A hundred years ago – the Hill equation

I have been meaning to post this piece for ages, but never seem to find the time to do the necessary re-writes! Since there is now a small lull before I get submerged under the next wave of exam marking, I have finally got round to it. It is adapted from an article I wrote for Physiology News, though I have changed some bits, and added the hyperlinks.


Teaching students one often finds, as I have said before, that even ten years ago is viewed as “from the ark”. Of course, there was science being done a hundred, or a hundred and fifty years ago, let alone ten. In physiology one can easily find key scientific discoveries that underpin much of the modern subject in the journals of a century and more back, all reported in ways that are quite recognisable to a modern eye.

For a few years now I have been writing a regular article series which takes a look back at papers in the physiology journals exactly one hundred years ago. Here is one such. It deals with one of the earliest works of AV Hill, who we have discussed before over at Stephen Curry’s blog.


AV Hill, probably photographed in his late 20s or early 30s.

AV Hill (1910)

“The possible effects of the aggregation of the molecules of hæmoglobin on its dissociation curves”



J Physiol 40 Suppl, iv-vii

First, a bit of background – The Physiological Society is famous, at least in part, for its meetings. And its dinners… In a post back in the Autumn about Charles Darwin and the late Victorian physiologists, I touched on the founding of the Society in 1876. The Physiological Society started as essentially a gentlemens’ dining club, with scientific papers being read before a substantial dinner at a London Club or restaurant.

Almost all the meeting books of the Society survive, so that one can trace the activities of various scientists – both the then-famous, and the later to be so – through the pages. [Links to more (much, much more) history about the Society can be found here ]. The Society also founded a journal – the Journal of Physiology, first published in March 1878. The papers read to the society at the meetings appeared in a special supplementary volume called the Proceedings .

Anyway, enough preamble:

Let me take you to the Proceedings for 1910, and a meeting of the Physiological Society that took place at King’s College London on January 22nd 1910. The meeting marks the first one attended, and first communication to The Society – one of only three papers in total read at the meeting! – of AV Hill (1886-1977), Nobel Laureate, doyen of British biophysicists, and giant of 20th century physiology. And also, of course, the originator of the Hill Equation, and the Hill coefficient, the guise in which non-physiologists are perhaps most likely to encounter him today.

Hill (christened Archibald Vivian, though he disliked both names and was always known as ‘AV’) was just twenty-three at the time on the 1910 meeting. He was working in the Cambridge Physiological Laboratory, having taken his Physiology degree final exams there the previous summer (1909) and his Mathematics finals two years earlier. He had published one single paper, the previous month (Dec 1909) in the Journal of Physiology. He was not yet a member of the Physiological Society (he was not elected until two years later, in 1912) and was introduced for the King’s meeting by his friend the respiratory physiology Joseph Barcroft.

Hill’s main scientific interest through his career, and the one that was to earn him the Nobel prize, was heat production in muscle, and muscle energetics and contraction. However, his earliest work on a number of diverse problems foreshadowed one of his wider contributions, the bringing of mathematics and quantitative thinking to physiology. Hill’s protégé Bernard Katz describes this in his Oxford Dictionary of National Biography entry on Hill:

”[Hill’s] first published papers were concerned mainly with a theoretical and quantitative analysis of experimental results obtained by himself and his senior colleagues in the Cambridge laboratory. They included an analysis of drug action in muscle tissue, of the reaction between oxygen and haemoglobin, and of the effects of electric stimuli on nerves.

Although Hill later regarded this work as being of little importance, it contained the first mathematical formulation of drug kinetics later generally known as the Michaelis-Menten or Langmuir equation. It also introduced the concept of co-operativity in complex chemical reactions, signified by a quantity which was widely referred to as the Hill coefficient.”

David Colquhoun, in an interesting article on the origins of quantitative approaches to drug-receptor interactions, gives a nice account of Hill’s December 1909 paper, which derived the Langmuir adsorption equation some ten years before Langmuir, and the January 1910 communication.

Hill derived the equations that would govern a reversible association between haemoglobin and a ligand, and compared these to the experimental oxygen dissociation curves measured by Barcroft and others. Hill sets out what would subsequently be known as the Hill equation, describing the fraction of the macromolecule saturated by ligand as a function of the ligand concentration. Hill’s equations also took into account possible self-association (multimerization, as we would now say) of haemoglobin. The resulting successive ligand (oxygen) binding events to multiple haemoglobin units give rise to what would eventually become known as the Hill coefficient.

Colquhoun notes that Hill (presciently?) did not attempt to ascribe precise physical meanings to the parameters in his equation:

“My object was rather to see whether an equation of this type can satisfy all the observations, than to base any direct physical meaning on [the parameters]”.

Colquhoun drily adds: “His caveat has often been forgotten since then.”

