Larmor, Sir Joseph

(1857-1942), theoretical physicist

by Isobel Falconer

© Oxford University Press 2004 All rights reserved

Larmor, Sir Joseph (1857-1942), theoretical physicist, was born at Magheragall, co. Antrim, on 11 July 1857. He was the eldest of the seven children of Hugh Larmor and his wife, Anna, elder daughter of Joseph Wright of Stoneyford, co. Antrim.

Education and early career
In 1863 or 1864 Hugh Larmor gave up farming to become a grocer in Belfast. Larmor attended first a national school in Eglinton Street, and then the Royal Belfast Academical Institution, being described at the time as a 'thin and delicate black-haired boy of most precocious ability both in mathematics and classics' (Eddington, 197). He proceeded in 1871 or 1872 with a scholarship to Queen's College, Belfast, graduating BA and then MA. In 1876, a year later than planned due to a severe illness, he entered St John's College, Cambridge, reading for the mathematics tripos.

At Cambridge, Larmor was coached by Edward Routh in the methods of analytical dynamics which were central to the tripos teaching of the time. Analytical dynamics was a mathematical method of solving physical problems by applying Lagrange's equations and Hamilton's principle of least action. It could co-ordinate phenomena and allow predictions to be made about the existence of other effects without any knowledge of the underlying mechanism. Maxwell's electrodynamics exemplified the method, and, by the early 1880s, were becoming a focal point for the research of the most able mathematics graduates. Larmor remained deeply committed to analytical dynamics throughout his life, the principle of least action being, for him, 'the ultimate natural principle--the mainspring of the universe. ... Before he would admit to understanding [a theory] ... Larmor required it to be put in the form of an action principle' (Eddington, 204).

In 1880 Larmor graduated as senior wrangler (J. J. Thomson was second), first Smith's prizeman, and was elected a fellow of St John's. In the same year he was appointed professor of natural philosophy in Queen's College, Galway. Despite being cut off from the Cambridge research community Larmor continued to study Maxwell's Treatise on Electricity and Magnetism, which prompted his first major piece of research, a theoretical study, 'Electromagnetic induction in conducting sheets and solid bodies' (Philosophical Magazine, January 1884). This work exemplified the type of mixed mathematics which Larmor was to use all his life; in an appendix to the same article he stressed that he had reduced 'the mathematical analysis to as narrow limits as possible, replacing it by a discussion of the physical phenomena' (Philosophical Magazine, April 1884), and he was always looking for general principles underlying phenomena, being impatient of attending to the mathematical details. This paper was rapidly followed by 'Least action as the fundamental formulation in dynamics and physics' (Proceedings of the London Mathematical Society, 15, 1884, 158-84).

Seeking to return to Cambridge, Larmor applied unsuccessfully for the Cavendish professorship of experimental physics in 1884. J. J. Thomson was elected, but in 1885 Larmor was appointed to succeed him in one of five recently created university lectureships in mathematics. He lived at St John's College for the rest of his working life, succeeding G. G. Stokes as Lucasian professor of mathematics in 1903.

The ether and matter
In Cambridge, Larmor's research was at first devoted mainly to traditional problems in dynamics and analytical geometry. About 1890, though, his interest in Maxwellian electrodynamics was stimulated by preparing a review article on magneto-optic rotation and recent theories of light propagation. The extremely comprehensive article eventually appeared in 1893 as a British Association report, 'The action of magnetism on light: with a critical correlation of the various theories of light propagation', and it led directly to the work for which Larmor was best known, the development of the idea of electrons as the electromagnetic basis of matter. His ideas marked a fundamental break with the nineteenth-century attempts to devise a mechanical, continuous, and essentially material ether which underlay all physical phenomena, including electromagnetism. Larmor argued instead for an electromagnetic ether, discrete strain centres (called electrons) in which formed matter.

While preparing his British Association report Larmor became aware of George FitzGerald's re-analysis of James MacCullagh's rotationally elastic ether. Larmor identified himself strongly both with the school of mathematical physics at Trinity College, Dublin, to which FitzGerald and MacCullagh belonged, and with the method of least action by which FitzGerald showed that MacCullagh's mechanical ether was formally equivalent to Maxwell's electromagnetic field. Larmor became convinced that if he could ascribe the correct properties to MacCullagh's ether, then it could provide a dynamical foundation for both electromagnetism and the propagation of light.

