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Ampère's Invention of Equilibrium Apparatus: A Response to Experimental Anomaly


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André-Marie Ampère's contributions to electrodynamics came at a late stage in an unconventional career. In 1820, he had reached the age of forty-five and had not as yet done any systematic research in physics. As a member of the mathematics section of the Académie des Sciences, his only significant contributions to the physical sciences had been some constructive criticisms of Fresnel's wave theory of light and three memoirs on chemical classification and gas theory. Meanwhile, his longstanding interests in metaphysics and epistemology had resulted in pointed methodological and philosophical attitudes which both motivated and structured his subsequent work in electrodynamics. Not surprisingly, events during the first few months of Ampère's research included many unplanned and unexpected encounters as this wildly enthusiastic theoretician grappled for the first time with the recalcitrant complexity of actual experimentation in an uncharted new domain.
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The British Society for the History of Science
Ampère's Invention of Equilibrium Apparatus: A Response to Experimental Anomaly
Author(s): James R. Hofmann
Reviewed work(s):
The British Journal for the History of Science,
Vol. 20, No. 3 (Jul., 1987), pp. 309-341
Published by: Cambridge University Press on behalf of The British Society for the History of Science
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BJHS, 1987, 20, 309-341
Ampere's Invention
of Equilibrium
A Response to Experimental
Andre-Marie AmpZere's contributions to electrodynamics came at a late stage in an
unconventional career. In 1820, he had reached the age of forty-five
and had not as yet
done any systematic research in physics. As a member of the mathematics section of the
Academie des Sciences, his only significant contributions to the physical sciences had
been some constructive criticisms of Fresnel's wave theory of light and three memoirs on
chemical classification and gas theory.' Meanwhile, his longstanding interests in meta-
physics and epistemology had resulted in pointed methodological and philosophical
attitudes which both motivated and structured
his subsequent work in electrodynamics.
Not surprisingly, events during the first few months of Ampere's research included many
unplanned and unexpected encounters as this wildly enthusiastic theoretician grappled
for the first time with the recalcitrant complexity of actual experimentation in an
uncharted new domain.
Historians have only recently begun to investigate this chaotic period in Ampere's
career; in general, there has been an excessive reliance upon the famous expository
memoir he published in 1826.2 The preliminary pages of that rich blend of conceptual,
mathematical and experimental argumentation have usually been glossed as Ampere's
attempt to imitate Newton's creation of gravitation theory through a 'deduction from
the phenomena'.3 This is, in fact, a fairly accurate rendition of the image Ampere
to broadcast in 1826; the general contour of this image should be clarified before its
sources are scrutinized in more detail.
Two highly suggestive experimental discoveries had provided a lasting foundation
for Ampere's efforts to create a new physics of 'electrodynamics'-the term he coined for
the dynamics of moving electricity. In July 1820, Hans Oersted showed that an electric
1 For a good discussion of why Ampere became interested in electrodynamics,
see K. Caneva, 'Ampere,
Etherians, and the Oersted Connection', British
Journal for the History of Science, (1980), 13, pp. 121-138.
2 A-M. Ampere, Theorie des Phenomenes ?lectro-dynamiques, Uniquement Deduite de l'Experience,
Paris, November 1826.
3 For some examples, see P. Duhem, The Aim and Structure of Physical Theory, reprinted, New York,
1974; A. Kastler, 'Ampere et les lois de l'electrodynamique', Revue d'Histoire des Sciences et Leurs Appli-
cations, (1977), 30, pp. 145-157.
* History Department, California State University-Fullerton, California, U.S.A. 92634.
In spite of whatever flaws remain, the present form of this essay owes much to the helpful criticism of David
Gooding, Rod Home and L. P. Williams.
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310 James R. Hofmann
current can change the natural orientation of a suspended bar magnet. During the
following September and October, AmpZere produced attractions and repulsions
wires conducting electric current; he attributed these phenomena to 'electrodynamic'
forces and argued that these forces were also responsible
for magnetic phenomena due to
internal electric currents within all magnetized bodies.
For reasons I shall address in due course, Ampere assumed that an adequate theory of
electrodynamic forces must include a force law expressing the attractive or repulsive
forces between any two segments of an electric circuit small enough to be considered
'infinitesimal' in comparison to the distance separating them. By 1826, he had assembled
an elegant and succinct derivation of his electrodynamic force law through the con-
ceptual and mathematical analysis of four carefully
chosen experimental demonstrations
of states of equilibrium.
Each of these demonstrations used a balanced set of electrodynamic forces to
produce a case of static equilibrium for a potentially mobile component of an electric
circuit. Assuming that an electrodynamic force acts along the line joining any pair of
circuit elements. Ampere applied the relevant laws of statics to provide a mathematical
statement about the observed state of equilibrium in each case. Interpretations and
applications of these equilibrium conditions in terms of infinitesimal
current elements
then provided the desired derivation of the electrodynamic
force law as a function of the
mutual orientation of any two elements and the distance between them. Such was the
formal and polished process Ampere presented in his 1826 memoir as a model exercise
Newtonian methodology.
There has never been any doubt that Ampere
had done considerable
spadework prior
to 1826. As Maxwell remarked in 1879:
We can scarcely
believe that Ampere really
discovered the law of action by means of the
he describes.
are led to suspect, what, indeed,
tells us himself, that he
discovered the law by some process
which he has not shown us, and that when he had
afterwards built
up a perfect
removed all
of the
scaffolding by which he
had raised
Historians have recently taken up the task of reconstructing Ampere's discarded
scaffolding. In particular, L. Pearce Williams and Christine
Blondel have tried to unravel
the chronology of the early events leading up to Ampere's discovery of electrodynamic
forces between electric currents.5 Blondel has provided an accurate survey of Ampere's
entire career in electrodynamics,6 and considerable attention has been given to Ampere's
study of induction between 1820 and 1822.7
4 J. Maxwell, A Treatise on Electricity and Magnetism, 3rd edn., 2 vols, London, 1891; reprinted,
York, 1954, ii, pp. 175-176.
5 C. Blondel, 'Ampere and the programming of research', Isis, (1985), 76, pp. 559-561; L. Pearce
Williams, 'What were Ampere's earliest discoveries in electrodynamics?', Isis, (1983), 74, pp. 492-508; L.
Pearce Williams, 'Reply to "Ampere and the programming of research"', Isis, (1985), 76, p. 561.
6 C. Blondel, A-M. Amp&re
et le Creation de l'Electrodynamique,
Paris, 1982.
7 J. Hofmann, 'Ampere, electrodynamics, and experimental evidence', Osiris, (1987), 3 (in press); E.
Mendoza, 'Ampere's experimental proof of his law of induction: i2ai ', European Journal of Physics,
(1985), 6, pp. 281-286; L. Pearce Williams, 'Why Ampere did not discover electromagnetic induction',
American Journal of Physics, (1986), 54, pp. 306-3 11; L. Pearce
Williams, 'Faraday and Ampere: a critical
dialogue', in: D. Gooding and F. James (eds), Faraday Rediscovered: Essays in the Life and Work of Michael
Faraday 1 791-1867, New York, 1985, pp. 83-104.
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Ampere's Invention of Equilibrium Apparatus 311
The topic of the present essay is quite different in that I am concerned with Ampere's
early experimental methods rather than any specific discovery as such. I intend to make
explicit how some of Ampere's most creative experimentation in 1820 set an important
precedent for his subsequent adoption of the equilibrium
experiment technique. Prior to
the middle of 1822 Ampere did not expect that this method could provide an adequate
means for a full derivation of his force law; his first set of equilibrium experiments was
not assembled until November 1825, and he continued to revise them thereafter. His
1826 memoir provides little information about how his initial responses
to experimental
novelty started this gradual implementation of a new experimental method. It is true that
Ampere did begin his research with a preference for the primarily deductive mode of
theory construction he eventually relied upon. Nevertheless, at the outset there was no
reason for him to suspect that such a procedure would ever become applicable to the
bewildering new domain of electrodynamics.
Ampere's experimental activities under these circumstances are intriguing
in several
respects. First, following his discovery of electrodynamic forces, Ampere's approach to
experimentation was almost always guided by his predetermined
tasks of specifying the
mathematical expression for his electrodynamic force law and the structure of the
electric circuitries he believed to exist within magnets. Thus, with rare but important
exceptions, Ampere did not engage in experimentation with the exploratory mentality
conducive to the pursuit of novelty for its own sake. Instead, his procedure was one in
which appropriate new phenomena were, quite literally, to be constructed and then
presented in an increasingly suggestive and clear manner so as to become readily
accessible demonstrations fostering the acceptance of Ampere's theoretical interpret-
ations. At the same time, as Ian Hacking has emphasized, 'experimentation
has a life of
its own';8 in his search for appropriate demonstrations, Ampere repeatedly encountered
novel experimental events which, malgre lui, he had to recognize as unexpected dis-
coveries. Secondly, the alacrity with which Ampere transformed seemingly anomalous
observations into bases for further theoretical progress
became the creative source for the
type of demonstrations that he eventually developed into the equilibrium experiment
This paper thus addresses the following questions concerning
the first
five months of
Ampere's research on his electrodynamic force law. The time frame within which the
questions are posed extends from September 1820 to February 1821; severe illness put a
halt to Ampere's systematic activity for several months thereafter. First, what were
Ampere's methodological views prior to 1820, and what bearing did they have on his
early experimentation in electrodynamics? What effect did the methods and goals of
other French physicists have on AmpZere's
conception of physical theory, and how did his
rivalry with physicists such as Biot influence the course of his early research? Most
importantly, how did Ampiere
transform initially anomalous experimental discoveries
into the demonstration that later became the prototype for his equilibrium experiment
technique? Finally, what indications are there that in 1821 Ampere
did notyet foresee the
full potential of the equilibrium method?
8 I. Hacking, Representing and Intervening, Cambridge, 1983, p. 150.
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312 James R. Hofmann
I. Ampere's methodological views prior to 1820
The most important source of information concerning Ampere's methodological views
just prior to 1820 is a set of lecture notes compiled for part of a course in logique he
taught at the Ecole Normale during 1817 and 1818.9 In particular, these notes reveal
Ampere's sensitivity to the logical structure of inferences intended to link scientific
theories to confirmatory experimental evidence. Ampere took great pains to distinguish
four different argumentative modes; he soon would put two of them into practice in his
own research in electrodynamics.
First, Ampere drew upon a long tradition to confront his students with yet another
application of the time-honoured terms 'synthesis' and 'analysis'.
He defined 'synthesis'
as a mode of reasoning that proceeds from relatively 'simple' premises to conclusions
that are more 'complicated'. 'Analysis', on the other hand, arrives at conclusions that are
more simple than the original premises. The relative simplicity or complexity of a
statement is dependent upon that of the state of affairs
it describes. States of affairs are to
be considered increasingly more complicated in-so-far as they are composite results of
many individual causal agents acting under various attenuating
For example, in the context of an imponderable fluid theory of electricity, a very
simple statement would be the claim that the force between two particles
of electric fluid
is inversely proportional to the square of the distance between them. On the other hand, a
claim that a large collection of electric fluid particles has reached a state of static
equilibrium on the surface of a sphere obviously describes much more complicated
circumstances resulting from the mutual interactions of many electric fluid particles.
Ampere next draws a second distinction between 'direct' and 'indirect' reasoning.
Direct arguments proceed from premises that have been acknowledged to be true; they
establish a conclusion that previously had been considered to be contingent. Indirect
reasoning takes a contingent hypothesis as its major premise and derives a conclusion
that can straightforwardly be recognized as true or false. Combining
this dichotomy with
that of analysis and synthesis results in four possible modes of reasoning:
indirect analysis, direct synthesis and indirect synthesis.
For the physical sciences, the most important example of indirect
is when a
physicist, for example, tentatively adopts a simple hypothesis and derives complicated
observable consequences from it that can be checked by experiment. In Ampere's
terminology, this would be indirect synthesis. On the other hand, Newton's presentation
of the universal law of gravitation is Ampere's favourite example of direct
analysis. That
is, one stage in Newton's argument involved taking as a premise
the approximate
the relatively complicated statement of Kepler's third law in order to derive the more
simple inverse square law for the attraction of each planet to the sun; he then could use
the approximately spherical shape of the planets to infer the even more simple inverse
square law for the gravitational attraction between any two arbitrarily
small volumes of
9 Ampere's notes for Lessons 25, 26 and 27 are most important and are to be found in the archives
of the
Academie des Sciences, carton 16, chemise 261.
