Macdonald, Hector Munro

(1865-1935), mathematician and physicist

by E. T. Whittaker, rev. Isobel Falconer

© Oxford University Press 2004 All rights reserved

Macdonald, Hector Munro (1865-1935), mathematician and physicist, was born on 19 January 1865 in Edinburgh, the elder son of Donald Macdonald, originally of Kiltearn, Ross-shire, and his wife, Annie, daughter of Hector Munro of Kiltearn. His earliest education was in Edinburgh, but after the removal of his parents to Fearn in Easter Ross he went to school there, and later to the Royal Academy, Tain, and Old Aberdeen grammar school. He graduated at the University of Aberdeen in 1886 with first-class honours in mathematics and was awarded a Fullerton scholarship. Proceeding to Clare College, Cambridge, as a foundation scholar, he graduated as fourth wrangler in 1889, was elected to a fellowship at Clare in 1890, which he held until 1908, and in 1891 was awarded the second Smith's prize.

In the last years of the nineteenth century Macdonald published many papers on pure mathematics, on the relations between convergent series and asymptotic expansions, the zeros and the addition theorem of Bessel functions, various Bessel integrals, spherical harmonics, and Fourier series. However, his permanent reputation as a discoverer rests chiefly on his research in mathematical physics, which originated in the announcement by Cambridge University in 1899 of the Adams prize subject for 1901--'The improvement of existing knowledge in respect of ... the modes and periods of free electric vibrations in systems of charged bodies, and the radiation from them ... the theory of wireless telegraphy': Macdonald's essay won the prize. The great advance he made was the solution of the problem of diffraction at the edge of a perfectly conducting (that is, totally reflecting) prism; his method could be extended to any transparent or metallic prism of which the optical constants are known. Macdonald's essay was published under the title Electric Waves in 1902.

About this time, Guglielmo (afterwards Marchese) Marconi succeeded in sending wireless signals across the Atlantic, and the problem of explaining the transmission mechanism attracted the attention of mathematicians. The question may be put thus: the electric waves generated by the sending apparatus differ from waves of light only in having a longer wavelength, which is, nevertheless, small compared with the radius of the earth; the curved surface of the earth may, therefore, be expected to form a sort of shadow, effectively screening the receiving apparatus at a distance; how, then, does it happen that in practice the waves penetrate into the region of the shadow? To Macdonald belongs the credit of having been the first to formulate the problem as one of diffraction, and of having, in a series of papers published between 1903 and 1914, solved it.

Macdonald's later papers (eight of which were produced when he was in his sixties) and his book Electro-Magnetism (1934) continued the main study of his life, the radiation, transmission, and reflection of electric waves. He never seemed to be affected by the tremendous upheaval caused by the discoveries of the twentieth century--relativity and quantum mechanics.

In 1904 Macdonald left Cambridge to take up the chair of mathematics in his old university of Aberdeen, where his ability as an administrator soon made him the most influential member of the senatus. In 1907 he was elected as one of the representatives of the senatus on the university court, of which he remained a member (except when absent on government service during the war) for the rest of his life, attending his last meeting only a week before his death. Having been brought up on a farm, and with the further experience of estate management gained as acting senior bursar of Clare, he naturally took up specially the oversight of the university lands and buildings; his conception of a cité universitaire for the neighbourhood of King's College has left a permanent impress on that area.

The value of Macdonald's scientific work was recognized by his election in 1901 to the fellowship of the Royal Society, of which he was awarded a royal medal in 1916. He was president of the London Mathematical Society in 1916-18, was elected into an honorary fellowship at Clare in 1914, and received the honorary degree of LLD from Glasgow University in 1934. He never married. He died at his home, 52 College Bounds, Aberdeen, after a short illness, on 16 May 1935.


E. T. Whittaker, Obits. FRS, 1 (1932-5), 551-8
The Times (17 May 1935)
personal knowledge (1949)
CGPLA Eng. & Wales (1935)

W. Stoneman, photograph, 1931, NPG
R. G. Eves, oils, 1933, Scot. NPG
R. G. Eves, oils, 1933, U. Aberdeen
photograph, repro. in Whittaker, Obits. FRS, facing p. 551
two photographs, RS

Wealth at death  
£30,887 10s.: confirmation, 29 July 1935, CCI
£554 19s. 5d.: eik further grant, 25 Nov 1935, CCI

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