JAMES CLERK MAXWELL Perspectives on his Life and Work Material Edited by raymond flood mark mccartney and andrew whitaker Copyrighted - Preview 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. 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Copyrighted - Preview CHAPTER 1 Introduction raymond flood Material James Clerk Maxwell’s work on electricity and magnetism was such that Einstein enthused: Since Maxwell’s time, Physical Reality has been thought of as represented by continuous fields ...and not capable of any mechanical interpretation. This change in the conception of Reality is the most profound and the most fruitful that physics has experienced since the time of Newton.1 While the distinguished physicist, Richard Feynman, predicted: From a long view of the history of mankind — seen from, say, ten thousand years from now — there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics.2 I will start by giving an overview of Maxwell’s life and will then consider his major areas of interest and his achievements.3 Copyrighted Maxwell’s Life - James Clerk Maxwell was born in Edinburgh on 13 June 1831. Two years later, the family moved to Glenlair, an estate that his father had inherited, about 90 miles southwest of Edinburgh. The family was financially well off and well established. James’s father, John, had trained as a lawyer but seems to have been more interested in what we might now call ‘design and technology’. His mother, Frances, was 40 when James was born and she died in December 1839. From all accounts James was a much loved, precocious, curious and intelligent child. After his mother’s death his father appointed a tutor for him, which was not a success – to put it mildly – and as a result James was sent to Edinburgh Academy and to live with relatives just under two years after his mother’s death. Preview P. G. Tait was another pupil at the Academy and they became lifelong friends, even though as adults they competed for the same job on more than one occasion. It was while James was at introduction | 3 Fig. 1.1 Method of drawing an ellipse with a piece of string. Edinburgh Academy that he published his first academic paper, at the age of 14, in the Proceedings of the Royal Society of Edinburgh. It arose out of his attempts to generalize the well-known process for drawing an ellipse by attaching a string to two pins and keeping the string stretched with the point of your pencil and then moving the pencil around to trace an ellipse (see Fig. 1.1). James investigated what happens when the string is folded back on itself towards each pin. Figure 1.2 shows the opening page of his paper, as it was later reprinted in his collected works. In the bottom left picture, the string starts at the left pin, goesMaterial round the pencil and then round therightpinbacktothepencilwhereitisattached.Sothelengthofthestringisthesum of the distance to the left pin plus twice the distance to the right. In the bottom right pic- ture, the string starts attached to the pencil, goes round the right pin, back to the pencil, then round the left pin, back to the pencil and is then attached to the right pin. So the length of the string is the sum of twice the distance to the left pin plus three times the distance to the right. The page shows some of the ovals that can be generated. And Maxwell did not stop with just two pins! Although Descartes had described ways of generating these curves, Maxwell’s method was new. Maxwell’s father, John, showed the work to a friend, J. D. Forbes, who was Professor of Natural Philosophy at Edinburgh University and who arranged for its publication. Apart from showing his talent at such an early age, it also demonstrates two of Maxwell’s lifelong characteristics: the ability to generalize and his ability with, and enthusiasm for, geometrical reasoning. In 1847, James enrolled at Edinburgh University, where he would study mathematics under Philip Kelland, natural philosophy under James Forbes and logic under Sir William Hamilton. He was 16 at the time and undecidedCopyrighted on his future career, in particular whether he should follow his father’s wishes and become- a lawyer. When he left Edinburgh University three years later he was decided on a scientific career or as he put it, I think most charmingly, to pursue ‘another kind of laws’.4 I want to pick out one investigation that Maxwell undertook at Edinburgh University because it illustrates that he was a gifted experimentalist as well as a theoretician – he was like Newton in this regard. This work was on the ‘Equilibrium of Elastic Solids’ and was published in 1850. Elasticity will come into our story again when we turn to electromagnetism later. In this paper Maxwell axiomatized the equations of elasticity and applied the results to a number of problems (see Fig. 1.3). Maxwell went up to Cambridge in 1850. He was at Peterhouse College for his first term, but then migratedPreview to Trinity College, possibly because there might have been better career oppor- tunities there. He graduated as Second Wrangler, with E. J. Routh taking the top spot of Senior Wrangler. In the subsequent competition for the Smith’s Prize, Maxwell and Routh were declared 4 | james clerk maxwell Material Fig. 1.2 ‘On the Description of Oval Curves and those having a Plurality of Foci; with Remarks by Professor Forbes’, published by James Clerk Maxwell at the age of 14. joint winners. In the Smith’s Prize examinationCopyrighted paper that year, one of the questions was on Stokes’ Theorem, connecting surface and- line integrals (see Fig. 1.4). Maxwell later made great use of this theorem in his work on electromagnetism. Maxwell had done well, not as well perhaps as Tait, who two years earlier had been Senior Wrangler and Smith’s Prizeman, but then Tait was not up against Routh. All of them had studied under the private tutor William Hopkins, as had Stokes, Cayley and William Thomson. In 1855, Maxwell became a fellow of Trinity. This year also saw him publish the paper ‘Experiments on colour as perceived by the eye’, as well as the first part of his paper on Faraday’s lines of force, which showed the first evidence of true genius. The second part of the paper was published the following year. In 1856, Maxwell received a letter from Forbes telling him of a vacancy in the Chair of Natural Philosophy at MarischalPreview College, one of the two university level colleges in Aberdeen at that time, and suggesting that he should apply. At the age of 24, Maxwell was young for a professorship and relatively inexperienced, but others had been appointed at similar ages: William Thomson introduction | 5 Fig. 1.3 The axioms from Maxwell’s ‘On the Equilibrium of Elastic Solids’, 1850. Material Copyrighted - Preview Fig. 1.4 Question 8, on Stokes’ Theorem, set in the Smith’s Prize examination paper taken by James Clerk Maxwell in 1854. 6 | james clerk maxwell to his chair at Glasgow at the age of 22, and Tait to his professorship of mathematics at Queen’s College, Belfast, at the age of 23. Opportunities did not come up very often, and a position at Aberdeen would also allow Maxwell to be closer to his father. However, his father died at Easter in 1856 before James heard that he had been appointed. His appointment to the chair and his time at Marischal College is described in John Reid’s Chapter 2, Maxwell at Aberdeen. The university year ran from November to April, when the students went home to help with their parents’ farms, trades or professions, so Maxwell was able to spend half the year at Aberdeen and the rest at Glenlair. In 1858, he married Katherine Mary Dewar, daughter of the Principal of Marischal College. She helped him in his scientific experiments, both in Aberdeen with his colour experiments and later in London on kinetic theory, in particular on the viscosity of air (see Fig.