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Ampere's Invention of Equilibrium Apparatus 313
Ampere made sure that his students realized that only after a preliminary stage of
exploratory discovery has been completed can textbook writers use direct synthesis to
give an axiomatic presentation of a theory for didactic purposes. The complex
phenomena encountered in experimental research require either direct analysis or
indirect synthesis as the only viable routes to the discovery and confirmation of simple
theoretical laws. Ampere thus concentrated on these two modes and made some
interesting remarks about his preferences. He pointed out that only in very rare cases
might it be possible to emulate Newton's paradigmatic use of direct analysis; more
commonly, recourse must be had to indirect synthesis and a theoretical claim must
tentatively be adopted as a hypothesis. Two of Ampere's comments on this stratagem
worth quoting.
Cette necessite
de changer
de methode n'est
pas moins evident
des qu'il s'agit de ... trouver
l'explication d'un phenomene que la nature nous offre dans toute sa complication.
La les
donnees etant par le fait meme plus compliques que les r6sultats qu'on cherche, la synthese
directe devient
et il faut bien recourir soit
a l'analyse
directe si on le peut, soit a la
synthese indirecte du tatonnement et des hypotheses explicatives. . . . Rappeler que pour
a la cause d'un ensemble de faits
il y a 2 marches-analyse directe, synthese
Aveu que la premiere
naturelle si l'on
pouvait l'employer-efforts inutiles
par quelques-uns
memes des
pour faire
These passages provide a clear statement of an important methodological priority
Ampere had adopted before beginning his research in electrodynamics.
From Ampere's
point of view, only de facto mathematical and physical complexity prevents scientists
from following Newton's exemplary deductive use of direct analysis. The inductive
confirmation of a hypothesis by repeated observation of its implications is less trust-
worthy; but this indirect synthesis is the typical pragmatic procedure
in science.
Looking ahead to Ampere's own work in electrodynamics, it is clear that his eventual
invention of the equilibrium experiment technique was fully in keeping with his pref-
erence for direct analysis. By deriving simple theoretical conclusions from complicated
but clearly demonstrated experimental circumstances, Ampere could claim to have
accomplished for electrodynamics the closest possible methodological correlation to
Newton's theory of gravitation. Prior to his successful invention of this technique,
Ampere was forced to rely upon indirect synthesis to confirm tentative hypotheses
through observation of their consequences. My primary project in this essay is to show
how Ampere's first recognition that equilibrium experiments might be a source for direct
analysis emerged from his reaction to anomalous results produced during his practice of
the hypothetico-deductive method of indirect synthesis. Ampere's enthusiasm for
deductive formalism based upon a small set of well-chosen experimental
was not typical of the French scientific community in which his arguments would be
scrutinized. But before turning to the 'Laplacian' scientific milieu in some detail, some
additional points should be made about the goals and structure
Ampere expected of a
physical theory.
10 Ibid.
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314 James R. Hofmann
First, as Kenneth Caneva has made clear,1'
by 1816 Amp&re
had adopted Fresnel's
luminiferous ether as an ontological basis for the unification of physics. From the time of
his earliest recorded thoughts about physics,-Ampere
had been dissatisfied
with the idea
of forces acting instantaneously through space to an object located 'at a distance'.12 One
reason for Ampere's sudden and enthusiastic activity in electrodynamics in 1820 was
that he hoped that it would offer new insights into the mechanics of an all-pervasive
composed of superimposed negative and positive electric
His ultimate
goal was
that optics, electrostatics and electrodynamics (including
would all become
domains determined by various types of etherial vibrations. Nevertheless, he recognized
that this ambitious project would have to be preceded by a determination
of the laws
governing directly observable phenomena. Thus, although the ultimate
goal of Ampere's
research programme was a reduction to an ontology of electric
fluids and the dynamics
their individual particles, he often used the term fait primitif or 'fundamental fact' to
refer to the force he claimed to exist between any two 'infinitesimal'
segments of an
electric circuit. These segments actually contained the motions of many electric fluid
particles, and the force between such segments thus was not truly 'primitive' from
Ampere's point of view. 13 Nevertheless, at this relatively
ontological level, Ampere
could still argue that his search for an electrodynamic force law was a natural
of the French tradition in physics established and promoted by Coulomb, Hauy, Laplace,
Biot and Poisson. This tradition deserves some detailed attention since the 'Laplacian'
response to Oersted's discovery set the context for Ampere's
own attempts
to link theory
to observation.
II. Laplacian physics and the Biot-Savart response to Oersted's discovery
A. Laplacian physics
In a series of thought-provoking essays during the 1970s, Robert Fox provided ample
reasons for historians to recognize 'Laplacian physics' as a distinct and important phase
in early nineteenth-century science.
14 The full range of accepted conclusions and disputed
questions generated by subsequent research in this area
need not be surveyed
here. I shall
clarify the issues that are of particular importance for Ampere's electrodynamics and
then focus on the Laplacian response to Oersted's 1820 discovery as carried out by
Jean-Baptiste Biot and F6lix Savart.
11 Caneva, op. cit. (1).
12 There are extensive manuscript notes on this subject preserved in the archives of the Academie des
Sciences, carton 10, chemise 203. They can be dated as written between 1801-1802.
13 Ampere emphasized this point in several publications including his famous 1826 memoir, op. cit. (2).
The most commonly cited version of this monograph is the slightly revised 1827 publication: 'Memoire sur la
theorie mathematique des phenomenes electro-dynamiques, uniquement deduite de l'experience .
Memoires de l'Academie Royale des Sciences de l'Institute de France.
Annee 1823, (1827), 6, pp. 175-387, on
p. 294.
14 R. Fox, 'The rise and fall of Laplacian physics', Historical Studies in the Physical Sciences, (1974), 4,
pp. 89-136; R. Fox, 'Scientific enterprise and the patronage of research
in France
1800-70', Minerva, (1973),
11, pp. 442-473.
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Ampere's Invention of Equilibrium
Apparatus 315
Although Laplacian physics was practised most actively between 1800 and 1820, it
owed much of its initial inspiration to Charles Coulomb's careful experimental
determination of the inverse square distance dependency laws for electric and magnetic
forces between 1785 and 1789. Thereafter, Haiiy, Laplace, Biot and Poisson became
spokesmen for what Biot called a renaissance de la ve'ritable physique.15 Following
Coulomb's example, this renaissance was promoted as a return to a rigorous physics
epitomized by Newton's theory of gravitation; its hallmark was to be the accurate
confirmation of mathematically formulated laws by quantitative experimental
measurements. In 1817, Biot gave the following summary of his conception of proper
scientific procedure in one of his influential textbooks:
L'etude de la nature physique,
consideree dans toute son etendue,
se reduit
toujours a ces
choses distinctes: l'observation des phenomenes;
la recherche
du mode
lequel ils s'accomplissent,
et qui est leur loi physique; enfin,
la determination des forces
abstraites et mecaniques
dont ils resultent
Laplacian physicists thus did not restrict themselves to the discovery of empirical
relationships governing directly observable phenomena; attractive and repulsive forces
were their most fundamental explanatory principles.
However, as the history of physics so amply demonstrates, explanations based upon
forces inevitably evoke further questions concerning the ontology from which these
alleged forces arise. In this respect, Laplacian physics underwent a major transition in
18 12. At that point Poisson published two important memoirs on electrostatics
in which
he calculated an impressively detailed set of consequences based upon the hypothesis of
inverse square-distance dependent forces acting between particles
of two imponderable
electric fluids. 17 The close match between these theoretical calculations and the extensive
data inherited from Coulomb made the existence of imponderable
fluids an integral part
of Laplacian physics thereafter. Earlier scepticism about the reality of unobservable
causes now gave way to a systematic attempt to repeat Poisson's success in electrostatics
within the domains of optics, heat and magnetism.
Biot, for example, had only been willing to accept the existence of imponderable
particles in optics prior to 1812; thereafter he became one of the most assertive pro-
ponents of the new point of view. In a passage written in 1816, he made an important
point about the distinct domains determined by the apparent
lack of interaction
the various imponderable fluids. For Biot, physics should be limited to the study of:
les phenomenes
produits par
les actions
invisibles, intangibles,
que l'6lectricite,
le magnetisme,
le calorique
et la lumiere.
jusqu'a present
15 J.B. Biot, 'Borda', Biographie Universelle, 5, (ed. Michaud), Geneva, 1812; 1854 edition, p. 60. For a
good discussion of the context for Biot's phrase, see E. Frankel, 'J.B. Biot and the mathematization of
experimental physics in Napoleonic France', Historical Studies in the Physical Sciences, (1977), 8, pp. 33-72.
16 J.B. Biot, Precis Ele~mentaire de Physique Experimentale, 2 vols, Paris, 1817; 2nd edn., 1821; 3rd edn.,
1824; quoted passage from 3rd edn., vol. 1, p. 5.
17 For a good discussion of the impact of Poisson's memoirs, see R.W. Home, 'Poisson's memoirs on
electricity: academic politics and a new style in physics', British
Journal for the History of Science, (1983), 16,
pp. 239-259.
18 For a thorough analysis of Poisson's contributions to the physics of ponderable matter, see D.H. Arnold,
'The Mecanique Physique of Simeon Denis Poisson: the evolution and isolation in France
of his approach to
physical theory (1800-1840)', Archive for History of Exact Sciences, (1983), 28, pp. 243-367; (1983), 29,
pp. 37-5 1; (1984), 29, pp. 287-307.
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316 James R. Hofmann
se distinguent par leurs effets, ou par les
conditions sous
lesquelles ils agissent, sans qu'on sache
encore s'il est possible de les reduire les uns dans
les autres,
leur etude doit necessairement
quatre divisions distinctes, en observant toutefois de faire ressortir avec
soin toutes les
qui pourrent servir un jour de les rapprocher.19
As became evident after 1820, this division of physics into disjoint domains was more
important to Biot than the above passage might indicate; his reaction to Oersted's
discovery would be guided by the presupposition that the electric and magnetic fluids do
not interact.20
However, before turning to Biot's confrontation with electrodynamics,
an important
methodological issue should be noted. We have seen how Ampere demoted the
hypothetico-deductive method of indirect synthesis to the status of a pragmatic
expedient to be adopted when the complexity of the observed
makes a direct
analysis impossible. On the other hand, Biot drew a distinction between the gradual
inductive discovery of empirical laws relating directly observable phenomena and the
hypothetico-deductive confirmation of more elementary forces pertaining
to unobserv-
able causes. During the height of the 1821 debates in optics and electrodynamics, Biot
summarized his views as follows:
L'observation, quelquefois
le hasard, decouvrent les
et determine
leurs lois
mais le dernier
elementaires qui
les produisent,
ne peut etre
mis en evidence
que par
la puissance
de la pensee.21
Biot thus expected the justification of elementary force laws pertaining
to magnetic
and electric fluids to come about through a successful match between measurements
calculations based upon speculative hypotheses. His exemplar was Poisson's electro-
statics, and he had no expectations that anything resembling Ampere's direct analysis
was an option for a practising physicist.
On the other hand, Biot's emphasis on 'elementary forces' paralleled Ampere's
demand for the discovery of a fait primitif as a causal basis for more complicated
phenomena within any experimental domain. Although Ampere ultimately hoped to
locate the most elementary causes of electric and electrodynamic
phenomena in oscil-
latory etherial motions, this project had to be preceded by the determination
of the laws
governing the directly observable effects produced by electric circuits. Within this
relatively crude ontological context, Amp&re argued that the 'fundamental fact' of
electrodynamics was a central force acting along the line joining any pair
of small current
elements; Biot opted for a transverse force produced by a current element acting on a
magnetic fluid particle. Biot's attempts to legitimate this claim should be discussed in
some detail since they created a hostile conceptual and methodological context for
Ampere's own research.
19 J.B. Blot, 'Lettre de Mr. Biot, membre de I'Academie
des Sciences,
etc. au Prof. Pictet, correspondant
l'Academie et l'un des redacteurs de ce recueil', Bibliotheque Universelle
des Sciences, Belles-Lettres,
et Arts,
(1816), 2, pp. 81-86, on pp. 84-85.
