James Clerk Maxwell (1831-1879), Scottish physicist, widely considered by twentieth and twenty-first century physicists to have been one of the most significant figures of the nineteenth century. His work fundamentally changed conceptions of electromagnetism and introduced the basis of field theory. He is also known for his work on thermodynamics and the kinetic theory of gases.
Education
James Clerk Maxwell was born in Edinburgh on June 13th 1831, into a modestly wealthy Scottish family. (Maxwell was the family name which his father was required to adopt, by the terms of a legal entailment, in order to inherit the estate). As a child, Maxwell was enrolled in the Edinburgh Academy. It was here that he met Peter Guthrie Tait (1831-1901), a contemporary who pursued a very similar career to Maxwell's own, and who became a life-long friend. Tait later recalled that as a schoolboy Maxwell spent his free time 'drawing curious diagrams and making rude mechanical models'.1 These pursuits contributed to Maxwell's rather uncomplimentary school nickname of 'Dafty', but bore signs of talent and originality —characteristics which his father sought to nourish by introducing James to the intellectual societies of Edinburgh. Thus encouraged by his father and the natural philosopher James Forbes (1809-1868), the fourteen year old Maxwell produced his first publication: a paper describing a simple mechanical means of drawing mathematical curves with a piece of string.2 This combination of algebraic mathematics with elements of geometry would remain a distinctive feature of Maxwell's work.
At age 16, Maxwell left the Academy for Edinburgh University. His studies there included Natural Philosophy under Kelland, Forbes and Gregory; Moral Philosophy under Wilson; and Mental Philosophy under Sir William Hamilton. Maxwell consumed these subjects eagerly, and his letters and notes from this period (November 1847 to October 1850) clearly demonstrate an extraordinary thirst for knowledge. At the same time, we can see the maturation of his own critical faculties, together with the want for original research, and his vacations were invariably spent engaged in experiment of some kind at the family home of Glenlair.
In October 1850, Maxwell came up to Cambridge. He applied and was admitted into Peterhouse —the college at which his friend Tait had arrived two years earlier (and which was rumoured to favour Scotsmen at this time). However, within a few months, and on the advice of several individuals including Forbes, Maxwell 'migrated' to Trinity, a larger college with a better reputation for mathematics. Trinity also offered an improved possibility for a fellowship, which even if it were not yet a consideration for Maxwell himself, was already on the mind of his father, who took a very active interest in managing his son's academic career.
Yet whilst Maxwell's change of college might have improved his prospects somewhat, the learning conditions within the University as a whole still left much to be desired. An 1852 Royal Commission reported 'a very general feeling of dissatisfaction prevalent respecting the present system of instruction'.3 This meant that students aspiring to a first-class degree often resorted to private tutors or coaches (indeed, this was the origin of the term 'coach' as trainer, meaning one who swiftly conveys a student to their intellectual goal, as a horse-drawn coach does to a physical destination). Thus by November 1851, Maxwell had become a student of William Hopkins, a tutor whose success in producing first-class mathematicians —such as Cayley, Kelvin, Stokes and Tait —had earned him the nickname 'wrangler maker'. With Hopkins' help, Maxwell graduated in 1854 as second wrangler (i.e. second-highest in the mathematics exam); the disappointment of being beaten by another of Hopkins' students, Edward Routh of Peterhouse, was slightly mitigated when the two of them were declared joint winners of the highly prestigious Smith Prize.
Electrical science
Having entered 'the unholy estate of bachelorhood', as he put it, Maxwell turned his attention towards electrical science.4 He found it a difficult subject, with its phenomena and internal relations 'more…complex than those of any other science hitherto developed'.5 He therefore sought to understand the subject, as he explained to Kelvin in 1855, 'by the aid of any notions I could screw into my head'.6
The most comprehensive collection of writings on the subject which Maxwell found was Faraday's three volume Experimental Researches in Electricity. These were not of a particularly mathematical nature —Faraday having had little formal training and having approached the subject from a strongly experimental, rather than theoretical point of view. However, whilst most other physicists saw this as a deficiency, Maxwell viewed this as a positive feature; whereas many saw Faraday's language as vague and unscientific, Maxwell saw this coarseness as an opportunity for Faraday's experimental results to be 'assimilated…in the nascent state'.7 Indeed, Maxwell made a conscious decision not to read any work on electricity by 'the mathematicians' —that is, the Continental researchers such as Gauss, Weber, Biot, Ampère and Coulomb, who approached the subject principally through a mathematical analysis of centres of forces acting at a distance —until after becoming familiar with Faraday's work on the subject.8 Besides a wariness of the 'tenuity and paleness' of symbolic mathematics —a cautiousness which Maxwell had acquired from William Thomson and William Whewell —this decision also reflects a desire to ground himself first in the phenomena, an empiricism which later found its application in Maxwell's appointment as Cavendish professor of natural and experimental philosophy and first director of the Cavendish laboratory, when it was established in 1874.
