
mcreased to five setting sliders and I0 result
dials. The multiplicateur slide was retaim,cl
from the 18205 machine but must have had a
new mechanism, while there was n o w a wing
nut on the sethng plate for switching between
addition and subtraction,dispensing with the
doubly numbesx~l resultdials.L"
['h~.se changes heralded a decade of further
development, the most intensive in the
anthmometer's history. A patent for a new
and more compact machine was obtained m
1850. ~ As well as the reduction m size, the
position of the handle was altered and a
zeroing mechanism added (Fig. 6). But this
model was, in turn, quickly superseded by
another new machine m 1852 (Fig. 7). z~As well
as incorporating some relatively ctvsmetic
changes, such as a new form for the add/
subtract switch and for the zeroing buttlm, the
1852 machine also marked a more fundamental departure in Thomas's approach and
strategy. While the succession of previous
models had incorporated mechanical changes,
they had nevertheless retained the same
functional elements. ]'he new m~lel of 1852
iettL~med the multiplicateur, making the
machine smmpler (and therefore presumably
13
Fig.7 The arithmometer as shown in an 1852 mstructhm manual
O~ote 10).
Fig.6
Ar~t/tmo,tctc,
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c. IS3, wrwatc tolh'ttto~.
cheaper to ctmstruct), but in effect less lra~werful. The u ~ r rather than the machine now had
to keep count of the turns of the handle,
especially' Ishen pertorming division
quently di~arded, which was engaged as part
of the tens c a m ' mechanism. Moreover, rather
than ~ stepped teeth the Smith~nian exampie's cylinders have 18, arranged in pairs.
pn~motional material em behalf of the machine
all offered the arithmometer to a wider
audience.
i h o m a s evidently expenmented with means
to supply this lack, ~ but it was not until 1 8 ~
that the absence was defimttveh' remedied by
the mtr~xtuction of quotient dials on the
carnage. '~ By this stage the arithmometer
had, outwardly at least, achieved its classic
torm, though it was not until the mid-ifl~Os
that the quot,ent dials received their own
zeroing mechanism.
Although further refinements would ctmtinue
to be introduced bv Thomas's business
successors and their competitors, by the
18~b; arithmometers were being produced in
a form which remained relatively stable until
the First World War. This familiar form of the
anthmometer may clothe it in a guise of
solidih" and permanence. But by surveying
the machine's technical development w e can
how shifting and fragile was its identity
over a period of ~0 years.
When presented through these media the
anthmometer was placed m open competition
with other devices. Although now often
presented as a lone pioneer,:" the arithmometer iostled with other machines for
attention and acclaim Far from being a selfevident success it was frequently ranked as
merely second best in its class. The public
career of the arithmometer in the 1840s and
"~)s suggests how much work was required to
establish the name and reputation of Thomas's
machine.
This sketch of the changing form of the
anthmometer has only coxered .~me of its
more ~vious and external alterations, th~w.,e
which reveal the changing options and
operations available to a u.,cer. But these do
ra~t n e c ~ r i l y represent the machine's m~st
mgmficant tran.~formations. The development
and ultimate abandonment of the multiplicateur required maior internal redesign, for
example However, contemporanes agreed
that the m ~ t challenging task for the devi.~r
of calculating machines lay m the creati,~ of
the tens carry mechamsm]r Without delving
into the me~:hanical mtricaoes, we can note
that Fhomas redesigned this element more
than an,, other: the anthmometer exhibits at
least 5 dt~,hnct mechamsms up to the 1860s.
Fhese alterahons re,,ponded to publicly' voiced
concerns al~ut the delicacy of the tens carD',
and sought to guarantee robustness by
redu(mg the reliance on springs as transmiiter,, of torce."
Fhe hidden revisions to the 4nthmometer's
renard,, extended beyond the ,,~.nsltive element
ot tens cam' to suchbasic features as the drive
tran~,m|sm~n, which was altered from a gear
tram to a ,,haft Such internal alterations
pro~,=de probably the best e~,tdence that the
performance of the machine was open to
=mpn~ement. Even that mt~t fundamental
mexhamcal organ of the machine, the stepped
Qhnder, did not remain unalter~l. Although
its wording and dlu~,tration is ob~ure, and
there is no .,,unlvlng machine available for
clanhtation, It e, clear from the 1820 patent
that [homa~'s radial design for the cylinder
incorporated an a d d m o n a l ha~th, subse-
14
Promotion and Competition
Focusing on the machine itself provides one
strand of development. But how did the
anthmometer fare in the public realm? The
anthmometer had first become public when it
was patented in 1820. This claim expired after
5 years and it was not until 18~1 that fresh
legal rights were obtained. From this I~int a
more systematic i~1i(3, was pursued, and the
15 year rights were extended and renewed in
1865 and 1880.
While the patent documents included mechanical description and illustration, such information was also made accessible by other forms
of publication Machines were offered to
learned and improving societies with the
expectation that they would be reviewed.
The rel~rts ,ha the construction and use of
the arithmometer for the ~cit'tP d'encouragement in 1821, 1822, 1851 - when it was
awarded a gold medal - and, after Thomas's
death, m 1878 have already been cited. A
machine was a l ~ presented to the Academic
des ~ i e n c e s in 18~4 and a report duly
followed later the .same year. TM
Patent specifications and ioumal reports thus
repeatedh" served as a medium for accounts of
the anthmometer, typicalh' focusing narrowly
on the form and operation of the machine
itself. However, the contexts in which the
machine was communicated and assessed
multiplied from the 184(h. Exhibitions, newspapers, popular scientific periodicals and
Thomas first ventured into the world of
exhibitions when the arithmometer was revived in 1844. A machine was entered in the
French national exhibititm of industrial products where it was classed amongst precisk)n
instruments in a category of 'diverse measures,
counters and calculating machines'. If Thomas
had hoped for substantial recognition and
reward, he was to be disappointed. The
arithmometer was granted an honourable
mention in the jury report but was clearly
considered inferior to the submission of thee
Hungarian emigr~ doctor Didier Roth, who
obtained a bronze medal for his adding and
calculating machines and counters. Roth had
been actively pn~moting his adding machines
since 1842 and had received a favourable
report from the Societ~ d'encouragement in
1843. The judgement of the 1844 jury was
mirrored in the coverage given to Roth in a
separate guide to the exhibitkm's highlights, in
which Roth's adding machine was described
and illustrated, while the arithmometer was
ignored. 21
The next French national exhibition took place
in 1849 and Thomas again tried his luck. On
this occasion he was awarded a silver medal
and the jury report devoted three pages to his
machine. 2z However, despite this higher
h~mour, he was again eclipsed, for a gold
medal went to the mechanicians Maurel and
Jayet for their "arithmaurel', a calculating
machine with automatic capabilities judged
to exceed those of the arithm~maeter.
Bulletin of the Scientific Instrument Society No. 52 (1997)
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Fig.9 The 1855 exhibition arithmometer lnote 31). By permission of
Andrew Neuhart/Neuhart Donl~es Neuhart.
Fig.8
The arithmaurel of Maurel and [aye(. From Lalanne (note 27).
A further competitive opportunity was s ~ m
offered by the 1851 Great Exhibition. But
again, Thomas was frustrated. The arithmometer was one of two calculating machines to
receive a prize medal, but the jury decided that
it was inferiorto a Russian entry devised by
Israel Abraham Staffel, onginally a watchmaker from Warsaw. The arithmometer was
illustratedin the officialcatalogue, but it was
Staffel's calculator, already successful at a
Polish exhibition and rewarded in St Petersburg, which was featured in the lllustrated
In planning for the 1855 exhibition Thomas
envisioned his chief rival to be the arithmaurel
which had captured so much interest at its first
public appearance in 1849 (Fig. 8). Subsequently awarded the prix de m6canique of the
Fondation Montyon this machine had been
undergoing continued development and was
evidently seen as a threat to the arithmometer's prospects. Thomas set about garnering
positive publicity for his most recentlydeveloped model.
