George Hartley Bryan

Quick Info

1 March 1864
Cambridge, England
13 October 1928
Bordighera, Italy

George Bryan made important contributions to kinematics, thermodynamics and the mathematical theory of flight. He wrote two important monographs and a whole series of undergraduate texts intended for private study.


George Bryan was the only child of Robert Purdie Bryan (1840-1865) and Fanny Martell (1841-). Robert Bryan was the son of the physician James Bedingfield Bryan (1813-1889) who, for example, published Nature and treatment of influenza in The Lancet in 1837, and Eliza Hartley (1811-1894). Robert matriculated at Merton College, Oxford on 17 June 1858 and, while studying there, he married Fanny Martell. He matriculated at Clare College, Cambridge on 3 May 1860 as a Fellow-Commoner and studied the Classical tripos. He was admitted at Lincoln's Inn on 12 January 1863 and was awarded a B.A (1st Class) from Cambridge in 1864. He died on 11 February 1865 and was buried Upton Cum Chalvey, Buckingham on 20 February 1865. His baby son George Hartley Bryan, the subject of this biography, was baptised at St John, Battersea on 14 June 1864 but he was less that one year old when his father died.

After the death of his father, George was brought up by his mother and his paternal grandparents. They spent much time abroad, in France, Germany and particularly Italy [5]:-
... especially the warmer climes of the Italian and French rivieras. This unusual upbringing gave him an excellent knowledge of languages and a lifelong fascination with the natural world, particularly of the rivieras ...
We obtain a snapshot of the family in 1871 at the UK Census when they are living in Thicket Road, Penge, Surrey. The head of the household is George's paternal grandfather, James B Bryan (age 58), giving his qualifications as M.D. Edinburgh and Member of the Royal Colleges of Physicians, London. Also in the house are James' wife Eliza Bryan (age 60), George Bryan (aged 7), the subject of this biography, and Fanny Bryan, George's mother. The family have three servants, a cook, a housekeeper and someone labelled as "music". Presumably the musician entertained the family and taught music to young George who certainly had a great passion of music all his life. There is also Sarah Whittle, who is an assistant, and a visitor David Williams who is a Church of England clergyman.

Ten years later, in 1881, we gain obtain details from the next UK Census when they are living in Fitzwilliam Road, Cambridge. James B Bryan, Eliza Bryan, Fanny Bryan and George Bryan are in the house with one servant, a parlour maid Ann Britton. They have one visitor, Mary D Richmond. On 10 April 1883 George Bryan was admitted as a pensioner at Peterhouse, Cambridge and began his study of the mathematical tripos. His upbringing to this stage had been unconventional and its effects are described in [3]:-
His mother lived to a good old age, and Bryan always spoke of her with the greatest affection. He was brought up by his mother and his grandparents. He was the idol of the household, and being supposed to be delicate he was never allowed to go to school. Even when he went to Peterhouse as an undergraduate he was not given the opportunity of becoming self-reliant, for he still lived at home. The result of such an upbringing, in which discipline was totally absent, was a rather noticeable eccentricity, which did not, however, cover up a remarkable simplicity, honesty, and kindliness of character.
Bryan graduated with a B.A. in 1886, being fifth Wrangler (ranked as the fifth best First Class student), and in the following year he was in the First Division of the First Class of Part II of the tripos, having concentrated on hydrodynamics, elasticity and thermodynamics, and, later that year, was bracketed with the Senior Wrangler, Alfred Cardew Dixon, as one of the two Smith's Prizemen for his dissertation on the stability of a rotating fluid. He had been taught by a number of famous mathematicians at Cambridge, including George Howard Darwin, James Glaisher, Walter Rouse Ball and Andrew Forsyth. His opinion of the Cambridge mathematical tripos, however, was pretty negative [12]:-
One peculiarity of this examination is that the syllabus goes a long way past the dividing point at which the mathematician and the physicist branch off in different directions. Another peculiarity is that it covers a number of subjects each of which, to be properly mastered, would take the whole number of hours that the candidate usually can devote to the entire syllabus. A third peculiarity is that greater importance is attached to the candidates' powers of devising artificial dodges for the solution of tricky problems than to his knowledge of first principles and their direct applications.
He submitted his first papers for publication in 1888 and, in 1889, he was elected a fellow of Peterhouse.

