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Parcours historique > Des lois pour l'électricité : Coulomb et quelques autres...

Some reflections on a "founding" instrument

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By Christine Blondel and Bertrand Wolff
Translated by Andrew Butrica

Coulomb wanted to give a pioneering dimension to his electrical and magnetic research. In removing electricity from "natural philosophy", in basing it on mathematics and scientific instruments, he reserved it for those with sufficient mathematical and mechanical skills, and he excluded the majority of "electricians" from this new research field.

The instrument of this break, which enabled Coulomb to apply "the melange of calculus and physics" to electricity that he advocated from 1773, was the famous "electrical balance". In France, throughout the nineteenth century, it became a monument of science, a symbol of the inductive method, "the first high-precision physics apparatus", the "keystone" of electrostatics. For a century, the physics treatises of Haüy and Biot, reference works in France as well as in translation abroad, shaped the portrayal of electrostatics. These treatises, followed by the manuals, such as those of Ganot, described in detail the balance, present equally in all the secondary school (lycée) collections in the form of more or less crude copies. These manuals systematically repeated the three numerical values given by Coulomb in 1785 in his first memoir on electricity [See the page Charles-Augustin-Coulomb, des fortifications de la Martinique à la mesure de la force électrique]. In this way generations of students became convinced of the power and simplicity of physics experiments by contemplating an instrument brought out of a physics cabinet for the duration of the lesson. If instead of just showing off the balance, the teacher had tried to use it, this simplicity would appear less evident [See the page Une expérience contestée, un accueil contrasté].

The Coulomb balance that appeared in Ganot's Traité élémentaire de physique ... from the first edition to the beginning of the twentieth century. (Shown here, the 1857 edition).

The electrometers of the "electricians"

In the article "Electromètre" in the Encyclopédie (1755), Jean-Baptiste Le Roy evoked "the benefits that one has gained from barometers and thermometers," especially since they had been fitted with precise graduations. He continued:

"if there is a part of physics where an instrument of the kind of which I have just mentioned is necessary, it is surely in electricity which is so changeable". If "one is not in a position to estimate or to know the variations of this force, one will be exposed at any time to draw false inferences from the simplest experiments".

According to him, it is due to the inability to compare this "force" of electricity that physicists:

"have embraced different feelings on diverse phenomena of electricity. [...] An electrometer would have soon put them in agreement, by making them see that the differences that they observed were born only from the electrical force."

But, on what phenomenon should one base an electrometer? At mid-century, two types of apparatus were intended to assess the "force of electricity". The first ones gauged it by the length of a spark.

Lane's bottle electrometer: the length of the spark that jumps between two balls whose distance is adjustable enabled the estimation of the quantity of electricity accumulated in the Leyden jar.
(Musée des arts et métiers, Paris)

Le Roy believed that these electrometers did not permit the making of reliable comparisons: for the same amount of electricity the length of the spark depends on the shape of the conductors. In his opinion:

"repulsion is the only sure and general way that one can use to measure electric force". And he concluded: "It is not too early to think of an instrument for measuring the force of electricity".

In fact, the second half of the eighteenth century saw the development of all kinds of electrometers based on the repulsion between wires, straws, and plates. Volta in particular pushed far in attempting to make true measuring instruments.

However, there was no consensus on what was being measured: the "force", "amount", "density", or "tension" of the electricity. And it remained extremely difficult to compare the measurements given by two different electrometers. There was, therefore, among the electricians of the 1780s, a demand for quantification that went unsatisfied.

A reconstruction of Volta's balance. By varying the counterweights on the right side of the beam, Volta balanced the attraction between the charged upper disk carried on the left side of the beam and the grounded lower disk. With this balance, he sought to standardize electrical measurements. By choosing a particular value for the counterweight, he defined a unit "degree of electrification" or tension. This unit was equivalent to more than 10,000 of our volts.
(Museo per la Storia dell'Università di Pavia)

The balance of the "mechanic" Coulomb

Unlike a Nollet, a Franklin, or a Volta, Coulomb would not have identified himself as an "electrician" when, after extensive work as a mechanical engineer, he turned to electricity. It was the study of the torsion properties of metallic wires that led him to construct a torsion balance, one possible use of which was the study of the force between small charged spheres. Although the original title of his first memoir on electricity was "Description of a new electrometer", on publication it became "Construction and use of an electric balance ..." It certainly distinguished him from the attempts of his contemporaries. The word "balance" was indicative of a desire to mathematize electricity on the model of mechanics.