20 For example, see the following announcement written in November 1820: J.B.
Biot, 'Advertissement sur
la seconde edition du Traite de Physique 1le6nentaire
de M. Biot', Annales de Chimie et de Physique, (1820),
15, pp. 331-335.
21 J.B. Biot, 'Sur l'aimantation imprim6e
aux metaux par l'electricite en mouvement:
lu a Ia
de l'Academie des Sciences, le 2 avril, parM. Biot',Journal des Savans, (1821), Avril,
pp.221-235, on p. 235.
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Ampere's Invention of Equilibrium
Apparatus 317
B. The Biot-Savart response to Oersted's discovery
Although most French physicists initially were sceptical about Oersted's claim that an
electric current could change the orientation of a suspended magnet, Arago established
the legitimacy of the new effect at a public demonstration for the Academie des Sciences
on 4 September 1820. Oersted's report had not been clear about the magnitude of the
reorientation; during the next two weeks AmpZere
discovered that when the interference
of terrestrial magnetism is eliminated, the magnet takes an orientation normal to a line
drawn from its centre to the conducting wire.22
Biot's response to these events was quite in keeping
with his penchant
for quantitative
data as a necessary basis for the determination of relevant force laws. As he wrote in
retrospect in 1821:
La premiere
chose qu'il falloit
la loi suivant
la force
du fil
a diverses distances
de son axe.23
To determine how the magnitude of the Oersted effect varied with changes in the
initial conditions, Biot and Felix Savart24
magnetized a small steel needle and suspended
it in a horizontal plane. An appropriately located bar magnet cancelled
out the magnetic
effect of the earth, and the magnetized needle was then exposed to a long vertical
conducting wire located at a carefully measured distance. It was observed
that the needle
always came to equilibrium with an orientation perpendicular
both to the wire and to the
line joining the needle to the wire. To study this effect quantitatively,
Biot noted that just
as a pendulum can be used to measure the strength of the earth's gravitational force,
either the frequencies or the periods of the oscillations of the needle,
when displaced
its equilibrium position, can be used to compare the strengths of the force bringing the
needle back to its position of equilibrium for various separations of the wire from the
needle. The operative force is proportional to the square of the frequency or inversely
proportional to the square of the period.
In their first short publication, Biot and Savart
their results as follows:
A l'aide de ces procedes,
MM. Biot et Savart ont &e
conduits au resultat
qui exprime
eprouvee par
une mol6cule de magnetisme
ou boreal placee a
une distance quelconque
d'un fil cylindrique tres-fin
et indefini,
magn6tique par le
le point ou reside cette
menez une
a l'axe du
fil: la force
qui sollicite la mol6cule est
a cette
et a l'axe de fil.
Son intensite
est reciproque
a la simple
Biot and Savart obviously carried
out quite a complicated set of inferences
in order to
be able to offer the above statements as the 'result' of their observations. Most
importantly, they claimed that they had discovered that the wire exerts a force on
22 L.P. Williams has recently clarified this point; see Williams, op. cit. (5), 1983, p. 498.
23 Biot, op. cit. (21), p. 228.
24 Felix Savart published extensively in the areas of acoustics and elasticity. Biot helped him to become
established within the Parisian scientific community, and Savart's
interest in electromagnetism
seems to have
been limited to this early stage in his career. See S. Dostrovsky, 'Felix Savart', D.S.B., vol. 12, pp. 129-130.
25 J.B. Biot and F. Savart, 'Note sur le magnetisme de la pile de Volta', Annales de Chimie et de Physique,
(1820), 15, pp. 222-223, on p. 223; also published as 'Sur la mesure de l'action exercee a distance sur une
particule de magnetisme',Journal de Physique, de Chimie, d'HistoireNaturelle etdesArts, (1820), 91, p. 151.
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318 James R. Hofmann
individual particles of magnetic fluid; their actual measurements, of course, pertained
only to the directly observable effect produced on the entire magnetized needle. As
resolute champions of the two-fluid theory of magnetism, Biot and Savart assumed that,
although the two types of magnetic fluid particles were constrained within individual
molecular regions, the net effect of their polarized separation
within those regions would
be the same as that which would be produced by a concentration of one fluid near each
pole of the magnet. By approximating the distance from the wire to each of these poles by
its distance from the centre of the magnet, the experimentally determined action of the
wire on the magnet could be interpreted in terms of action on magnetic fluid particles
located at each pole. The observed inverse proportionality to distance was thus said to
apply to a force acting on individual magnetic fluid particles.
Following their presentations of these conclusions to the Academie on 30 October,
Biot and Savart carried out a second set of measurements
using wires still positioned in a
vertical plane but with a single bend at the height of the suspended magnet. Based upon
the slightly retrospective account Biot presented in April 1821, the new conclusions he
presented to the Academie on 18 December can be summarized as follows.26 First, the
initial set of data with straight wires now was specifically
as measurements of
a resultat compose brought about by the action of the entire wire on a particle of
magnetic fluid. Second, the inverse dependency of this total force with respect
to distance
from the wire could be shown to be a mathematical consequence of an inverse square
distance dependency for more elementary forces assumed to act upon the magnetic fluid
particle from each 'infinitesimal' segment of the wire. The second set of measurements
with bent wires then was interpreted as evidence that these elementary segmental
were also proportional to the sine of the angle formed at the point where a line drawn
from the magnetic particle to the wire segment meets the wire.
Biot's justification for these claims was an interesting combination of rhetoric and
error. First, he claimed that Laplace had 'deduced' the inverse square dependency
of the
segmental force from Biot's first set of data.27
More accurately, Laplace's claim was
simply a hypothesis confirmed by Biot's data; in Ampere's terms this was indirect
synthesis rather than direct analysis. Secondly, the angular
of the segmental
force did not really account for Biot's original report of his second set of data; he
corrected this several years later by altering the empirical
law he had used to summarize
his measurements.28 In any event, in spite of his claim that his conclusion about the
angular dependency of his segmental force had been 'analysed by calculation',29 Biot
again had been practising Ampere's indirect synthesis; he assumed that the segmental
26 To my knowledge, no direct report of Biot's 18 December presentation
has survived. Biot gave a fairly
detailed summary of both sets of measurements at the public session of the Academie on 2 April 1821, and he
published this discourse shortly thereafter; see Biot, op. cit. (21). Most of this publication was incorporated
into the second edition of Biot's Pr&cis, op. cit. (16), and was expanded into a much larger
version in the 1824
third edition.
27 Biot, op. cit. (21), p. 229.
28 Biot, op. cit. (16) 3rd edn., vol. 2, pp. 742-746; the relevant
passages from the 1821 and 1824 editions
are conveniently contrasted in Memoires sur l'flectrodynamique, vols 2 and 3 of Collection de Memoires
Relatifs a la Physique, 5 vols, Paris, 1885-1887; vol. 2, pp. 116-120.
29 Biot, op. cit. (16), 2nd edn., vol. 2, p. 123.
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Ampere's Invention of Equilibrium
Apparatus 319
force was proportional to the sine of the relevant angle and then derived a measurable
implication from this hypothesis. The second set of data he and Savart had gathered
used as confirmatory evidence. This data actually only directly pertained to the total
composite action of conducting wires on magnets. Biot's references
to 'deduction' and
'analysis' of more elementary forces were simply rhetorical attempts to lend an aura of
certainty to what were actually inductive confirmations of hypotheses. The systematic
quantitative procedure of this confirmation was precisely the indirect
synthesis Ampere
expected to be necessary in the new domain of electrodynamics.
Before turning to AmpZere's
activities in detail, Biot's ultimate ontological com-
mitments should be reiterated. Although he claimed to have discovered a mathematical
expression for forces assumed to act upon magnetic fluid particles
from each tiny section
of a conducting wire, Biot considered this to be only a preliminary
step towards a full
explanation based upon an understanding of 'une veritable aimantation moleculaire
imprimee aux particules des corps metalliques par le courant voltaique qui les
traversait.'30 The most elementary forces for Biot thus were assumed to act between
molecular fluid particles in the wire and in the magnet. Not surprisingly, Biot never
explained how a wire's 'molecular magnetism' was produced without violating the
conventional Laplacian prohibition of any interaction between electric fluid and
magnetic fluid. Instead, he concentrated upon arguing that his segmental force could at
least account for electrodynamic phenomena on a less fundamental level. Ampere's
fledgling attempts to create his own physics of electrodynamics thus took place in
competition with a powerful rival research programme headed by one of France's most
prestigious scientists.31
Ultimately, Biot and Ampere were determined to reduce electrodynamics to the
action of magnetic or electric fluid, respectively. Meanwhile, given that this issue could
not be resolved experimentally in 1820, the rivalry demanded a choice for one of two
alternative 'fundamental facts' as a temporary but important basis for explanation at an
ontological level that actually was not considered to be fundamental
or final.
With this context in mind, we should expect that as Ampere
searched for evidence for
his electrodynamic force law, he was also constantly alert for any opportunity to convert
initially perplexing experimental events into demonstrations readily
in terms
of his own research programme. This was indeed the scenario in which he took his first
step towards a direct analysis of his force law through the construction and inter-
pretation of equilibrium phenomena.
III. AmpZere's initial production of equilibrium
Now that the Laplacian conceptual and methodological context has been clarified,
Ampere's efforts to discover and justify a mathematical expression for his electro-
dynamic force law can be studied in detail. My primary goal is to explain how Ampere's
30 Biot, op. cit. (16), 3rd edn., vol. 2, p. 773, and as quoted in Memoires, op. cit. (28), vol. 2, p. 127.
31 The rivalry had become quite heated by the time of the annual public session of the Academie on 2 April
1821. Biot took the occasion to claim that Ampere's discovery of attractions and repulsions between con-
ductors should be understood in terms of the magnetic states of the conductors. See Biot, op. cit. (21).
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320 James R. Hofmann
encounter with experimental anomaly during 1820 was the instigation for his invention
of the apparatus that became an early prototype for the equilibrium experiment
technique he explicitly promoted during 1822. I begin with Amp&re's formulation of a
tentative hypothesis during October 1820. I describe his original plans to test the
implications of this hypothesis and his attempts to duplicate the action of magnets using
electric circuits. These efforts led to unexpected experimental
events which Ampere soon
construed in terms of what I refer to as his 'addition law' for electric circuit elements. On
4 December 1820, Ampere used this law as a premise in his first
public derivation of the
angular factor in his force law. During the following month, he invented an apparatus
designed to produce a suggestive state of equilibrium, and he argued that this
phenomenon should be interpreted as an experimental basis for the addition law. This
was the beginning of Ampere's gradual replacement of indirect synthesis by direct
analysis, a transition he did not advance further until over a year later. A brief chron-
ology of particularly relevant events is provided in an appendix.
A. Ampere's first force law hypothesis: October 1820
As Kenneth Caneva has argued in great detail,32
Ampere's enthusiastic reaction to
Oersted's discovery was facilitated by his lack of commitment
to Laplacian concepts and
institutions. Rather than try to incorporate the new effect into one of the disjoint
Laplacian categories of magnetism or static electricity, Ampere interpreted it as an
indication that a new type of force arises due to moving electricity.
Ampere, magnetic
fluid simply does not exist; instead, magnetic effects are produced by closed electric
circuits within planes normal to the axes linking the poles of magnetized bodies.
This implied that it might be possible to duplicate the interactions between magnetic
poles using conducting wires coiled into spirals; it was probably during such an investi-
gation that Ampere discovered the existence of attractive and repulsive forces between
linear wires bearing electric currents.33
By the 9 October meeting of the Academie des
Sciences, he used the apparatus shown in Fig. 1 to demonstrate an attraction between
parallel linear conductors bearing currents in the same direction and a repulsion when
currents flow in opposite directions. AB is a fixed conductor, and CD is free to swing on
pivots located at E and F.
In keeping with the reductionist mentality he shared with his Laplacian colleagues,
Ampere saw his next task to be the formulation of a mathematical law for an
electrodynamic force acting between any pair of electric circuit
small enough to
be considered 'infinitesimal' in comparison to measurable
In principle, such
a formula could be mathematically integrated over the path of any electric circuit,
32 Caneva, op. cit. (1) and Caneva, 'What should we do with the monster? Electromagnetism
and the
psychosociology of knowledge', in: E. Mendelsohn and Y. Elkana (eds) Science
and Cultures,
Sociology of the
Sciences, Dordrecht, 1981, 5, pp. 101-13 1.