Bryan published The waves on a rotating liquid spheroid of finite ellipticity in 1889. He begins the Introduction as follows:-
The hydrodynamical problem of finding the waves or oscillations on a gravitating mass of liquid which, when undisturbed, is rotating as if rigid with finite angular velocity, in the form of an ellipsoid or spheroid, was first successfully attacked by M Poincaré in 1885. In his important memoir, "Sur l'Équilibre d'une Masse Fluide animée d'un Mouvement de Rotation," Poincaré has obtained the differential equations for the oscillations of rotating liquid, and shown that, by a transformation of projection, the determination of the oscillations of any particular period is reducible to finding a suitable solution of Laplace's equation. He then applies Lamé's functions to the case of the ellipsoid, showing that the differential equations are satisfied by a series of Lamé's functions referred to a certain auxiliary ellipsoid, the boundary-conditions, however, involving ellipsoidal harmonics, referred to both the auxiliary and actual fluid ellipsoid. At the same time, Poincaré's analysis does not appear to admit of any definite conclusions being formed as to the nature and frequencies of the various periodic free waves.

The present paper contains an application of Poincaré's methods to the simpler case when the fluid ellipsoid is one of revolution (Maclaurin's spheroid). The solution is effected by the use of the ordinary tesseral or zonal harmonics applicable to the fluid spheroid and to the auxiliary spheroid required in solving the differential equation. The problem is thus freed from the difficulties attending the use of Lamé's functions, and is further simplified by the fact that each independent solution contains harmonics of only one particular degree and rank.
Over the next few years Bryan undertook a remarkable amount of work, essentially having two parallel careers, both of which on their own have an amazing output. One of these is as a writer of textbooks for the University Correspondence College, the other is as a researcher tackling novel lines of research.

The University Correspondence College, founded in London by William Briggs in 1887, was set up to provide tutorial assistance to students who were studying for external University of London degrees. Briggs also set up the University Tutorial College, giving tutorial assistance to students in London, and the University Tutorial Press with its own printing and bookbinding works. Briggs and Bryan began to collaborate in writing textbooks for the University Correspondence College from about 1890, beginning with The elements of coordinate geometry (1891). But as well as writing texts with Briggs, Bryan was persuaded by Briggs to collaborate with others writing textbooks. C W C Barlow had been a fellow student of Bryan at Cambridge, being sixth Wrangler in the same tripos examination that Bryan was fifth Wrangler. Bryan and Barlow's first textbook for the University Correspondence College was Elementary Mathematical Astronomy, with examples and examination papers (1892). These books were very popular and so Bryan was not only involved in writing many new textbooks but also bringing out new editions of his previous books.

For more information on over twenty textbooks written by Bryan for the University Correspondence College, including extracts from reviews and prefaces, see THIS LINK.

Bryan's research output during this period was also exceptional; he published eight papers in 1889-90: The waves on a rotating liquid spheroid of finite ellipticity (1889), On the stability of elastic systems (1889), Application of the energy test to the collapse of a long thin pipe under external pressure (1889), On the Stability of a Plane Plate under Thrusts in its own Plane, with Applications to the "Buckling" of the Sides of a Ship (1890), On the beats in the vibrations of a revolving cylinder or bell (1890), An application of the method of images to the conduction of heat (1890), On the stability of a rotating spheroid of perfect liquid (1890), and On the deformation of twisted strips (1890).

