# John Henry Michell

### Quick Info

Maldon, Victoria, Australia

Camberwell, Victoria, Australia

**John Henry Michell**was an Australian mathematician, who made important contributions to the fields of hydrodynamics and elasticity.

### Biography

**John Henry Michell**'s parents were John Michell and Grace Rowse. John Michell was born on 11 December 1825 in Marytavy, Devon, England and Grace Rowse was born on 26 October 1828 in Kenwyn, Cornwall, England. John Michell was a miner, the son of the miner Thomas Michell and his wife Elizabeth Saunders. Grace Rowse was a daughter of Anthony Rowse and Ann Wilcocks. Again this was a mining family and, around 1828, Anthony Rowse had moved to Marytavy, Devon, to become the manager of a copper mine. John and Grace Michell were married on 21 April 1853 in Tavistock, Devon and, in the following year, they emigrated to Port Phillip, Australia. There were good reasons for this since mining deposits in Devon and Cornwall were becoming exhausted. In 1851 rich gold deposits had been found in Victoria, Australia, so many left England looking for a better life. In fact Grace was one of a large family and at about this time all her brothers, trained as miners by their father, were taking up mining in various parts of the world. John and Grace Michell had five children: Elizabeth Ann Michell was born in April 1855 in Creswick Creek, Victoria, Australia; Grace Michell was born in July 1857 in Ballarat, Victoria, Australia; Amelia Michell was born in February 1861 in Maldon, Victoria, Australia; and John Henry Michell, the subject of this biography, was born in October 1863, also in Maldon, Victoria, Australia, a small rural mining field. As a young child John was taught reading, writing and arithmetic at home by his older sisters. In 1870 the family returned to England to spend time with their parents and relatives and their fifth child, Anthony George Maldon Michell, was born in Islington, London, England in June 1870. George Michell, as he was known, went on to become a well-known engineer who wrote the obituary [7] of his older brother. George Michell:-

... invented the Michell Thrust Bearing, a tilting-pad device which made possible much of the modern development of steam and water turbines and of propeller drives for large fast ships.The family were still in England at the time of the April 1871 census, and were living at 3 Millbrook Villas, Tavistock, Devon.

Returning to Australia in 1873, the family lived at Maldon until 1877. There, in December 1874, Michell's father showed him the transit of Venus by means of smoked glass. It was in Maldon that John Michell attended elementary schools and, since he showed great promise, his parents moved from Maldon to the suburbs of Melbourne in 1877 so that he could attend Wesley College there. This school had opened in 1866 and, two years before Michell entered, the school colours had been changed to light blue and white to match both Cambridge University and the University of Melbourne. Henry Martyn Andrew (1845-1888) had become the third headmaster of the school in 1876 and, a few years earlier in 1872, he had been a Wrangler in the mathematics tripos at Cambridge. Andrew, described as "a severe but inspiring teacher" certainly seems to have inspired Michell who came top in all the mathematics classes and was awarded the Draper and Walter Powell scholarships at Wesley College. Michell graduated from Wesley College in 1881 and, in that year, entered the University of Melbourne.

At the University of Melbourne Michell had to take a broad course of study including geology, political economy and classics in addition to mathematics. However, at this time there was only one mathematician on the faculty at the University of Melbourne, namely Edward John Nanson (1850-1936), who had been Second Wrangler in the mathematical tripos at Cambridge in 1873. Nanson was an expert on the mathematics of Cayley, Salmon and Sylvester and wrote many papers on determinants [7]:-

... in the handling of which he had extraordinary facility.Michell graduated with a B.A. in 1884 and he was strongly encouraged by both Nanson and Andrew, who was by this time professor of natural philosophy at the University of Melbourne, to continue with his mathematical studies at the University of Cambridge. This would, of course, put severe financial pressure on Michell's parents but they were quite prepared to make the necessary sacrifices. But Michell was not sent to England on his own for his whole family left Australia and set up home in Cambridge. Once there Michell's younger brother George continued his education in Perse Grammar School, Cambridge.