London News. z~
After his succession o f defeats Thomas
embarked on a far more active promotion of
the arithmometer. His next challenge was to be
the 1855 exhibition in Paris and he evidently
determined to secure international victory on
French soil. Thomas campaigned both through
the press and in commissioned publications.
He also engaged in the rituals of patronage,
rituals that we might more readily associate
with the decoratively elaborate calculating
machines of the 18th century.
In the early 1850s Thomas distributed examples of the arithmometer to numerous
crowned and titled heads of Europe. Surviving
examples of these presentation machines are
individually ornamented with engraved dedications on scrollwork inside the case lid. u
Thomas's direct reward for these arithmometer gifts was a series of at least a dozen
honours granted between 1851 and 1855. He
was named to a stream of chivalric orders,
received gold and diamond gifts in recompense for his invention and, in 1857, was
elevated from Chevalier to Officer of the
L~gion d'Honneur3~ Aside from this personal
accumulation, Thomas was able to make
abundant use of these decorations in promotional material for the arithmometer, listing
them to indicate the endorsements he had
received from the European elite. Such t~forts
to raise the profile of the anthmometer placed
it within a world of honour and prestige, far
removed from the commercial marketplace to
which the machine is usually assigned in
historical accounts. Clearly the a r i ~ e t e r
cannot be identified as an exclusively industrial product. ~"
The arithmaurel and the arithmometer were
iuxtap~r,ed in the pages of the Annales des
Ponts efChauss~s in 1854 when each was made
the subject of a separate memoir. Both reports
were favourable but, apart from noting that
the arithmaurel made use of the stepped
cylinder which had earlierbeen incorporated
by Thomas, there was littlein the way of direct
comparison,v The stakes were raised by an
1854 article in the scientific review Cosmos, in
which the abb~ Moigno not only looked
forward to the forthcoming exhibition struggle
between the two machines but also gave his
opinion of the likely outcome. Moigno moved
the contest away from the staid and careful
prose of official reports and presented it as
journalistic high drama.~ He acknowledged
his own previous championing of Maurel and
Jayet but now sought to press the claims of
Thomas. Not only had Thomas's prioritybeen
overlooked but the superior ix)tentialof the
arithmometer had lain unrecognised. The
arithmaurel was still to be clas,q~cl as a
machine of the highest ingenuity. Yet Moigno
reminded his readers that the best could he the
enemy of the good. Maurel and Jayet had
produced a powerful machine but had not yet
been able to either expand its operational
capacity or render it suitable for the commercial market. Thomas on the contrary had
already supervised the construction of many
arithmorneters and there was no mechanical
hindrance to the expansion of the machine's
capacity. The arithmometer may have a p
peared slower and more in need of human
action and intelligence,but Moigno turned
such evaluations on theirhead. The simplicity
and solidity of the arithmometer identified it
as the 'classical' instrument, representing the
absolute good, while the anthmaurel was
Bulletin of the Scientific Insmmwnt Society No. 52 (1997)
damned by its transcendence, a romantic
instrument symbolising only a beautiful ideal.
Thomas presumably prmnpted or supported
these publications in some way but, whatever
the manoeuvres, they are now lost. ~ His
intervention is much clearer in another text
from the period tmmediately preceding the
Paris exhibition. The innocuously titled His-
toire des hombres et de la numiration micamque
appeared in 1855 over the name of JacomyRd~gnier, otherwise apparently best-known for
a lengthy treatise on coniugal morality.
Whatever expectations its title suggests, this
work turns out to be a lO0 page promotional
puff for Th~nas. Mustenng not iustthe history
of mechanical calculation but the hiskny of
arithmetic itself, Thomas is celebrated in
extravagant terms. Where the surpassing
acuity of a Pascal or a Leibniz had failed,
Thomas had finally succeeded in creating a
genuine calculating machine. Extraordinarily
purple passages elevate the anthmometer to
the status of a finely horled pniduct of genius,
its clarity of p u ~
matching a deeply
considered simplicity of ctmstruction. But
whereas "['hornas'sachievement ought to have
been the glory of the age and of the French
nation, his rewards had been few and
middling, with ~cL~nition bestowed more
readily bevond the Ixmndanes of France than
within them.
The supply of personal anecdote and quota(ion reveals Th(wnas's participation in this
promotional venture, and its message suggests
his direct support. Dark comments on the
inadequacy, of jury. p n ~ u r e s witne~ his
disappointment at previous exhibition verdicts
on the anthmometer. Sigmficantly, the t~nh.'
other machines to be given appreciatwe
mentkm are the three which had already
defeated the anthmt~meter, But each L~quickly
dispatched. Roth's machine, although a prao
tical device, is merely for addition. ]'he
arithmaurel rests on Thomas's prior mnova(ion of the stepped cylinder mechanism and is
in any case both mechanically dehcate and
prt~dbitively expensive, qualities which apply
likewise to the Staffel machine. Of these three,
only the anthmaurel would stand as rival to
the arithmometer at the forthcoming exhibi-
15
t~n, and Thomas had hit on a strategy to
outflank this competitor.
Moigno had reported on the difficulties facing
Maurel and Jayet in building an anthmaurel
with a results capacity of 8 figures. Thomas
laced no such problems, in the previous four
years he had seen the completion of m o ~ than
200 lO-figure and 50 16-figure machines. ~ To
drive home this advantage of capacity Thomas
created a giant machine especially for the
exhibition. Some 6 feet long, equipped with 15
setting sliders and 30 R,sult dials,and encased
in fine cabinetwork the result was evidently
meant to capture more than technical interest
(Fig. 9)?I
Advance reports of this calculating leviathan
were already circulating befone the exhibition
itself. The record of a meeting of the Acad~mie
des Sciences in the pages of Cosmos again
allowed the abb~ Moigno the opportunity, to
trumpet the anthm(nneter's merits. As well as
citing the conclusions of recent reports he
announced that Thomas's giant machine
would "strike a final grand blow' against
obj.
resistance or inertia which might
stillImpede the arithmcnneter's progre-~? 2
After this extensively orchestrated preparation, the initial signs from the exhibition itself
were encouraging. A guidelx~k reported in its
section on preosion instruments that the giant
anthmometer was the centre of lively interest.
Thomas would have been satisfied to note that
the anthmaurel appears onlv as an afterthought, an additional item also worth viewrag. Yet m this moment of triumph there was a
small ck~ud on the horiztm. The same volume
reported a late arrival, too recent to be
properly integrated into the topically arranged
text, but still justi~mg a mention in the
national account of Sweden and Norway. No
detads were given other than to report that it
was a quite remarkable calculating machine. ~
The machine was the Scheutz difference
engine. Inspired by Babbage and carried
through to completion with more limited
means, the second version of the Scheutz
engine had been brought to London in the
autumn of 1894. A working machine which
could automaticalh, calculate and pnnt mathematical tables by ihe method of differences, it
received Babbage's blessing and was taken to
Pans in August 1855. Ek--spite its late arrival,
the machine and its impact were widely
reported. A newspaper commented, 'we do
not believe that the Universal Exfa~sition
~upplies a single machine where inventive
genius is more completely revealed, than the
calculating machine' of Georg and Edvard
Scheutz."
Jury and journalist were largely at one: the
Scl~eutzes received the accolade of a gold
medal, leaving the anthmometer once again
with no more than an honourable mentitm."
The carefully staged struggle between the
arithmomet~ and anthmauwl had bec(~ne a
diverting side show rather than the main
event. The arithmometer's claims as an
elevated prt~uct of genius were dismissed
when faced with the ~)wers of the difference
engine. A substantial review of the exhibiti~n
quickly dealt with the two French calculating
rivals heft)re moving on to the much more
16
astonishing achievement of the Swedish engine. With its almost intelligent qualities and
its ability to replace the work of learned
savants by the handle-turning operations of
an ordinary man, the difference engine seemed
to open up a rhapsodic world of possibilities in
which intellect was overtaken by mechanism?*
Humbled once more, the a r i ~
would
nevertheles6 remain a regular entrant to
subsequent exhibitions where it was duly
RVorted and often rewarded. But never again
would it be so carefully groomed for success,
and yet so notably thwarted. While the
exhibitions provided a dramatic public arena,
their reports did however point to another
dimension of the arithmometer's public career.
