Brodie, Benjamin Collins, Jr.

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Brodie, Benjamin Collins, Jr.

(b. London, England, 5 February 1817; d. Torquay, England, 24 November 1880)


Brodie was the son of a prominent surgeon who was also a president of the Royal Society. He attended Harrow and then entered Balliol College, Oxford. After graduating, he left England for the famous chemical laboratory at Giessen, where, in the summer of 1845, he worked under Liebig on the analysis of beeswax. He returned home about 1847 and continued his chemical studies in a private laboratory in London. He was elected a fellow of the Royal Society in 1849. In 1855 he became Waynflete professor of chemistry at Oxford, a position he held until 1873.

Brodie pursued the investigation of waxes that he had begun in Germany, and soon discovered and named cerotic acid, cerotin, and melissic acid. A few years later he examined graphite and discovered graphitic acid. Brodie discussed his findings in this early work in terms of the accepted language of the atomic theory, representing the new substances by conventional formulas. He soon abandoned this treatment, however.

Brodie is interesting as a historical figure on account of his drastic proposals for an alternative approach to chemistry, which he first put before the Royal Society in 1866. By this time a skeptical attitude toward Dalton’s atomic theory had arisen. Chemists welcomed the convenience of the theory as a summary of known facts and employed its language, but they were not prepared to discuss the question of the ultimate divisibility of matter. It was sufficient to know that certain masses were undivided by the powers of chemistry. Gerhardt’s statement that chemical formulas did not represent actual atomic arrangements, but merely the relations between substances in chemical change, was quoted with approval by Brodie, who placed it at the head of his 1866 paper.

This was not enough for Brodie, however. The advertisement in a chemical journal of a set of balls and wires as an aid to the study of chemical combination was evidence enough for him that the science of chemistry had gone “off the rails of philosophy.” Only an accumulation of errors could have produced such a “bathos.” He therefore proposed to substitute an exact language, free from any association with Dalton’s theory. He said that this would be independent of any hypothesis on the nature of matter. Its symbols would simply express the facts.

The new symbols represented chemical operations performed on space. Brodie regarded the method as an applied algebra and stated that he had been guided by algebraic procedures in geometry and logic. He made several references to George Boole. Just as in geometry a symbol could indicate the operation on a unit of length by which a line was generated, so in chemistry a symbol could represent an operation on space which produced a weight. All substances were considered to be perfect gases. The chemical unit of ponderable matter was that which occupied 1,000 cc., the “unit of space,” at standard temperature and pressure. The symbol α represented the operation on the unit of space from which a unit of hydrogen resulted. The compound that resulted from the successive operations α and χ had the symbol αχ. The logarithmic relation α + χ = αχ was one of the fundamental equations of the calculus.

In Brodie’s scheme only weight would be considered; the form, color, and other properties of matter would be neglected. He would investigate the distribution of weights in chemical change by the appropriate symbols, which were derived with the aid of experimental data on gases. For example, the decomposition of water vapor, in which two volumes of water produce two volumes of hydrogen and one of oxygen, was represented as 2ϕ = 2ϕ1 + ϕ2, where ϕ, ϕ1, ϕ2 are the symbols of units of water, hydrogen, and oxygen, respectively.

Let ϕ = αmξn, ϕ1 = α, ϕ2 = αpξq, where α and ξ symbolize uncompounded component weights (prime factors) and m, n, p and q are positive integers. By the fundamental logarithmic relationship 2ϕ = 2ϕ1ϕ2, or (αmξn)2 = α2αpξq, so that 2m = 2 + p and 2n = q. Density data were brought into the calculation and the equations were finally solved, subject to the condition of a minimum number of prime factors. The unique solution is then m = 1, n = 1, p = 0, q = 2. The symbol for the unit of oxygen is therefore ξ2 and that for water is αξ.