On 10 October 1884 Michell was admitted as a pensioner at Trinity College, Cambridge. As a pensioner, he would have had to support himself financially. His tutor at Cambridge was James Whitbread Lee Glaisher. He became a scholar in 1885, indicating that by this time he had won a scholarship. He sat Part I of the mathematical tripos in 1887 and was bracketed as Senior Wrangler along with three other students, one of whom was Henry Baker. (Having four students come first equal is, perhaps, a unique event in the Cambridge tripos.). His coach for the mathematical tripos was the famous Edward Routh and he attended lectures by Andrew Forsyth, Joseph Larmor, Joseph John Thomson (the Cavendish Professor of Experimental Physics, and later the discoverer of the electron), and George Stokes. Michell was also First Class in Part II of the tripos in 1888 and, in the following year, he was a Smith's prizeman. The only other Smith's prizeman in that year was Henry Baker. His brother George Michell had graduated from Perse Grammar School after spending three years there, but remained with the family in Cambridge and attended lectures at Cambridge University as a matriculated non-collegiate student. George Michell, writes in [7] about his brother Henry's time at Cambridge:-

Michell put all his energy into his training for these contests, doubtless feeling that he owed it to his parents to qualify himself for obtaining some remunerative employment without delay, and that securing a high place in the lists was the only means available to him, compatible with his temperament, for securing that end. It is probable that the strain which he imposed on himself caused permanent injury to his health and spirits. at any rate, it is certain that, both at the time and later, he deplored the effort spent in acquiring the arts of 'problem-solving' in the manner of the Cambridge examinations of those days and that he put them aside as soon as the examinations were over in order to plunge into the reading of such authors as Cauchy, Clebsch, Riemann, Weierstrass and PoincarĂ©. For Riemann especially he had an admiration which was profound and lifelong.In 1890, still at Cambridge, Michell was elected to a Fellowship at Trinity College. In this year he published five papers:

*The small deformation of curves and surfaces with applications to the vibrations of a helix and a circular ring*;

*On the exhaustion of Neumann's mode of solution for the motion of solids of revolution in liquids, and similar problems*;

*Vibrations of a string stretched on a surface*;

*On the stability of a bent and twisted wire*; and

*On the theory of free stream lines*. This last mentioned paper was, perhaps the most remarkable [7]:-

... by a new mathematical transformation, a complete solution was obtained, in forms readily available for detailed application to concrete cases, of the two-dimensional flow of non-viscous fluid. Earlier attacks on the problem, even by Helmholtz and Kirchhoff, had yielded only the solutions of a few special cases not of the highest importance.For a list of all Michell's publications, see THIS LINK.

For a discussion of the problem studied in

*On the stability of a bent and twisted wire*see THIS LINK.

Soon after accepting the Trinity fellowship, Michell was offered a lectureship at the University of Melbourne. He accepted and later in 1890 he took up the post in Melbourne. T M Cherry writes in [3]:-

On returning to Melbourne the household, reduced shortly afterwards to the four unmarried children and their mother, built a solid house, where with mutual support and in orderly Victorian comfort they lived until, in the fullness of time, their sands ran out. Few families can have been more closely knit. Round the house the brothers established a most remarkable garden reminiscent of a tropical forest. The upper storey consisted mainly of palms of many species and the middle storey of exotic shrubs, mostly South African and Australian (at this time any non-European shrubs in Melbourne gardens would have been called 'exotic'). The visitor never saw a leaf on the paths or otherwise out of place. It was said that this was the only foreign site on which the Lord Howe Island palm (much used for indoor civic greenery) had ever set seed; but the brothers explained that there was no magic in this - it was simply that their specimens were the only ones outside the Island that had achieved the requisite age. In contrast to the palms there were fruit trees again exotic - cumquat, guava, feijoa, and a 30-foot mulberry tree - this last completely enclosed in a cage to foil the blackbirds ...We note that this quote suggests that Michell's father died soon after they returned to Australia and indeed he died at Camberwell, Melbourne, on 16 July 1891. It also suggests that one of the children had married and that was the eldest daughter Elizabeth Ann who married John Dabb in 1877. The other four children never married. Michell's mother died in 1921.