Beyond the realm of spectacle and rivalry the
arithmaxnet~'s performance as a commercial
product was h'eqoently noted. Hem too the
eady news was not good.
The 1849 exhibition jury report remarked
simply that the arithmometer had never
entered into the commercial world, even
though it could be delivered at a reasonable
price. The situation was little changed by 1855
when the jury again t~2ognised the machine's
potential to be modestly priced, even though it
was as yet little knownY By this time Thomas
had distributed many examples of the arithmometer as presentation machines but he
evidently expected that an increasing number
of purchases would be made. Certainly, the
250 machines apparently assembled by 1854
would not all have been intended for Europe's
learned societiesand royalty. But whether such
completed machines had already been sold is
uncertain. Apart from Moigno's 18~ reference, the only other 19th-century source to
quantify, the anthmometer's pniduction is
Sebert's report of 1878 which records sales of
500 machines up until 1865, 300 for 1865-70,
400 for 1870-75 and finally 300 for 1875-78Y
Even by the late 1870s it would seem that no
more than I{10arithmometers were being sold
each year. The machine was far from being a
successful object of mass production.
Advocates of the arithmorneter sought to
account ft~r what they took to be its low rate
of adoption and offered suggesticmsto expand
its use. The most extended corcsideration of
public responses to the machine was penned
by the civil engineer G.-A. Him in 1863. Him
offered the arithmometer as one of two
inventions which had failed to achieve the
public and commercial acclaim which he
believed they. merited (the other device was
the hydrostat of Kaeppelin). His memoir was
seif-consciously presented as a case study in
technological diffusion: having used the
machine since 1855 and frequently demonstrated it to friends and colleagues he sought
to document common reactions to the arithmometer and to identify and defuse the
objections which he perceived as hindering
its progress. ~
Him records that after initialexclamatioRs of
wonder at the machine's capacities, most
observers first begin to doubt and then to
criticise.Surely, as a machine, it must get out
of order? Doesn't it require more of an effort to
learn than calculation with the pen? Won't a
user either lose the habit of calculation, or
simply become mathematically lazy.'~ Isn't it
restrkled only to the four rules of ant~aetic?
How can it replace the slide rule, which has
the advantage of portability?
Him effered practical reassurance and permnal experience to allay anxieties about mechanical reliability and he presented the Mide
rule and the afithmonwter as complementary
devices, their particular strengths suited to
distinct envinmments and calculating tasks. '~
The balance of his paper was devoted to an
exposition of advanced techniques which
extended the a n n ' s
reach beyond
the apparent restrictions of the four bask:
arithmetical rules.
However, Him suggested that moot of the
doubts about the arithmometer hinged on one
question which every onlooker always ended
by asking: hew much does the arithmometer
cost? Him acknowledged that the answer
typically frightened off nmst enqumers. However, Thomas was not creaming off exces~ve
profits. Rather, the elevated price arose from
the machine's manufacture process. Currently
constructed one by one using hand methods,
Him considered that the price could be halved
if the machine was manufactured in quantity
using the mechanical techniques of a large
workshop. 42
Price had been identified from the outset as a
crucial issue for the anthmometer. The very
first report of 1821 had worried that the
arithmometer would always be an expensive
device. In 1854 it was identified as the only
obstacle to the wider use of the machine. ° No
systematic index of the anthn~)meter's price
has yet been constructed, and it would in any
case be complicated by the variety of different
models and capacities which were available
from the 1850s onwards. However, fragmentary evidence does suggest that deliberate
efforts were made to cut the price of the
machine?4
Users and Uses: the Example 04 England
The evidence of reports, exhibitions and
contemporary comment suggests thal sustained pncluction of the anthmometer - either
individually or in small batches - first began
seriously in about 1850. The machine was not
an overnight success. Frequently outshone in
public by its rivals, it was sold at a rate of no
more than 100 a year before the 1880s. The
fragility of the machine's identity and market
both puzzled and disturbed advocates such as
Him. Him's memoir offered an analysis of the
perceived obstacles to the diffusion of the
ari.thnum~ter, much in the manner (dr more
recent economic historians and market researchers. Can the historian do more? Even if
impn~sskmistic, Him had the advantage of
witnessing and reporting directly on the
reactions of contemporaries. Nevertheless
the~ are sources which can complement his
picture and which enable us to move from a
model of passive diffusion to consider the
ways in which the arithmometer was actively
appropriated and adopted by users. We need
to take thLs mute if we are to understand how
a device appanmtly so beset by problems not
only survived but became the foundation for
an industry. Focusing on users and their
diverse uses of the machine helps to recast
the problem, transforming it from the negative
Bulletin of the Scientific Instrument Society No. 52 (1997)
terms of 'resistance to innovation' and towards
a n~re productive investigation of how the
anthmometer came to figure reliably in the
calculating routines of human 'computers'.
The first report for the S o c ~ d'encouragement in 1821 noted that Thomas envisaged his
machine primarily as a kml for large commercial organisatinns or banks. He apparently
imagined that it 'ought to render important
servicesin counting houses, banks, exchan~,
and every place where __,f~uent and rapid
calculations are necessary.' D~ubtless this
vision of the p~ential market was conditioned
by Thomas's own experiencesboth as an army
administrator with the French forces in Spain
and Portugal and as director of the Ph(,nix
insurance company from 1819Y'
However, the exhibition reports from the 1840~
and '50s repeatedly state that the machine was
not estahlL~d in the commercial realm. An
indication of some of the early French
institutional users is given in an instruction
manual of 1865 which cites the Western and
Northern railways as well as the Caisse des
consignations and the Creusot works? 7 A
post-1865 promotional leaflet suggests the
expansion of the targeted market beyond
commerce and finance through its references
to astronomy, geometry, architecture and
industry.'*
In the 1850s the arithmometer was principally
available from the offices of the Soleil
insurance company in Paris, of which Thomas
was general director. However, by at least the
1860s, agents w e ~ being appointed outside
France. Exports were claimed to account for
50% of production in 1862 and 60% in 1878.~
In Germany, the arithmometer had been
to as early as 1823,~ and its revised
form was publicised in an 1862 booklet by
Franz Reuleaux. st Early satisfied purchasers
included the Preu~ische statistische B0ro,
which bought its firstmachine in 1864 and
another larger one the following year. Further
Pairs of machines were added in both 1878
and 1879.s= The first evidence of intenest from
the United States likewise comes from the
1860s and '70s?~
The national example 1 want to focus on is,
however, that of England, principally for the
pragmatic reason of access to archives and
sources. The arithmometer was known in
England at least as early as its 1851 appearance
at the Great Exhibition.As well as his support
in the Pages of Cosmos and despite his faltering
command of English, the abb@ Moigno
demonstrated an example at the 1854 meeting
of the British Association. s4 Although it is clear
that a few arithmetical adventurers purchased
machines in the 1850s,s~ it is primarily for the
1860s and later that we have detailed evidence
of the me of the arithnmmeter.
A London-produced promotional leaflet provides one of the most vivid windows onto the
anthmometer's use in ,England. After describing the machine and noting its exhibition
awards most recently at Moscow in 1872 the leaflet prints a list of the machine's users. A
total of 33 corporate bodies, from government
departments to colleges, ol~ervator~ and
insurance companies, are included, foUowed
Su~.tinofthesc~t~U~entSodety
by 40 individuals and firms representing
engineers, bankers, actuaries, doctors and
chemists ~' The 1872 List was evidently intended to demonstrate that the arithmometer
had already arrived, and that it was wellestablished in a wide range of professional
pursuits. But by naming a ~
of exemplary
owners in order to persuade prospective
customers this leaflet provides a point of entry
to a rich network of users.