A.V. Hill – the man and his science

Speaking many years later about how he had come to take up physiology, Hill said:

“A short answer… is, because Walter Morley Fletcher was my tutor at Trinity [College]…During my first year [at Cambridge] I began to lose interest in some of the things [in mathematics] that to me seemed rather remote from reality and hankered after something more practical. I realize now that I was much better fitted to engineering than to mathematics, but physiology proved in the end to be much like engineering, being based on the same ideas of function and design.”

Fletcher persuaded Hill to complete his Mathematics degree before pursuing new directions. As Hill tells us:

“In 1907 I took the Mathematical Tripos [Final year exams], which in those days was an extraordinary business, with fourteen three-hour papers and great public interest as to who would be Senior Wrangler [i.e. achieve the top mark of the year]. It was too much like the Grand National with all its obstacles. I did quite respectably in fact [Hill finished third in the class], but nobody encouraged me to go on with it; which was a very good thing. So I sought Fletcher’s advice again, and decided soon to become a physiologist.”

In the summer of 1910 Hill published the first instalment of his scientific life’s work on muscle energetics (Hill, 1910). This work was to culminate in the Nobel Prize in 1923 – though ‘culminate’ is perhaps the wrong word, given that Hill continued to publish papers on muscle energetics until the early 1960s (the last ones in J Physiol., in 1961 and 1962, with his final PhD student Roger Woledge).

Though Hill is often associated with University College London, the institution where he spent all his later career (after 1923), the Nobel Committee honoured him for his muscle work carried out in Cambridge (1909-19) and Manchester (1920-23). During the Manchester years Hill, who had been a keen athlete, developed a parallel interest in human exercise physiology, and is credited with originating the idea of ‘oxygen debt’.

Hill married into the Keynes academic dynasty (his wife Margaret was the sister of the economist John Maynard Keynes, and aunt to Professor Richard Keynes). Among Hill’s four children, his son David or ‘DK’ Hill (1915-2002) followed in his father’s footsteps to become a muscle physiologist, Professor and FRS. Nicholas Humphrey, Hill’s grandson, has written a touching memoir of helping his grandfather with his experiments as a child in the early 1960s in a chapter of the book Curious Minds: How a Child Becomes a Scientist.

Outside the laboratory

AV Hill was an early example of a scientist who engaged in many spheres beyond the laboratory, and it would take a decent-sized book to do justice to even a selection of his activities. He worked in wartime ‘operational’ research in both World Wars, and was an independent MP for Cambridge University during the Second War. He served The Physiological Society and Royal Society in many capacities, and was an early populariser of science, giving the 1926 Royal Institution Christmas Lectures. Perhaps the ‘extracurricular’ activity for which he is most remembered is his leading role in the 1930s in the Academic Assistance Council which helped Jewish academics flee from the Nazis.

Hill had used his Thomas Huxley Memorial lecture in November 1933 to denounce the Nazi persecution of the Jewish people, especially of scientists who had been forced out of Germany. This triggered an extended argument, in the pages of Nature in early 1934, with the German physics Nobelist Johannes Stark who had become an enthusiastic Nazi. Stark insisted that Jews were not being persecuted, only people guilty of “high treason” against the Nazi state. Hill’s response was withering:

“With Prof. Stark’s political anti-Semitism I need not deal… it appears absurd. It is a fact, in spite of what he says, that many Jews or part-Jews have been dismissed from their posts in universities … No doubt in Germany, after this reply, my works in the Journal of Physiology and elsewhere will be burned.”

The correspondence famously ended with Hill commenting, with characteristic dry wit, that since his previous letter he had received many donations to help the AAC’s cause – but he felt he could not really take the credit, as the donors’ generosity surely owed something to Stark’s (racist-ideological) arguments. Bernard Katz, himself a Jewish refugee from the Nazis, sought Hill out partly because of the correspondence (see e.g. here, and would later write that the letters:

“Gave me the first glimpse of A.V. Hill’s personality…[which] I found… so attractive that I made every effort to go and work with him”.

Katz also quoted a favourite saying of Hill’s:

“Laughter is the best detergent of nonsense”.

The definitive scientific biographical source on Hill is Bernard Katz’s monumental (78 page!) Royal Society Biographical Memoir; for a shorter introduction Katz’s DNB entry is a useful starting point.


Colquhoun D (2006). Trends Pharmacol Sci 27, 149-157.

Hill AV (1909). J Physiol 39, 361-373.

Hill AV (1910). J Physiol 40, 389-403.

Hill AV (1969). J Physiol 204, 1-13.

Katz B (1978). Biogr Mem Fellows R Soc 24, 71-149.

About Austin

Middle-aged grouchy white male. Hair greying but hasn't all fallen out yet. Spreading waistline ill-concealed by baggy jumper.Semi-extinguished physiology researcher turned teacher. Known for never shutting up. Father of two children (aged 6 and 2) who try to out-talk him. Some would call that Karmic Revenge.
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