He published even more research papers in 1891, but there is a particularly significant paper he published that year which we should say a little more about. The British Association for the Advancement of Science was due to hold their 1891 meeting in Cardiff and Bryan was keen to offer the meeting a review of thermodynamics. Bryan had not published on thermodynamics so it is not obvious where his interest came from. The source was Joseph Larmor who, after spending five years in Galway, had returned to St John's College, Cambridge in 1885 and taught the Part II tripos course that Bryan studied. At any rate, the British Association asked Bryan and Larmor to jointly report on thermodynamics to their 1891 meeting and they presented the "Report of a committee, consisting of Messrs J Larmor and G H Bryan, on the present state of out knowledge of Thermodynamics, specially with regard to the second law" to the meeting and "Part I. - Researches relating to the connection of the Second Law with Dynamical Principles. Drawn up by G H Bryan" was published in 1892 in the proceeding of the meeting. The report praises Boltzmann and criticises Clausius. For example:-
Boltzmann seems to have been next to take up the subject, but his claim to priority has been disputed by Clausius , whose investigations appeared about five years later. Boltzmann was undoubtedly the first to regard the subject from a statistical point of view. ... The methods of proof employed by Clausius in [his 1870] paper are very laborious and complicated, while his arguments are artificial and, in places, not very intelligible.
Boltzmann was delighted with the Report and after attending the Tercentenary Celebrations of Trinity College, Dublin in July 1892, he visited Bryan in Cambridge. This meeting marks the start of a friendship between the two who had much in common in addition to thermodynamics, namely a love of nature, and a love of music, both being gifted musicians. At the British Association meeting in Oxford in 1894, Bryan presented the second part of the thermodynamics report, this time as the sole author. Boltzmann attended the meeting and eagerly took part in the discussion after Bryan's lecture. The Proceedings of the meeting contains the paper "Part II. - The Laws of Distribution of Energy and their Limitations (With an Appendix by Prof Ludwig Boltzmann.)" Bryan had undoubtedly made his presence known to the mathematics and physics world as a leading expert. There was another aspect of the British Association meeting in Oxford in 1894 which proved important in Bryan's career, namely discussions between those studying the theoretical possibilities of aeroplanes and the engineers who were actively experimenting with manned flight. Boltzmann was enthusiastic about the possibilities and Bryan soon became enthusiastic too.

Bryan's leading role in kinetic theory led to his election as a Fellow of the Royal Society in 1895. The British Association held their 1896 meeting in Liverpool and Bryan, now showing his theoretical interest in flight, presented the paper On the Sailing Flight of Birds. While at this meeting, he received the news that he had been appointed as a Temporary Lecturer in Mathematics at the University College of North Wales in Bangor and on 14 December 1896 he was elected to the Chair of Pure and Applied Mathematics at Bangor. He was now thinking hard about stability of flying machines and delivered lectures and papers on the topic such as Artificial flight in Science Progress (1897). Let us emphasise our "two careers" point here by noting that, by 1897, he had at least twelve textbooks in print, many of which had already gone through several new editions.

It looks at this stage as though Bryan was handling the extremely heavy load that he had chosen to put on himself. This, however, was not the case for the very small mathematics department at Bangor was in difficulties. All teaching and examining mathematics was Bryan's responsibility with only one assistant to help him. We quote James Boyd [9]:-
... having been cocooned at Cambridge for so long, Bryan had no notion of how to go about organising work in a small - very small - department. So with the assistant unwilling and the professor unwitting and at times unwell throughout the 1897-1898 session, it was small wonder that the very stability of the Mathematics Department was threatened by the near total breakdown in communication between professor and assistant. A Committee of Inquiry was set up. When the committee duly reported in early 1899, Bryan was discomfited to learn that while blame was indeed attributed to his assistant, his own leadership was found wanting. Bryan suffered a nervous breakdown and withdrew to Cambridge for the Summer Term of 1899.
I [EFR] believe that Bryan had another problem not mentioned by Boyd, namely that he was suffering from overwork. Given his incredible output in the ten years leading up to these difficulties, surely this must have been a major contributing factor to his problems at Bangor. Perhaps there was an indication that he understood this when he wrote in Boltzmann's obituary:-
Mathematical research is a dangerous occupation if carried too far, and the consequences that may have been the result of this intense concentration of thought should prove a warning to others not to allow themselves to be too deeply absorbed in any particular investigation. The difficulty of tearing oneself away from a particular line of work till it has been finished constitutes a grave danger ...
Also Bryan does not appear to have been the sort to try to avoid confrontation and did not mince his words when handing out criticism. Look, for example, at his criticism of the London Mathematical Society in 1904 [11]:-
... the London Mathematical Society is not taking the place it ought to take among English scientific societies. Its library is stowed away in a dark attic and is practically inaccessible. Its members are not styled "Fellows." It has no lack of contributors to its Proceedings, but it makes no effort to improve the status of mathematicians in this country in the way that is undoubtedly done for other branches of science by the leading societies in Burlington House.
In 1899 Bryan received a major honour when he awarded the Gauss Medal of the German Mathematical Society. He was also invited to write an article on thermodynamics for the Arnold Sommerfeld's Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen . In fact Sommerfeld visited Bryan in Bangor in September 1899 to make the invitation in person. Bryan wrote the 90-page article Allgemeine Grundlegung der Thermodynamik which was published in the 1st part of the 5th volume of the Encyclopaedia in 1903. He received a second award in 1901 when the Institution of Naval Architects awarded him their gold medal for his mathematical theory, published in his paper The steading of ships, concerning the reduction of oscillations of a ship with certain types of keel.