The 1872 list names 'Mr. Brunel, C.E.,
Westminster', who can be readily identified
as the engineer Henry Brunel, son of Isambard
Kingdom Brunel. in March 1866 Brunel wrote
to a c o ~ t :
I have just Sot what my mother irreverently
calb 'a new toy' - to wit a cakulating machine
price £12 which does all the common operations of arithmetic viz addition, multiplication,
subtraction& division in the twinkling of an
eye. It is reallya very useful articleworth its
weight in brass.-~
Later the same month, the machine . still
described as 'very u ' ~ u l ' and now identified
as French - was recommended to another
corres~mdent. ~ From a subsequent letter it
appears that Brunel's machine had been
ordered for him by his engineer colleague
William Froude,~ and it was to Froude that
Brunel reported in May of 'the grand use of
my cak. machine this afternoon getting out
some quantities'. The context of the letter
suggests that Brunel sought arithmetical aid
as he worked on a tunnelling machine scheme
for the proposed Channel Tunnel.'*
Confirmation that Brunel's calculating machine was indeed the anthmometer and that
it was treated as more than just a passing
novelty comes in the following year. Brunel
had evidently persuaded Froude to take a
closet look at what was presumably a new
model and had asked Thomas's I.o~on agent
to make the 'Arithmetic Machine' available.
That the service may have been performed
before, though not entirely to Brunel's satisfaction, is suggested by I~s alterthought: "Please
make sure that the key of the box is sent with
it.'*' If Froude had not actually bought the
machine previously, Brunel's enthusiasm was
infectious: Froude's name also appears on the
1872 list of the arithmometer's purchasers.
By 1868 Brunel had learnt to call the machine
an arithmometer and was ordering another
example. He immediately reported his acquisition in terms which suggest both his intm~ate
familiarity with the machine and also the way
in which itscapadty and power had become a
matter of friendly rivalry: 'I have a £20 Calc:
Machine as big as Clarke'swith a fizzerfor the
"tilebeggars'.~ As the mote prosaic language
o4 the order makes clear,Bruners "fizzer'was
the eraser knob and mechanism for the small
quotient dials, introduced in 1865.~
The evidence of Brunel's correspondence
indicates how, beneath the outward face of
anonymous market phenomena and purchase
decisiom, personal friendships and recom~tiom
were vital in hastering the commercial success of the a n ~ .
Moreover,
his enthusiastic efforts help us to rethink the
character of the machine's 'diffusion'. Brunel
No. S2 (19,r~
demonstrates the extent to which users were
more than mere passive vectors for the spread
of an unchanging object. Writing to the agent
in 1868 to enclose his delayed payment, Brunel
listed four faults in the machine which could
be remedied without great trouble. The last (ff
them, concerning the operatkm of the setting
sliders, was simple to correct at the manufacturing stage but troublesome afterwards and
had afflicted the four most recent of the five
machines bought by Brunel and his friends. M
Brunel's suggestions were not warmly received. Wnting from Froude's in March 1869
he remarked that 'I now get m y Anthmometers through Adie m y Instrument Maker
as the regularagent did not take pains to serve
me well'.Bypassing the agent, Brunel got Adie
to buy directly from Paris and then to make
alterations according to his preferred pattern,
as well as adding a leathercarrying case. By
this stage Brunel was acting as an intermediary himself, obta~ng his 'improved' arithmometers through Adie and then sending new
machines to friends while also receiving
damaged or worn examples for repair. It
should perhaps be no surprise that Hawkshaw
and Noble, two of the engineers with whom
Bmnel carried on his traffic in arithmometers,
also appear in the 1872 list of purchasers.~
In addressing problems with his friends'
machines, Bnmel was led into highly detailed
examinations of their mechanisms.Mechanical
defects which januned the machine could be
diagnosed a M repaired but more worrying
were instances when the machine was found
to be giving the wrong results. Errors of this
kind u n d e r m i r ~ the t m ~ on which resular
operation was founded. Brunel therefore went
to ~ t
lengths to identify the sources of such
subtly unsettling faults.In one instance, with
the help of diagrams and much explanation,
he tracked down a problem to wear and tearin
the carrying mechamsm, but only when the
carriage was in one particular position." Such
faults could have cast a long shadow over the
reliability of the arithrnometer among isolated
users but, by capturing the fault,devising a
~ y
and passing it on to correspondents,
Brunel helped to keep the machine above the
level of unrecoverable suspicion. In d~ng so
he helped to build up a repertoire of cautiorLs,
tricks and fixes well beyond the more anodyne
recommendations of the official insmx-fion
manuals.
Henry Brunel enables us to recover the
network of active interest through which the
arithmometer's engineering trajectory was
accomplished. While the purchase of other
machines can be documented, in the present
state of research it often remains difficult to
identify particular motivations. For example,
the 1872 list includes the South Kensington
Museum; the corresponding machine, purchased in 1868 and marked for the Science
and Art Department, survives in the Science
Museum, London?~
Other personal connections are occasionally
hinted at. Both the Cambridge Observatory
and Pm4ess~ Bashforth appear in the 1872list.
John Couch Adams, director of the Cambridge
Observatory from 1861, is reported to have
remarked that an arithmometer was 'in
constant use the~ in the observatory, and that
17
it is most valuable in shortening the tedious
prc~esses of asmmomical calculations'."~ Ba~forth was second wrangler at Cambridge in
1843 when Adams was senior wrangler and
they. became ckx~e associates, collaborating on
a treatise c,n capillary, action as late as 1883.
However, after his appointment as professor of
applied mathemati~ at Woolwich in 1864,
Bashforth's primary interest [as"in ballistics. In
reducing the results of ex~,nments with his
chrism,graph and in calculating ballistic tables,
Ba~forth relied on the arithm~nneter as 'a
most valuable assistant'. '~
(.hae of the m ~ t pnnnment areas in which the
arithm(nneter came into use m England was in
insurance. Actuaries were pnahably the first
pmk-'ssKmal group to adopt itand adapt their
work to its capabilities. From the l ~ ) s there
was a steady stream of artici~ showing i~w
the speciali'.~l and repetitive calculati(ms
required to c~mstTuct actuarial tables could
be reworked to take advantage o4 features of
the anthmometer. More than iust exposition.
there was also active debate about the merits
of machine cakulation TM The 1872 lLst illustrates the extent to which u'Lsurance companies
were not just considering the possibility of
adopting arithmometers but were already
making their purchases. A total o[ 17 offic~
had already bought machines from the
London agent. Nor do such references
necessarily represent only a single machine.
An~mg those l/~ed was the Prudential, which
underwent dramatic expanskm hr, n the mid18~)s as it pioneered mass 'industrial insurance' beyond the s ~ a l l v elevated market to
which companies had largely restricted themselves. The company's investment in, and
reliance on, the arithmometer spiralled as its
business grew. Aside hx~n daily calculation,
the arithm(~neters were put to work when the
company fulfilled its legal obligation to
conduct quinquennial valuatitms of every
pi)licy. The 1877 valuation took 300 clerks 6
mlmths to c(nnplete and it was reckmwd that,
with about 2.5 million policies in force,
4,635,8gl calculati(ms were carried out. The
Prudential's Henry, Harben recorded that 'We
had 24 arithmometevs at work on the business,
and without them it would have been
impossible. '~
Essential as the anthmometer was becoming to
the l'rudential's bu~ness, the machine could
not be treated as a fully reliable resource. The
company's archives presen'e a few fragmentary but revealing records of repair work
camed out on their anthm(m~L~tersdunng the
1870s. Springs would snap and other more
serious mechanical defects were not uncommon. The effort of the quinquennial valuation
severely tested the machines' robustness: in
one month alone in 1877 12 machines required
attention for tree or more repairs,r2 To guard
against the dangers of both operator and
mechanical error, the Prudential typically
carried out its calculatkms in parallel, usin~
tree machine to check the results of another/'
But the company was so concerned with
guaranteeing reliability that it sponsored the
development of an English versi(m of the
anthmometer in the h ~ e of obtaining improved performance. An 1879 letter to The
T~rnes announced 'a premium of £300 in
addition to the full price of 20 perfect
English-made machines'. When the prize was
18
paid in January 1882, £200 went to the
instrument makers Elliott Brothers.74
The Pnidential's initiative was evidently I~wn
of frustra~m at the perceived inadequacies of
a dry'ice that they could m~ kruger do without,
a device they, had built into their admini~
trative procedures. Henry Brunel's respimse to
his ,similarexperience had been to commisskm
his regular mslrument maker to carry (rot
alteratitwL~. But government departments also
faced the same problems with which ctnnmercial b~aties and individual engineers were
struggling.
