Scales and Balances

This article appears in Joseph D. Martin and Cyrus C. M. Mody, eds., Between Making and Knowing: Tools in the History of Materials Research, WSPC Encyclopedia of the Development and History of Materials Science, vol. 1. Singapore: World Scientific, 2020.

In Ancient Egyptian mythology, entry into the afterlife was secure only after the weighing of the heart (figure 1.4.1). The gods would place the deceased’s heart on a scale opposite the feather of Maat, symbolizing the seven cardinal virtues of truth, justice, propriety, harmony, balance, reciprocity, and order.(4 p374) Those whose hearts were in equilibrium with Maat could pass into the afterlife; hearts heavy with misdeeds would be devoured by Ammut—a chimerical, crocodile-headed goddess—consigning the soul of the deceased to oblivion.(4,10)

Although it concerns the fates of the dead, this story hints at the practices of the living in the ancient world, and the importance weighing held for them. Ancient civilizations curious about the nature of weight soon realized that two arms of equal length balanced on a fulcrum could be used to establish either that two objects weighed the same, or that one weighed more than the other. Balances of this type have been found dating to as early as the fourth millennium BCE. The moral consequence evident in the weighing of the heart hints at the import such balances held for civic life of the ancient world, guiding the equitable conduct of trade and commerce.(6) That same moral consequence carries through to the modern world, where the personification of Justice is commonly portrayed blindfolded, holding a set of scales.

Like many of the tools discussed in this volume, scales and balances make clever use of materials in order to better understand them. In the ancient world, that meant crafting stone weights to be used as the standards against which objects of unknown weight could be tested. This fundamental aspect of weighing changed little over the subsequent millennia. Even into the twentieth century, many scales and balances and their standard weights, although much refined in their construction and operation, would have been perfectly intelligible to an ancient Egyptian or Mesopotamian shopkeeper (figure 1.4.2).

Over the next several millennia, improvements to weighing techniques came in the form of improved scales, but also in refinements to the systems that ensured the accuracy and precision of standard weights. The precision required for weighing of the sort that greases the wheels of day-to-day life in a settled society—for trade, assaying, and minting, for example—depended as much (or more so) on the robustness of standards as it did on the form of the scales set by them. As the following examples show, further refinements to weighing techniques were frequently inspired by the use of scales in investigations into the properties of matter.

Antoine Lavoisier and the Chemical Balance

Chemical problems in the late eighteenth century provided ample motivation to seek out more precise ways of weighing. Chemical investigations posed distinctive problems that called for precision balances. Assayers, whose job it was to determine the composition of metals, had long demanded precision scales, but they worked with a small class of substances whose properties were well known. Combined with the firm standards that were in place in much of Europe by the eighteenth century, this meant they received little trouble from standardized balances optimized for relatively small weights. But the research programs that emerged in the eighteenth century, in particular on the composition and properties of air, drove demand for increasingly sensitive scales for a wider variety of types of measurements.

Of special interest were scales that could hold heavy loads (on the order of kilograms) while also maintaining their sensitivity. Antoine Lavoisier (1743–1794), the virtuoso French natural philosopher, sought out scales that could manage containers big enough to hold considerable quantities of air, so that he might observe the results of chemical reactions on the weights of different airs. Precision weight measurements were crucial in the wide-ranging debate over the nature and existence of phlogiston, the hypothesized matter of fire. The precision balances Lavoisier commissioned permitted the measurements by which he noticed that many metals gain weight during calcination (burning), posing a problem for the notion that phlogiston was a substance with a finite weight.(9 p176) The suggestion that phlogiston might have negative weight slowed the bleeding of a mortally wounded theory, but Lavoisier’s oxygen theory, flawed though it was, won favor over the phlogiston theory in large part on the basis of Lavoisier’s precision measurements.(2)

Balances offering the precision sensitivity required by the eighteenth century chemical laboratory had a limited commercial audience, and hence were unlikely to be developed in the absence of the demand provided by well-resourced experimenters. It is in Lavoisier’s experimental practice that we begin to see something resembling the sort of networks characteristic of a modern chemical or materials laboratory. Lavoisier’s laboratory was a site of practice not only for experienced instrument makers, but also for apprentices, so that the process of designing and refining instruments became intertwined with the training of their makers.(1) The social world that grew up around wealthy gentlemen natural philosophers therefore created a market for superlative precision that would not have existed otherwise.

Coulomb, Cavendish, and the Torsion Balance

Charles Augustin Coulomb (1736–1806) came to natural philosophy from a background in military engineering. His engineering training gave him both a sensitivity to the properties of materials and an appreciation for rigorous mathematical precision. While working to develop an extremely sensitive compass—one capable of detecting small local variation in the Earth’s magnetic field—by suspending a magnetized needle from a silk thread, he became interested in what happens to thin wires when they are twisted.(3)

In the 1780s, Coulomb worked out that the force a twisted thread exerts against the direction in which it was twisted—what we would call the “reaction torque” and what he termed “the momentum of the force of torsion”—is proportional to the angle through which it has been rotated. After formulating the law governing the reaction torque of a wire, Coulomb realized that a sufficiently thin wire could be a sensitive tool for measuring extremely small forces.(5) The result was the torsion balance (figure 1.4.3), which Coulomb used to verify the supposition that electrostatic charges exert forces that decrease with the square of the distance, and to articulate his eponymous law.

