Coulomb designed an instrument for measuring electrical forces. Experimenters knew that bodies repel if they carry the same kind of electrical charge, moving away from one another. One might measure the force by measuring their mutual repulsion. Coulomb had studied the properties of wires under torsion. He had found that when a wire is twisted by a certain amount, it exerts a proportional force against that torsion. For example, if you twist a wire to a given angle, it reacts by pushing back with a certain force, and if you twist it to an angle twice as large, then it pushes back with a force twice as strong. Coulomb realized that he could use this property of wires under torsion to measure electrical forces.
Coulomb constructed an apparatus that he called the “torsion balance.” He provided an illustration, which, like the image of Ben Franklin flying a kite, has been reprinted countless times—in fact, it has been characterized as the one diagram of any experimental device that has been “reproduced more often than any other diagram.”7 Inside a glass cylinder, Coulomb hung a thin, silver wire. Onto it he attached a thin vane, horizontally, carrying a small ball of pith on one side and a paper counterweight on the other.8 Nearby, a rigid stick held another small pith ball at the same height. By imparting electricity onto the two balls, Coulomb could make them repel. One ball remained fixed in place, while the other ball (suspended from the vane and wire) moved away. In turn, the wire, being twisted by this repulsive force, exerted a reactive force in the opposite direction. At some point, the force of repulsion reached a balance against the wire's reactive force, and the movable ball stopped moving.
Once the balls were separated by a constant distance, held in place by the balance of the two forces, Coulomb could twist the top of the device to force the suspended ball to come closer to the stationary ball. Then he could measure how much any given twist affected the separation between the balls.
Now, Coulomb wanted to test the force equation. Once the bodies separate, to measure the force of electrical repulsion means to assign a number to it. The farther away the two balls are, the greater the force pushing them apart, and the farther the balls separate, the more the wire is twisted. Therefore, the torsion of the wire expresses the force. If the balls separate by, say, 30 degrees, we expect that the wire is twisted by 30 degrees, and so we may well say that the force is “30.” That number represents the force, quantified in terms of how much the wire is twisted. Now, in this case, the number also represents the distance (the angular separation) between the two balls.
Coulomb could increase the force between the balls by forcing them closer together. And he did so by turning a knob at the top of his instrument, where the wire was attached, bringing the one ball closer to the other. Thus the force between them increased, and it could be quantified by taking note of the total torsion on the wire. Coulomb had marked degrees all around the knob, to show how much torsion he had added to the wire. Meanwhile, the two balls continued to repel, thus adding extra torsion onto the wire. Thus, in his device:
Meanwhile, the distance between the two balls is measured easily, approximately, by the angular separation between the two balls. And to measure that separation, Coulomb used a strip of paper, divided into 360 degrees, pasted all around the large glass cylinder, at about the height of the two pith balls.
Now, since he could measure the distance between the balls, plus the force acting between them, he had two terms, d and F, with which to test the equation in question. One way to do so is to use the algebraic property we identified: that at half the distance the force is quadrupled.
So, Coulomb compared how much the separation changes when the balls are forced closer together. First, he imparted electricity onto the two balls. He reported that the suspended ball moved away from the stationary ball until the two were separated, steadily, by 36 degrees. Thus, the total torsion on the wire, at that stage, was 36 degrees as well.
Next, Coulomb, turned the knob enough to add four times as much force as before, to see what separation would result. He expected that if he quadrupled the force, the balls should become separated by half the initial distance. The balls should then rest at 18 degrees. So how much should one twist the knob to quadruple the force of repulsion? The total torsion of the wire should be 36 × 4 = 144. But the total torsion of the wire, as we pointed out above, consists of the angle on the upper dial plus the separation between the two balls. (The knob pushes the ball in one direction while the repulsion pushes it away in the opposite direction, causing a greater total torsion on the wire.) To have a total torsion of 144, we need to include the separation of the balls, 18. So Coulomb knew that one should twist the knob to: 144 − 18 = 126, in order to get a total force of torsion 144.
Next, one would expect that if the force were quadrupled again, 144 × 4 = 576, then the separation should become half as large, 18/2 = 9. So, to obtain that separation, one would need a total torsion of 576 on the wire, consisting of 567 degrees on the upper dial plus 9 degrees on the lower ruler.
In short, the inverse square equation of electrostatic repulsion predicts that if the initial separation between the two balls is 36, then one would obtain the following results by forcing the balls closer together, as we have described:
These are purely abstract, theoretical results, assuming the simple algebraic equation that expresses the expectation that electrical force varies inversely with the square of the distance. Compare the theoretical numbers with the numbers that Coulomb reportedly obtained in his experiment:
These numbers, the only data that Coulomb published on the matter, are remarkably close to the predicted series. Coulomb concluded that he had found that the fundamental law of electrostatics was an inverse square law. In his paper, Coulomb did not allude to any witnesses to his experiments. Yet he presented his apparatus to the Paris Academy of Sciences and wrote that his results were “easy to repeat, and immediately disclose to the eyes the law of repulsion.”9 Just as Ben Franklin said about his kite experiment: easy.
