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Miller, William Lash


(b. Galt, Canada, 10 September 1866; d. Toronto, Canada, 1 September 1940)


During the last decade of the nineteenth century and the early part of the twentieth century Miller played a leading role in the development of chemistry in Canada. In accordance with the tradition of the time, classical studies formed a significant part of his undergraduate training at the University of Toronto, although this was leavened with courses in mathematics, physics, chemistry, biology, mineralogy, and geology. After receiving his B.A. degree in natural philosophy in 1887, Miller went to Germany. After spending some time in Berlin and Göttingen he proceeded to Munich, where he took his Ph.D. under Baeyer in 1890. He then moved to Leipzig to work in Ostwald’s laboratory. This was a turning point in Miller’s life, and he continued to spend his summers with Ostwald after he had become a member of the staff of the department of chemistry at Toronto and had received his second Ph.D. at Leipzig in 1892. It was at Leipzig that he first became acquainted with the elegance and applicability to chemistry of the thermodynamic approach of Josiah Willard Gibbs.

In a series of papers published largely in the Transactions of the Connecticut Academy of Arts and Sciences (1873–1883), Gibbs had laid the foundation for chemical thermodynamics; but it was left to Ostwald and Miller to translate Gibbs’s highly theoretical treatment into laboratory terms. Most of Miller’s academic life was devoted to this activity. In one of his first scientific papers (1892), he showed that the electromotive force of an electrochemical cell having a metallic electrode of mercury, lead, or tin was independent, at the melting point, of whether the metal was in the liquid or the solid state, and hence the factor determining the electromotive force at constant temperature and pressure must therefore be the chemical potential, or Gibbs free energy.

Miller was particularly adroit in applying and extending Gibbs’s theories to polycomponent systems. When one of his students found that the addition of salt to an aqueous solution of alcohol raised the partial pressure of alcohol, an effect opposite to that predicted by then-current theories, he was able to show that this was a logical consequence of thermodynamic reasoning and proved it in the paper “On The Second Differential Coefficients of Gibbs Function ζ”(1897). His appreciation of the importance of having quantitative values for these second differential coefficients dominated his approach to both teaching and research. It also led, in later years, to some controversy between the Miller school of thermodynamics and that of G. N. Lewis at Berkeley. In retrospect, this controversy was seen to relate to a choice of formalism rather than logic. Lewis chose to use two quantities, the standard state and the activity coefficient, which are related to the first derivative of the Gibbs free energy; Miller used the second differential coefficient of the Gibbs free energy. Whereas Miller’s choice was mathematically more elegant, and possibly a better method for the beginning student, the Lewis approach was more practical insofar as getting accurate data for real systems is concerned. Miller realized this difference, and saw to it that his students were exposed to the two approaches.

During his long career at Toronto, Miller had a record of outstanding research in several areas of physical chemistry: chemical equilibriums, rates of reaction, electrochemistry, transference numbers, over-voltage, high-current electric arcs, and diffusion. In his later years he was attracted by problems of a biochemical nature, particularly by growth factors for simple cells like the yeasts.

In 1894, when Miller was promoted to lecturer in chemistry, he introduced research as a regular part of the fourth year of the undergraduate honors program, a step that has been followed in many other disciplines and institutions. He was made associate professor in 1900 and professor in 1908. When World War I broke out, the head of Miller’s department took leave to enter active military service and Miller became de facto head. He remained in that capacity until his retirement in 1937.

Miller’s leadership in research was paralleled by his active role in many professional societies and academies in Canada, Great Britain, and the United States. As early as 1910 he was chairman of the Canadian Section of the Society of Chemical Industry. He was one of the chief organizers of the Canadian Institute of Chemistry (its president in 1926) and of the Canadian Chemical Association. All three societies were eventually amalgamated to form the present Chemical Institute of Canada. In 1926 Miller was the first Canadian to be made an honorary member of the American Chemical Society and served for many years as an associate editor of its Journal. He was active in the establishment of, and as an associate editor of, Journal of Physical Chemistry. His distinction as a scientist and his leadership in his profession were recognized when he was made a commander of the Order of the British Empire.


I. Original Works. Miller’s works include “Über die Umwandlung Chemischer Energie in Elektrische,” in Zeitschrift für physikalische Chemie, 10 (1892), 459–466; “On the Second Differential Coefficients of Gibbs Function ζ. The Vapour Tensions, Freezing and Boiling Points of Ternary Mixtures,” in Journal of Physical Chemistry, 1 (1896–1897), 633–642; “The Theory of the Direct Method of Determining Transport Numbers,” in Zeitschrift für physikalische Chemie, 69 (1910), 436–441; “Mathematical Theory of the Changes in Concentration at the Electrode Brought About by Diffusion and by Chemical Reactions,” in Journal of Physical Chemistry, 14 (1910), 816–885, written with T. R. Rosebrugh; “The Influence of Diffusion on Electromotive Force Produced in Solutions by Centrifugal Action,” in Transactions of the Electrochemical Society, 21 (1912). 209–217; “Toxicity and Chemical Potential,” in Journal of Physical Chemistry, 24 (1920), 562–569; “The Method of Willard Gibbs in Chemical Thermodynamics,” in Chemical Reviews, 1 (1924–1925), 293–344; “Numerical Evaluation of Infinite Series and Integrals Which Arise in Certain Problems of Linear Heat Flow, Electrochemical Diffusion, etc.,” in Journal of Physical Chemistry, 35 (1931), 2785–2884, written with A. R. Gordon.

II. Secondary Literature. See C. J. S. Warrington and R. V. V. Nicholls, A History of Chemistry in Canada (New York, 1949), and the obituaries by Frank B. Kenrick, in Proceedings of the Royal Society of Canada, 3rd ser., 35 (1941), 131–134, and by Wilder D. Bancroft, in Journal of the American Chemical Society, 63 (1941) 1–2.

Donald J. Le. Roy

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