In the history of computing the General
Register Office tGRO), Britain's centre hvr
official statistics, is known for c~nnmisskming
the third Scheutz difference engine, manufactured by Bryan Dimkin & Co. and delivered in
18~. ~ "Alt]~ough this machine assisted in the
calculation and printing of William Farr's
Engli~ Life Tabh" (1864), it was afterwards
dec~nnmissioned and placed in storage. The
GRO turned away harm the ambiti(ms of the
difference engine to the more limited means of
the arithmometer.
Treasury letters record the GRO's purchase
arithmometers in 1870, 1872, 1873 and 1877
and, although the utility of the machine was
repeatedly reported and endorsed, qualifications were entered [Tom the beginning. The
first letter seeking authorisation for purchase
asked not for the price of the machine (£20) but
for £25: 'some improvements have been
suggested after trial and experience in this
Department, which may cost ped~aps some
two or three pounds additi(mal'. TM Like Brunel,
and perhaps because of his example, custom
alterations were seen to be necessary before
delivery. Such improvements were not however enough to render the machines fault-free,
and running repairs were still required.
Although it was ultimately left to the
Prudential's private initiative, the GRO considered the same chauvinistic solution later
sponsored by the insurance clnnpany. Responding to "['reasuryenquiries, the GRO took
the view that 'the liability of "Ar/thmometers"
to get out of order and their noise would be
greatly diminished if they were made by more
accurate and better workmen - perhaps
Englistunen'. ~
The Treasury did not however resort to
offering English incentives but hoped to
prevail upon the current manufacturer. Having received another report in 1873 fixnn Sir
Francis (later Lord) Sandford on a machine
supplied to the Education Department, the
Treasury suggested that Sandford and the
G R O should together 'commun/cate with the
Inventor of the "ArithrrKwneter" in order to
ascertain if improvements could not be
intrt~uced in the construction of these
machines'.TM Thomas had died in 1870 and
British government efforts to encourage new
developments met with no more success than
Brunel's. Four years later the GRO addressed
the need for improvements in the machine:
'this has been fix,~quentlyrepresented to the
manufacturers in France and to theirAgents in
this Country, but the reply is that the demand
for them isso limited that no alterationcan be
made in them; consequently they hx-~quently
require repairs.'~ This remarkably telling
comment indicates that the machine was
offered as being 'go~d enough'; cl~te the
importunities of unruly English use~ the
arithm(aneter's manufacturecs did not think
that it merik,,d further investment and development.
The inmiductkm of an Engl/~-made arithmometer in the 188(h was evidently meant to
capitali~ on the dissatisfied sentiments of
English use~ of the Thomas machine. Later
GRO documents show how the c o m p a r ~
between the Thomas arithmometer and its
English c~nnpetitor was analysed, playing off
cost against long-term reliability. ~' But rather
than continuing with this sto'ry and highlighting the frailties of the arithn'anneter !
want to conclude my account of English users
by returning to the early 187[h.
The 1872 list of purchasers brings together
ct~npanies and individuals fnwn many fields,l
have shown how engineers, astronomers,
actuaries and statisticians engaged with the
machine, celebrating its utility and actively
probing its weaknesses. Was the juxtaposition
of these different intellectual and professional
roles merely an arte4act of a promotional
leafl~? Did the arithrnometer move along
Parallel but distinct tracks in the pro~essional/sing world of later lgth century England?
A meeting of the Society of Telegraph
Engineers in April 1872 suggests that the links
an~mg advocates and users of the anthmometer were not constrained by disciplinary or
professional boundaries. The Society gathered
to hear a paper on 'the application of the
calculating machine of M. Thomas de Colmar
to electrical computations' by Thomas T.P.
Bruce Warren. The paper reveals the extent to
which Warren had taken his cue from recent
accounts of the actuarial use of the arithmometer; actuaries had pointed the way in
showing how calculating procedures should
he reworked in order to benefit from the
capabilitiesof the machine. Perhaps even more
significant Ls the printed discussion which
follows the published version of the paper. *t
The contributing audience did not consist of a
narrowly bounded group of telegraph engineers, or indeed electricians defined mote
broadly. General Hannyngton of the India
Office, one of the prime actuarial proponents
o( the arithmometer, was present and his
views were supplemented by those of Henry
Harhen, the secretary of the Prudential.
Another actuary to speak up was Peter Gray
and comments also came from Dr Royston
Piggott ER.S. All of these figures and their
institutions are recorded in the 1872 list. The
discussion ranged from electrical work
through actuarial experience to trigonometrical and surveying issues, as well as the
handling and maintenance of the machine.
The judgement of Siemens, the Society's
President, captures the effect of this informed
cross-disciplinaryaudience in persuading new
users of the arithmometer's potential. Siemens
confessed that he had initially had doubts
about the suitability of the arithmometer as a
topic for his society's meeting. 'But the more he
had seen and heard about it, the more he was
satisfied the subject was one of great interest to
Telegraph Engineers; they had so much to do
with calculatio~ of an intricate kind.'
Bulletin of the Scientific bmrumem Society No. 52 (1997)
Con¢Ismims
seneromty in subsequently passing on *he
results of his own research.
I began by citing a widely-held view o4 the
anthmometer as the first commercially manufactured calculating machine. While my
account casts doubt on less cautious claims
(such that it was the first mass-produced
calculator), "2 that initial general statement
remains intact as a concise caption for the
arithmonw~ - thnugh only for the deveksped
form available towards the end of Thomas's
long life. Thomas's business success in insurance meant that the low rate of machine
production and its apparent lack of profit
were not pmbhems which need have troubled
him.s~ On the contrary, Thomas advertised his
extraordinary investment. In his promotional
Ixmk of 1855, Jacomy-R6gnier announced that
Thomas had spent 300,000 francs on developing the arithmometer, setting that figure
against Leibniz's reputed costs of 100,000
francs and Babl~ge's notorious government
subvention of £17,000 (reckoned as equivalent
to 425,000 francs).N Ifwe are to labelThomas's
work on the arithmometer, it is more likely to
fall within the category of vanity publishing
than mass production.
The burden of this paper has been to examine
the lengthy and complex process by which the
arithmon~.=ter's eventual soccess was achieved
- if indeed the process was ever completed. At
the end of my period, in the late 1870s, it is
clear that the arithmometer occupied an
increasingly established and tangible calculating niche but, while its usefulness was praised,
a search was already underway for a superior
replacement. The perceived need for an
alternative was taken as a symptom of the
arithmometer's inadequacies, but the assumption that the desL,~cl replacement should be
functionally (and even visually) identical can
equally be interpreted as a mark of the
machine's success.
Clearly it is not enough to date the arithmometer to 1820 and then interpret its subsequent history as simply a question of
diffusion. The mechanical and public identity
of the machine was worked and n.~vorked,
and its users adapted not just their own
computing work but altered the machine itself.
These three elements - the machine's development as a mechanism, its public evaluation
and reputation, and the activitiesof its users do not exhaust the history of the arithmometer, the details of its manufacture, for
example, are still largely obscure. Nevertheless, only by jointly attending to the diverse
elements of the arithmometer's persona can
we can begin to grasp the machine's career,
from fragile p r o ~ T ep to de facto standard.
Acknowled~
I would like to thank the Scienti~ ~ t
Society for supporting this work with a
research grant. Many individuals - too many
to list here - have helped by supplying
information on individual machines or allowing access to theircollections.Particularthanks
are due to Michel Bardel, Paolo Brenni,
Dominique Brieux, Judit Brody, Friedrich
Kistermann, Doron Swade, Peter Traynor and
Geoffrey Tudor. I would especially like to
thank Robert Otnes for prompting me to begin
this work many years ago and for his
ihdletin~eScienti~lnsmm~tseci~
anthmometer, in the 1920 exhibition cehebrating the centenary of the arithrm~eter: see
Bulletin(1920), pp.620-1.