When Michell became a lecturer at Melbourne he became a colleague of Nanson, his former professor. In fact he became the only other member of Nanson's Department of Mathematics and so had to work extremely hard. Certainly he took his responsibilities as a teacher very seriously which meant that his workload was even greater than it might have been [7]:-

Michell took his work as a teacher very seriously and gave to it almost the whole of his time and mental energy. His notes for his class lectures were recast repeated, in fact almost every year, with immediate regard to the character of the prospective classes as indicated by the intending students themselves in their entrance examinations and subsequently. He was always most solicitous that his students should get an accurate record of his lectures, and, to ensure this, his rule was to writ every word on the blackboard. The pace therefore appeared to be slow, but this was deceptive; he achieved economy of words by omitting unessentials, and his judgement in this matter was so sure that he covered more than the normal extent of ground rather than less. He also took a great deal of trouble in setting his examination papers. Nearly all the problems were original, and it was rare for him to set anything that could be recognised as a repetition.During the first years as a lecturer in Melbourne, Michell published eighteen papers in addition to the five he published in 1890. The most important of these papers, according to Ernest Oliver Tuck (1939-2009) [11], was

*The wave resistance of a ship*(1898). Tuck writes:-

The paper is concise and to the point, occupying 17 small pages in total, the main formula being derived within the first 8 pages. The paper reads like a modern research article, apart from the lack of partial derivative notation, which Michell wanted but did not get from the printers. The problem is simply to obtain that portion of the drag force on a steadily moving ship which is due to the loss of energy into its wave pattern. Hence viscosity is neglected, this being justified by arguments pioneered by Froude for separating wave and viscous drag, but in Michell's own introductory words by boundary-layer-like arguments that could be said to anticipate Prandtl's by a decade or more. Once viscosity is neglected, classical inviscid-fluid theory indicates that the flow is irrotational almost everywhere, and a velocity potential exists. The task of determining the velocity potential is then a boundary-value problem for Laplace's equation ...However, there is remarkable final part to the paper that Tuck highlights:-

However, a little-known feature of the ship paper is that, almost as an afterthought, Michell also includes on its last two pages a mini-study of the shallow water case, i.e. of the limit as the water depth vanishes ... This shallow-water analysis is itself of remarkable historical interest, since it uses what we would now identify as an analogy between sub- or super-critical hydraulics, and sub- or super-sonic aerodynamics. Since manned flight was still a decade away, and supersonic flight a half century away, this is truly remarkable work, that would make these two pages significant even if the infinite-depth portion were discounted. However, it must be said that quite similar and now better known aerodynamic work was being done by Joukowski at about that time (though published later ...). Michell gives no indication that he has seen any of Joukowski's work, and it hardly seems likely in view of his geographical isolation that he had done so. At the very least, Michell's application of the hydraulic analogy to the ship context is original, and personally I believe that (based on nothing more than these two pages) he should be given at least equal credit with Joukowski for this whole research area.As we mentioned above, Michell published 18 papers between 1892 and 1902. In the year 1902 he was elected a fellow of the Royal Society of London. He published no further research after 1902 although in that year he was only 39 years old. Although Michell was under great pressure as a teacher, Tuck [11] suggests that the most significant reason for his giving up research was the lack of recognition he received. Michell's brother seems to, at least partially, support this when he writes [7]:-

Michell never showed concern for recognition of his work, but the absence of any response to such a paper as the 'Ship Waves' inevitably discouraged the making, or at least the publication, of investigations involving, for him, so much anxious labour.The idea that lack of recognition made him give up publishing research may, however, be an over simplification. What more recognition could one receive than to be elected a fellow of the Royal Society of London? This happened in 1902, exactly the date when he stopped publishing. Could the opposite be true - that he stopped publishing because he had received recognition as a world-leading researcher and so, in some sense, had proved himself as a researcher? There seems no possibility that we will ever know the answer, but it is certain that the world of mathematics would have benefited greatly from another 30 years of Michell's research publications. Let us note that Michell's brother also became a fellow of the Royal Society of London, being elected in 1934. There cannot be many instances of two brothers both being fellows of the Royal Society.

