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

By Anders Lundgren

According to a well-established tradition in the history of chemistry, the chemical revolution at the end of the 18th century was a product of the increased use of quantitative methods and of the balance, leavened by the law of the conservation of matter. Despite this emphasis on quantification in accounts of the transformation of 18th-century chemistry, most historians of chemistry have dismissed the topics of quantification, mathematics, and measurements in a few words.^[1] To redress the balance, I propose two approaches for studying the changing use of numbers in 18th-century chemistry.

The first approach stresses the influence of economic interests. During the 18th century, chemistry was often classified as an applied science. Mineralogy, metallurgy, and assaying, as aspects of applied chemistry, gave rise to an increased use of the balance and thereby a new role for numbers in chemistry. The second approach assays the influence of experimental physics. Before the beginning of the chemical revolution, important parts of experimental physics had been subjected to quantification.^[2] Many chemists during the 18th century

invoked physical concepts in explaining their subject matter: witness the assimilation of Newtonian forces and chemical affinities. Lavoisier was only one of a company of chemists who saw themselves as physicists.^[3] Consideration of the influence of experimental physics on laboratory instruments and chemical theories will also speak to the use of numbers in chemistry.

The Balance

The close association of chemistry with practical arts has figured prominently in the history of technology. In the index to the eight-volume History of technology edited by Charles Singer et al., for example, references to chemistry fill almost one page, whereas there is no reference at all to physics.^[4] Historians of the chemical revolution have not dwelt on this association with technology, presumably because they have regarded the revolution as a transformation in theory.^[5]

In the beginning of the 18th century, traditional chemical theory had little to do with the daily practice of chemistry. Existing theory was antiquated, almost entirely qualitative, and infused with compounds of Aristotelian elements and Paracelsian principles. As chemical descriptions of processes and substances were refined, old theories

lost their empirical foundation. Theories capable of organizing the growing body of empirical observations were in order. Mining practice, one of the most important practical fields and one that contributed to a changing use of numbers in chemistry, will be a focus here. The shape of the resulting systems bore the imprint of mining practice.

By 1700, the balance had long been in use in both metallurgy and assaying.^[6] The hydrostatic balance determined density and controlled purity of different substances, especially the noble ones, and assisted in the control of less than noble practices. After introducing the balance in testing gold sand imported from Guinea, the British noticed a marked decrease in "the swindling the natives practiced."^[7] But the method could be used only to determine mixtures of metals, never to decide chemical composition. In fact, the hydrostatic balance was afflicted by so many sources of error that it gave results scarcely better than assayer's needles and touchstones. (The needles were gold-silver mixtures of known composition; by matching the color of an unknown sample to that of a needle, the assayer could quickly estimate its makeup.)^[8] Despite the fact that the balance played a modest role in practical metallurgy, knowledge of density did not bring the chemist to a better understanding of chemical processes or of the chemical characteristics of a given substance.

The chemical (as opposed to the hydrostatic) balance does not appear in illustrations of laboratories of the 17th and early 18th centuries.^[9] Chemists did not use it in their daily work. Only in

commercial mining, which typically involved amounts of material far larger than anything of interest to the chemist or the assayer, was the balance at home. The most sensitive chemical balances were used exclusively for the weighing of noble metals. In De re metallica (1556), Georgius Agricola treats the balance in a section on the assayer's work and the purity of metals, and emphasizes that the most sensitive must be confined to weighing "the bead of gold and silver," since ores and other large weights would injure it.^[10] The balance played no part in the production of gold, but only in the measurement of the final, refined result.

Echoes of Agricola's attitude toward sensitive balances can be heard to the end of the 18th century. In 1689 J.J. Becher distinguished three types of balances with respect to sensitivity; his categories recurred in the writings of Johann Cramer in the mid, and of Sven Rinman in the late, 18th century. According to Rinman, the most sensitive balances, which could register changes as small as 1/128 ass (about 0.4 milligram), should be used only to weigh "the smallest bead. . .of the noble metals."^[11] Agricola, Becher, Cramer, and Rinman all assigned the same tasks to the balance. They did so independently of any theoretical commitments. Theories in chemistry retained their qualitative character until the end of the 18th century. However, from about 1750 the balance began to take on importance in the shaping of chemical theory.

