(b. Carnoustie, Scotland, 17 May 1839 [perhaps 1838]; d. Oxford, England, 25 August 1916)
Esson’s father, also William Esson, was a bridgebuilding engineer, and consequently the family often moved. Esson was an only child. He attended the Royal Academy in Inverness and the grammar school in Cheltenham, then studied mathematics at St. John’s College in Oxford. In 1860 he was elected a fellow of Merton College, later becoming a tutor of Merton, where he was a lecturer in mathematics. His teaching was so successful that other colleges sent their students to hear him. In 1872 he married Elisabeth Meek, a pastor’s daughter; they had two sons and one daughter. Esson became a deputy professor in 1894 and in 1897 obtained a professorship of geometry. Between 1898 and 1913 he was chairman of the board of the faculty of natural science. He had been a fellow of the Royal Society since 1869. He was a passionate mountain climber and a member of an alpine club.
Although Esson was a mathematician and a professor of geometry, he published almost nothing in his own field; he contributed greatly, however, to the employment of higher mathematics in chemistry (this science had so far been satisfied with the application of arithmetic). Esson worked in his youth as a chemistry demonstrator under Vernon Harcourt, a professor of chemistry at Oxford, and the collaboration between the two researchers continued after Esson himself rose to the rank of professor. Together they considered many problems of chemical kinetics.
In 1864 they investigated the reaction of potassium permanganate with oxalic acid and, in the course of their study, nearly succeeded in formulating the law of mass action (“On the Laws of Connexion Between the Conditions of a Chemical Change and Its Amount,” in Proceedings of the Royal Society, 14 , 470–475). (The law was formulated at the same time, but in a simpler and more general form, by the Norwegians C. M. Guldberg and Peter Waage, who are generally credited with it.)
By examining the reaction process, Esson and Harcourt reached the conclusion that “in unit volume of a dilute solution at constant temperature the rate of chemical change varies directly with the mass of each of the interacting substances,” or “the velocity of chemical change is directly proportional to the quantity of substance undergoing change.” They presented the law of reaction velocity in exponential form: y = ae−ax, where x is the time, a the initial concentration and a a constant. Or, in the case of α binary reaction where u = ae−(a+β)x, it follows that it takes an infinite time for the chemical reaction to go to completion.
In a later article (“On the Observation of the Course of Chemical Change,” in Philosophical Transactions of the Royal Society, 157 , 117–137), Esson and Harcourt discussed the reaction between hydrogen peroxide and hydroiodic acid. They established that “in the presence of a large excess of iodide, the reaction is of the first order in respect of the hydrogen peroxide.” In studying the effect of temperature on the reaction they found that K and Ko (the velocity coefficient at the two absolute temperatures T and To) are related to the temperatures
To be sure, Esson’s formulations were rather too complicated for his contemporaries. Their merits were not recognized until the laws of chemical kinetics were fully stated on the basis of other considerations and the work of many other researchers.
I. Original Works. Besides the articles in the text, Esson’s writings, all with Harcourt, include “Characters of Plane Curves, a Law of Connexion Between Two Phenomena Which Influence Each Other,” in International Congress of Mathematicians (1912); and “On the Variation With Temperature of the Rate of a Chemical Change,” in Philosophical Transactions of the Royal Society, 212 (1913), 187–204, a summary of their work in this field. A more detailed version of the 1865 paper is in Philosophical Transactions of the Royal Society, 156 (1866), 193–221. It appears under Harcourt’s name only, but Esson’s participation is mentioned in the text.
II. Secondary Literature. See the article “William Esson,” in Proceedings of the Royal Society, 93A (1917), 54; and J. R. Partington, A History of Chemistry, IV (London, 1964), 585–587.