In order for the experiment to work at all, it was essential that the electric charge be imparted only onto the pith balls and that it remain there rather than spread onto the other parts of the apparatus. For that purpose, it would help to use plastic as an insulating material separating the pith balls from their supports. But in 1785, synthetic plastic was not available. Instead, Coulomb used natural thermoplastic polymers manufactured from the sticky resin secreted by various species of lac insects. Such insects live mainly in soapberry and acacia trees in India, wherefrom their sticky resin was collected and exported by Venetian merchants to Spain and France. Thus, Coulomb used a compound, so-called Spanish wax (though it contains no wax) to coat the single strand of silk into a thin, rigid, horizontal vane for the suspended pith ball, and he further insulated it with an additional coating of gum-lac on the tip. Likewise, the stationary pith ball was also supported by a rigid stem of Spanish wax.
As far as I know, in 1785, Coulomb's torsion balance was the most sensitive instrument ever devised for measuring forces. To turn the thin wire a full 360 degrees would require merely a force so tiny that it would lift just one 40 millionth of a pound.
The French soon became convinced that Coulomb had indeed proven a fundamental law of nature. Over the next two hundred years, Coulomb's experiment became known as an excellent example of how experiments establish physical laws. Many physics textbooks reprinted Coulomb's diagram of his torsion balance. Also, various instrument makers produced versions of the torsion balance, which were purchased by physicists in Europe and America.
Still, books seem to have referred to Coulomb's data alone, rather than adding any other data whatsoever. Eventually, this lack of reports corroborating Coulomb's results raised some questions.
In the early 1990s, Peter Heering, at the University of Oldenburg, in Germany, carried out historical research to find out whether past scientists had operated the torsion balance as successfully as Coulomb. But Heering found no evidence that any other physicists had ever obtained results as good as C
oulomb's single report. Instead, he found that several German physicists in particular, in the 1800s, had reported difficulties operating the torsion balance. Of course, maybe there were others who had no such difficulties obtaining results similar to Coulomb's. But if so, why does it seem that no such results were ever reported in print?
Accordingly, Peter Heering decided to replicate Coulomb's experiment. Heering and his colleagues at Oldenburg constructed a replica of the torsion balance, following Coulomb's original prescriptions such that the dimensions of every part of the instrument were copied closely. Still, not all materials were duplicated; for example, the wire was not pure silver but copper, it was not clamped but soldered, and the needle was not made of silk and Spanish wax but of PVC. Nevertheless, the properties of each part were presumably equivalent to those prescribed by Coulomb, so it all should have yielded comparable results. Once all the components were in place, it took six more months of daily work to stabilize and calibrate the device before being able to take meaningful measurements. Heering carried out many experiments. But in none of the experiments did results similar to Coulomb's emerge. Finally, Heering reported: “in none of the experiments was it possible to obtain the results that Coulomb claimed to have measured.”10
As shown in the graph above, in Heering's results, the data does not confirm the central line, which stands for the results predicted by the inverse square law of electrostatics. Even though Heering gathered much more data in this trial than Coulomb reported in his, Heering confirmed that the delay in taking more readings did not affect the result (because the pith balls did not lose much charge in that time). Using this data and some trigonometry to calculate the exponent n in a presumed inverse law 1/r n, we get a result of n = 1.28 instead of the theoretical n = 2.
Compare that to Coulomb's reported results, as graphed here, which give an exponent of n = 1.91. Clearly, Coulomb's reported numbers seem to very nearly select the curve that belongs to an inverse square law. The only way that Heering managed to obtain results nearly as “good” was by altering the experimental setup.
The suspended needle behaved erratically. Heering reported that “it was absolutely impossible to measure the exact position of the movable pith ball because of these oscillations.”11 Heering noticed that whenever the experimenter, himself, approached the torsion balance, the movable pith ball oscillated. It became evident that electrical charge on the body of the experimenter affected the behavior of the experiment. So, to shield the device, Heering surrounded it entirely with a wire mesh, known as a “Faraday cage.” Only then did Heering obtain results that were almost comparable to Coulomb's. But Coulomb described no such metal insulation around his device. Moreover, such a metal cage was devised only decades later by Michael Faraday, in the 1830s, so it seemed unlikely that Coulomb would have a comparable arrangement, especially since he did not mention anything of the sort.