Synthesis and Analysis Quantified

By synthetic quantification, I mean a recipe that states the amount of each ingredient in numbers and the relative proportion needed to produce a substance with specified properties. In analytical quantification, the chemist determines the proportions among the constituent parts of a given compound substance. Synthetic quantification had a long tradition in pharmaceuticals, mineralogy, and metallurgy, as in the production of different kinds of brass.^[12] Analytic quantification scarcely existed before the middle of the 18th century.

Synthetic quantification did not demand exact balances. The figures given in recipes were only approximate: ingredients did not come pure and the recipes were the result of trial and error. A chemist tried one part of A and one of B, then two of A and one of B, and so forth, and then, by comparing the different products, chose the better recipe. A case in point is Johann Heinrich Pott, whose Chymische Untersuchungen of 1754 included extensive "Tabellen von denen Würckungen der verschiedenen Mischungen derer Erden." The tables recorded Pott's attempts to obtain a certain iron product able to withstand high heat. He mixed ingredients in various proportions,^[13] but the abundance of expressions like "about 4 parts to 1," "a little more was added," "a greater part," "most of it," in his tables suggest that we should not ascribe much weight to the numbers offered. Pott and his contemporaries resorted to these imprecisions because they lacked standards for measurements and uniform scales and weights.^[14] Compounding this lack was a plethora of impurities, which could cause successive weighings to give very different results even if carried out in exactly the same way. This last problem particularly afficted the medical branch of applied chemistry, pharmacy.^[15]

In pharmacies balances played much the same roles as in metallurgy and assaying.^[16] A pharmacist sold substances by weight, as indicated by the prominent position of the balance on the shop counter, and compounded drugs by weight according to the recipes in the pharmacopoeias. As in the case of the assayer, however, the pharmacist's method of measuring was independent of theory. The role of chemistry in the business was confined to qualitative aspects and in practice influenced the making of very few pharmaceuticals.

As practitioners of an art, apothecaries were trained by apprenticeship.^[17] The theory of their business was reserved for philosophical chemists who hobnobbed with savants. Carl Wilhelm Scheele confined his chemical work to his spare time, and Torbern Bergman explicitly reserved the theoretical part of pharmacy for the chemist.^[18] In all this pharmacy resembled metallurgy. Many metallurgists in Germany had either practiced as or trained under an apothecary.^[19] However, commercial demands on pharmacy did not lead, as in mining, to an increased use of analytical quantification. Synthesis, not analysis, was important for the apothecary; whose financial well-being did not depend on successful analysis. Nor was quantitative analysis important in medicine: with the techniques then available, it would have been impossible to subject the concerns of physicians to quantitative analysis.^[20]

The increasing use of analytical quantification in assaying during the 18th century was a consequence of the expanding number of known ores and minerals. In Sweden, for example, where mining

products were the backbone of the economy, discovering new sources of ores took high priority, especially after the failure of the Falun Copper Mine at the beginning of the century. This failure prompted search for substitutes that might have the same economical importance as copper.^[21]

In this process chemistry played a central part. Laboratories were built close to the different mines, in places like Ädelfors, Falun, and the little-known Skisshyttan, where Axel Fredrik Cronstedt organized a small chemical research center. The nature and activities of these relatively unknown laboratories need to be examined. They proved equal to their task; they helped solve the problems raised by mining and the iron industry—for example, how carbon influenced the quality of steel.^[22]

The significance of chemistry for metallurgy was further emphasized by the fact that the government Board of Mines employed a laboratory worker from the late 1630s, and regularly operated a Laboratorium chymicum from the 1680s.^[23] The main task of the laboratory was to prepare pharmaceuticals for the mining industry. From the beginning of the 18th century, it concentrated increasingly on mineral analysis, assaying, and mineralogy. In keeping with its original assignment, the first directors of the laboratory were physicians; but in 1718, when Georg Brandt became its director, the responsibility of running it was transferred to a mineralogist.