Larmor's work, 'A dynamical theory of the electric and luminiferous medium', appeared in three parts between 1894 and 1897 in the Proceedings of the Royal Society. Between the three parts, and even within some parts, his theory changed considerably. FitzGerald, who refereed the first part, criticized it heavily and was largely responsible for urging Larmor to solve some of the problems by introducing 'discrete electric nuclei' into his theory. For these Larmor adopted the name 'electrons', a term already proposed by FitzGerald's uncle George Johnstone Stoney for the discrete quantities of electric charge found on the ions in electrolysis.

'Electrons' were introduced in an appendix to part 1 of A Dynamical Theory and profoundly affected Larmor's understanding of the relationship between the electromagnetic ether and matter. Previously these had been distinct substances and no one had succeeded in explaining how they interacted. Now if, as he supposed, matter was composed purely of positive and negative electrons, and electromagnetic effects were due to the motion of electrons, then the whole of physics would be unified into a problem of the electrodynamics of moving bodies (Larmor, Dynamical Theory, pt 3, 1897).

Like Lorentz, whose Versuch he had read in early 1895, Larmor initially thought of his electrons as about as massive as the hydrogen ion. But the discovery by Zeeman, Lorentz's student, in 1896, of the broadening of spectral lines in a magnetic field, and work by J. J. Thomson, Emil Wiechert, and Walter Kaufmann on cathode rays in 1897, both provided important experimental support for the electron idea and indicated that electrons were only about a thousandth of the size of a hydrogen ion. In analysing and explaining the Zeeman effect Larmor arrived at the three results which now bear his name: the Larmor precession, which describes the precession of electron orbits in a magnetic field (at a frequency known as the Larmor frequency, which has become important in understanding nuclear magnetic resonance); the Larmor theorem, which allows the effect of the magnetic field to be neglected to a first order approximation by transforming into a suitably rotating frame of reference; and Larmor's formula for the power radiated by an accelerating electron ('On the theory of the magnetic influence on spectra: and on the radiation from moving ions', Philosophical Magazine, December 1897).

The electronic theory of matter also enabled Larmor to predict the apparent absence of motion of the earth through the ether as shown by Michelson and Morley's experiment of 1887. To British Maxwellians, Larmor and FitzGerald included, who liked to think of the ether as stationary, the Michelson-Morley negative result was puzzling. In 1889 FitzGerald had suggested speculatively that it could be explained if moving matter contracted slightly in the direction of its motion through the ether. Larmor now, in 1897, showed that electron theory predicted this effect; rather than being an anomaly to be explained away, the Michelson-Morley experiment became central evidence for the validity of his theory.

In analysing the Michelson-Morley effect Larmor confronted the problem of correlating the electromagnetic fields measured by an earthbound observer, with the fields that would be measured by an observer who was stationary in the ether. By 1900 he had arrived at the space-time transformations which were later given by Lorentz and Einstein, and are now known as the Lorentz transformations. Larmor was the first physicist to state these, in his influential book Aether and Matter (1900), the published version of the essay with which he won the Adams prize in 1899.

Larmor's work paralleled in many ways that of Lorentz on the continent, and his electronic theory of matter bore many similarities to the electromagnetic theory of nature developed from Lorentz's work. But there were fundamental differences between the two views, the most important of which was that Larmor (unlike Lorentz and, later, Einstein) believed that the equations of electromagnetism were not fundamental but were a manifestation of the dynamical properties of an underlying ether. In practice, though, he did not investigate these ethereal properties, but worked simply with the electromagnetic equations. And his sophisticated techniques, presented in Aether and Matter, allowed Larmor's students to work with Lorentz's model, as developed by Einstein, without abandoning ether physics. Indeed, Ebenezer Cunningham, who is widely credited with introducing relativity theory to Britain, initially adopted Einstein's 1905 relativity theory merely as an adjunct to Larmor's work. It was not until about 1912 that the fundamental incompatibility between relativistic physics and the electronic theory of matter was widely recognized.

