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Coulomb’s 1787 Newtonian force law: The Electrical Pendulum. Still in Advanced Textbooks. Feynman. Restaging Coulomb’s Legacy. The “restaging” of Coulomb’s torsion balance brought forward a number of issues dealing with precision, acceptance, rethoric, replicability, luck!.

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Coulomb’s 1787 Newtonian force law: The Electrical Pendulum

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Feynman

### Restaging Coulomb’s Legacy

The “restaging” of Coulomb’s torsion balance brought forward a number of issues dealing with precision, acceptance, rethoric, replicability, luck!

### Restaging Coulomb’s Legacy

Feynman:

The Torsion Balance is not precise

### Restaging Coulomb’s Legacy

• Feynman:

• Corroboration of the inverse square law is established through Gauss’s law and the corresponding zero field in a (not necessarily spherical) conductor.

### Restaging Coulomb’s Legacy

• Feynman: Coulomb’s law is wrong

### Hermeneutical “Coulombian” Circle!!!

• Textbook Physics Corroborates History

• History Corroborates Textbook Physics

• Are other circles possible?

• Let us try a

• Hermeneutical “Voltaic” Circle!!!

### Force and Tension: A comparison of the Torsion Balance and the Electrometer

Tension for the electrometer: Volta’s devices

Volta against Coulomb

Torsion for tension: Kelvin’s elecrometers

Coulomb and the Newtonian forces

The torsion balance and the electrical pendulum

The corroboration of Coulomb’s law

Is it a fundamental law?

### Force and Tension: A comparison of the Torsion Balance and the Electrometer

• Not so different after all: both based on repulsive electrical forces in equilibrium, in one case with elastic torsion, in the second case with weight.

• The measurement of forces or tensions largely depends on the theoretical background

### Torsion for Tension

Kelvin’s Electrometers show that the two instruments are not intrinsecally different

### Volta refused Coulomb’s lawWhat did he want to quantify?

• Volta wanted to measure a tension force, an effort to push outwards; but mostly he wanted to measure a tendency (intensity, tension) towards equilibrium and thus a quantity that tends to diminish approaching equilibrium.

• Newton’s force does not diminish towards equilibrium, but Leibniz’ vis mortua does

• Volta’s in-tension is better understood in a Scholastic and Leibnitian context

### 1782: Contributions towards the discovery of water composition

• Paris experiments with Lavoisier and Laplace

### 1792: Contact Electricity between Metals

Memoria seconda (14 May):

“E’ la diversità de’ metalli che fa”

A bimetallic arch acts also on nerves alone, and on the tongue

Transunto (June), Memoria terza (November):

Metals “veri motori di elettricità”

First class conductors (metals) of different kind have an electromotive power that is generated in the contact point between them and the second class conductors (liquids)

### Volta’s Theory: 1783 Calore

• il caloretende continuamente ad espandersi; che si diffonde, e comunica dai corpi più caldi ai meno caldi, fino a tanto, che si venga ad un'azione equilibrata, cioè, che sian ridotti essi corpi ad una temperatura eguale

• il calore, per l'innata sua tendenza all'equilibrio, si distribuisce ne' corpi a proporzione della loro capacità

• un altro esempio tratto dall'elasticità dell'aria, la quale può in certa qual maniera

### Volta’s Theory: 1783 Calore

• rappresentare l'espansibilità del calore, per cui tende egualmente, che quella all'equilibrio. L'esempio, che abbiamo preso dall'elasticità dell'aria, avremmo potuto prenderlo egualmente dalla velocità, che si comunica da un corpo all'altro per mezzo del semplice urto, dall'elettricità, che si propaga da uno in altro conduttore per ricomporsi ad equilibrio ec. e in generale da ogni cosa, che si riparte, e si distribuisce giusta le stesse leggi di equilibrio

### Factorisation

• Tutto avrebbe stabilita, e confermata questa proposizione: che le capacità rispettive di due corpi sono in ragione reciproca delle mutazioni, che soffrono in più o meno, mercè quel riparto, che li conduce ad uno stato di azione equilibrata

• C1DT1=C2DT2

### Volta’s theoretical works: Interdisciplinarity

• We know that Volta did not confine himself to electricity, but that he dealt at the same time with heat, pneumatics and chemistry

• Is his concept of in-tension confined to electricity or is it common to all fields of his researches?

### Volta’s Theory: 1778-80 Saggio Teorico e Sperimentale

analogia fuoco-fuoco elettrico

affinità, ossia forze attrattive delle minime parti di ciascun corpo verso il nostro fluido

forze mutue attrattive distinte dalla universale gravitazione

capacità: il fluido non già è ripartito nella semplice ragione delle masse e dei volumi; ma in ragione delle rispettive forze attraenti

### Volta’s Theory: 1784 Lezioni Compendiose

lo stato, ossia l’intensione dell’elettricità

Egli è facile il concepire, che l’azione dell’elettricità, è in ragione composta della sua intensità, e della capacità de’ conduttori

### Volta’s research programme

• For Volta the electric fluid is one and in a state of equilibrium, that is neutral. This depends on the mutual forces between the particles of the body and the fluid, forces that are balanced. When this state of equilibrium is modified, for instance through friction, because of the unbalance, an electric charge is perceived (accumulation or diminution of fluid) that tends to regain the equilibrium state. This tension is characteristic of the body and depends on its capacity to store charges according to the relation Q=CT.