Nolt~ and I [ ~
1. See, respectively, D. Baxandall and Jane
Pugh, Calculating Machines and Instruments:
Catalogue of the Collections in the Science
Museum (London, 1975), p a l , Uta C. Merzbach, C,eorg Schrutz and the First Printing
Calculator (Washington, 1977), p.37 and
Michael Lindgren, Glory and Failure: the
Difference Engines of ]ohann Mailer, Charles
Babbace and C,¢vrg and Edmrd Scheutz (Cambridge, Mass., 1990), p.290. For further references, among many others, note Michael R.
Williams, 'Early calculation', in William Aspray (ed.),Computing b~
Computers (Ames,
1990), p.50 and Gerard L'E. Turner, NinefeenthCentury ScientificInstruraents(Londcm, 1983),
p.283
2. Jean Margum, Histoiw des instruments et
machines d caiculer (Paris, 1994), pp.83-89.
3. Published in the Bulletin de ia Societt
d'encouragement pour i'industrie nationale (hemafter Bulletin). For this and other arithmometer
articles from the Bulletin 1 cite page numbers
from the reprinted versions published in
celebration of the machine's centenary in
1920, while also giving the year of first
publication. The report by Sebert was dated
13 December 1878, Bulletin (1879/1920),
pp.694-720, see p.707. The centenary issue o(
the Bulletin was the major source for Ernst
Martin's account of the arithmometer in The
Calculating Machines (Die Rechenmaschinen):
tlu'ir History. and Det~iopment, trans, and ed.
hy Peggy Aldrich Kidwell and Michael R.
Williams, Charles Babhage Institute Reprint
Series for the History of Computing, 16
(Cambridge, Mass., 1992), pp.53-57.
4. Hartmut Petzold, Rechnende Maschinen:
eine histori~he Untersuchung ihrer Herstellung
und Andu~adung yore Kaiserreichhis zur Bundesrepublik.Technikgeschichte in Einzeldarstellungen, 41 (D0sseldorf, 1985), p.102. For the
English machines of Tate and Edmondson see
Baxandall and Pugh (n~e I), p.12.
Patent no. 1420, 18 November 1820.
Thmnas's letter of request to the Minister of
the Interior,dated 6 October 1820, is reproduced in J.Joly,'Un grand invenieur alsacien:
5.
Charles-Xavier Thomas', IJI Vie en Alsace,
p.132. This article is the most authoritative
biographical source on Thomas and a copy
was kindly supplied by Friedrich Kistermann.
1 have not yet verified the date of the article
but it must have a l ~ e a ~ l in the Strasl~urg
periodical in 1935or shortly afterwards, when
a monument to Thomas was erected in Colmar
(see Maurice d'Ocagne, "Thomas de Coimar,
inventeur de I'arithmornc~re, Revue sc/ent~que,
73 (1935), pp.783-785).
6. The a n ~
was g'st examined by
Br~uet and Francoenr, and Francoeur's report
of 26 December 1821 is Bulletin (1822/1920),
pp.660-662. The subsequent memoir by Hoyau
is ib/d., pp.662-670.
7. N M A H , Washington, inv. 326,649. This
machine, or one very like it, was exhibited by
Darras, the then manufacturer of the Thonum
No. 52 (1997)
8. On Devrine, G.H. Baillie,Watchmakers and
Clockmala'rs of the World, 3rd ed. (l,ondon,
1951/1966), p.84 lists him as Paris, 1824,
though Tardy, Dictionnmre des horh~ers frant-ais,
part I (Paris, 1971), p.184 gives only a later
reference to a Devrine at the CaherieViv~,nne
in 1870. Devrine also made instruments: the
M u s ~ des Arts et M~,tiers has a balance
bought from him in 1809 (inv. 168). The
existence of this machine, and Devrme's r6he
in its manufacture, creates a problem for any
attempt to identifythe early arithmometer as a
radical break with the past. Cf. Annegret
Kehrbaum and Bernhard Korte, Calculi:Bilder
des Rechnens ernst und heute/Ima~ of Computing in Olden and Modern Times (Opladen, 1995):
'Thnmas's machine also inaugurated a new
epoch in the technical production of calculating machines. In the past practically all
calculating machines had been made by
watchmakers ...'(p.70). To further reinforce
the point, note that d'Ocagne (note 5, p.785)
states that Thomas was initiallyhelped by
Piolaine, 'un jeune ouvrier horloger de
Neuilly-sur-Seine'. I have been unable to
confirm this independently, but note that
Tardy (part 2 (Paris, 1972), p.523) lists a
member of the Piolaine family at Nenilly-surSeine in 1838 and Baillie has Pioiame ills at
Paris in 1825 (p.253).
9. The circular design of the patent's mulfiplicateur recalls Leibniz's machine. Although
often considered to have been lost to view for
almost 200 years, images of Leibniz'scalculating machine were available in the 18th
century; see the 1744 engraving in Kehrbaum
and Korte (note 8), p.61.
I0. Instructionpour se servir de l'anthra,,ni,
tre
(Paris, 1852; facsimile edition by Alain Brieux,
Paris, 1982), preface, p.2. The claim was
accepted and promoted. The abb~ Moigno,
Cosmos,4 (1854), p.76 writes extravagantly and
implausibly of Thomas 'qui, depuis trente ans,
n'avait pas ors~ un seul instant d'ameliorer
son oeuvre'. Equally, the c~mtemporary report
in the Comptes Rendus Hebdoraadaires des
Siances de i'Acadimie des Sciences, 39 (18~),
pp.1117-1124, on p.1123, writes that 'Quant A
I'anthm~,
qui ne se u~uve pas encore
darts le commerce, c'est avec le plus h~morabhe
d ~ i n ~ t
que, depuis trente am, M.
Thomas n'a orsc~ de la perfectionner pour he
rendre utile, de sunplifler pour qu'il pot 6tre
livr~ A un prix mode'.
II. See Joly (note 5) and note that Thomas's
name features repeatedly in EJ. Richard,
Histoire des institutionsd'assurance en France
(Paris, 1956).
12. For 1844, [Exposition des produits de
i'industrie franc,aise en 18441, Rapport du lury
central(Paris,1844),II,p.504. A machine dated
1848, again the property of Darras, was
displayed at the arithmometer centenary exhibition (note 7), pp.620, 622. What was
presumably the same machine was ofDred at
Drou~-Ri~,
Paris,17 November 1995, lot
124; its present whereabouts are unknown.
19
13. Patent no. 6261, 8 December 1850; additit'm, 19 August 1851. An English patent to the
same effect was taken out in 1851, no. 13,504.
14. Cf. Bulletin,51 (1852), p.615.
15. An 1851 report [or the Socktttt d'encouragement by Benoit remarks in a f i x ~ t e that,
without expanding the size of the arith~ ,
it should be possible for the machine
to record quotients on special dials: Bulletin
(1851/1920), p.691. The addition to the 1850
patent (note 13), filed a few months alter
8enoit's report, suggests a complex mechantsrn for recording quotients which never seems
to have been implemented. Note that a
machine o4 c. 1851 in the Mus/,e des Arts et
MiStier, Paris (inv. 40571) has a series of
independent dials on the settingplace, without
any mechanical connectkm, on which partial
quotients could have been manually inserted.
16..Sebert (note 3), p.703. Note however that
the 1855 exhibition machine discussed below
already had quotient dials.
17. Francoeur (note 6), p.661, Comptes Rendus
(note I0),p.l120, Sebert (note 3), p.098.
18. For example, Rapport du juW central sur les
pwduits de I'agriculture et de I'industrie exposis
en 1849 (Paris, 1851), !1, pp.549-1, see p.550.