Symbols of other substances, obtained by similar reasoning, formed three distinct classes. One group of substances, typified by hydrogen, was represented by a single letter, that is, only one operation on space was needed for their production. The group of doublelettered symbols indicated that two successive operations were needed to form the substances concerned. This was the case with oxygen, ξ2 or ξξ. The third group included chlorine, αχ2, nitrogen, αν2; and hydrogen peroxide, αξ2. These substances could not be formed by fewer than three operations on the unit of space.

Brodie discussed the exciting implications of his symbols. Substances regarded as elements were of the same symbolic form as substances known to be compounds. The ξ2 component of hydrogen peroxide indicated the presence of oxygen. But how were χ2, ν2, and ξ to be interpreted? They could not be dismissed as imaginary units, since, Brodie argued, they had been discovered in the course of analysis. Nor would he positively claim that ν, ξ, and χ represented real pieces of matter. He preferred to call such symbols “ideal.”

He could not exclude the possibility that chlorine, for example, might really consist of α and χ. This view that the elements might be compounded had earlier been favored by Davy and Prout. Brodie speculated that at some remote age, when the earth was very hot, the simple forms of matter—α, χ, ξ, and so forth—might have existed. As the earth’s temperature fell, these formed combinations, like chlorine, which were so stable that they never decomposed again. The primitive materials might still exist, however, on the sun and in distant nebulae. The independent existence of χ and ν might be detected by a spectroscopic examination of heavenly bodies. Indeed, a recent investigation of a nebula had shown its spectrum to be like that of nitrogen, but less complex. Later, he also seized on some erroneous experiments on chlorine as evidence of its compound nature.

Brodie failed to convince chemists to abandon their association with atoms. The weakness of the calculus of operations was indicated by Naquet, who translated Brodie’s work into French. He pointed out that there was no way to distinguish isomers, compounds such as acetaldehyde and ethylene oxide, which have identical compositions by weight but exhibit completely different properties. This anomaly was readily explained on the atomic theory by assuming different arrangements of particles in space. Brodie had restricted his treatment to weights, and without additional suppositions his calculus could not explain the different qualitative changes resulting from identical gravimetric redistributions. The spatial properties of matter assumed particular importance in the stereochemistry of Van’t Hoff and Le Bel, which appeared in 1874. The excess explanatory capacity of the atomic theory won the confidence of chemists, and Brodie’s calculus was never adopted. It was left as a curious relic of the positivistic tendencies of nineteenth-century chemistry.


I. Original Works. Some of Brodie’s scientific papers include “An Investigation on the Chemical Nature of Wax,” in Philosophical Transactions, 138 (1848), 147–158, 159–170, and 139 (1849), 91–108; “On the Atomic Weight of Graphite,” ibid., 149 (1859), 249–259; “On the Decomposition of the Simple Weight X Effected by Victor Meyer,” in Journal of the Chemical Society, 35 (1879), 673–682. A list of Brodie’s other scientific papers is given in the Royal Society Catalogue of Scientific Papers.

Brodie presented his calculus in “The Calculus of Chemical Operations,” in Philosophical Transactions, 156 (1866), 781–859, and 167 (1877), 35–116. A less formal exposition, together with some reactions to the calculus, can be found in Brodie’s “On the Mode of Representation Afforded by the Chemical Calculus, as Contrasted With the Atomic Theory,” in Chemical News, 15 (1867), 295–305. A corrected version of this was later published as Ideal Chemistry (London, 1880).

II. Secondary Literature. Brodie’s work has been discussed in W. H. Brock and D. M. Knight’s “The Atomic Debates: Memorable and Interesting Evenings in the Life of the Chemical Society,” in Isis, 56 (1965), 5–25; and in W. V. Farrar’s “Sir B. C. Brodie and his Calculus of Chemical Operations,” in Chymia, 9 (1964), 169–179. A. Naquet’s critique of Brodie’s calculus may be found in “Considerations on the Two Memoirs of Sir B. C. Brodie on the Calculus of Chemical Operations,” in Philosophical Magazine, 7 (1879), 418–432. Some additional information on Brodie can be found in J. R. Partington, A History of Chemistry, IV (London, 1961–), 425–427.

D. C. Goodman

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Brodie, Benjamin Collins, Jr.

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