An Elementary Treatise on Electricity: Second Edition

By James Clerk Maxwell

Albert Einstein characterized the work of James Clerk Maxwell as the "most profound and the most fruitful that physics has experienced since the time of Newton." Max Planck went even further, declaring that "he achieved greatness unequalled," and Richard Feynman asserted that "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 nineteenth century will be judged as Maxwell's discovery of the laws of electrodynamics."
Maxwell made numerous other contributions to the advancement of science, but the greatest work of his life was devoted to electricity. An Elementary Treatise on Electricity appeared at a time when very few books on electrical measurements were available to students, and its compact treatment not only elucidates the theory of electricity but also serves to develop electrical ideas in readers' minds. The author describes experiments that demonstrate the principal facts relating an electric charge as a quantity capable of being measured, deductions from these facts, and the exhibition of electrical phenomena.
This volume, published posthumously from Maxwell's lecture notes at the Cavendish Laboratory — which he founded at the University of Cambridge — is supplemented by a selection of articles from his landmark book, Electricity and Magnetism. A classic of science, this volume is an eminently suitable text for upper-level undergraduates and graduate students.

• Language: English
• Publisher: Dover Publications
• Release date: Feb 4, 2013
• ISBN: 9780486174631

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INDEX

INTRODUCTION TO THE DOVER EDITION

According to Albert Einstein, the greatest change in... our conception of the structure of reality since Newton laid the foundations of theoretical physics was brought about by Faraday’s and Maxwell’s work on electromagnetic phenomena.¹ By thus linking the names of Michael Faraday (1791–1867) and James Clerk Maxwell (1831–1879), Einstein paid homage to one of the greatest and most extraordinary scientific collaborations. Maxwell’s An Elementary Treatise on Electricity is the final, unfinished expression of the understanding he achieved by studying and extending Faraday’s work.

Consider the contrasting but intertwined lives of these two men. The son of a blacksmith, Faraday began as a bookbinder’s apprentice in London. He did not merely bind books but also read them, especially those on science, which fascinated him. He begged to be taken on as a bottle washer at the nearby Royal Institution, where Humphrey Davy took him under his wing. Without any higher education, Faraday’s astonishing abilities and energy led him to become the greatest experimental physicist of his time. Though he could not understand a single equation, he thought deeply about his exhaustive experiments and reached radically new insights. This immensely practical man also became a great thinker and visionary He came to view the invisible space between bodies as the true seat of electric and magnetic phenomena, not the bodies themselves. In that seemingly empty space was the new reality that Einstein hailed. Magnets were not really pieces of matter but bristling, invisible lines of force or fields, as Faraday named them. He eventually decided that light itself was a high state of vibration of those fields.²

Maxwell, in contrast, came from a wealthy Scottish family and distinguished himself at Cambridge especially for his mastery of mathematical physics. But he grew up in rural Galloway; as a schoolboy in Edinburgh, he was mocked for his country clothes and manners. He had a deep feeling for the grounded and practical, the realities of country and working life. Accordingly, he was not content with the purely theoretical but was drawn to experiment and concrete problems, beginning with his studies of Saturn’s rings and of color theory; in fact, he produced the first color photograph (1861). Faraday’s blend of practicality and imagination struck a chord in Maxwell, who began his study of electricity by resolving "to read no mathematics on the subject till I had first read through Faraday’s Experimental Researches."³ Both men called themselves natural philosophers; the term physicist was only coined in 1830 and Faraday hated it. Though Faraday styled himself an unmathematical philosopher, Maxwell decided that Faraday’s method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbol. Maxwell claimed merely to translate Faraday’s insights into such symbols and reveal him for the very high order of mathematician he really was.⁴ In this, Maxwell’s own humility and generosity stand revealed next to his genius. Such ungrudging recognition and amplification of the work of another living thinker is rare among the great.⁵

The result was Maxwell’s magnum opus, A Treatise on Electricity and Magnetism, first published in 1873. In it, Maxwell aimed to take up the whole subject in a methodical manner, though confined almost entirely to the mathematical treatment, referring the reader to Faraday for a strictly contemporary historical account of some of the greatest electrical discoveries and investigations. Maxwell demonstrated the immense importance of Faraday’s fields, which give a fundamental insight into reality lacking in the alternative approach in terms of action at a distance taken by Continental theorists.⁶ This was a deep advance in natural philosophy to which Einstein was profoundly indebted and whose significance is still unfolding in modern physics.