Maxwell reports that he read Faraday's Experimental Researches with delight, extracting from them several ideas to aid his own growing conception of electromagnetism.9 Among these was the notion of lines of force — a semi-physical, geometric arrangement of lines around charges which, just like iron filings around a magnet, indicated the direction in which a point charge would move if it were to be introduced at any location.10 This idea was of great significance in drawing attention to the space around charges, and so introducing the idea of a potential field, rather than simply considering charges as sources of action-at-a-distance, or as elements of a material substance which flowed only through conductors.11
Another idea which Maxwell 'appropriated' was an analogy between charge distribution and heat flow which Kelvin had published in 1842.12 It was through a combination of this and the line of force that Maxwell attempted his first discourse on electricity —his 1855 essay On Faraday's Lines of Force.13 In essence, this paper took Kelvin's 1842 analogy between electric charge and heat flow, but in place of heat assumed 'an imaginary fluid' whose properties could be described with standard hydrodynamic equations, following Stokes. Assuming positive and negative charges as sources and sinks of the fluid, Maxwell argued that the fluid would flow from source to sink along precisely the same lines as Faraday's 'lines of force'. In fact, the lines of force (or rather, the space between lines) could be considered exactly as thin tubes of steadily-flowing, continuous, incompressible fluid.14
In terms of the history of field theory, this paper was a very significant step, since it brought Faraday's physical, geometrical conceptions under the control of powerful analytical mathematics.15 In terms of our understanding of Maxwell's methodology, the paper is also highly significant, since it displays a characteristic and conscious use of what Maxwell called physical analogy: a compromise between physical hypothesis, which he felt restricted and channel one's thinking, and pure mathematics, which sometimes lacked sufficient connection with the phenomenon under discussion.
The use of mechanical models and analogies within Victorian physics is a substantial subject it itself, and also features heavily in the work of such figures as William Thomson and Oliver Lodge. It was also a fundamental part of Maxwell's next foray into electromagnetism, through his paper On Physical Lines of Force. This paper sought to turn the physical analogy of Faraday's Lines of Force towards physical explanation. As the title suggests, it was Maxwell's attempt to construct a physical basis for the previously imaginary lines of force, and to use this to account for other electromagnetic phenomena. Moreover, he was by now quite convinced of the value of Faraday's electrotonic state, and sought to find some way of mechanically describing this change in media.16 As he noted, the behaviour of magnetised iron filings in forming filaments around a magnet 'naturally tends to make us think of the lines of force as something real...and we cannot help thinking that in every place where we find these lines of force, some physical state or action must exist in sufficient energy to produce the actual phenomena'.17
Maxwell suggested that magnetic action could be explained by considering the lines of magnetic force around a magnet as if they were vortices within a continuous fluid medium. The centrifugal force of such vortices would act to make them shrink along their length and repel similar vortices —just like magnetic lines of force. This scheme had the added virtue of providing a possible explanation for the 'Faraday Effect' —the rotation of the plane of polarisation of light by a magnetic field, reported by Michael Faraday in 1845, which was used by William Thomson to argue for a genuine rotation within magnetised media.18
Maxwell expanded this model over a series of papers, before deriving an expression for the propagation of waves through the vortex medium. Precisely how realistically he viewed the vortex medium is a matter of some debate, but it was largely through this model that Maxwell arrived at two famous ideas:
That a changing magnetic field should always be related to a changing electric field, so that where a standard conduction current is not present, a changing magnetic field should be related to a theoretical 'displacement current'.
ii.) That 'the rate of propagation of transverse vibrations through the elastic medium of which the cells are composed...agrees so exactly with the velocity of light...that we can scarcely avoid the inference that light consists in the transverse vibrations of the same medium which is the cause of electric and magnetic phenomena'.19
Two years later, Maxwell felt able to make an even bolder claim. In his 1864 Dynamical Theory of the Electromagnetic Field, Maxwell argued not simply that the optical and electromagnetic media were the same, but that:
iii.) 'light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field'.
Although Maxwell's 1873 Treatise on Electricity and Magnetism is often cited as the crucial step in the development of electromagnetism, these papers from the 1860s contain the basis of all of Maxwell's electromagnetic work — identifying light as an electromagnetic wave (rather than a wave in a material aether), and introducing the hypothetical entity, the displacement current, which made possible a theoretical explanation of the propagation of electromagnetic energy in space. However, it required several other individuals (such as Lodge, FitzGerald, Heaviside and Larmor), working for some years after Maxwell's death in 1879, before this innovative work was interpreted, simplified and distilled into the set of rules we now know as Maxwell's Equations. Nevertheless, the 1888 announcement by Heinrich Hertz that he had transmitted and received electromagnetic waves was almost universally received as a glorious confirmation of Maxwell's work, and secured Maxwell's status within popular and scientific culture as a Victorian physicist without equal.
Last modified 28 September 2002