In German-speaking central Europe, interest in chemistry likewise grew with the economic importance of mining. Many German chemists, like Becher and Johann Heinrich Gottlob von Justi, also occupy distinguished places in the history of German economic thought.^[24]

When the French government wanted information on mining from the rest of Europe, they sent out a mining engineer with a thorough training in chemistry, Gabriel Jars.^[25]

Jars' appointment symbolized an important development in our history. Around 1700, empirical knowledge was sufficient to permit miners to decide the value of well-known minerals: a trained eye could sort samples by sight. But traditional knowledge was inadequate to manage the many new minerals discovered during the 18th century. Assayers found themselves in need of chemical knowledge. Only chemists armed with the methods of analytic quantification could answer the question, "How much iron does this ore contain, and how much of it can be made available?" In his Anfangsgründe der Probierkunst (1746), Johann Cramer declared that the assayer must be able to decide the composition of different substances "[i]n order to know what and how much of a [constituent] might be found in the substance under study, or could profitably be obtained from it."^[26]

The growing need for analytical quantification raised the balance to a more prominent position in the assayer's workplace, the forerunner of the chemical laboratory. When Cramer described his laboratory, or "Arbeitsstätte," in 1746, ovens and cupels were still the most important instruments, but balances also received attention; Cramer claimed that his newest balance could give "the weight of the smallest body exactly." Still, weight is not everything, and Cramer acknowledged that even the most sensitive balance had to be supplemented by needles and touchstones in order to determine the composition of important substances.^[27]

From mineralogy, analytical quantification spread into other fields of chemistry, including wet analysis. Mineral water was a favorite subject of study, even though its constituents were not intended for individual sale. Analysis facilitated subsequent synthetic quantification of naturally occurring mineral waters deemed to be especially valuable.^[28] Another sort of wet analysis, titrimetry, also became more important during the second half of the 18th century. Here, too, commercial concerns were at work, since analysis helped in determining the purity of sulfuric acid, among other substances.^[29]

Toward the end of the century analytical quantification seeped into ordinary textbooks of chemistry. Bergman's edition of H.T. Scheffer's lectures, Chemiske föreläsningar (Uppsala, 1775), is an instructive example. The material Bergman added almost doubled the size of the original, published thirty years before. In Bergman's additions, the composition of chemical substances is given in the form "100 parts of A contains x parts of B, y parts of C," and so on;^[30] no such formulas appeared in Scheffer's original text.

By Bergman's time it was common for chemists to describe composition quantitatively.^[31] Formulas did not necessarily afford great precision, however. Analytical quantification was a more difficult assignment than synthetic quantification; the same analytical procedure could yield very different results even when applied twice by the same chemist to the same substance. Insensitivity of the balances and, more importantly, difficulty in procuring and identifying pure substances, contributed to the variations. Early analytical quantifica-

tion thus represented a new use of numbers—whatever their exactness—but did not at first assist in the development of chemical theory.

Constant interaction between chemistry and mineralogy would change the situation. Analytical quantification led to important changes in mineralogical classification systems. Up to the middle of the century, these classifications remained a species of natural history—relatively simple and qualitative, based on the external characteristics of minerals. The more substances mineralogists needed to classify, however, the greater the difficulties they experienced in relying only on external characteristics.^[32] Classification by internal characteristics—that is, by chemical composition—offered an attractive alternative or supplement. The shift from classification on the basis of external physical properties to that based on internal, chemical composition began around 1750. Cronstedt's system of 1758 is an early example.^[33] He denied the value of description from external factors and plumped for one based on chemical composition. His program gave chemistry a new role as a describer of mineralogical species. Although Cronstedt did not use numbers to express chemical composition in numbers, the growing importance of analytical quantification made it just a matter of time before others did so as a natural part of chemical description.