33 See Williams, op. cit. (5), 1983 for evidence on this point.
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Ampere's Invention of Equilibrium
Apparatus 321
Annale, dFe (hAin ef
. PAyit yiz7 e N /
Rt y . F^
/ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7l
A L~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a
1. Amp'ere's
apparatus for demonstration
of forces
between parallel linear
including those AmpZere
believed to exist within magnets.
34 Precedents set in other
physical domains by Poisson, Biot, Laplace, Fourier and Fresnel
encouraged AmpIre's
unhesitating resolution of an electric current into a collection of elementary
The most important source of information concerning
his force law during October 1820 is one of the many fragmentary
manuscript drafts
composed during this period.3 From this document we learn that Amp'ere
assumed that
34 As early as the 8 January 1821 meeting of the Academie, Ampere proposed that the electric currents
within magnets might be confined to circuits around individual molecules. This was only presented as a
possibility at this point due to lack of experimental evidence and because Ampere
assumed that the summation
of these molecular currents would be equivalent to large scale currents to which he could more readily
apply his
force law. The notes for Ampere's lecture are preserved in the archives of the Academie des Sciences,
carton 8,
chemise 166.
35 This important manuscript fragment seems to be a rejected draft for the concluding part of the long
memoir Ampere eventually presented to the Academie on 26 December 1820: Ampere, 'Suite du memoire sur
l'action mutuelle entre deux courans electriques, entre un courant electrique
et un aimant ou le globe terrestre,
et entre deux aimans', Annales de Chimie et de Physique, (1820), 15, pp. 170-218. The manuscript is
preserved in the archives of the Academie des Sciences, carton 8, chemise 158. It has been partially edited in
C. Blondel, 'Sur les premieres recherches de formule electrodynamique par Ampere (octobre, 1820)', Revue
d'Histoire des Sciences et Leurs Applications, (1978), 31, pp. 53 -65.
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322 James R. Hofmann
the force should be an attractive or repulsive force directed along the line linking two
circuit elements.36 Secondly, he speculated that the force should vary as the inverse
square of the separation of the elements, 'conformement
a ce qu'on observe
pour tous les
genres d'actions plus ou moins analogues a celui-la'.37
For the special case where both elements are perpendicular
to the line connecting
them, Ampere drew some implications from his observations of the relative magnitudes
of the forces between finite circuit components with this orientation.
He had noticed that
the force was maximally attractive for parallel currents, became zero when they were
mutually perpendicular, and became increasingly repulsive when they are anti-parallel.
Ampere argued that the total force between finite circuit
components should thus include
a factor which was a function of odd degree in the cosine of the angle between the
directions of the two currents. The manuscript account then continues as follows:
Au reste, cette fonction du cosinus de l'angle
de la direction des deux courants
peut avoir une forme simple que quand
on considere
des portions
de ces
courants. I1 est probable
se r6duit alors a la premiere
de ce cosinus,
et c'est du
moins la premiere supposition
qu'il convient d'essayer
dans la comparison d'une hypothese
la loi des attractions et repulsions
les resultats
de l'experience.
Ampere then speculated further that, in the more general case where the two elements
are not perpendicular to the line joining them, the force should depend upon the angles a
and 18
which they make with this line. Also, the cosine of the angle y between two planes,
each of which passes through the connecting line and one of the elements, should replace
the cosine of the angle between the direction of the two currents which was argued
for in
the simpler case. The three angles a, ,8 and y are exemplified
in Fig. 2.
Although Ampere did not leave any record of the full mathematical expression he
constructed at this point, his original thoughts concerning
the dependency
of the force on
the angles a and /3
were probably those registered by Babinet in the Expose des
Nouvelles De'scouvertes sur le Magnetisme et l'Electricite.
Although not published until
early in 1822, the Expose' was almost completed by July 1821.39
In sections 15 and 16
Babinet included an analysis of how the electrodynamic force should vary as a function
36 When Ampere began teaching physics at the College de France in November 1824, he and Joseph
Liouville composed a long manuscript draft entitled 'Theorie mathematique des phenomenes electro-
dynamiques'. Although never published, this treatise includes a symmetry proof by Liouville in support of
Ampere's longstanding assumption that the electrodynamic force lies along the line joining two current
elements. The manuscript is in the archives of the Academie des Sciences, carton 11, chemise 208 bis.
37 Archives of the Academie des Sciences, carton 8, chemise 158; edited by Blondel, op. cit., (35) p. 64.
3 8 Ibid. A similar argument appears in one of Ampere's earliest publications in electrodynamics:
des memoires lus par M. Ampere a l'Academie des Sciences dans les seances
des 18 et 25 septembre,
des 9 et 30
octobre 1820', Annales Generales des Sciences Physiques, (1820), 6, pp. 238-257, on pp. 247-248.
39 A-M. Ampere and J. Babinet, Expose des Nouvelles D&ouvertes sur l'Electricite
et le Magnetisme de
MM. Oersted, Arago, Ampere, H. Davy, Biot, Erman, Schweiger, De La Rive, etc., Paris, 1822. Ampere
mentions the completion date in a 23 January 1822 letter to Faraday edited in S. Ross, 'The search for
electromagnetic induction 1820-1831', Notes and Records of the Royal Society, (1965), 20, pp. 184-219; on
pp. 217-218. Babinet composed most of the Expose but with important
additions and corrections
by Ampere.
A valuable set of proof sheets for the first nineteen sections has survived;
these provide considerable
insight into
Ampere's thinking during this period, particularly
in the case of passages which Ampere
did not correct at this
time but which he later realized were incorrect;
archives of the Academie
des Sciences, carton 11, chemise
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Ampere's Invention of Equilibrium Apparatus 323
Figure 2. Ampere's representation of the mutual orientation of two current elements: a, ,3
and y.
of the angle a, and his argument parallels the reasoning Ampere had applied to
observations of how the forces between finite conductors vary with the angle y. Babinet
concluded that the force between two current elements vanishes whenever one of them is
directed along the line connecting them.40 Ampere apparently had again drawn a
conclusion from his investigation of forces between circuit components large enough to
be individually manipulated. Combining this reasoning with the manuscript
of the dependency on cos y, it is very likely that as early as mid-October 1820 Ampere
concluded that the force between current elements was proportional to the following
r-2 sin a sin/ 3cos y. (1)
This would make the electrodynamic force vanish whenever a or ,B becomes zero, that
is, when at least one of the current elements is directed along the line connecting them.
It is clear that Ampere had arrived at this tentative hypothesis by relying upon what
he considered to be reasonable presuppositions and plausible conjectures suggested by a
few simple observations. The contrast between his procedure
and that of Biot is striking.
Nevertheless, at this point AmpZere
still expected that he too would necessarily have to
amass a large collection of quantitative data as confirmatory evidence; indirect
seemed to be the only applicable method of justification.
B. Ampere's initial plans to provide evidence for his hypothetical force law;
October 1820
With a plausible force hypothesis in hand, Ampere dedicated much of the second half of
October to designing and constructing experimental apparatus.
Unlike Faraday, Ampere
40 Ampere and Babinet, op. cit. (39), p. 19.
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324 James R. Hofmann
left no systematic daily record of his research.
A reconstruction of the chronology of his
activities must be based upon a judicious assessment of sketchy manuscript notes and
subsequent recollections that are not always entirely trustworthy. We do know that as
early as 25 September he had already started experimental investigations
of the second
major tenet of his electrodynamics, his conviction that magnetic phenomena are caused
by electric circuits in planes normal to the axis linking magnetic poles. Expecting to be
able to duplicate the action of magnets using appropriately designed electric circuits,
Ampere began by coiling conducting wires into spirals and helices. The planar spirals
were intended to imitate circuitry at the pole of a bar magnet, and helices represented the
circuitry of the entire magnet.
Ampere's earliest helices were balanced on a pivot like that of a compass needle;
perhaps as early as 25 September he found that this apparatus
as expected to
the presence of a bar magnet.41
This was encouraging, but Ampere could not detect any
corresponding response to the directive action of terrestrial
magnetism. Suspecting
friction was preventing his helix from rotating, Ampere switched to a more mobile
suspension by late September.42
As shown in Fig. 3, the helix now is centrally suspended by a vertical
extension of the
same wire that makes up the helix. This is accomplished using a circuit
in which the helix
Figure 3. One of A
mpere'5 axially compensated helices.
3. One of Ampere's
41 Ampere, op. cit. (38), p. 240, and 'Suite de memoire sur I'action mutuelle
entre deux courans electriques,
entre un courant electrique et un aimant ou le globe terrestre,
et entre deux aimans', Annales de Chimie et de
Physique, (1820), 15, pp. 170-218; on p. 172.
42 Ampere, op. cit. (41), 'Suite', p. 173.
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Ampere's Invention of Equilibrium
Apparatus 325
is assembled using two glass tubes. After descending vertically to the central point of
suspension, the wire goes inside one of the tubes and passes along its axis to the end of the
tube. There it emerges and is wrapped around this tube so as to return to the central
point. The wire is then wrapped around the second tube, enters the end of the tube, passes
back along the axis of the tube to the central point again, and then descends vertically.
The circuit thus includes a two-part helix enclosing an axial current flowing in the
direction opposite to the longitudinal components of the helix spires. Ampere assumed
that neither the axial current nor the longitudinal components of his helix spires would
interfere with the earth's directive action on the circular currents of the helix which were
intended to duplicate the circuitry of a bar magnet.
Nevertheless, in spite of its greater mobility, this device also failed to respond to
terrestrial magnetism; Ampere thus was confronted by a serious anomaly for his theory
of magnetism.
This situation persisted during the first two weeks of October, the period in which
Ampere formulated his initial force law hypothesis. By the middle of the month he had
designed an apparatus to start testing the accuracy of his formula, and he described his
plans in a manuscript draft that he probably composed late in October. Some of these
passages are worth quoting in length.
C'est sur ces considerations generales que j'avais construit une expression de l'attraction de
deux courans infiniment petits qui n'etait a la verite qu'une hypothese, mais la plus simple qu'on
put adopter,
et celle par consequent qu'on devait d'abord essayer. J'ai cherche a en tirer les effets
qui devait en resulter, tant pour des courans electriques
mais d'une grandeur finie,
que pour des courans circulaires
comme ceux que j'ai montres
exister dans les aimants
et pour les courans qui ont lieu
dans des
de cuivre
en helice, a cause des
que j'avais
faites sur cette derniere
sorte de courans. Je me proposais
les resultats
de ces calculs avec des
experiences oui
l'intensite d'action
de deux courans
rectilignes, (d')une longeur
finie et dont
l'angle pouvait
varier a volonte;
J'avais construire pour
appareil que j'ai montre
le 17 octobre demier
et Gay-Lussac, je m'en suis procure
un autre
observer l'action de deux
Les experiences que j'essayai
avec ces deux instruments
me firent
deux faits
nouveaux qui en compliquaient
les resultats
et m'obligerent par consequent
a suspendre
verifications qu je m'etais propose
de faire, a I'aide
de ces appareils,
des raultats de mes
Both of Ampere's deux faits nouveaux were of major importance
for his subsequent
research; in each case a discovery resulted from the unexpected behaviour of new
apparatus. One of these discoveries became the instigation for Ampere's interest in
equilibrium demonstrations. His other discovery should be discussed first, however,
because this will make clear how Ampere originally intended
to accumulate evidence for
his force law hypothesis in October.
The apparatus involved was the one AmpZere
claims to have shown to Biot and
Gay-Lussac on 17 October. It was similar to that shown in Fig. 1 except that the
originally fixed conductor AB was replaced by one that could be given a variable
43 Ampere, Archives of the Academie des Sciences, carton 8, chemise 158; edited by Blondel, op. cit. (35),
p. 65. A revised version of part of this passage appeared in Ampere's 1820 memoir, op. cit. (41), p. 182.