Because of its groundbreaking character, Maxwell’s exposition in Treatise had many difficulties, which he himself acknowledged. In conversation, he noted that his aim was not to expound his theory definitively but rather to educate himself by presenting what he had seen so far. As C. W. F. Everitt has observed, it is a studio rather than a finished work of art.⁷ For instance, we read sixty pages before coming upon his Plan of this Treatise. Maxwell even advocated reading the four parts of Treatise in parallel rather than in sequence, so as to bring out the complex echoing and restatement occurring throughout. But where Newton crafted his Principia to demonstrate the supremacy of mathematical laws, Maxwell enlisted mathematics to elucidate the ultimate physical priority of fields. If Faraday could not have understood the book that vindicated him, perhaps another, more elemental, approach was needed. In fact, Faraday himself in a letter to Maxwell had asked for just such a thing: When a mathematician engaged in physical actions and results has arrived at his conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as I to express them so?—translating them out of their hieroglyphics that we also might work upon them by experiment.⁸

Maxwell surely remembered that request, but his untimely death at age forty-eight interrupted his preparations for a second edition of Treatise. He was also unable to complete An Elementary Treatise on Electricity, which remained a fragment. Its publication in 1881 was undertaken by William Garnett (1850-1932), who had been his student, later his demonstrator (laboratory assistant) at Cambridge and first biographer, in collaboration with Lewis Campbell.⁹ Garnett took Maxwell’s unfinished draft for Elementary Treatise and decided to fill the lacunae with sections drawn verbatim from the larger Treatise. This was clearly a makeshift meant to allow the work to serve as an alternative to the first part of Treatise. However, Maxwell’s completed sections show that his intention was to write a much more basic work. Thus, Garnett’s interpolated sections from Treatise (whose numbers are marked with asterisks in the text) stick out rather awkwardly, especially because they tend to be much more mathematical than what Maxwell had written for the new work. Yet Garnett did manage to avoid using any calculus in the sections he chose to interpolate, which does help save the elementary character of the work.

Maxwell’s larger plan for Elementary Treatise was to use the most elementary mathematics possible not just to be easier, but in order to emphasize how the physical had become the theory I take this as Maxwell’s final homage to Faraday, reshaping his own presentation to accord better with Faraday’s own physical and intuitive approach because he became more convinced of the superiority of methods akin to those of Faraday, and have therefore adopted them from the first. But this choice also reflected deep preferences of Maxwell’s own. Besides his advanced investigations, Maxwell was deeply committed to reaching out to larger audiences in a thoughtful way, as in his elementary Theory of Heat (1871). Indeed, he had given regular evening classes to working people in Aberdeen and London until 1866.¹⁰

In 1871, Maxwell returned to Cambridge in response to the Duke of Devonshire’s initiative to set up the Cavendish Laboratory of Experimental Physics, meant to challenge and transform British attitudes toward science by emphasizing experiment, not only theory. As the first Cavendish Professor, Maxwell enthusiastically gave himself to this new venture. He supervised the building of the Cavendish Laboratory, kept it going out of his own pocket, and encouraged what he called heroic experiments of extreme precision.¹¹ Though his Cambridge lectures in 1873–74 assumed a high level of mathematical sophistication, he also noted at that time that Experimental Physics, treated without the higher mathematics, may be learned in a sound & scientific manner.¹² Accordingly, in 1875 he began to write his Elementary Treatise to give a more accessible, but also more fundamental, account than that in the earlier Treatise.¹³

In his Elementary Treatise, Maxwell’s intent is not to oversimplify or popularize; he seeks to present a thorough treatment, not easy but still accessible to beginning learners. When he uses the word elementary, he does not mean to disparage or minimize, as if the elements of a subject were shameful preliminaries for its real, advanced substance. Rather, he is thinking of Euclid’s Elements, more widely read in his time than ours, to which he refers several times. Euclid and Maxwell both consider the elements to be crucial beginnings, the foundation on which everything rests, worthy of close attention and thought¹⁴ In his Elementary Treatise, Maxwell tries to reveal those foundations. But here again he would probably repeat his disclaimer about Treatise, that rather than pretending to definitive statement, most of all he was trying to educate himself. By following his attempt to educate himself, we in turn may learn.

The present edition reprints the second edition (1888), for which Garnett had hoped to omit the sections he interpolated from Treatise. In the end, he decided to let his original version stand, though he made some corrections and added notes, shown in square brackets in the text. However, the only previous reprint in the last century copied the first edition, so that this Dover edition is the first to reprint Garnett’s final version since it appeared in 1888.¹⁵ In the endnotes, I have also used square brackets to enclose my commentary In addition, I have silently corrected some obvious misprints that remained in the 1888 text.

At the end of his preface to the Treatise, Maxwell wrote it is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state. Most of all, he wanted "to communicate to others the same delight which I have found myself in reading Faraday’s Researches." In its turn, An Elementary Treatise on Electricity invites us to join Maxwell’s voyage of education and delight.