In 1923 Nanson retired and Michell became Professor of Pure and Mixed Mathematics at Melbourne. Up to that time he had lectured mainly on applied mathematics topics (known as mixed mathematics at this time) but, from 1923 until his retirement in 1928, he lectured on topics across the whole range of mathematics. He was able to appoint a number of mathematicians to his department in Melbourne including Maurice Belz with whom he collaborated in writing his only book, the two volume

*The Elements of Mathematical Analysis*(1937) published nine years after his retirement. The authors write in the Preface:-

In writing the present book we have tried to make it conform to three main conditions. ... (i) The book should assume as known only those elements of Algebra, Geometry and Trigonometry which are taught in the secondary schools to all those preparing to attend any lectures in Mathematics at a university. ... (ii) The second main condition is that the book should form a practical or working text provided with an abundance of illustrative examples treated at length and of other examples to be solved by the student. ... (iii) The third condition is that the subject should be expounded on the basis of the theory of real numbers, geometrical notions being employed only illustratively and not as replacing abstract discussions ....Frederic Miller, in the review [10], writes:-

The authors have succeeded admirably in meeting their aims.P J Daniell, in the review [4], writes:-

We have here a course in Calculus written by authors with a mathematical conscience and an ability to teach. Every attempt is made not only to be rigorous and clear but also to explain at some length what is being done. It is a great pleasure to find such a work on calculus.Other than mathematics, Michell's interests were music, reading and, as we noted above, gardening. Cherry writes [2]:-

He found relaxation in classical music - he was a capable performer on the organ - in wide reading and in gardening; he was a learned connoisseur and lover of plant life, especially Australian trees and shrubs.Michell retired in 1929, becoming an Honorary Research Professor, and continued to live at Camberwell, Melbourne, Victoria, Australia where, after a short illness, he died in 1940. He was buried in Boroondarra Cemetery, Victoria.

Today, Michell is probably best remembered by the J H Michell Medal which is awarded annually (if there is a candidate of sufficient merit) by the Australian and New Zealand Industrial and Applied Mathematics which is a Division of the Australian Mathematical Society. The award is made to someone who has made an outstanding contribution to applied and/or industrial mathematics, must have worked mainly in Australia and/or New Zealand, and be less than ten years from the award of their Ph.D.

### References (show)

- F W Niedenfuhr and J R M Radok (eds.),
*Collected Mathematical Works of J H and A G M Michell*(Groningen, 1964). - T M Cherry, Michell, John Henry (1863-1940),
*Australian Dictionary of Biography***10**(1986). http://adb.anu.edu.au/biography/michell-john-henry-7568/text13209 - T M Cherry, George Maldon Michell. 1870-1959,
*Biographical Memoirs of Fellows of the Royal Society***8**(1962), 90-103. - P J Daniell, Review: The Elements of Mathematical Analysis. I. II, by J H Michell and M H Belz,
*The Mathematical Gazette***22**(249) (1938), 197-198. - A Goriely, Twisted elastic rings and the rediscoveries of Michell's instability,
*J. Elasticity***84**(2006), 281-299. - G J McCarthy, Michell, John Henry(1863-1940),
*Encyclopedia of Australian Science*(4 February 2010). http://www.eoas.info/biogs/P000642b.htm - A G M Michell, John Henry Michell. 1863-1940,
*Obituary Notices of Fellows of the Royal Society***3**(9) (1941), 363-382. - Michell (John Henry),
*National Library of Australia*. http://trove.nla.gov.au/people/495047?c=people - Michell (John Henry),
*University Library, University of Melbourne*. http://hdl.handle.net/11343/59936 - F H Miller, Review: The Elements of Mathematical Analysis. I. II, by J H Michell and M H Belz,
*Science, New Series***119**(3095) (1954), 549-550. - E O Tuck, The wave resistance formula of J H Michell (1898) and its significance to recent research in ship hydrodynamics,
*J. Austral. Math. Soc. Ser. B***30**(1989), 365-377.

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Written by J J O'Connor and E F Robertson

Last Update October 2016

Last Update October 2016