19 Comptes gendu¢ (note I0) and lb/d.,38
(18~I, p.315. Thomas also attempted to enter
the anthm~wneter for the Acad~mie's prix de
n~canique in this year but the entry was
deferred until 1855: i[,/d.,39 (1854),p.1221. The
machine, with an engraved dedication to the
Academte, survives in the Musde des A m et
Metiers. ins'. 74/"9.
20. Marguin (note 2), p.lll: 'Pendant un
demi-siecle, la machine y regna seule.'
21. For Thomas and Roth at the 1844 exhibiti(m, see the jury.report (m~te 12), 11, pp.503.504 The catalogue of the Bibliotheque Nationale listsRoth's published leafletson his adding
machine. The re~wt (m Roth's adding machines and counters appeared, along with a
historical classification of calculating devices,
m Bulh'tm (1843/1920), pp.673-684. The exhibition guide mentieming Roth is Jules Butut,
Exposztn,n de I'industrie francai~ ann& 1844.
Lh'~r~ptum method~que, 2 vols (Pans, n.d), 1,
pp.00-2 Roth (whose first name is also given
as David) appears in Marguin (note 2), which
illustrates both his adding and his (unfinished)
calculating machines (pp. 114-117).
22 See note 18.
23. [Exhibition of the Works of Industry of All
Nations, 18gl ], Rqx~rfs by. the Juries (i.xmdon,
1852), p.310. Illustrated London News, Exhibition
Supplement, 20 September 1851, pp.354-5.
24. An 1850-style example dedicated to
Marie-Th6rese Louise de ~urbon, regent of
the duchies ot Parma and Plaisance, was
otfewd at Drouot-Richelieu, Paris, 10 May
19t~0, lot 114. Another presentation machine,
probably from after 1852 judging by the form
of the add/subtract switch, is in "the Heinz
Nixdorf MuseumsForum, Paderbom, inv. no.
E-19q4-bS1. A more modest level of decorahon was reserved for personal presentations
20
rather than those d~tmed for the crowned
heads of Eun~e; see the example dated 22
July 1852 and dedicated to Mine Zenoide de
Jacquemain, 'souvenir affectueux de l'[nventeur' (Musc~m, The Hague, inv. 9006; http://
museon.museon.nl / objecten/ 567.him). Presentation examples were still being offered
after Th(anas's death by his ~m: see Bulletin
(1920), p.625 for the machine offered to the
emperor of Brazil in 1872 by Thomas de
Ik~ano.
25. Thnnas had been created Chevalier of the
L~
d'Honneur in 1821, for his military
service rather than the arithnwaneter Ooly,
note 5, p.131).
26. For an account stressing the industrial
character of the anthmometer and contrasting
it with impractical earlier machines destined
only for the collections of princes and nobles,
see Kehrbaum and Korte (note 8), pp.70, 64.
27. On the arithmaurel, see Lalanne in Anhales des Ponts ef Chabs,~,s, 3rd set., S (1854),
2nd trimestre, pp.287-310. Lemoyne's report
on the anthmometer directly follows at pp.311332; itsreference to Maurel and Jayet comes at
the end of a historical review on p.328.
28. E Moigno, 'Arithmomt~e ou machine A
cak'ul',Cosmos, 4 (1854), pp.72-79. A descriptive account of the arithn~mleter also appeared in a subsequent number of Cosmos: 4
(1854), 186-96. Moigno was one of the leading
vulgarisateurs of science, emphaslsmg spectacle
and controversy rather than 'normal science';
see Susan Sheets-Pyenson, 'Popular science
periodicaL~ in Paris and London: the emergence of a low scientificculture, 1820-1875',
Annals of Science, 42 (1985), 549-72, pp.556-7.
29. Robert Fox, 'Edison et la presse fl'angaise A
l'exposition intemationale d't~lectricitttde
1881', in his Science, lndust~, and the S~ial
Order m Post-Rez~olutmna~. france (Aldershot,
19951 has shown how big business interests
were able to buy influence and favourable
press coverage on a massive scale at the
electricity,exhibition of 1881. Thomas may
have pursued similar tactics,but on a much
smaller scale.
30. Cosmos, 4 (1854), p.77.
31. The machine remained with the firm and
is listed in a 1915 inventory of materials and
machines drawn up for Darras: 'Grande
machine A calculer d'Exposition 1855 dans
son grand meuble en bois noir incrust~ et gami
de cuivre hbriqu~e par M Th(wnas de Colmar.
Prix reduit convenu 1.000 [francsr (inventory
copy m Mathematics Files, National Museum
of American History, Washington). Darras
exhibited the machine at the 1920 exhibition,
Bulletin (1920), pp.621,623. It is now in the
collection of IBM: A Calculator Chronicle: 300
Years af Counting and Reckoning Tools (Armonk,
n.d.), pp.14-15.
34. On the Scheutz engme, see L ~ g r e n (no~
1). The engine's year=long stay in Paris is
discmsed on pp.19"3-203 and the newspaper
citation is on p.196.
35. [Expmition Universelle de 1855l, Rapports
du jury mitre international (Paris, 1856), p.405.
36. L&)n Brisse, Album de I'Expasition Uni~crsd/e, 3 vols (Paris, 1856-9), H, p.194.
37. Rapm~ (note 18) 0, p.551 and ~pports
(note 35),p.4~3.
38. Sehert (note 3), p.704. Sebert's figures
have provided the primary kamdation for the
few existing analyses of factors affecting the
production and ad(~tion of the anthmometer.
See Ludoif yon Mackensen, 'lk,,dingungen for
den Rechnischen Fomchritt: dargestellt an.
hand der Entwicklung und ersten Venvertung
der techenmaschinenerfindung im 19. Jahrhundert', Technikgeschichte,36 (1969), pp.89102 and F.W. Kistermann, q'he slow acceptame of mechanical calculating machines some reflections and remarks', Pnc.e~:ngs of
the Cultural Histo~. of Mathematics, 6 (1996),
pp.32-43. The only independent way of
assessing the reliabilityof the data of Sehert
and Moigno is by studying surviving machines and their serial numbenng system.
Preliminary indications suggest that S~,,Tt's
figures tally reasonably well with machine
serial numbers. What is not yet clear is
whether the serial numbers provide a reliable
guide to the number 04 machines actually
c ~ .
An unknown number of exampies from the early 1850s do not carry serial
numbers. Nor is it clear that serial numbers
wece assigned in a continuous sequence. Such
msues will only be clarified when a more
comprehensive survey of surviving machines
has been carried out.
39. G.-A. Him, 'Notice stir i'utiliM de Farithmom#tre et de l'hydrostat', Annales du G~ie
Civil, 2nd part, 2 (1863), pp.113-7, 152-64.
40. This fear had been expressed by the Royal
Academy of Sciences in Madrid, whose report
on the arithnmmeter had worried about the
social consequencesof the machine's adoption.
Thomas once mo~ relied on the journal
Cosmos, presumably in the person of the abl~
Moigno, to vigorously rebut this view: Cosmos,
$ (18~), pp.660-1.
41. Earlier neports had already concluded that
the arithmometer had an important place
alongside rather than as a ~placement for
existing technologies such as slide rules and
logarithmic tables. See, for example, Lemoyne
(note 27), esp. pp.320-3.
42. Lemoyne (note 271, p.329 had al~ady
considered that, if 10,000 examples were to be
commissioned, the machine could be built for
less than 100 francs, instead of its then curmat
price of 300. Him's half-price comment was
later repeated in Sebert (note 3), p.707.
32. Cosmos, $ (18~), p.663.
43. Francoeur (note 6), p.661 and Lemoyne
(note 27), p.329.
33. H. Tresca (ed.). Visited I'Exposaion Universelle de Paris, en 1855 (Paris, 1855), p.353
(arithmometer and arithmaurel) and p.25
(Swedish machine).
44. In 1856 the arithmometer was included
among the recommended specialities advertised on the inner leaves of Cosmos. lO-figune
machines (5xOxlO) were priced at 250fr, and
Bulletin of the Scientific lnsmunem Society No. 52 (1997)
16-tiKures (Sx0x16) at 500ft. Franz Reuk~ux
(note 51, p.40) complained of the high price of
the machine in 1862 but the prices he quotes
are significantly less than 1856: the same 10
and 16-figuae machines were now only 15oft
and 500fr respectively. Additional models
wene also available to Reuleaux, though the
most expensive was still only 400ft.
