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8 The Changing Role of Numbers in 18th-Century Chemistry
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Experimental Physics and Chemistry

During the 18th century, the word "physics" meant both general knowledge of nature and "experimental philosophy." In the second, newer sense, physics was quantified or quantifiable—it attempted to formulate mathematical laws from experimental results obtained by means of specially constructed instruments.[39] It is the influence on chemistry of experimental physics that concerns us here.

Around 1700, there were few connections between physics and chemistry. John Keill's and John Freind's efforts to use Newtonian concepts in calculating chemical affinity did not attract many followers.[40] The influential 31st Query to Newton's Optics referred affinity to atoms interacting by Newtonian forces. No one succeeded in handling the subject mathematically, however, and at the end of the century some chemists working in the Newtonian tradition, like Bergman, declared it to be impossible. Newtonian views of atomism and affinity had little or no effect on concrete chemical work. A common approach to the relations between matter theory and chemical thinking may be seen in the work of Ernst Stahl, who accepted a corpuscular philosophy but based his chemical understanding of


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matter on laboratory work. He made a clear distinction between chemistry and physics, saw chemical elements as compounds, and did not consider it the task of the chemist to penetrate deeper.[41] Throughout the 18th century, the atomic theory hovered in the philosophical background against which chemists carried out their work.

The difficulty of applying physical theory to chemical phenomena derived from the fundamental difference between the two disciplines: physics dealt with properties common to all substances, whereas chemistry dealt with their special characteristics. The chemist described unique substances and did not aim at discovering general laws. Even Proust's theory of definite proportions did not explain why these proportions existed. Proust is said to have had little interest in any sort of theory.[42] As late as 1810, when Berzelius considered definite chemical proportions, he could not decide whether the proportions "obey laws, common for all substances, or depend on circumstances unique for each substance."[43]

Working chemists saw physics as very different from chemistry.[44] Johann Friedrich Henckel, in his influential Pyrotologia oder Kiess-Historie (1725), mentioned "gravitas specifica" as a property to be studied with the hydrostatic balance, but the insights thereby gained would be physical rather than chemical. Even though determination of specific weights was still part of metallurgy, Henckel did not own a hydrostatic balance; the remarks about specific weight in his book were instead contributed by his less well-known colleague, Dr. Meuder. To learn chemical properties, Henckel argued, there was no way to avoid tedious laboratory work, despite the opinions of philosophers "who did not like to dirty their hands with coal."[45] Pott liked


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to say that physics was the study of the superficial, far from the reality examined in chemistry: "it is an important difference, that superficial physics only describes the external and largely changeable shape of objects, while a reasonable chemistry can discover and bring to light through its experiments the inner forces and characteristics, fundamental composition, and partes constituantes of objects."[46]

In spite of the disparaging rhetoric, ideas borrowed from physics took hold in chemistry, particularly in the English development of pneumatic chemistry with its emphasis on empiricism, instrumentalism, and, ultimately, measurement.[47] Here the influence of Stephen Hales and Joseph Priestley on continental chemistry, and especially on Lavoisier, deserves particular emphasis.[48] Experimental physics made crucial contributions to chemistry—among them, a new attitude toward instruments and the quantitative facts they yielded, and a new methodology, which included an instrumentalist interpretation of theories.

Instruments and Facts

As the use of instruments characteristic of experimental physics spread to chemistry, new sorts of facts seized the chemist's attention. In 1750, Pott could say of fire as a chemical substance: "Although in its subtlety it cannot be investigated by number, measure, or weight, yet chemistry discovers a goodly number of its attributes."[49] The impact of experimental physics changed matters. The means of production of chemical facts in themselves remained much the same—distillation, vaporization, and precipitation, according to the tradi-


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tional practices of assayers, pharmacists, and others in chemical trades—but, thanks to the influence of physics, facts yielded up by the balance assumed greater importance.