Therefore, Heering argued that “Coulomb did not get the data he published in his memoir by measurement.”12 Another historian, John Heilbron, remarked that “It appears from Heering's careful and resourceful labor that Coulomb either faked his numbers altogether or obtained them under experimental conditions materially different from those he reported.”13
Meanwhile, Christian Licoppe argued that in Coulomb's various papers, his rhetoric of purported instrumental precision was tailored to his primary audience, mathematicians of the Paris Academy who were ready to believe that electricity obeyed a simple mathematical law, like Newton's law of gravity, and to accept the rather unique and private results of a fellow member.14 There seemed to emerge consensus that a disparity exists between Coulomb's elegant and simple narrative of 1785 and complications that arise in actual practice. In particular, Coulomb's wonderfully accurate numbers seem unlikely in light of Heering's results as well as Coulomb's admission in his original memoir that his balance suffered from defects that he planned to correct later. Accordingly, some historians have advanced conjectures about tacit procedures or practical knowledge that Coulomb might have exercised but left unreported. If the movable pith ball, once charged, oscillated for a while before settling, then how could Coulomb possibly make his three readings in only two minutes? Heilbron conjectured that Coulomb may have guessed where the moving ball would come to rest and reported that guess as an actual reading of its position. Heilbron also proposed: “Probably Coulomb put some torsion on the wire by twisting the knob even for the first data pair, although in the narrative he says that in its first position the needle balanced between the electrical force of the balls and the torsion given the wire by their repulsion alone. Coulomb's convenient round number for his first measurement (f = q = 36°) suggests that he had his hand on the micrometer knob for the first setting and that he had a special way of estimating the equilibrium position of the needle.”15
The apparent discrepancy between the text and the practical subtleties led to various speculations about the actual operational procedures involved as well as past practices of scientific reporting. It also led to perceptive questions about possible unidentified material factors in the laboratory environment. Christine Blondel wondered whether Coulomb glazed his apparatus with an insulating varnish. Jed Buchwald wondered whether Coulomb used a short-range telescope to make his readings while staying a distance away from the apparatus. Maria Trumpler, and Heilbron, even commented that perhaps factors such as a wig and a silk shirt could affect the charge on the experimenter.
Furthermore, students at the Massachusetts Institute of Technology, under the guidance of Jed Buchwald, attempted to replicate Coulomb's experiment. But their results were not even as good as Heering's. And in France, Bertrand Wolff operated a torsion balance and observed unstable needle behaviors similar to those reported by Heering, which rendered the device utterly inconclusive for testing Coulomb's law. A documentary video concluded: “Since the results announced by Coulomb were in such good accord with the inverse square law, one may think that from among numerous measurements, he selected those which confirmed the previous hypothesis of a law analogous to Newton's law of universal gravity.”16 A plausible conclusion, but speculative. Strangely, in over two centuries, and despite hundreds of discussions about the torsion balance in textbooks and journals, no documents showing actual data comparable to Coulomb's three data pairs have surfaced.
Today, a widespread and disturbing habit exists in physics classrooms. Students in many lab classes try to reproduce one or another basic experiment, but often, they do not get the results predicted by the physical theory. Then, when writing the report that will determine their grade, they proceed to “fudge” the results. Students discreetly adjust data to make it seem as if they were closer to the theory than was actually the case. Wouldn't it be disturbing to find that, originally, famous scientists also fudged the data in their experiments? Don't we hope that, rather than the theory determining whether the results are correct, experiments decide whether a theory is valid?
So whom should we believe: Coulomb and the French Academy of Sciences and the many old teachers and books that parroted Coulomb's report? Or should we believe the physicists and historians who, two centuries later, having the resources of high-tech experimental physics and the benefit of critical hindsight, argued that Coulomb's report was suspicious? It might seem that the apparent triumph of Coulomb's law was artificial and socially constructed.
But there's an alternative. Belief in science should not have to be decided by appeals to authority or by popularity votes. Instead, we could well carry out the experiment and see what results. Maybe then one's judgment would not be an opinion.
In light of Heering's account, Coulomb's experiment seemed so fascinating and puzzling that once I actually tried to carry it out. I'm not a physicist, and I had no prior significant experience replicating old scientific experiments, but teaching history sometimes leads to such attempts. In spring 2005, at the California Institute of Technology, I put together a torsion balance following Coulomb's specifications and benefiting from
advice from historian of science Jed Buchwald. I tried various materials for some of the components, starting with foam balls and relatively thick wires, as a metallurgist told me that it would be “impossible” to make a wire as thin as Coulomb claimed to use. Failing also to follow some of Coulomb's prescriptions, I fitted components in various ways. For example, I could not find a way to clamp a very thin copper wire (thinner than Coulomb's; the metallurgist was wrong), so instead I tied it at the top, where it hung. Also, I attached the fixed pith ball to a wooden rod instead of a rod made of sealing wax. Later I used rods made from a white plastic coat hanger. To insert electricity into the system, I attached a metal pin with a round tip onto a plastic rod and rubbed it on a bundle of cat hair. For months, I did not obtain results similar to Coulomb's. It was quite an unsuccessful effort.
Gradually, I made a series of adjustments, identifying components that seemed responsible for the erratic effects. For example, I managed to clamp the wire firmly to flattened metal, inserted in turn into the tip of a mechanical pencil. Also, for a while I used a thread covered in sealing wax as the needle that held the suspended pith ball. And it exhibited erratic oscillations such as Heering had described. (By this point, my original skeptical doubts increased, for how could such a crude tabletop instrument test a fundamental law of physics, given that it does not even use a vacuum?) But in my case, it turned out that the oscillations were caused by a leak of electric charge from the pith ball onto the waxed thread, as I finally found the waxed thread itself was attracted by the other charged pith ball. So, I replaced the waxed thread with a thin stick of blue plastic that I made by melting a disposable Gillette razor.
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