### Volta’s research programme

• The tension tends to expell charges (excess of fluid) towards other bodies, in a different state. If (conducing) bodies are in contact, the charge is divided in relation to the capacity of the bodies. If a discharge is produced, the effect depends both on the tension and on the quantity of charge. Moreover the tension (?the charge) produces an electrical atmosphere (a sphere of activity) that acts at (great) distances and thus diminishes with the inverse of the distance and not with the inverse square.

### Volta’s research programme

• This in turn produces an unbalance in the electrical fluid of the bodies immersed in this atmosphere, an actuation (induction) is produced, and these bodies acquire a potential electricity, and thus a tension. Charges of opposite sign face each other and an attraction follows. On the basis of this attraction principle all the electrical phenomena can be explained, keeping in mind the tension (expandibility of the fluid) and the actuation produced by the atmospheres.

### Volta’s research programme

• When instead charges of the same sign face each other the tension (and the consequent attraction) manifests itself towards other bodies (including air) and thus the apparent effect of repulsion is attributed to these attraction towards other directions.

### Volta’s research programme

• Summarising Volta introduces two quantities: not only the total amount of the “quality” (charge) but also the state of the body (its tension). One extensive (additive) and the other in-tensive (non additive) related together through the specific capacity of the bodies to store the extensive quantity. Thus the intensive quantity is given by the ratio between the extensive one and the capacity (“volume”): T=Q/C

### Volta’s research programme

• The same relation connecting Charge, Capacity and Tension can be applied to Heat (fire, caloric fluid), to the air and to the quantity of motion. In other words if we have definite quantities of some “qualities” that are conserved during the process, the state of these quantities is characterized by a tendency towards equilibrium that depends on the capacity of the body that stores the given quantity. A small capacity (extension), implies a great in-tension towards equilibrium.

### Volta’s research programme

• Thus a quantification of qualities is achieved. Capacity is extensive (additive) as the quality it refers to, in-tension instead is intensive (non additive). The product of the intensive factor by the extensive factor is a constant depending on the various situations.

### Volta’s research programme

• This kind of approach, even if Volta does not outlines the effects of the riequilibrium of the fluids (of the qualities) and he does not introduce the concept of work (about to be born) is linked to principles of equilibrium, cause-effect, conservation, to tendencies to reestablish the perturbed equilibrium, through the actuation of potential (virtual) qualities. There are no references to Cartesian mechanicism, nor to Newtonian forces. Rather a scholastic terminology mediated by Leibniz and Boscovich.

### Volta’s research programme

• Obviously I am not pre-dating the formulation of energy conservation: Volta’s conserved quantities are usually substances (electric fluid, heat, air) and not functions (except perhaps in the case of quantity of motion), obviously again there is no conversion (of substances!) but extended use of analogies

• But, as usual, this is not the end of the story

### The Galvani-Volta debate: chronology

Galvani

1781 1o Esperimento

1786 2o Esperimento

1791-2 Commentarius

1794 3o Esperimento

1797 Memorie

Volta

1792 Prime reazioni

1792 Teo spec.contatto

1795 Teo gen.contatto

1797 Elettrom. cond

1799 Pila

1801 Identità due fluidi

### Galvani: 1791-2 Il “De Viribus”

• Diviso in 4 parti

• 1. Contrazioni con elettricità artificiale (primo esperimento)

• 2. Contrazioni con elettricità atmosferica

• 3. Ipotesi elettricità animale, contrazioni con arco monometallico, maggiori contrazioni con archi bimetallici (secondo esperimento)

• 4. Tesi elettrofisiologiche basate sull'elettricità animale

### Volta: 1792 Prime Reazioni

• Prima memoria (24 marzo-5 maggio): Dall’incredulità al fanatismo al dubbio

• a) Accettazione elettricità animale e archi “conduttori”

• b) Due metalli necessari per contrazioni con animali interi

• c) Ipotesi metalli “elettromotori”

• d) Spiegazione alternativa del primo esperimento di Galvani: atmosfere immateriali

### Volta: 1792 Teoria speciale del contatto

• Memoria seconda (14 maggio):“E’ la diversità de’ metalli che fa”; Arco bimetallico agisce sui soli nervi, sulla lingua

• Transunto (giugno), Memoria terza (novembre): i metalli “veri motori di elettricità”

• I conduttori di prima classe (metalli) di specie diverse hanno un potere elettromotore che si genera nel punto di contatto tra essi e i conduttori di seconda classe (umidi)

### Volta: 1795 Teoria generale del contatto

“E’ la diversità de’ conduttori che è necessaria”

Terza lettera a Vassalli (7 ottobre): “Esse (esperienze) mostrano soltanto, che sono io andato troppo innanzi asserendo, che non si potrebbe mai coll’applicazione di soli conduttori umidi, ossia di 2a classe, senza l’intervento cioè di alcun metallo o conduttore di 1a classe, eccitare le convulsioni nelle rane”

### Galvani: 1797 Memorie a Spallanzani

• “Egli vuole questa elettricità la stessa che quella comune a tutti i corpi; io, particolare e propria dell’animale: egli pone la causa dello sbilancio negli artifizi che si adoprano, e segnatamente nella differenza dei metalli; io, nella macchina animale: egli stabilisce tal causa accidentale ed estrinseca; io, naturale ed interna: egli in somma tutto attribuisce ai metalli, nulla all’animale; io, tutto a questo, nulla a quelli, ove si consideri il solo sbilancio”