The British natural philosopher John Michell (1724–1793) independently developed a similar device. Michell’s torsion balance made its way into the extensive instrument collection of his friend Henry Cavendish (1731–1810). Like Coulomb, Cavendish was interested in the nature of force laws. Isaac Newton had established the inverse-square relation for gravitational attraction, but his law of universal gravitation included a constant, G, the value of which remained difficult to establish experimentally. The precision offered by Michell’s torsion balance permitted Cavendish to measure the gravitational attraction between two ordinary objects in the laboratory, in his famous 1798 experiment, and to establish an accurate value for G.

The torsion balance and a related innovation from around the same time, the spring scale, first manufactured in Britain by the instrument maker Richard Salter in the 1770s, represented a transition in scale design. Whereas equal-arm balances relied on principles that had at least been informally understood for millennia, this new class of tools relied on identifying and formalizing a natural regularity and developing knowledge of how materials behave in accordance with it. In the case of the torsion balance, this was Coulomb’s account of reaction torque; in the case of the spring scale, it was Hooke’s law.

Precision Weighing as a Standard Practice

Scales and balances contributed to fundamental advances in physical and chemical science, but they also continued their function as standard pieces of laboratory apparatus. A precise, well-calibrated scale is necessary for preparatory work for a great many other tools, or for evaluating their results—for instance in preparing samples or in determining the results of an analysis. As in the past, ensuring the reliability of such instruments requires vigilantly maintained standards and carefully controlled systems of calibration and certification. Readers interested in standards more generally should consult Sharon Ku’s contribution to this volume, but it will be worthwhile here to discuss weight standards in particular.

Up until the late-nineteenth century, most countries (and some smaller political units) maintained their own domestic weight standards. The British Imperial pound, for instance, was not quite one French livre. Local variation among standard weights created difficulties both for trade and for international scientific exchange, leading in the late-nineteenth century to the establishment of the SI (Système Internationale) system of units. On May 20, 1875, seventeen countries signed the Meter Convention, which established the meter as a standard international unit of length and the kilogram as an international unit of mass. Both would be maintained by artifact standards—physical objects defined has having a characteristic weight or length.

The kilogram was, until very recently, defined as the weight of a platinum-iridium cylinder—the International Prototype Kilogram (IPK; figure 1.4.4)—kept in carefully controlled conditions at the International Bureau of Weights and Measures in Paris. Every SI scale in the world could trace its calibration back to this object.

But changes in how the metrological community defines and maintains standards have now caught up with even this most long-lived of artifact standards. The world’s metrological community voted in November 2018 vote to start the process of redefining the kilogram in terms of a fundamental unit, Planck’s constant—a change that went into effect on May 20, 2019.(8) What has changed? For most researchers in materials laboratories, very little. Their scales still work as before, and they talk about weight in the same terms.

The transition is deeper, however. Just like the emergence of torsion balances and spring scales represented a new way of thinking about measuring weight through a deep understanding of physical law, redefining the kilogram in terms of Planck’s constant is a way of driving the girders of the mass standard into the firm bedrock of a fundamental physical quantity. For all the precision and control behind the manufacture and maintenance of the IPK, its real weight does drift ever so slightly over time, which means that the kilogram was, on some level, a moving target since it was first manufactured in 1889.

It is worth mentioning in closing, however, that the current most precise measurement of Planck’s constant relies on a Kibble balance. Like the torsion balance, the Kibble balance takes a subtle, delicate, but known force, in this case the electromagnetic force exerted by a current-carrying wire, and uses it to determine an unknown, counteracting force. The cutting edge of precision weighing remains the frontier of understanding material properties, and so the redefinition of the kilogram away from a material object will not make the properties of materials any less important for the practice of weighing.

References

1.     Beretta M. Between the workshop and the laboratory: Lavoisier’s network of instrument makers. Osiris. 2014;29:197–214.

2.     Chang H. We have never been Whiggish (about phlogiston). Centaurus. 2009;51(4):239–64.

3.     Heering P. Regular twists: replicating Coulomb’s wire-torsion experiments. Physics in Perspective. 2006;8(1):52–63.

4.     Karenga M. Maat, the moral ideal in ancient Egypt: a study in classical African ethics. New York: Routledge; 2004.

5.     Martínez AA. Replication of Coulomb’s torsion experiment. Archive for History of Exact Sciences. 2006;60(6):517–63.

6.     Petruso KM. Early weights and weighing in Egypt and the Indus Valley. M Bulletin. 1981;79:44–51.

7.     Privat-Deschanel A. Elementary treatise on natural philosophy. JD Everett, trans., London: Blackie, 1872.

8.     Quinn T. From artefacts to atoms: the BIPM and the search for ultimate measurement standards. Oxford: Oxford University Press; 2011.

9.     Stewart J. The reality of phlogiston in Great Britain. Hyle. 2012;18(3):175–94.

10.  Taylor JH, editor. Journey through the afterlife: the ancient Egyptian book of the dead. Cambridge, MA: Harvard University Press; 2010.