Other scientific work
Only about half the works collected in Larmor's Mathematical and Physical Papers (2 vols., 1929) are about electromagnetism. The rest are 'mainly General Dynamics and Thermodynamics including the dynamical history of the Earth, Formal Optics, and Geometry' (J. Larmor, Mathematical and Physical Papers, 1929, 1.v). His interest in the dynamics of the earth's motion dated from 1896 when he published 'On the period of the earth's free Eulerian precession' (Proceedings of the Cambridge Philosophical Society, 9, 1896, 183-93), which was followed by four papers over the next twenty years. In 1906 and 1915, with E. H. Hills, he introduced a new kind of analysis of the irregular motion of the earth's rotation (Monthly Notices of the Royal Astronomical Society, 67, 1906, 22-34; 75, 1915, 518-21). Other papers investigated isostasy and, elsewhere, the sun's magnetism.

Larmor had first considered the effects upon the earth of a conducting layer in the upper atmosphere in his paper 'Electromagnetic induction in conducting sheets and solid bodies' (1884), where he showed how such a layer could screen the earth from external magnetic fields. He returned to the topic of the ionosphere in 1924, his interest stimulated by the experiments of Edward Appleton, another fellow of St John's. Since 1901, when Marconi had demonstrated that radio signals could be transmitted around the earth from Cornwall to Newfoundland, the mechanism guiding the radio waves had been a subject of debate. In 1902 Heaviside and Kennelly both suggested that a conducting layer in the upper atmosphere reflected the waves. After the First World War, Appleton began investigating the existence, nature, and height of this Heaviside layer, as it became called, by examining the fading of radio signals between London and Cambridge. Larmor became interested in the mechanism by which the radio waves were reflected or refracted by this layer: should one consider the ionized air as a conductor or as a dielectric? The central problem was that the layer had to bend the waves considerably without absorbing them at the same time. Assuming that the waves were refracted Larmor concluded that the lack of absorption was possible only if the air pressure was very low and the conductivity of the ionosphere was very small, so that it behaved like a feebly conducting dielectric. He published his results in 'Why wireless electric rays can bend round the earth' (Philosophical Magazine, 48, 1924, 1025-36). Larmor's results suggested to Appleton that the effective electrical particles in the Heaviside layer were free electrons rather than molecular ions, a conclusion that he was later able to verify.

Deeply interested in the history of thermodynamics Larmor was concerned to 'disentangle the romantic history of the evolution of foundations in that domain, with the mainly statistical outlook which its generality imposes' (Larmor, Collected Papers, 1929, 2.v). His obituary notice of Lord Kelvin for the Proceedings of the Royal Society (1908) contains an extensive survey of the developments of thermodynamics. He also contributed an obituary of Josiah Willard Gibbs to the same journal (1905), revised Maxwell's edition of the papers of Henry Cavendish (1921), and edited the collected works of James Thomson (1912), the fourth and fifth volumes (1904-5) of the works of G. G. Stokes, and the fourth, fifth, and sixth volumes (1910-11) of those of Lord Kelvin.

Public life
A quiet and reserved man, Larmor nevertheless took on more than his full share of public duties. Some insight into his character and conception of public service can be gained from his comments on Henry Cavendish, who, Larmor judged, had been unfairly judged misanthropic:

The tracking out of great discoveries which will be a possession to the human race for all time has indeed to be its own supreme intellectual satisfaction; and once an investigator has realized, in however modest a way, his capacity for such achievement, he can feel that he is serving humanity in the most perfect manner open to him by concentrating upon that work. Yet the temptation to continual postponement of ordinary social intercourse inevitably involves increasing isolation, and growing habits of solitude ... in the cooperative tasks which united the scientific men of the time ... he was always ready to take unsparing pains, and to devote himself without limit to the assistance of his colleagues. (Larmor, preface to The Scientific Papers of the Honourable Henry Cavendish, 2 vols., 1921, 1.ix-x)
These comments might apply, in lesser measure, to Larmor himself. Larmor had few friends, but being kindly by nature 'while he lived, and they lived, he lost none' (Thompson, 13).

Elected a member of the London Mathematical Society in 1884 Larmor served on its council from 1887 to 1912, being at various times vice-president (1890-91), treasurer (1892-1912), and president (1914). In 1914 he received the De Morgan medal of the society.