The experimental space redefined: the exclusion of spectators

Eighteenth-century engravings show experimenters wearing laced ruffles and experimenters in long robes, at the same time actors and objects of the electrical experiments. Strange devices, from which leaped impressive sparks, caused terrible electric shocks. The experiment was a spectacle that brought together amateurs and the curious, who testified and attested to the truth of these unusual facts.

The extreme sensitivity of the instruments used by Coulomb required the exclusion of spectators. The experimenter himself had to take draconian precautions in order not to spoil the measurements. The choice of place and of furnishings was far from being unimportant: cellars cut in stone to install Cassini's magnetic compasses, a room tightly closed, dry weather, distancing from any body susceptible of causing electrical interference.

Physics thus left public spaces, salons, and cabinets, to set up in the laboratory, closed to the public. The arbiters of experimental proof are no longer high society audiences, but other physicists equally well-versed in experimental techniques. The experiment was hardly ever reproduced except by a small number of savants belonging to learned or educational institutions.

A depersonalization of the accounts

The drawings accompanying Coulomb's texts never show the body, not even the hands of the experimenter. It is the instrument and not the man, the measurements and not the sensations, that stand out. Coulomb still frequently wrote in the first person as in the oldest accounts: "I found that ...", "I place today before the eyes of the Academy ...", but the impersonal turns of phrase asserted themselves in the conclusions. He did not inform us, or very seldom, about the months of daily work and the difficulties that he personally sustained in his experiments. Above all, the meticulous descriptions of the experiments and the tables of numerical results were supposed to allow anyone to reproduce the experiment "easily", even if in this particular instance it was very far from being the case.

A prior belief in the existence of simple and universal mathematical laws

If the three numerical values given by Coulomb in his first memoir sufficed to win over the support of the group of French physicists and mathematicians of the Academy of Sciences, it was because the latter shared a solid faith in the possibility of translating physical phenomena by means of simple and universal physical laws. After mechanics, it was in electricity, a science until then qualitative and descriptive, that the mathematical law became a new resource. In addition, this law was supposed to have a simple form: Coulomb and many of his peers limited themselves to 1/dⁿ laws with a whole-number exponent.

This vision was far from being shared universally in the rest of Europe. For some, all physical phenomena were composite and could not be reduced to a simple law. Coulomb and his colleagues acknowledged the complexity of physical phenomena. However, they believed that one could seek a single cause by either eliminating other phenomena with an appropriate experimental arrangement or calculating the effect of these phenomena when considered as perturbations. So, for example, Coulomb calculated electrical losses through the air or through matter [See the page Les lois fondamentales de l'électricité et du magnétisme].

Nonetheless, if, around 1800, one contemplated controlling or calculating the errors to which one could assign a cause, the management of the "observational errors"-one would call them today the uncertainties of measurement-might surprise the modern reader. The contrast indeed is great between the rigor displayed in theoretical calculations and the not yet codified use of quantitative experimental data. Accounting for and evaluating errors became the object of reflection during the 1820s and 1830s.

Coulomb spoke easily of the admirable "exactness" of his balance, where we distinguish between remarkable sensitivity and questionable accuracy and fidelity. He sometimes gave results of measurements to four places, though the fluctuations between two measurements reached 10%. On the other hand, the selection of measurements according to their "quality", that is to say their agreement with theory, was a practice considered to be logical and it was vindicated. Regularly, Coulomb stated that he had chosen some observations "among an infinity of others", in order not to unnecessarily enlarge his memoir. René-Just Haüy, one of the leading disseminators of Coulomb's work, wrote in 1818:

"the numerical expressions of these forces, deduced by the mechanical means that he [Coulomb] employed to measure them, never represented strictly the law to which he assumed these forces were subjected; but they touched it so closely that he had the right to reject the difference among the small errors inseparable from observation". And "we are all the better founded in regarding our experiments as decisive when they give only slight differences with the results of our theories, we should rather be surprised that they should give none".

It was enough that the experimenter attained, among a collection of measurement results, some values consistent with the anticipated law to consider the latter as validated.

It is a good thing that Poisson, Gauss, and many others took this law as a starting point for their work, which in turn helped to confirm it.