Peter Pesic

1

Albert Einstein,Maxwell’s Influence on the Evolution of the Idea of Physical Reality, Ideas and Opinions (New York: Crown Books, 1982), pp. 266–270, at 266.

2

Michael Faraday’s Experimental Researches in Electricity (Dover, 2004; also reprinted in Santa Fe, NM: Green Lion Press, 2000) remain essential reading, referred to henceforth as Experimental Researches; a well-chosen selection and excellent introductions and notes are given by Howard J. Fisher, Faraday’s Experimental Researches in Electricity: Guide to a First Reading (Santa Fe, NM: Green Lion Press, 2001), reiferred to below as Guide. L. Pearce Williams, Michael Faraday (New York: Simon & Schuster, 1971) gives an excellent and detailed biographical account that also addresses Faraday’s philosophical and religious views, as does Geoffrey Cantor, Michael Faraday, Sandemanian and Scientist: A Study in Science and Religion in the Nineteenth Century (New York: St. Martin’s Press, 1991).

3

James Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd edition (Dover, 1954), vol. 1, p. viii, hereafter to be cited by volume number and page or section number as Treatise 1:viii. Thomas K. Simpson gives a superb guide in Figures of Thought: A Study of Maxwell’s Treatise (Santa Fe, NM: Green Lion Press, 2005), as well as an excellent presentation of three of Maxwell’s earlier writings in Maxwell on the Electromagnetic Field: A Guided Study (New Brunswick, NJ: Rutgers University Press, 1997).

4

For treatment of the interchange between Faraday and Maxwell, see John Hendry, James Clerk Maxwell and the Theory of the Electromagnetic Field (Bristol: Adam Hilger, 1986); Thomas K. Simpson, "Maxwell’s Treatise and the Restoration of the Cosmos," in The Great Ideas Today (Chicago: Encyclopædia Britannica, 1986), pp. 218–267; P. M. Harman, The Natural Philosophy of James Clerk Maxwell (Cambridge: Cambridge University Press, 1998) gives a superb treatment of Maxwell’s whole oeuvre in its historical and philosophical context. The work of Fisher and Simpson has also helpfully emphasized the larger philosophical and rhetorical, even literary, implications of the work of Faraday and Maxwell. I have also considered the context and implications of field theory in Seeing Double: Shared Identities in Physics, Philosophy, and Literature (Cambridge: MIT Press, 2002), pp. 69–84.

5

Albert Einstein’s unselfish admiration of Hendrik Antoon Lorentz and Max Planck may be comparable; as counterexamples, consider Isaac Newton and G. W. Leibniz.

6

However, Maxwell scrupulously acknowledged the merits of Carl Friedrich Gauss, Wilhelm Weber, and Ludwig Lorenz. See Olivier Darrigol, The electrodynamic revolution in Germany as documented by early German expositors of ‘Maxwell’s theory’, Archive for History of Exact Sciences 45, 189–280 (1993).

7

C. W. F. Everitt, James Clerk Maxwell, Physicist and Natural Philosopher (New York: Charles Scribner’s Sons, 1975), pp. 80–81, who notes that the conversation was recounted by Joseph Larmor in 1908.

8

Faraday’s letter of November 13, 1857 in The Selected Correspondence of Michael Faraday, ed. L. Pearce Williams (Cambridge: Cambridge University Press, 1971), vol. 2, pp. 884–885.

9

Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (New York: Johnson Reprint, 1969); beside Everitt’s excellent work, for nontechnical biographies see Ivan Tolstoy, James Clerk Maxwell: A Biography (Chicago: University of Chicago Press, 1981) and Martin Goldman, The Demon in the Aether: The Story of James Clerk Maxwell (Edinburgh: Paul Harris, 1983).

10

James Clerk Maxwell, Theory of Heat, ed. Peter Pesic (Dover, 2001). Another work Maxwell wrote for a general audience was Matter and Motion (1877; Dover, 1991).

11

See Everitt, Maxwell, pp. 175–177.

12

The Scientific Letters and Papers of James Clerk Maxwell, ed. P. M. Harman (Cambridge: Cambridge University Press, 1995), vol. 2, p. 964 (1873). Reprinted by Dover, 2003.

13

In 1876, he began also to give lectures at a much more elementary level (along with Garnett); see the introduction to Scientific Letters and Papers of James Clerk Maxwell, vol. 3, pp. 3–5,16, and Garnett, Life of Maxwell, 348-358, 364–366. See also Andrew Warwick, Masters of Theory: A Pedagogical History of Mathematical Physics at Cambridge, 1760–1930 (Chicago: University of Chicago Press, 2003).

14

For Maxwell’s treatment of the elementary, see Simpson’s commentary on Maxwell’s Matter and Motion in The Great Ideas Today (Chicago: Encyclopædia Britannica, 1986), pp. 351–356.