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326 James R. Hofmann
orientation in a vertical plane.44
By varying the orientation of this conductor, Ampere
intended to compare observed effects on the mobile conductor CD with calculations
based upon the application of his force hypothesis. However, during his preliminary
investigations he was surprised to see the mobile conductor influenced by terrestrial
magnetism; he quickly realized that his helix devices had failed
to respond
in this way due
to their small radial dimensions.45
A serious anomaly thus was resolved by a discovery
using apparatus designed for an entirely different purpose. Subsequently, in order to
compensate for the magnetic action of the earth on large suspended current loops,
Ampere simply used pairs of loops traversed by currents
in the proper directions so that
the torques produced on the two loops by terrestrial magnetism are in opposite
directions. Using this method he designed a replacement for the first uncompensated
apparatus he had shown Biot and Gay-Lussac on 17 October; thus, he was in a position
to settle down to a laborious comparison of calculations and data which would hopefully
provide confirmatory evidence for his force hypothesis. There is no indication that
Ampere ever put this project of indirect
synthesis into practice. Instead, his research
quite a different direction due to the second of the faits nouveaux he probably discovered
shortly after 17 October.
C. Anomalous helices and Ampere's addition law: October-November 1820
To review, on 9 October Ampere had publicly displayed repulsions and attractions
between linear conductors using the apparatus shown in Fig. 1. Secondly, perhaps as
early as 25 September he had been using centrally suspended helices coiled around axial
currents, as shown in Fig. 3, to produce the expected rotational reorientation of a helix
due to the attraction or repulsion of one of its ends by the pole of a bar magnet.
At some point during the hectic month after 25 September, AmpZere also attempted to
demonstrate how the mutual action of two helices duplicates
that of two bar magnets.
left no record of when he did this for the first time; in his most detailed discussion of the
subject he reported that he made the test by using helices in place of the linear conductors
in the apparatus shown in Fig. 1.46 Although this instrument was not shown to the
Academie until 9 October, it is possible that Ampere built it and modified it with helices
at some point during the preceding two weeks. An early date is suggested by Ampere's
report that he had made the resulting observation 'long-temps avant d'en connoitre la
cause'.47 On the other hand, in what is probably the earliest relevant
44 Ampere, op. cit. (41), p. 182.
45 Ibid.
46 Ampere, op. cit. (41), p. 173.
47 Ampere, 'Notes de M. Ampere sur les lectures qu'il a faites a l'Academie des Sciences', Journal de
Physique, de Chimie, d'Histoire Naturelle et des Arts (abbreviated hereafter
as Journal de Physique), (1820),
91, pp. 166- 169; on p. 168. Ampere's claim about this observation and much of the rest of the chronology in
'Notes' were repeated in G. de Laumont, 'Note sur les experiences electro-magnetiques
de MM. Oersted,
Ampere et Arago, relatives a l'identite de l'aimant avec l'electricite', Annales des Mines, (1820), 5, pp.
535-546; on p. 544. Ampere identifies Laumont as the author of this unsigned report in a 21 February
letter to Roux-Bordier; Correspondance du Grand Ampere, L. de Launay (ed.), 3 vols, Paris, 1936-1943
(abbreviated hereafter as Correspondance), vol. 2, p. 567.
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Ampere's Invention of Equilibrium Apparatus 327
Ampere implies that this observation gave him the second of the faits nouveaux that
delayed his plans to verify calculations based upon his hypothetical force law.48 Since
Ampere explicitly says that he showed the apparatus responsible for one of these 'new
facts' to Biot and Gay-Lussac on 17 October, this seems to imply that neither of the two
discoveries took place until after that date. In short, the available evidence
does not allow
any clear-cut determination of the date of Ampere's
with two helices; the
reference to 17 October and the apparatus involved make the second half of October a
plausible conjecture.49
Ampere obviously was not concerned about leaving a precise chronology of his early
research. In the present case this is particularly unfortunate;
Ampere's second 'new fact'
constituted a serious anomaly for his conviction that magnetic phenomena could be
duplicated using spirals and helices. Much to his surprise,
when he replaced the linear
conductors in the apparatus of Fig. 1 by simple helices wound around glass tubes without
axial currents, he found that the two parallel helices duplicated the interactions of two
linear currents rather than two bar magnets. That is, they attracted each other when
Ampere expected them to repel and vice versa. AmpZere's
reaction to this discovery was
typical of his general attitude towards experimental
novelty. Considered simply as a 'new
fact', the unforeseen event would have held little in interest for him if it had not violated
his theoretical expectations. Faced with an apparently
serious anomaly, AmpZere did not
publicize it until he could produce other phenomena to bolster an argument
for how the
anomaly could be defused and transformed into confirmatory
This process began when Ampere noticed how the misbehaving
helices differed from
those he had been using hitherto. Up to this point, Ampere had assumed that, when he
coiled a wire into a helix to imitate a magnetic circuitry, the longitudinal dimension of
each spire was too small to have any noticeable effect. Probably during the last week in
October or the first week in November, Ampere decided that this assumption had been
incorrect; he now argued that the unexpected behaviour of his helices was due to the
cumulative effect of the longitudinal components of the spires being equivalent to a linear
current along the axis of each helix. In apparatus such as that shown in Fig. 3, Ampere
had unwittingly compensated for this longitudinal current by running a current back
down the axis of the helix in a direction opposite to that followed by the longitudinal
components of the spires. He had done this simply to implement his new suspension
method or, as he put it, 'sans que j'en prevu les avantages'.50
But when Ampere replaced
the linear currents in the apparatus of Fig. 1 with helices, he had no reason to include
compensating axial currents. In this situation, since the radii of his helices were relatively
small, Ampere realized that the interaction between the longitudinal components of the
48 See the quoted passage referenced by (43).
49 L. Pearce Williams has argued for a 25 September date but can cite no textual evidence. Why would
Ampere say that his anomalous discovery suddenly delayed his plans to test his force law hypothesis if he made
that discovery prior to the detection of electrodynamic forces between linear currents?
As always, it is possible
that Ampere simply confused the order of his own discoveries. For further
discussion of this issue, see Williams
and Blondel, op. cit. (5).
50 Ampere, op. cit. (41), p. 176.
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328 James R. Hofmann
spires of the two helices became predominant over the radial circular
components and
thus had produced an effect equivalent to an interaction between two linear currents.
This was the argument Ampere presented to the Academie on 6 November 1820. He
realized that his reasoning hinged upon the legitimacy of treating each of the 'portions
infiniment petites'51 of an electric current as if it were made up of distinct components,
and then determining what force would be contributed by each individual component
treated in isolation from the others. The legitimacy of adding together
forces imagined
be produced by various components of the elements of an electric current became a
permanent principle of crucial importance for the mathematical
expression of Ampere's
electrodynamics. He always referred to it as a loi, and I shall call it Ampere's 'addition
Unfortunately, Ampere's initial statements of this principle
were far from clear. This
was partially due to the fact that, by the time Ampere presented
the law to the Academie
on 6 November, his thoughts were already leaping ahead to possible applications. He
naturally realized that he had to present experimental
evidence in support of the addition
law; simultaneously, however, he was already trying
to incorporate
the addition law into
a derivation of the angular part of his force law. The experimental
project called for a
clear, concise statement of the law in question followed by experimental evidence of
obvious confirmatory value. But Ampere's impatience to use the law as a premise for
derivational purposes infected his early terminology with the ambiguities he was
struggling with on the more abstract level of mathematical idealization. Further study of
Ampere's addition law requires us to penetrate the smokescreen of assertive rhetoric
about 'facts' and 'laws' that surrounded his gradual creation of a new conceptual
framework. This calls for a brief digression in order to clarify
the issues at stake.
Throughout the month prior to 6 November, AmpZere
had been grappling
with the
central theoretical concept of his electrodynamics, namely, the idea of a segment of an
electric current that could be considered 'infinitely small' in comparison to measurable
magnitudes but to which a three-dimensional direction could also be assigned. His
explanation of anomalous helix behaviour had relied upon a further resolution of
current elements into components; it is not surprising
that Ampere
had difficulty
explaining the meaning of this operation. First of all, even 'infinitely small' circuit
segments were assigned lengths in order to represent
them geometrically.
For Ampere,
these lengths were a relative measure of the number of elementary
molecular processes
taking place within a current segment at any instant; these are the oscillations of the two
electric fluids responsible for the electrodynamic forces contributed by the segment.
Thus, as Ampere wrote in an 1820 draft,
... une portion
une action
a sa longeur,
la subdivisant
en un nombre
de parties egales,
son action est la somme
des actions
de toutes ces parties, lesquelles
entre elles ...52
Hopefully, the idea Ampere tried to convey on 6 November was that the force in any
direction due to an infinitely small current
element was equivalent
to a sum of individual
51 Ampere, op. cit. (41), p. 174.
52 Ampere, Archives of the Academie des Sciences, carton 8, chemise 158. For one of Ampere's fullest
published discussions of this issue, see Ampere, op. cit. (13), pp. 199 and 296-302.
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Ampere's Invention of Equilibrium
Apparatus 329
forces in that direction when these forces are imagined to be produced by the components
into which the original element has been resolved.53
Drawn geometrically,
the length of
each component would represent the maximum strength
of the force it could exert when
parallel to another current element at a specified distance.
In addition, however, Ampere also wanted his forces to be proportional to the
'intensity' of electric currents. This quantity would represent
the number of molecular
processes taking place at any point in the circuit during
a given unit of time; intensity thus
does not correspond to the length of Ampere's geometric depictions of current elements.
It is not clear that Ampere himself ever seriously misunderstood this distinction; his
instinctive insight into the implications of his mathematical models seems to have been
unimpaired by the ambiguous language that persisted even in the initial published
version of the derivation he presented on 4 December.
What we can be sure of is that Ampere's early statements of his addition law so
thoroughly confused current element 'length' with current 'intensity' that few of his
readers could have made much sense of them. For example, in one of his earliest and most
detailed published discussions of the law, Ampere wrote that in order to understand
... il faut
ligne representant
grandeur et
direction la
de deux forces
qui sont semblablement
representees par
deux autres
et supposer,
directions de ces trois lignes,
de courans
dont les
soient proportionnelles a leurs
La loi dont il s'agit
consiste en ce que la
de courant
electrique, dirigee
resultante, exerce,
que se soit, sur un autre courant ou sur un
une action
attractive ou repulsive egale a celle
qui resulterait,
dan la meme direction,
de la reunion des deux portions
de courans
suivant les composantes.54
If one is not misled by the preliminary comments about 'intensities',
the statement of
the addition law in the last sentence of this passage is fairly accurate. At the 6 November
meeting of the Academie, Ampere tried to provide experimental evidence for his law
using the helices that had suggested it. According to his recollections of this meeting, he
gave a helix a compensating axial current and showed that the earlier anomalous
attractions and repulsions now were cancelled out so that his apparatus remained
stationary in a state of equilibrium. Ampere left no detailed record of how this
demonstration was carried out. He may have used some combination of the apparatus
shown in Figs 1 and 3, or he may have wrapped a helix around a vertical glass tube.55
Our ignorance on this point is unfortunate because this may well have been Ampere's
first encounter with the type of static situation that he would rely upon in his subsequent
53 To my knowledge, no immediate record was made of what Ampere said at the 6 November meeting of
the Academie. For what are probably the earliest recorded recollections by Amp6re
himself, see Ampere, op. cit.
(47), p. 168. A page of Ampere's notes for his presentation is in the Archives of the Academie des Sciences,
carton 8, chemise 160.
54 Ampere, op. cit. (41), p. 174.
55 In Ampere's most detailed description of his demonstrations, he refers to an instrument of the type
shown in Fig. 3; Ampere, op. cit. (47), pp. 168-169. For a few additional details, see Laumont, op. cit. (47), pp.
543-546; Ampere, op. cit. (41), pp. 175-176 and 208-209; and a set of notes for Ampere's 26 December
1820 lecture to the Academie, Archives of the Academie des Sciences, carton 8, chemise 164.
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330 James R. Hofmann
equilibrium experiments. Considering how many issues were on Ampere's
mind at this
time, it is not surprising that he did not immediately attribute
any special significance
this particular observation. He apparently spent most of his lecture on 6 November using
the apparatus of Fig. 3 to show how a compensated helix interacts as expected with bar
magnets and compass needles.