Although there are some signs that he was easing off a little after his nervous breakdown, he was still undertaking a large amount of research and he had become totally committed to working on stability of flying machines.

On 17 July 1906, Bryan married Mabel Grace Williams (1870-1958) at the Cathedral Church in Bangor. Mabel, the daughter of the iron merchant Frederick Williams and his wife Frances, was the headmistress of the Bangor primary school; George and Mabel had one child, a daughter, Margaret, born in 1909.

Bryan became President of the Mathematical Association in 1907 and he set up the local branch of the Association in North Wales. He was delighted with the way this local branch operated; see his description in his Address as the Retiring President [12] at THIS LINK.

In 1907 Bryan published the book Thermodynamics. An introductory treatise dealing mainly with first principles and their direct applications. The Preface begins as follows:-
When I accepted an invitation to write the article for the 'Encyklopädie' on the General Foundations of Thermodynamics, it was understood that the article should deal, as far as possible, exclusively with the laws of thermodynamics and consequences immediately deducible from them, and that all properties of particular substances and states which depended partially on experimental knowledge or other hypotheses should be left for another article. I had long felt the want of a book in which thermodynamics was treated by purely deductive methods, and it has been my object in the following pages to develop the subject still more on this line than was possible in an article professing to be to some extent an exposition of the history and actual state of knowledge of the subject.
For a longer extract from the Preface see THIS LINK.

In 1911 he published Stability in Aviation: An Introduction to Dynamical Stability as Applied to the Motion of Aeroplanes. The Preface begins as follows:-
Up to the present time the problem of stability has received very inadequate attention in connection with aviation. From the point of view of the practical aviator, this is, perhaps, little to be wondered at. It would scarcely be possible for him to devote months of concentrated attention to long and laborious stability investigations when it is no exaggeration to say that very frequently his success or failure depends, above all things, on the names of the towns at which he starts and lands. If a prize is offered for flight from Folkestone to Flushing, it is useless for him to fly from Harwich to the Hook, even on much more stable machine than that used by the winner of the prize.
For a longer extract from the Preface, and extracts from two reviews, see THIS LINK.

The author of [7] writes:-
Bryan took a great delight in the beauties of Nature, in scenery, plants and insects and had a passion for music which led him far. At one period - when piano players first appeared, a considerable amount of his time and energy was spent in developing an invention for their improvement and led him into friendly disputation on the principles involved with musicians and physicists. In his later years Bryan found the ties of his university duties rather irksome and sought an opportunity for unfettered research; this was provided for him in 1917 by a three years' grant from the Department of Scientific and Industrial Research, which time he devoted to the dynamics of aeroplane motion and to considering methods of dealing with the motion of compressible fluids.
We mentioned above his term as President of the Mathematical Association. In his Address as retiring President he spoke much about his ideas regarding teaching mathematics and the status of mathematics in Britain; see a version of his address at THIS LINK.

He also served terms as President of the Institute of Aeronautical Engineers, and the Cambridge Entomological Society. He served on the Council of the London Mathematical Society from 1894 to 1896. He retired from his chair at Bangor in 1926 and purchased a villa in Bordighera in his beloved Italy [10]:-
His two years of retirement at Bordighera were made happy by friendly intercourse with the Italian peasants, whose language he spoke so well, and 'Il Professore' was known and loved in many a mountain village far off the beaten track of the ordinary tourist.
He attended the International Congress of Mathematicians in Bologna in September 1928 with both his wife and daughter. He died a month after attending the Congress after a short illness.