The major innovation at midcentury was not high accuracy in measurements, but rather numerical measurement per se. Exactness was not essential to the formulation of the theory of definite proportions. Proust derived his ideas about the chemical significance of proportions from his work in ordinary practical metallurgy, the inaccuracy of which left plenty of room for the debates between himself and Berthollet over the nature of chemical combination.[50] The arguments central to Lavoisier's classical investigations on the supposed conversion of water to earth did not depend on great accuracy;[51] they did, however, rest on a numerical base. Nor did his studies of fermentation indicate the importance of exact measurement in the concrete study of chemical processes. To be sure, Lavoisier gave the law of the conservation of mass in mathematical form in order to demonstrate its exactness, but he never came close to exactness in actual experiments.[52] None was needed. The balance merely gave a gravimetric criterion for identifying and describing a unique chemical substance.[53]

Lavoisier thus relied on a rhetoric of numbers. The complication of chemical reality, which could not be idealized, might have compromised the rhetoric. But Lavoisier and others explained away


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large numerical discrepancies by invoking unknown chemical processes. In the water conversion experiment, for example, the numerical shortfall was blamed on a chemical reaction between the glass and the water.[54] Still, the precision balance and the law of the conservation of matter conferred upon numbers a rhetorical value similar to what they enjoyed in physics and other fields during the late 18th century. Lavoisier made good use of the eloquence of the balance when arguing for the new chemistry.

Imponderables posed special technical problems. Lavoisier and Joseph Black wished to subject imponderables to quantitative study, but the usual array of chemical instruments offered no help. Other experimental devices were called for, such as the thermometer, which had not been an instrument for the chemist, and above all the calorimeter, recently constructed. These new instruments, introduced into chemistry from physics, became central to the study of chemically important substances. Deliberately constructed to yield quantitative results, they contributed to the introduction of numbers into chemistry. The study of heat stood at the intersection between physics and chemistry. Lavoisier and his physicist colleague Laplace met the problem of measuring the amount of heat participating in a chemical reaction by inventing the ice calorimeter.[55] Bergman, both physicist and chemist, found a way to measure the relative phlogiston content of two metals. He knew that a metal lost its phlogiston in acid solution but could regain it when another metal was added to the solution. He therefore dissolved a certain weight of one metal in acid and then weighed the amount of a second metal necessary to precipitate entirely the first from solution. In his chemistry, the amounts of phlogiston in the two metals were proportional to the weights so determined.[56]


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Instruments and Theory

The influence of experimental physics on chemical theory was still negligible in the middle of the century. Although interest in Newtonian ideas about affinity then began to increase, and although affinity was supposed to be a distance force, the tables remained descriptions of empirical facts, in practice irrelevant to any theory of affinity. This generalization holds for the work of the thoroughgoing Newtonian Etienne François Geoffroy and also for Bergman, who brought the affinity tables to their fullest form.[57] Also, the Newtonian concept of the ether did not attract attention during the heyday of phlogiston and affinity studies. It later influenced Lavoisier.[58]

The influence of physics on chemistry was most evident on the continent in France, which, perhaps not coincidentally, had a relatively weak tradition in mining.[59] In Germany and in Sweden, chemists took less interest in physics because of the difficulties of applying it to mineralogy and because of the tendency of Stahl and his followers to keep Newtonian mechanics away from practical chemical work. Chemists who did show interest in physics in the last decades of the 18th century typically had some attachment to the universities. That in any case was true of Sweden.[60]

Relations between mathematics and chemistry were strained by the inability of the one to calculate anything of interest for the other. This was especially true in atomic theory. As Joseph Black put it, the assumption that a certain attractive force existed between certain atoms was void, since "all the mathematicians of Europe are not


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qualified to explain a single combination by these means."[61] Macquer, though appreciative of Newtonian methods, thought that some mathematics was needed to formulate a general theory of chemistry; "but that [he said] does not fall into our line of work." As a pharmacist he recognized the complicated reality of the chemist: "Perhaps chemistry is not yet sufficiently advanced to be made the subject of calculation, perhaps it will never be [since] the problems that it will present mathematicians might be so complicated that they would be beyond all human effort."[62] Bergman, who was close to Pierre-Joseph Macquer and Guyton de Morveau, had a thorough knowledge of physics, admired Newtonian methods, and was capable in mathematics. None of these tools seemed useful for the study of the atom. For Bergman, empirical knowledge of atoms was itself impossible; certainly they could not be studied quantitatively.[63]