The determination of composition by weight consequently was not inspired primarily by attempts to formulate a classificatory system, but by the need to describe individual species more accurately. The balance and analytical quantification contributed to improved description, but only within a basically qualitative scheme of classification.

(The order in a system of mineralogical classification, for example, continued to depend on the qualitative properties of the substances to be classified.) It was only with Joseph Louis Proust's system of definite proportions in the 1790s that improved descriptions were incorporated into a quantitative classificatory scheme. Proust arrived at his basic concepts while working as a chemist and mineralogist for the Spanish Government.^[34] The research that inspired the theory of definite proportions, which immediately found its way into the mineralogical classification systems and gave a forceful impetus to the change from qualitative to quantitative description, concerned economically important oxides of iron.

Mineralogy thus began to transform itself from a technical art into a science. In it chemistry played important roles, providing both the overall qualitative pattern for classification and exact, quantitative descriptions of mineral species. This dual role finds a parallel in the tension between practice (economic interest) and theory (scientific interest) in the development of mineralogical classifications. Economic interest argued for a system based on monetary value; chemists preferred a system based on composition. Bergman even tried to amalgamate the two systems into one.^[35]

Bergman envisioned a scientific mineralogical system whose classes were determined by the most dominant ingredient of the mineral where dominance was defined quantitatively. Value can also be quantified, however, and it was therefore both possible and advantageous in practice to include in one class all minerals containing gold and silver regardless of their content of noble metal.^[36] Similarly, any mineral that derived its economic or metallurgical properties from one particular component might be placed in the class of that component, not in the class of the quantitatively dominant component.

Every systematizer used both qualitative and quantitative methods in the laboratory. The blowpipe, for example, never ceased to be an important tool for the mineralogist. According to Berzelius, miner-

alogical classification approached "mathematical certainty" thanks to the theory of chemical proportions.^[37] But he also insisted that the constituents of a compound must be found "in their nature as well as in their quantity." He combined the results of his undisputed mastery with the blowpipe with a consistent application of numbers. The game can also be played on pharmaceuticals. Berzelius was the first to do so systematically.^[38]

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

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

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-

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

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]

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

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

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

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

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.

Conclusions

During the 18th century an increasing body of chemical facts was expressed in quantitative form. Economic pressures in mineralogy and the general influence of experimental physics inspired the development of new mineralogical systems, in which quantitative descriptions of the units to be classified were an essential feature, and forced a change in the use of the balance for analytic as well as synthetic quantification, which eventuated in the theory of definite proportions.

Experimental physics did not influence chemistry by the direct application of basic physical concepts of affinity or the atom or by the direct use of mathematics. Rather, it encouraged the use of instruments yielding quantitative data: balance, thermometer, and calorimeter. On the epistemological level, it brought an instrumentalist view of theories and so contributed fundamentally to the reinterpretation of known facts that lay at the heart of the chemical

revolution. Instrumentalism was at work, for example, in the phlogistic debates and in the attempts to define an element. Quantification in chemistry did not result in generalized laws until it was augmented by the atomic theory; even then the theory bore the mark of chemistry as a whole—the task of describing the unique. Finally the rhetoric of number played an important role in propagating Lavoisian chemistry.

The change can be summarized in the sorts of questions that were put to the balance. In the beginning of the 18th century, the main question was "How much is needed to produce this substance?"—a question of synthetic quantification. Later in the century, the question shifted to one of analytic quantification: "How many parts of different constituents make up this substance?" With the atomic theory, the question became "What is the atomic weight of this element?" The evolution of questions reflected the growing theoretical importance of the balance. No great increase in the accuracy of the balance prompted or accompanied this change. The exact measurements necessary for a quantitative physics were not necessary for a chemical revolution; what was required was increased awareness within chemistry of the significance of measurement.