References (show)

  1. Anon, Review: Elementary Mathematical Astronomy, with examples and examination papers, by Crossley William Crosby Barlow and George Harley Bryan, Nature 45 (1173) (1892), 579.
  2. Anon, Review: Worked Examples in Co-ordinate Geometry, by William Briggs and G H Bryan, Nature 49 (1255) (1893), 52.
  3. Anon, Review: Text-Book of Dynamics, by William Briggs and G H Bryan, The Journal of Education 41 (8) (1016) (1895), 131.
  4. Anon, Review: The Tutorial Trigonometry, by William Briggs and G H Bryan, The Journal of Education 47 (1) (1160) (1898), 11.
  5. Anon, Review: A Middle Algebra, based on the Algebra of Radhakrishnan, by William Briggs and G H Bryan, The Educational Times and Journal of the College of Preceptors 51 (1898), 505-506.
  6. Anon, Review: Matriculation Mechanics (3rd edition), by William Briggs and G H Bryan, Nature 94 (2343) (1914), 88.
  7. L B, George Hartley Bryan, Biographical Memoirs of Fellows of the Royal Society 1 (2) (1933), 138-142.
  8. A Barton, Review: The Tutorial Algebra (6th edition), by W Briggs, G H Bryan and G Walker, The Mathematical Gazette 39 (330) (1955), 336-337.
  9. T J M Boyd, George Hartley Bryan, Ludwig Boltzmann, and the Stability of Flight, Physics in Perspective 14 (2012), 4-32.
  10. S Brodetsky, Prof G H Bryan, F.R.S., Nature 122 (3083) (1928), 849-850.
  11. G H Bryan, The London Mathematical Society, The Mathematical Gazette 2 (43) (1904), 396.
  12. G H Bryan, The Address of the Retiring President, The Mathematical Gazette 5 (78) (1909), 44-51.
  13. J M C, Review: Text-Book of Dynamics, by William Briggs and G H Bryan, Amer. Math. Monthly 4 (4) (1897), 125.
  14. J M C, Review: Geometry of the Similar Figures and the Plane, by C W C Barlow and G H Bryan, Amer. Math. Monthly 4 (4) (1897), 126.
  15. H P C, Review: Elementary Mathematical Astronomy, with examples and examination papers (3rd edition, 8th impression), by Crossley William Crosby Barlow and George Harley Bryan, Nature 113 (2827) (1924), 7.
  16. N M Gibbins, Review: Tutorial Algebra. I. (5th edition), by W Briggs, G H Bryan and G Walker, The Mathematical Gazette 25 (264) (1941), 127-128.
  17. N M Gibbins, Review: Tutorial Algebra. II. Advanced Course (5th edition), by W Briggs, G H Bryan and G Walker, The Mathematical Gazette 26 (272) (1942), 237-238.
  18. R L Goodstein, Review: Tutorial Algebra. Vol. II (6th edition), by W Briggs, G H Bryan and G Walker, The Mathematical Gazette 41 (338) (1957), 314-316.
  19. F W H, Review: Mechanics of Fluids, by G H Bryan and F Rosenberg, The Mathematical Gazette 1 (11) (1897), 120.
  20. H Hilton, Review: Stability in Aviation: An Introduction to Dynamical Stability as Applied to the Motion of Aeroplanes, by G H Bryan, The Mathematical Gazette 6 (99) (1912), 343-344.
  21. W H Humphries, Review: Stability in Aviation: An Introduction to Dynamical Stability as Applied to the Motion of Aeroplanes, by G H Bryan, Science, New Series 35 (901) (1912), 543-544.
  22. A Hunter, Review: Elementary Mathematical Astronomy, with examples and examination papers (5th edition), by Crossley William Crosby Barlow and George Harley Bryan, The Mathematical Gazette 29 (283) (1945), 39.
  23. A E H Love, George Hartley Bryan, J. London Math. Soc. 4 (1929), 238-240.
  24. G M M, Review: Advanced Mechanics. Vol. II. Statics, by William Briggs and G H Bryan, The Mathematical Gazette 1 (10) (1897), 95-96.
  25. R M Milne, Review: Matriculation Mechanics (3rd edition), by William Briggs and G H Bryan, The Mathematical Gazette 7 (114) (1914), 433.
  26. F S M, Review: The Tutorial Trigonometry, by William Briggs and G H Bryan, The Mathematical Gazette 1 (12) (1897), 143-144.
  27. D J Wright, Bryan, George Hartley (1864-1928), applied mathematician, Oxford Dictionary of National Biography (2004).

Additional Resources (show)

Written by J J O'Connor and E F Robertson
Last Update January 2021