**Professor Hector Munro Macdonald**, one of Europe's foremost mathematicians, died on the 16th of May, 1935.

Professor Hector Munro Macdonald brought the world of science half way to an understanding of how Guglielmo Marconi was able to transmit wireless signals across the Atlantic. Marconi knew how to transmit and receive radio waves, but he didn’t know how they managed to navigate the curvature of the earth to get across the ‘pond’. That was the major problem tackled by Macdonald. Coincident with Macdonald publishing his Adams Prize winning essay on electric waves, Marconi was successfully transmitting the first wireless signals across the Atlantic. However, unless Marconi had been feigning his successful reception of those signals, science had been posed a major ‘problemo’. According to the then current theory, that should’ve been impossible. An answer was proposed by Scotland’s own Professor Hector Munro Macdonald.

Light and wireless waves are both electric waves of different wavelengths, but both have a wavelength, which is very small compared with the radius of the Earth. Light does not bend round the Earth, yet wireless waves do as is proved by transmitting them across the Atlantic. The answer that Macdonald came up with was that the means was due to refraction. That is partially true, but not completely so as experimental evidence later showed, since wireless waves bent round the Earth more than could be explained by refraction alone. The answer, as we now understand, is due to reflection of waves of particular wavelengths by the upper atmosphere. Nevertheless, Macdonald’s early theory was most certainly an important step towards such an understanding.

Macdonald’s great publication, which established his reputation in the world of science, and which led to his being elected a Fellow of the Royal Society, was his volume on ‘Electric Waves’. Macdonald’s main body of scientific work was on electric waves and he solved several difficult problems regarding diffraction of these waves by summing series of ‘Bessel functions’. Incidentally, Friedrich Wilhelm Bessel was the director of Frederick William III of Prussia’s Königsberg Observatory and its professor of astronomy. He was born in Minden, Westphalia, in 1784. Bessel worked out a method of mathematical analysis, involving what are now known as ‘Bessel functions’, which are a special class of coefficients that have become an indispensable tool in applied mathematics, physics and engineering.

Hector Munro Macdonald was born on the 19th of January, 1865, in Edinburgh. Soon after he started school in Edinburgh, the family moved to a farm near Fearn, in Easter Ross; a long way from Edinburgh. Hector attended the Hill of Fearn Public School, before attending the Royal Academy in Tain. He then completed his school education at the Old Aberdeen Grammar School, before entering Aberdeen University, in 1882.

After studying mathematics at Aberdeen University, Macdonald graduated with First Class Honours in Mathematics and Natural Philosophy, in 1886, winning the Simpson Mathematical and Arnott Experimental Physics Prizes, and a Fullerton Scholarship.

As did many Scottish mathematicians of that era, Hector Munro Macdonald went to Cambridge to take the Mathematical Tripos after completing his first degree in Scotland. Entering Clare College as a foundation scholar, he graduated with a First Class degree. Macdonald was awarded a fellowship at Clare in the following year and, in 1891, was awarded the second Smith’s Prize. Macdonald began his research career at Cambridge working on topics in pure mathematics. That work was on the relations between convergent series and asymptotic expansions, the zeros and the addition theorem of the ‘Bessel functions’, various ‘Bessel integrals’, spherical harmonics and ‘Fourier series’.

Macdonald’s research changed direction, however, when in 1899, Cambridge University announced that the topic for the 1901 Adams Prize would be “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 ... [and] the theory of wireless telegraphy.” Macdonald’s essay won the Prize and later working up from the foundation of his paper, he published the book, ‘Electric Waves’, in 1902. Macdonald also published a volume on ‘Electromagnetism’, in 1934.

Whilst at Clare, Macdonald became acting senior bursar. His experience in that role, coupled with that from his early life on a farm, meant that he was, quite naturally, a good candidate to take up the oversight of the University lands and buildings. So, he did just that. Macdonald’s conception of a ‘cité universitaire’ for the neighbourhood of King’s College has left a permanent, positive impression on that region. Macdonald was elected to the Royal Society in 1901, but left Cambridge to return to Scotland in 1904, after he was appointed Professor of Mathematics at Aberdeen University. In 1907, Macdonald was appointed to the Court of Aberdeen University and he remained on that administrative body for the rest of his life. Macdonald was awarded the Royal Society’s Royal Medal in 1916 and, during 1916-18, served as President of the London Mathematical Society.

It was said of Macdonald that “he spoke little, and when he spoke he was always brief, but what he said was usually decisive and always undeviatingly to the point.” He was a man of few wasted words. Interestingly, Macdonald also had the capacity to make himself rapidly an authority on any subject to which he gave his attention. Macdonald’s great passion was mountaineering and he climbed most of the highest peaks of the Bernese and Valaisian Alps in between theorizing on electric waves. Although a true Highlander, Macdonald was apparently never a fluent Gaelic speaker, nevertheless, his grandmother taught him to read the Gaelic Bible and he was a regular at the annual Gaelic Service in King’s College Chapel, and he was often seen at students’ Gaelic society meetings. Not surprising, since those folks knew how to enjoy a wee ‘Cailidh’.

Professor Hector Munro Macdonald died in a nursing home in Aberdeen, to which he was removed to undergo an operation only the week before, on the 16th of May, 1935. His death was unexpected, judging by the fact that in the week of his demise he was reappointed as the University’s representative Governor on the Highlands and Islands Education Trust for another five years. Macdonald was buried in the old Churchyard of St. Machar’s Cathedral.

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