45. Francorur (note 6), p.661.
,~. jofy (note 5), pp.130-1.
47. Instruction pour ~ servir de I'aritkmom~tre
(Paris, 1865). Copy with arithmometer in
NArodnl technick~ muzeum, Prague, inv. no.
6337. The 1852 boofdet (note 10) mentions only
Benoit, who produced the 1851 report on the
arithomometer for the Soci~t~ d'encouragement. Scbert's report of 1878 provides some
additional names (note 3), p.707.
48. Reproduction mchided with entry for inv.
M559 in the loose-leaf catalogue of the
Brunsviga collection (copy in Mathematics
Collection files at Science Museum, London).
49. [Exposition Universelle de 1862 J
Londres}, Section Franchise: C#,,iogue Officiel
(Paris, 1862), p.109 and Sebert (note 3), p.704.
50. Din[tiers polytechnisches]oun~l, 11 (1823),
p.121f., dted by von Mackensen (note 38),
p.100.
51. Franz Reuleaux, Die Thonsas~he Rechennmschine (Freiberg, 1862). The pamphlet was
extracted from Reuleaux's article in Der
Civilingcnieur, S (1862). The piece was also
republished in Dinglo's polytechnisches Journal,
165 (1862), pp.334-62 and a second edition
appeared in 1892.
52. Petzold (note 4), p.106. For the use of the
arithmometer in t r i g ~ l
tabulations,
see August lunge, Tafelder u,irklichen Ldn[teder
Sinus und Cosinus (Leipzig, 1864), preface.
53. Peggy Aldrich Kidweil, 'American scientists and calculating machines - horn novelty
to commonplace', Annals of the History of
Computin[t, 12 (1990), pp.31-40, see pp.32-34.
54. Report of the Twenty-Fourth Meeting of the
British Association for the Advancement of
Science; held at Lit~pool in September 1854
(London, 1855), 'Notices and abstracts of
miscellaneous communications to the sections', pp.l-2 and Cosmos, 5 (1854), pp.463-4.
55. In the discussion following C.V. Boys,
'Calculating machines', Iournal of the Societyof
Arts, 34 (1886), p.387, Thomas Ackland mentioned that he had bought a Thomas machine
in 1851.
56. Copy in Mathematics Collection Technical
File inv. 1980-1779, Science Museum, London.
The leaflet can be dated to either 1872 or 1873
from its reference to an as-yet-unpublished
paper given at the Society of Telegraph
Engineers (discussed below). ! shall refer to it
as the '1872 list'.
of Pnqcision (Princeton, 1995), pp.311-351, see
57. Brund to Adams, 18 March 1866, Bristol
Umvemty Library, Brunel Collection, Letter
Book Vll, f.106 (hereinafterBrund Collection).
71. Cited by Martin Camphell-Kelly, 'Largescale data processing in the Prudential, 18501930', Accounting, Business and FinancialHistory, 2 (1992), pp.117-139, see p.123.
58. Brunel to J. Dobson, esq., 27 March 1866,
Brunel Collection, VII, f.15.
59. Brunel to de Fontaine Moreau, 13 July
1868, Bnmel Collection, IX, 1.115.
60. Brunel to Froude, 31 May 1866, Brunel
Collection, VII, f.157.
61. Brunel to L. de Fontaine Moreau, 26
November 1867, Brunel Collection, VIII,
f.326. Brunel wrote to Froude about the
arrangement on the same day; ~ . , L322.
62. Brunel to Gamble, 14 June 1868, Bnax,q
Collection, IX, L99.
63. Bnmel to L. [de] Fontaine Moreau, 10June
1868, Brund Collection, IX, f.97.
64. Brune4 to de Fontaine Moreau, 13 July
1868, Brunel Collection, IX, ff.114-5.
65. Brunel to Captain Noble, I0 March 1869,
Brunel Collection, IX, 1.237. The 1872 list is
apparently mistaken in assigning Captain
Noble to the Postal Telegraph Offices. B n m d
addressed Noble at Armstrong's Elswick
Works at Newcastle; on Noble see David J.
Jeremy, Dictionary of Business Btography, 5 vols
(London, 1984-5), IV, pp.444-6. For Adie, see
Brune] to Adie, 28 December 1868, Brune[
Collection, IX, f.169 and 11 March 1868, Brunel
Collection, IX, L236. Adie is Patrick Adie, who
began a London offshoot of his father's
Edinburgh business in 1844. T.N. Clarke,
A.D. Momson-Low, A.D.C. Simpson, Brass &
G/ass (Edinburgh, 1989), pp.75-84.
66. Brunel to Captain Noble, 29 April 1869,
Brunel Collection,IX, f.284.
67. Science Museum, Mathematics Collection,
inv. 1868-I.The machine isengraved "S.& A. D.
S. K. MUS'. Kevin Johnson kindly confirmed
from the museum archives that the machine
was bought in Parison II January 1868 for £16.
pp.329-31.
72. Prudential Asmarance Company, CalculatinK Machine Papers. Prudential-owned arithmometers from the 1870s still survive:, see
figure 1.28 m Williams (note 1), p.50.
73. Henry Hadx, n in the discusmon to "rhorims T.R Bruce Warren, 'On the application of
the calculating m ~ h i n e of M. Thomas de
Colmar to electrical computations',/ournal of
tke Society of Telegr~,h En~neers, I (1872), p.165.
74. For the Times letter, see CamphelI-Kelly
(note 71), pp.127-8. Payment is recorded in the
Prudential Assurance Company Board Minutes, 19 January 1882. Several a r i ~
signed by EOiott Brothers sunqve, for example,
Science Museum, London, Mathematics Collection inv. 1989-636.
75. On this engine, see Lindgren (note 1),
pp.211-35. Note that Donkin's name appears
on the 1872 a r i t ~
list.
76. Public Record Office (PRO), RG129/2/
III, 29 January 1870. I am indebted to Doron
Swade for providing me with t T a n ~
of
this and other Treasury-GRO documents.
77. P R O RG2912/162, 28 July 1873.
78. PRO RG29/6/109, 5 August 1873. On
Sandford and his career m the Education
Department, see the Dictions. of National
B~,~.
79. PRO RG2912/250, 16 March 1877.
80. PRO RG2913/129 and RG2917/80 from
1893 and cf. Boys's paper (note 55) which
compares English arithmometers with the
inkmor workmanship of the Thomas machine.
81. Warren (note 73). The paper m pp.141-164
and the discu~ion appears at pp.164-8. Warran was electrician to Hca~:~,,r's Telegraph
Works, who appear in the 1872 list.
68. Transactions of the Devonshire Associ~tion for
the Admncement of Scwnce, Literature end the
Arts, 7 (1875), p.174, l owe this reference to
82. Stan Augarten, Bit by. Bit: an Illustrated
History. of Computers (London, 19841,pp.37-8.
Jackle Britton. The Cambridge Observatory
was listed as a purchaser in the 1865 edition of
the i n s ~
manual (note 47).
83. CI. Him (now 39), p.l13 on the machine's
relativelack of profitability.
69. For Bashh~rth, see Dict~anary of National
B~graphy, 1912-1921, pp.35-6. The reference to
the a r i t h ~
appears in his Supplement to
a Mathematical Treatise on the Motion of Proh'ctiles ( ~ o n , 1881), p.126.
70. Andrew Warwick, 'The laboratory of
theory, or what's exact about the exact
sciences.~, in M. Norton WLSe (ed.), The Values
Bulletm of the Scientific instnanent Society No. 52 (1997)
84. Jacomy-Regnier, Histoirt des m)mbres et de
1¢ nund,ratmn ra~'anique (Paris. 1855). pp.28, 58,
68.
Author's address:
Museum of the Histtn~. a~ fa'wnce
Bn~d Street
O~,,d o x l 3AZ
stephen.pohnst~@mhs.ox.ac.uk
21