At any rate, we can conclude that Ampere's initial demonstrations in support of the
addition law were examples of the hypothetico-deductive mode of reasoning Ampere
called indirect synthesis; effects produced using compensated helices confirmed the
implications of the addition law and Ampere's theory of magnetism. But the state of
equilibrium Ampere observed with one of these helices also set a precedent that he would
build upon several weeks later.
Meanwhile, Ampere realized that he had to respond to the rival Laplacian inter-
pretation of Oersted's discovery as presented to the Academie by Biot and Savart on 30
October. As part of this response, he used the addition law to present his first public
derivation of part of his electrodynamic force law.
D. Ampere's first public discussion of his force law: 4 December 1820
Although by 1826 Ampere had at least some justification for claiming that he could
derive his force law from a well-chosen set of equilibrium experiments,
this certainly
not the case in 1820. On 4 December he presented a derivation of the angular factor in
the law using symmetry arguments and his addition law. The full details of this deriva-
tion are not relevant to my concern to clarify how investigations of the addition law
stimulated Ampere's gradual invention and application of the equilibrium technique. At
this point I shall simply summarize the general structure and presuppositions of
Ampere's argument and explain how it relied upon the addition law. This will establish
the context for Ampere's attempts to improve the experimental
basis for the addition law
and justify his mathematical manipulations of idealized current
elements. As will soon
become apparent, Ampere's 'derivation' was an artful combination of idealization,
mathematics and approximation. His invention of the equilibrium experiment technique
during the following eighteen months was directly inspired by his extended efforts to
legitimate controversial stages in his argument.
I have already mentioned that Ampere's 4 December derivation concerned only the
angular factor in his formula. At this time he simply continued to assume that the force
would include a separable inverse square function of the distance between two current
elements.56 Secondly, he also assumed that the force would act along the line joining the
elements and that, when the direction of one of the two elements is reversed,
the mutual
force also reverses its direction but retains its original magnitude. He used the last of
these assumptions to argue for a useful symmetry principle: the electrodynamic
between two current elements should vanish when one element is located in a plane, that
56 Ampere, 'Note sur un Memoire lu a l'Academie royale des Sciences,
dans la seance
du 4 decembre 1820',
Journal de Physique (1820), 91, pp. 226-230.
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Ampere's Invention of Equilibrium
Apparatus 331
passes through the centre of the other element
and cuts it at a right
angle.57 Like
addition law, this symmetry
principle applies to the
of inflniment
petites portions of a circuit
depicted for mathematical
purposes as tiny
directed line segments.
At the Academie on 4 December,
Ampere presented a derivation of the angular
in his force law using the above
principle and
his addition
law. He began by
giving two current
elements a mutual
determined by the three angles
a, f8
and y, as shown in Fig. 2. He then resolved each
element into components along
conveniently chosen directions and considered
the forces between
all possible
pairs of
components when one component
is chosen from each of the two current
Geometrically, the components of a current
element have no common
point of inter-
section; they only combine to form
the total
a process
that now would
be called vector addition.
For the
of his derivation,
the components
of each element to be slightly
so that all
three of an
components could be depicted
as having their
midpoints at
the point
chosen as
the midpoint of the element itself. This was justified by the relatively
involved in comparison
to the distance between
the two current
With his components
in this way, Ampere
could apply
his symmetry
principle to conclude that there were no forces between some
of components;
then invoked the addition law to add together
the remaining
forces. The
force between two current elements is given by the following
g and
h are
the current
k is an undetermined
r-n is
the distance
which AmpZere
to be such
n = 2,
a sin:3 cosy+k cos
a cos,8). (2)
This expression
was more complicated
the hypothesis
adopted in October; it included
an additional term
by the magnitude
of the
parameter k which was left undetermined
by the derivation
on 4
In physical
k represented
the relative
of the
collinear current elements in comparison
to the force that would exist if they were
and separated by the same distance.58
During the remainder of December, Ampere
on the basis of some limited
evidence that k was small
to be treated
in comparison
to measurable
reduced his force
law to the form of his initial
and Ampere
to believe
that this truncated
was correct
1822. At that point an anomalous
a renewed
of the
general formula
(2) resulting
in the discovery
k = -%.59
57 Ibid., pp. 226-227. A more detailed argument is provided in a manuscript
draft for Ampere's memoir:
Archives of the Academie des Sciences, carton 8, chemise 162.
5 8 Ibid., p. 229. Ampere adopted the notation of n and k for his two parameters
during 1821. He originally
simply used r- for the assumed distance dependency and wrote the parameter
k as a ratio n/m to express the
fact that it determines the relative strength of two forces.
59 This point is discussed in detail in J.R. Hofmann, 'The great turning point in Andre-Marie Ampere's
research in electrodynamics: a truly "crucial" experiment', 1982 Ph.D. dissertation, University
of Pittsburgh,
University Microfilms order no. 8318183.
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332 James R. Hofmann
However, in December 1820 these later developments were far in the future. At this
point it was imperative that Ampere devote attention to the experimental
basis for the
addition law; this was the problem that soon fostered
his production
of new equilibrium
E. Ampe're's first equilibrium apparatus: December 1820-January 1821
During the month following the 4 December meeting of the Academie,
with two closely related projects. First, because Biot and Savart were promoting their
own Laplacian programme in electrodynamics, Ampere devoted considerable
energy to
what turned out to be unsuccessful attempts to design a decisive experimental
test that
would discredit their approach in favour of his own.60 Secondly, when these efforts
resulted in an acknowledgment that the observable implications of the two programmes
were presently indistinguishable, this amplified Ampere's realization that he needed to
call upon a new mode of argumentation if his own conception of the fait primitif of the
electrodynamic domain was to be accepted as the correct
In particular, Ampere had to motivate the acceptance of his addition law, a crucial
premise in his derivation of the angular factor in the electrodynamic
force law. In view
of Ampere's predisposition for direct analysis, it is not surprising
that he thought of
improving the design of one of the experiments he had used in his initial presentation of
the addition law to the Academie on 6 November. This had been his demonstration
an axially compensated helix does not exert any of the forces to be expected from a linear
current. Although Ampere presumably performed or at least described such an
experiment for the Academie on 6 November, the fact that he never published an
accurate description of the original experiment is indicative of the chaotic state of affairs
he sought to remedy during the following December.
Ampere's project was determined by the mathematical technique
he had used in his
4 December derivation. How could he provide a readily repeatable
demonstration that
could be interpreted as a legitimization for a mathematical analysis of the force
attributed to a current element as if this force was a sum of forces produced by
geometrically depicted components of the original element?
This was the problem that
soon generated Ampere's interest in equilibrium phenomena. Clearly, there would
always be a gap between physically manipulated circuitry
and the idealized
geometry of
infiniment petites current elements. Ampere's task was to make this gap relatively
easy to
cross by means of an experimentally stabilized stepping-stone.
Although we do not know how Ampere went about presenting
his ideas verbally,
publications and notes leave a fairly clear record of his strategy. First, the disastrous
confusion of current element length and current intensity was purged from subsequent
statements of the addition law. For example, late in 1820, when Gillet de Laumont
composed an exposition of Ampere's research,
he relied
heavily upon passages
written by
Ampere for his own publications. In the description of the 6 November presentation
60 The primary sources for these arguments are the unpublished manuscripts pertaining to Ampere's
lectures to the Academie during December 1820 and January 1821: Archives of the Academie des Sciences,
carton 8, chemises 162, 163 and 166. They are discussed in Hofmann, op. cit. (59).
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Ampere's Invention of Equilibrium
Apparatus 333
the addition law to the Academie, Laumont
replaced Ampere's
original phrase,
infiniment petites de courans electriques, dont les intensities
leurs longueurs',61 by a much more accurate reference to, 'courans electriques dont les
forces attractives ou repulsives sont proportionelles a leurs longueurs'.62
This certainly was a more correct statement of the significance
attributed to
the lengths of his geometric representations of current elements. But in addition to this
conceptual clarification, Ampere decided to formulate an experimentally testable
assertion that he hoped would readily suggest the necessary
transition from experience
his idealized mathematical model. In passages published early in 1821, he claimed,
somewhat misleadingly, that the addition law 'se reduit a' the following statement:
Si l'on fixe la direction d'un courant
electrique deux points
rapproches, et qu'on
substitue 'a la petite
portion de courant comprise
entre ces points une
autre portion
de ce meme
courant, suivant une ligne
pliee ou contournee d'une
quelconque, mais se termninant
aux memes points
sans s'en ecarter
nulle part a une
distance finie,
cette substitution ne
en aucune maniere
exercee dans quelque
direction que
ce soit par la petite
portion de
courant que l'on considere, sur une
autre portion de courant
electrique eloignee de la premiere
d'une quantite finie.63
This assertion was in fact a testable claim about wire segments large enough to be
manipulated experimentally. The phrase 'infiniment rapproche's'
can simply be para-
phrased as 'very close together in comparison to other lengths or dimensions of the
circuit'. The addition law itself actually applied to the idealized geometry of current
elements and could not be argued for directly; Ampere thus was hoping that it would be
accepted as an obvious 'deduction' if he could provide a striking demonstration in
support of its experimentally testable analogue.
Ampere made this project public at the 26 December meeting of the Academie.
According to the surviving manuscript notes for Ampere's presentation, he stated the
testable assertion as quoted above and then described the apparatus he had designed,
'pour m'assurer directement de l'exactitude de cette loi'.64 Ampere's own sketch is
shown in Fig. 4. EG and FH represent two glass tubes equidistant from a central
point N
which acts as a point of suspension for either a mobile linear
segment or, as shown
in Fig. 4, a small magnet. Either linear or slightly bent conductors are to be inserted in
grooves inside the glass tubes. Ampere's description of the experiments he planned to
perform is worth quoting because this is probably the message he conveyed to the
Academie on 26 December.
verification de la loi dont
je viens
de parler consiste a s'assurer
la substitution
d'un de ces
I'autre dans
une meme rainure ne change
a I'action
61 Ampere, op. cit. (41), p. 174.
62 Laumont, op. cit. (47), p. 544.
63 Ampere, 'Note sur deux memoires lus par M. Ampere a l'Academie royale des Sciences,
le premier
la seance du 26 decembre 1820; le second dans les seances des 8 et 15 janvier 1821', Journal de Physique,
(1821), 92, pp. 160-165; on p. 161. The same passage appears in Ampere, 'Exposition du moyen par lequel il
est facile de s'assurer directement, et par des experiences precises, de 1'exactitude
de la loi des attractions et
repulsions des courans electriques, suivie de quelques observations sur cette loi. Memoire lu le 26 decembre
1820', Annales des Mines, (1820), 5, pp. 553-558; on p. 554.
64 Ampere, Archives of the Academie des Sciences, carton 8, chemise 164.
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334 James R. Hofmann
i Ig htXl9
Figure 4. Ampere's drawing for the apparatus described
for the Academie
on 26 December 1820.
un petit aimant suspendu en N. On peut faire une sortie de contre epreuve
de cette experience
placant deux courans dirig6s en sens contraire dans la meme rainure
par une lame de
papier, en se servant pour cela d'un meme fil conducteur dont une extremit6 arriverait par le
tube EG, par exemple, et l'autre reviendrait en l'entourant de quelques spires se rendre dans la
coupe a mercure U situee pres de la coupe R, et qui remplacerai
alors l'autre
coupe S. I1
n'y aurait
aucune action sensible.
Cette derniere exp6rience ne serait, au reste, que celle que j'ai faite sur un conducteur
rectiligne enferme dans un tube de verre, et qui revenait ensuite autour de ce tube en l'entourant
de ses spires, experience dont j'ai deduit la loi dont il est ici question, avec seule difference
lieu d'un fil conducteur plie en helice on peut employer un qui soit contoume d'une maniere
Des que cet instrument sera acheve, je ferai les experiences auquel il est destin6.65
There are several points to be noted here. Although Amnpere planned his circuit to
pass through both of whatever conductors were placed within the two glass tubes, he did
not originally attempt to demonstrate a state of equilibrium
for the suspended magnet or
conductor. Instead, expecting to always observe some rotational reaction, he only
claimed to be able to duplicate a linear conductor's contribution to any observed effect
by replacing the linear wire with a bent and twisted conductor. Almost as an after-
65 Ibid.
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Invention of Equilibrium
Apparatus 335
thought, Ampere also described 'a kind of counter-test of this experiment'
in which only
one tube is used, but with a linear conductor inside and an arbitrarily
twisted conductor
coiled on the outside. This arrangement was expected to result in the suspended part of
the apparatus remaining unaffected and in a state of equilibrium.