Larmor was elected a fellow of the Royal Society in 1892, became a member of the associated Philosophers' Club, a dining club which existed to discuss new ways of promoting the society's scientific aims and improving its methods and organization, and in 1901 became physical secretary, a responsible and influential position which he held until 1912. In this position he was knighted, in 1909, and later received the society's royal medal (1915) and Copley medal (1921).

Possibly prompted by concern for the Irish question, Larmor entered parliament as a Unionist, being MP for Cambridge University from 1911 to 1922.

One of his characteristic reminiscences was the defeat of the alternative vote, which he claimed to have secured by a long speech, leading the bewildered House deeper and deeper into mathematics until the whip gave him the signal that the wanted absentees had arrived. (Eddington, 206)
Larmor was for many years a member of the council of St John's College. Here he was often critical and conservative, ensuring that important points were not overlooked, and questioning modern trends. But at a more informal level Appleton recalls that he was 'friendly, considerate and generous in the attention he gave to [his younger colleagues]' (Appleton, 66). D'Arcy Thompson alleges that he was disappointed not to have been elected master of his college. His continuing commitment to Cambridge and St John's was shown by bequests which he made for medical help for junior members of the university, to the University and College Servants' Association and for prizes to be awarded annually to men of St John's College who were adjudged the most outstanding on general, rather than purely academic, grounds.

In 1932, about the time that he began suffering from pernicious anaemia, of which he eventually died, Larmor retired from Cambridge. He returned to Ireland, living at Drumadillar, Demesne Road, Holywood, co. Down, near Belfast, with four of his brothers and sisters, including his brother Alexander, who had followed Larmor to Cambridge and had subsequently become professor of natural philosophy at Magee University College, Londonderry. From there Larmor followed with interest general advances in geophysics and astrophysics, often contributed letters to Nature and The Observatory on the physical problems that they raised, and pursued metaphysics. His brothers' and sisters' deaths left him isolated, for nearly a year before he himself died at Holywood on 19 May 1942.


A. S. Eddington, Obits. FRS, 4 (1942-4), 197-207
W. B. Morton, 'Joseph Larmor', Proceedings of the Belfast Natural History and Philosophical Society, 2 (1942-3), 82-90
D. W. Thompson, 'Joseph Larmor', Year Book of the Royal Society of Edinburgh (1941-2), 11-13
J. Z. Buchwald, From Maxwell to microphysics: aspects of electromagnetic theory in the last quarter of the nineteenth century (1985)
B. J. Hunt, The Maxwellians (1991)
A. Warwick, 'Frequency, theorem, and formula: remembering Joseph Larmor in electromagnetic theory', Notes and Records of the Royal Society, 47 (1993), 49-60
A. Warwick, 'On the role of the FitzGerald-Lorentz contraction hypothesis in the development of Joseph Larmor's electronic theory of matter', Archive for History of Exact Sciences, 43 (1991-2), 29-91
A. Warwick, 'Cambridge mathematics and Cavendish physics: Cunningham, Campbell and Einstein's relativity, 1905-1911, part 1', Studies in History and Philosophy of Science, 23 (1992), 625-56
E. Appleton, 'Sir Joseph Larmor and the ionosphere', Proceedings of the Royal Irish Academy, 61A (1960-61), 55-66
Venn, Alum. Cant.
The Times (14 Oct 1936)
CGPLA NIre. (1942)
WWW, 1929-40

RS, Larmor correspondence
St John Cam., MSS |  CUL, Stokes collection, papers and correspondence
CUL, Kelvin collection, correspondence
CUL, Rutherford collection, correspondence
UCL, Lodge MSS, correspondence

photograph, 1912, repro. in Hunt, Maxwellians, 211
F. McKelvey, portrait, 1940, Queen's University, Belfast [see illus.]
W. Stoneman, photograph, NPG
photograph, repro. in Eddington, Obits. FRS, facing p. 197
photograph, repro. in Morton, 'Joseph Larmor', facing p. 82

Wealth at death  
£9901 8s. 5d.: probate, 9 Nov 1942, CGPLA NIre.

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