What chemists did take from experimental physics was an instrumentalist attitude toward theories. William Cullen and Joseph Black, following one methodological approach inherited from Newton, insisted that empirical knowledge and theoretical explanations should be kept separate.[64] The first part of Black's classical treatise, Experiments on magnesia alba (1750), is given over to experiments; the second, to their interpretation and theoretical explanation.[65] The instrumentalist approach fit well with a new view of theories during the late 18th century. English chemists wrote about the caloric


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theory of heat in an instrumentalist way and did not commit themselves about its absolute truth.[66]

Instrumentalism triumphed in chemistry with Lavoisier's definition of an element.[67] It was perhaps his most important contribution to a new theoretical role for numbers in chemistry. The definition of a chemical element as the simplest substance available in the laboratory ignored philosophical questions concerning the structure of matter and denied elementary status to the old elements and principles. Lavoisier's definition turned the concept "element" into empirical operations independent of any hypothesis about the structure of matter; at the same time he made the definition the starting point for the construction of theories.

Lavoisier's view of chemical elements represented a break from the earlier concept of chemical facts as so many benchmarks in the search for absolute truth.[68] Lavoisier's definition augmented by the atomic theory, gave numbers a new function in chemistry. This theory can be regarded as a combination of definite chemical proportions, derived from practical chemistry, with the instrumentalist notion of a simple body, derived from experimental physics. Dalton's atomic theory used numbers to express its central concept—atomic weight. With the help of Dalton's rules of simplest combination and the assumption of definite proportions, the different weights could be interrelated. The balance thereby acquired a definitive role in the construction of chemical theory.

Although the atomic theory gave to chemistry numbers invested with theoretical significance, it did not provide generalized laws in mathematical form. The study of discrete atomic weights thus made it possible to combine theory and practice in a quantitative way without commitment to the existence of atoms. The atomic theory


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eventually overcame philosophical opposition by its success in explaining experimental facts and by distancing itself from physical atomic theory.[69]

Phlogiston Modified

It might seem inappropriate to treat the phlogiston theory here, since it is rightly considered a qualitative system. But as the dominant theory of 18th-century chemistry, and as a theory undermined by Lavoisier's brand of "quantification," the modifications of phlogiston theory in the face of quantitative facts have a claim on our attention.

Phlogiston functioned as a qualitative classifier and offered a rational explanation of the behavior of combustible substances. Like Aristotelian elements and Paracelsian principles, phlogiston could not be isolated in pure form, and it could not easily explain details of chemical processes. Yet there was one important difference: the existence and properties of phlogiston had been inferred from many and repeated empirical observations. It was easy to demonstrate that smoke, heat, fire, and perhaps also matter escaped from burning bodies. Moreover, phlogiston theory was developed by chemists who considered chemistry a practical science and who had a deep knowledge of metallurgical and mineralogical practice.

Swedish and German chemists close to mineralogy generally adhered to the theory and pushed it to its limits. Bergman's attempts to calculate the phlogiston content of different metals is especially interesting in showing how a chemist could combine Newton and Stahl.[70] Adherence to Newtonian method might thus go hand in hand with acceptance of the phlogiston theory. Bergman insisted on strong empirical foundations and on an instrumentalist interpretation


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of theories. He distinguished between chemia vulgaris , or traditional descriptive chemistry, and chemia sublimior , or transcendental chemistry; he compared the objects of the latter to the "fluxions and infinitesimals of the more sublime or transcendental geometry."[71] An instrumentalist interpretation of phlogiston theory helped its adherents to make the switch to the oxygen theory. Quantitative facts alone did not kill the phlogiston theory. Increased accuracy of measurements certainly played no important part in its demise. A very crude balance was sufficient to show that weight increased during combustion. The details of the shift deserve careful investigation, and the influence from experimental physics should be taken as a starting point for reinterpretation of the role of phlogiston in the history of chemistry.


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