Ampere clearly
did not
consider this to be a major improvement over his 6 November helix experiment, and he
did not yet place any particular importance on the use of equilibrium
But on 26 December, Ampere had not yet constructed his apparatus;
he apparently
had some unexpected experiences as he grappled with it during the following two
months. To my knowledge, Ampere left no records of his initial observations and
reactions. All that is certain is that by the time he wrote up a slightly retrospective memoir
for the February 1821 volume of the Journal de Physique, Ampere
was ready to launch
into an elaborate description of the famous apparatus
he would later
depict in engravings
such as that shown in Fig. 5.66
In contrast to the tentative circuits described on 26 December, this new apparatus
was specifically designed to produce a state of equilibrium;
the resulting
thus became the first and prototypical member of the set of equilibrium experiments
from which Ampere eventually would claim to derive his entire force law. As shown in
Fig. 5, the circuit includes a vertical suspended linear segment, GH, equidistant
from two
longer conductors. One of these is a linear segment, QP, and the other is an arbitrarily
twisted conductor, SR, which follows a random, two dimensional path of tiny bends.
The suspended conductor, GH, is free to rotate about a vertical axis, Fl, and the circuit is
designed so that the linear and twisted conductors exert oppositely-directed repulsive
forces on GH. Ampere accomplished this by making use of an axially-compensated helix,
gf, a technique that creatively embedded the humble origins of his apparatus
within its
own final structure.
According to Ampere's assessment of this circuit, if the linear and bent conductors act
with unequal strengths:
... le conducteur mobile seroit
devie par
a la difference
de ces
actions, au
lieu que si la loi enoncee plus
haut est exacte,
ce conducteur
doit rester dans la situation
oiu on
l'avoit mis avant d'etablir
les communications,
en equilibre entre deux forces
egales. C'est en
en est en effet
ainsi, que l'experience
1'exactitude de cette loi.67
The 'law' Ampere refers to as demonstrated here is the analogue to the addition law
phrased in terms of 'small portions' of wire which are actually large enough to be
individually manipulated. His argument that this assertion is demonstrated by the
observed state of equilibrium hinges upon the fact that an arbitrary non-systematic
set of
66 Ampere, op. cit. (63), pp. 161-163. To my knowledge, the engraving depicted in Fig. 5 was used for the
first time in Ampere's republication of his Annales des Mines article; Ampere, op. cit. (63). This reprint
appeared in Ampere's collection of memoirs which in its second edition was given the title, Recueil d'Obser-
vations Electro-dynamiques Contenant Divers Memoires, Notices, Extraits de Lettres ou d'Ouvrages
Periodiques sur les Sciences, Relatifs a l'Action Mutuelle de Deux Courans
a Celle qui Existe entre
un Courant Electrique et un Aimant ou le Globe Terrestre,
et a Celle de Deux Aimans l'Un sur l'Autre, 2nd
edn., Paris, 1822, pp. 87-92. For details on the two editions of this collection, see Williams, op. cit. (5), 1983,
p. 494.
67 Ampere, op. cit. (63), 1821, p. 162.
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336 James R. Hofmann
Figure 5.--
The final desgnofAm s
5. The final
Ampcre's first
bends had been given to the twisted conductor, SR. That is, any specific
little bend in SR
could have been slightly different than it actually was without preventing
the resulting
state of equilibrium. For Amp'ere,
this meant that, although what was observed was a
state of equilibrium produced by the combined action of the entire linear and twisted
conductors, this observation justified the 'law' he had asserted for any individual small
portion of the circuit.
Furthermore, as far as Ampiere
was concerned, the addition law for individually
unobservable current elements could be 'deduced' straightforwardly
from the preceding
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Ampere's Invention of Equilibrium
Apparatus 337
preliminary conclusion. Ampere never published a detailed discussion of this step in his
argument; he seems to have expected that, once his readers had accepted the conclusion
he had already argued for, they would naturally extend it by imagining the circuit
segments in his apparatus to become increasingly small. Ampere himself was quite
willing to pursue this reasoning until it applied to current elements so small as to be
mathematical idealizations that could only be depicted and manipulated
Nevertheless, Ampere also realized that some of his colleagues were reticent about
following his lead in this matter. To ensure that they at least accepted the validity of his
experimental discoveries, Ampere published a retrospective expository memoir early in
1821. In the process of summarizing his research during 1820, Ampere drew a careful
distinction between the experimental 'fact' produced by his equilibrium apparatus, and
'les lois mathematiques des attractions et repulsions de deux fils metalliques faisant
partie d'un circuit voltaique'.68 Among these laws he included the following accurate
statement of the addition law as he had used it in practice:
Que si l'on considere une de ces portions infiniment
petites comme la diagonale
son action sur I'autre est egale
a la somme des actions
sur cette
derniere, trois portions
du premier
suivant les trois
arretes qui
les trois dimensions du parallelepipede,
et de meme longueur que
Ampere rather optimistically presumed that the addition law would be accepted as a
straightforward implication of his equilibrium demonstration together with his inter-
pretation of the import of that demonstration for the individual small circuit
segments of
his apparatus. This expectation continued during the composition of the Expose'Ampere
and Babinet completed by July 1821. Once again, the addition law was said to be
legitimated by imagining an infinitesimal current element to be replaced by three
components, 'qui d'apres l'experience fait le meme effet'.70
Ampere's strategy is not too surprising considering the Laplacian
milieu in which he
was arguing. Biot too had formulated his own conception of the electrodynamic fait
primitif in terms of an infinitesimal current element acting on a particle
of magnetic fluid.
In contrast to Ampere, however, Biot treated his current elements as if they were
punctal; he did not develop a theory dependent upon their orientation. The importance
of Ampere's first equilibrium demonstration thus was due to the support it provided for
his efforts to initiate an alternative research programme built around a force law for
directed current elements. The success of this programme depended largely upon the
degree to which it achieved an accurate and comprehensive
explanation of
electrodynamic phenomena. My concern in this essay is to explain how Ampere
deliberately produced some of these phenomena in retaliation to what seemed to be
serious experimental anomalies. Furthermore, by incorporating compensated helices
into the circuitry of his first equilibrium apparatus, Ampere
made the engraving
shown in
Fig. 5 a visual display of the conceptual and experimental route he had followed.
68 Ampere, 'Expose sommaire des divers memoires lus par Mr. Ampere a I'Academie
Royale des Sciences
de Paris, sur l'action mutuelle de deux courans electriques, et sur celle qui existe entre un courant electrique
et le
globe terrestre ou un aimant', Bibliotheque Universelle des Sciences, Belles-Lettres et Arts, (1821), 16,
pp. 309-319; see pp. 311 and 318.
69 Ibid., p. 318.
70 Ampere and Babinet, op. cit. (39), p. 44.
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338 James R. Hofmann
Ampere's invention of the equilibrium experiment technique obviously did not come
about in a single flash of inspiration. It is true that his longstanding preference
for the
direct analysis of simple theoretical assertions from more complex experimental obser-
vations did give him a predisposition to pursue this procedure in the electrodynamic
domain; this distinguished Ampere from his more inductively minded Laplacian col-
leagues such as Biot. Nevertheless, Ampere's first systematic use of equilibrium
apparatus only came about as an unexpected result of a gradual refinement of the
demonstrations he had performed with axially compensated helices during
the first
in November 1820. These initial demonstrations were designed in response to the
anomalous behaviour of the uncompensated helices he had hoped would duplicate the
interaction of two bar magnets. Ampere now attributed these effects to the longitudinal
components of his helix spires. More fundamentally, he argued that all electrodynamic
attractions and repulsions could be understood as cumulative effects due to the sum-
mation of forces attributed to appropriate components of individually unobservable
current elements.
Following his application of this addition law to derive
the angular
factor in his force
law, Ampere temporarily shifted his attention to a more directly testable version of the
law stated in terms of circuit segments large enough to be individually observable in
experimental apparatus. By 26 December, he had designed equipment to produce
phenomena he hoped would compel acceptance of this relatively large-scale
analogue to
the addition law. Most of the initial demonstrations he planned at this time were not
intended to establish states of equilibrium; only his subsequent experience with his
apparatus revealed that such effects not only were technologically feasible but might
even be particularly appropriate. Early in 1821, this investigation resulted in the
invention of the famous bent wire equilibrium apparatus depicted in Fig. 5.
At this point, Ampere's argumentation passed through a sequence
of construals and
interpretations.7t He began by giving his new equilibrium effect extensive publicity by
means of detailed descriptions of his apparatus. He was particularly
conscientious about
this due to the less than enthusiastic response generated by the haphazard juxtaposition
of experiment and theory he had presented in his most widely read 1820 memoir in the
Annales de Chimie et de Physique. His consternation about this subject is evident in a
March 1821 letter to Bredin.
Quelque longue que ffit une lettre que je t'ecrirais
sur tout cela, elle ne serait
pas plus claire
mon memoire. Personne ne le comprend?
Je suis suir que ce qu'ils cherchent
a comprendre
71 For an interesting discussion of 'construals' as 'flexible, quasi-linguistic messengers between the
perceptual and the conceptual', see D. Gooding, 'How do scientists reach agreement about novel observa-
tions?', Studies in History and Philosophy of Science, (1986), 17, pp.205-230. Gooding's examples are drawn
from the electrodynamics of Ampere's English contemporaries:
Davy, Faraday and
Barlow. This group rejected
Ampere's reduction of electrodynamics to central forces. Engravings
such as those shown in Figs 1 and 5 are
examples of Ampere's efforts to highlight the phenomena he held to be of primary
importance for a correct
understanding of electrodynamics. As such, his diagrams and descriptions were suggestive construals of
electrodynamic phenomena which Ampere then subjected to highly theoretical interpretation.
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Ampere's Invention of Equilibrium
Apparatus 339
la th6orie dont je ne voudrais pas qu'on s'occupat encore, on l'adoptera de reste quand les faits
seront bien connus. Ce sont les faits, les faits qu'il s'agit
de bien
Est-ce que les physiciens de Lyon ne peuvent pas distinguer dans
memoire, malgre le
peu d'ordre qui y regne parce que je 1'ecrivais a mesure de nouvelles experiences, les faits
nouveaux des th6ories?72
Ampere's optimism that his version of electrodynamics would win acceptance once
the 'facts' were known was not so heady as to prevent him from providing some
explanatory encouragement. He gave brief but pointed arguments for how his equi-
librium apparatus produced effects that could be interpreted as an experimental basis for
the large-scale analogue to the addition law when stated in terms of the individually
observable segments of his circuitry. This is an outstanding example of AmpZere's
use of
what he called direct
He was less helpful, and less successful, in promoting the
acceptance of the addition law itself. In fact, Ampere's attribution of forces to com-
ponents of 'infinitesimal' current elements initially generated some highly critical
reactions. His reliance upon a carefully designed state of equilibrium clearly did not
result in a sudden victory over the rival Laplacian programme headed by Biot.
For example, as late as 5 July 1822, Ampere's close friend Maurice reported the
following objections from a correspondent who wished to remain
Ce n'est pas tant la contention
d'esprit necessaire pour
saisir les actions des courants
qui me
repugne dans cette th6orie que le grand nombre d'hypotheses toutes gratuites I'abus de la
consideration des infiniment
on peut
tout ce
qu'on veut,
le melange de
idees dynamiques
dont l'introduction n'est
pas suffisamment
ni l'influence
nettement caracterisee.73
Ampere's attempt to motivate his conceptual and mathematical treatment of 'infini-
tesimal' current elements obviously had failed to convince this critic.
The status of Ampere's research programme was further undermined by Biot's
promotion of a rival programme publicized by a great display of systematically collected
quantitative data. Although Biot and Savart were at a disadvantage
due to their reliance
upon a non-central, transverse force between a current element and a particle of
magnetic fluid, Biot claimed that this was only a temporary expedient that would become
unnecessary when the 'impressed magnetism' of conductors was understood in terms of
central forces between magnetic fluid particles. This project never materialized, but it
was still promoted enthusiastically by Biot during 1821.74
Like Biot, Ampere claimed that he too would eventually reduce his force law to more
elementary forces; in Ampere's case these forces were assumed to act between the electric
fluid particles of the ether. But Ampere made no more progress on this reduction than
Biot did on his. As a result, during most of 1821 the competition between Biot and
Ampere continued to call for a pragmatic choice between two force laws which were
admitted to be temporary expedients. In this contest Ampere failed to generate wide
acceptance of his construal of electrodynamic phenomena. Ampere's reliance upon the
72 Ampere, Correspondance, vol. 3, p.-907.
73 Ibid., p. 924.
74 Biot, op. cit. (21).
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340 James R. Hofmann
addition law met considerable
resistance due to the delicate
which he
claimed to 'deduce'
it from his equilibrium
in 1821 Ampere
had no expectations
that the equilibrium method
might provide a basis for further derivations relevant
to his force
1820 and
1821, his attempts
to stipulate
the values of the parameters
k and
n in his force formula
(2) were simply hypothetico-deductive
confirmations of consequences
drawn from his
assumptions that
k =0 and
n = 2. This
the method
and prior to April 1822 he had no hopes of being
to do without it. At that
confrontation with another anomalous
inspired Ampere's
invention of a
second equilibrium
His analysis
of this
the relation-
ship 2k = 1
-n, and this sparked
Ampere's hopes
the entire
derivation of his force
law might eventually
be based
an analysis
of states
of equilibrium.75
By 1826, a full set of four
took a central
in Ampere's
most polished attempt to improve
the reception
of his ideas. His first equilibrium
thus set an unexpectedly important precedent
the degree to which
considered the
framework of Ampere's electrodynamics
to be well-founded was to a large extent
dependent upon their willingness
to follow him in his reductionistic
cases of equilibrium
as a route to understanding
of electrodynamic
Major events
the early
months of Ampere's
research on his
force law
25 September Ampere
for the Acad6mie
conducting planar
spirals attract
and repel
each other
and respond
to bar
poles. Arago
follows Ampere's
and magnetizes
a needle
by wrapping
it with a
conducting wire.
2 October Ampere presents
the Academie
with the first
of his resume article to be
in volume 15 of the Ann. Chim. Phys.; by this time
between linear
9 October At the Academie,
electrodynamic forces
between linear
(Fig. 1).
September Ampere uses a centrally suspended
conducting helix wrapped
around an axial
to early
October current
to duplicate
the rotational
of a suspended bar magnet to
another bar
(Fig. 3).
75 This transition in Ampere's thinking is the primary
topic of Hofmann, op. cit. (59).
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Ampere's Invention of Equilibrium
Apparatus 341
17 October Ampere shows Biot and Gay-Lussac the new apparatus with which he dis-
covered the action of terrestrial
magnetism on a suspended current
During the Probably shortly after 17 October, Ampere gets anomalous results when he
month after substitutes two helical conductors without axial currents for the linear con-
25 September dcutors in the apparatus he presented
to the Academie
on 9 October (Fig. 1).
30 October At the Academie, Ampere demonstrates the action of terrestrial
on a
suspended current loop. Biot and Savart
present the Academie with their first
report on their quantitative measurements of Oersted's
6 November At the Academie, Ampere presents his addition law for electrodynamic forces
and uses it to interpret the action of helices. He uses a helix around an axial
current to duplicate the action of a bar magnet on another bar magnet (Fig. 3).
He mentions that the motion of ether particles might be the basis for the
addition law.
4 December At the Academie, Ampere presents his symmetry principle and uses it and the
addition law to derive the angular factor in his electrodynamic
force law. Biot
gives a preliminary statement of the result of his recent measurements with
11 December At the Academie, Ampere reports on an experiment which he claims implies
that k = 0; he explains why an experiment by Gay-Lussac and Thenard
erroneously seemed to indicate that k had a positive
that k = 0,
he draws an analogy to the radiation of heat. He reports an inconclusive
attempt to use quantitative measurements to demonstrate the superiority
of his
theory to Biot's.
18 December Biot and Savart report to the Academie on their second set of measurements on
a variation of Oersted's discovery.
26 December At the Acad6mie, Ampere describes an apparatus
with a suspended
magnet to
test his addition law (Fig. 4). He presents
the second part of his resume
to the Academie for publication in volume 15 of the Ann. Chim. Phys.
Late December Ampere designs an equilibrium apparatus
with a suspended linear conducting
or early wire to demonstrate his addition law (Fig. 5).
January 1821
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... Do início ao fim de suas pesquisas eletrodinâmicas Ampère sempre assumiu que a força entre dois elementos de corrente se dá ao longo da reta que une seus centros, seguindo o princípio de ação e reação. Em um artigo de 1820, por exemplo, afirma o seguinte, [Hof87,pág. Naépoca ainda não existia notação vetorial, que só passa a existir de maneira mais completa por volta de meados do século XIX, [Cro85]. ...
... Como Ampère nunca mencionouângulos orientados nemângulos negativos, concluímos que para ele eram iguais oângulo que vai de ds para ds ′ e o que vai de ds ′ para ds. Logo em nossas figuras não utilizaremosângulos orientados, embora Hofmann tenha representado osângulos de Ampère como sendo orientados, [Hof87] e [Hof96, pág. 241, Fig. 5]. ...
Full-text available
Apresentamos a força de Ampère entre elementos de corrente e discutimos detalhadamente as grandezas que aparecem nesta lei. Analisamos o caminho percorrido por Ampère para chegar na sua força entre elementos de corrente. Mostramos suas primeiras experiências, as formulações iniciais de sua força, as experiências de Biot e Savart, assim como a influência da experiência da rotação contı́nua de Faraday na determinação do valor final da força entre elementos de corrente de Ampère. Apresentamos os diversos casos de equilı́brio introduzidos por Ampère e sua relevância metodológica na obtenção de leis quantitativas na fı́sica. Mostramos as contribuições de Savary na elaboração das conseqüências quantitativas da força de Ampère e o impacto que elas tiveram sobre Biot, Savart e Ampère. Discutimos alguns dos principais trabalhos, cartas e manuscritos de Ampère, desde 1820 até sua obra máxima de 1826, o Théorie des Phénomènes Électro-dynamiques, Uniquement Déduite de l’Expérience. Apresentamos uma tradução completa desta obra e das notas que a acompanham.
... Ampère begins his reasoning in his main book by proposing that the elemental agent of electrodynamic force consists in the product of an infinitesimal portion of a conductor wire (ds) by the constant current intensity (i) through it. After this current element hypothesis, the mathematical form of Eq. (1) and the values of the parameters n and k were determined by the equilibrium experimental method, as devised by Ampère himself [2,14]. 2 He presented four 'cases of equilibrium' in order to deduce the expression of his force. We remark that he developed many other equilibrium experiments, some of them being the first alternative to arrive at his force. ...
Full-text available
In 1822, Ampère published the final form of his law for the electrodynamic force between current elements. Since then, it has been said that he carried out all his work in electrodynamics assuming both Newton's 3rd law and the absence of elementary torques as
... Assim, Ampère acabou por desenvolver o método dos casos de equilíbrio (ASSIS; CHAIB, 2011, p. 97) e (HOFMANN, 1987). Este, felizmente, era possível de ser aplicado, e ao mesmo tempo fornecia um resultado mais geral e confiante que o outro método citado. ...
Full-text available
J. Bertrand costuma ser conhecido por suas contribuições para a mecânica e para a matemática, mas pouco se sabe sobre sua predileção para a eletrodinâmica. Assim, de maneira inédita, apresentamos a contextualização e a tradução comentada, do francês para o português, do artigo “Demonstração dos teoremas relativos às ações eletrodinâmicas”. Nesse artigo, Bertrand deduz catorze teoremas fundamentais da eletrodinâmica. Entre outros pontos, tece considerações a respeito da validade da 3a lei de Newton na eletrodinâmica, deduz a Força de Ampère de apenas dois fatos experimentais – diminuindo o número dos casos de equilíbrio necessários de quatro para dois – obtém o teorema equivalente ao divergente do campo magnético (uma das equações de Maxwell), faz considerações sobre o potencial eletrodinâmico, e deduz a relação entre um dipolo magnético e um circuito fechado plano.
... Many recent publications deal with Ampère's work and his force law [103,114,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157]. Further papers are quoted in these books and works. ...
Full-text available
German translation by H. Härtel of the book The Electric Force of a Current: Weber and the Surface Charges of Resistive Conductors Carrying Steady Currents (Apeiron, Montreal, 2007).
Full-text available
The primary target of this essay is the thesis that the acceptability of a set of guiding assumptions is judged largely on the basis of the success of its associated theories at making novel predictions, a thesis promoted by Imre Lakatos and, subsequently, by Elie Zahar and John Worrall. Ampère's efforts to promote acceptance of his program in electrodynamics between 1820 and 1823 provide a clear test for the historical significance of the type of novelty Michael Gardner has labelled 'use novelty'. My conclusions bear most directly upon John Worrall's revisions of Lakatos's ideas, in that Worrall incorporated 'use novelty' into his concept of 'genuine empirical support'. With this understanding of 'novel prediction' at stake, I present evidence that Ampère did call attention to the importance of novel predictions prior to the beginning of his research in electrodynamics in 1820. However, when 'novel prediction' is understood in terms of 'use novelty', Ampère’s argumentation does not rely upon a significantly clear-cut stipulation of this concept.
Narrative accounts misrepresent discovery by reconstructing worlds ordered by success rather than the world as explored. Such worlds rarely contain the personal knowledge that informed actual exploration and experiment. This article describes an attempt to recover situated learning in a material environment, tracing the discovery of the first electromagnetic motor by Michael Faraday in September 1821 to show how he modeled new experience and invented procedures to communicate that novelty. The author introduces a notation to map experiment as an active process in a real-world environment and to display the human agency written out of most narratives. Comparing maps of accounts shows how knowledge-construction depends on narrative reconstruction. It is argued that invention processes can be interpreted in the same way as discovery, and a study is proposed to compare packaging learned skills into demonstration devices with the innovative strategies of inventors such as Edison. If situational knowledge is as important as is claimed, computationalists need to join science studies scholars in coming to grips with nonverbal and procedural aspects of discovery and invention.
A new epoch in the history of physics began in the summer of 1820 when Hans Christian Oersted announced his discovery that a compass needle was affected by an electric current. All over Europe, as the news came to them, natural philosophers repeated, extended and theorised about Oersted’s basic experiment.1 Nowhere was the fever more intense than in Paris where, in a few short weeks, André-Marie Ampere created a new science which he later named electrodynamics. By the end of 1820, Ampere had published a number of papers in which he tried to account for all magnetic phenomena by means of the forces exerted by electricity in motion — forces that he had discovered and which he insisted were completely different from the ordinary and well-studied forces of static electricity. In spite of his striking discoveries and in spite of the apparent ability of his new theories to account for new phenomena, Ampere’s ideas were greeted with scepticism. Among those who were not convinced of the basic correctness of Ampere’s view was Michael Faraday. In 1821 and 1822 Faraday published papers that criticised Ampere’s theories with sufficient force to compel Ampere to modify his views.2 Ultimately he presented his theoretical results in a manner quite different from those which marked the beginnings of electrodynamics. In this essay I explore in detail the bases of Faraday’s critique and point out exactly its effect upon Ampère.
This investigation begins with the recognition that what passes for knowledge at different times and among different people is not a universal invariable. This is evident not only when one compares primitive with modern societies, or the East with the West, but also with respect to the divergent approaches to understanding the natural world which have been cultivated by Western scientists. The question is why there are such cross-cultural and personal differences. Education, the influence of tradition and of community standards, the apparent logic of theories and force of facts — all these explanatory factors commonly employed by historians are important in understanding a scientist’s work. However, the historian is repeatedly forced to recognize that enculturation, logic, and the supposed compelling force of facts all operate selectively. The question is whether or not there are generalizable ways of accounting for the differential de facto selection that individuals make from the pool of explanatory alternatives. Putting the question this way suggests an answer in terms of biographical particulars, or of individual psychodynamics. Although such explanations are not in principle to be shunned, the supraindividual, social aspects of the problem gain prominence when one recognizes the historical occurrence of groups of people sharing the same sets of attitudes.