15

The reprint of the 1881 edition by Dabor Science Publications (Oceanside, NY, 1977) has an introduction by Joseph Anthony Mazzeo.

CHAPTER I.

EXPERIMENT I.

Electrification by Friction.

1.] TAKE a stick of sealing-wax, rub it on woollen cloth or flannel, and then bring it near to some shreds of paper strewed on the table. The shreds of paper will move, the lighter ones will raise themselves on one end, and some of them will leap up to the sealing-wax. Those which leap up to the sealing-wax sometimes stick to it for awhile, and then fly away from it suddenly. It appears therefore that in the space between the sealing-wax and the table is a region in which small bodies, such as shreds of paper, are acted on by certain forces which cause them to assume particular positions and to move sometimes from the table to the sealing-wax, and sometimes from the sealing-wax to the table.

These phenomena, with others related to them, are called electric phenomena, the bodies between which the forces are manifested are said to be electrified, and the region in which the phenomena take place is called the electric field.

Other substances may be used instead of the sealing-wax. A piece of ebonite, gutta-percha, resin or shellac will do as well, and so will amber, the substance in which these phenomena were first noticed, and from the Greek name of which the word electric is derived.

The substance on which these bodies are rubbed may also be varied, and it is found that the fur of a cat’s skin excites them better than flannel.

It is found that in this experiment only those parts of the surface of the sealing-wax which were rubbed exhibit these phenomena, and that some parts of the rubbed surface are apparently more active than others. In fact, the distribution of the electrification over the surface depends on the previous history of the sealing-wax, and this in a manner so complicated that it would be very difficult to investigate it. There are other bodies, however, which may be electrified, and over which the electrification is always distributed in a definite manner. We prefer, therefore, in our experiments, to make use of such bodies.

The fact that certain bodies after being rubbed appear to attract other bodies was known to the ancients. In modern times many other phenomena have been observed, which have been found to be related to these phenomena of attraction. They have been classed under the name of electric λεκτρον, having been the substance in which they were first described.

Other bodies, particularly the loadstone and pieces of iron and steel which have been subjected to certain processes, have also been long known to exhibit phenomena of action at a distance. These phenomena, with others related to them, were found to differ from the electric phenomena, and have been classed under the name of magnetic phenomena, the loadstone, μ γνης, being found in Magnesia a.

These two classes of phenomena have since been found to be related to each other, and the relations between the various phenomena of both classes, so far as they are known, constitute the science of Electromagnetism.

EXPERIMENT II.

Electrification of a Conductor.

2.] Take a metal plate of any kind (a tea-tray, turned upside down, is convenient for this purpose) and support it on three dry wine glasses. Now place on the table a plate of ebonite, a sheet of thin gutta-percha, or a well-dried sheet of brown paper. Rub it lightly with fur or flannel, lift it up from the table by its edges and place it on the inverted tea-tray, taking care not to touch the tray with your fingers.

It will be found that the tray is now electrified. Shreds of paper or gold-leaf placed below it will fly up to it, and if the knuckle is brought near the edge of the tray a spark will pass between the tray and the knuckle, a peculiar sensation will be felt, and the tray will no longer exhibit electrical phenomena. It is then said to be dischargerd. If a metal rod, held in the hand, be brought near the tray the phenomena will be nearly the same. The spark will be seen and the tray will be discharged, but the sensation will be slightly different.

If, however, instead of a metal rod or wire, a glass rod, or stick of sealing-wax, or a piece of gutta-percha, be held in the hand and brought up to the tray there will be no spark, no sensation, and no discharge. The discharge, therefore, takes place through metals and through the human body, but not through glass, sealing-wax, or gutta-percha. Bodies may therefore be divided into two classes: conductors, or those which transmit the discharge, and non-conductors, through which the discharge does not take place.

In electrical experiments, those conductors, the charge of which we wish to maintain constant, must be supported by non-conducting materials. In the present experiment the tray was supported on wine glasses in order to prevent it from becoming discharged. Pillars of glass, ebonite, or gutta-percha may be used as supports, or the conductor may be suspended by a white silk thread. Solid non-conductors, when employed for this purpose, are called insulators. Copper wires are sometimes lapped with silk, and sometimes enclosed in a sheath of gutta-percha, in order to prevent them from being in electric communication with other bodies. They are then said to be insulated.

The metals are good conductors; air, glass, resins, gutta-percha, caoutchouc, ebonite, paraffin, &c., are good insulators; but, as we shall find afterwards, all substances resist the passage of electricity, and all substances allow it to pass though in exceedingly different degrees. For the present we shall consider only two classes of bodies, good conductors, and good insulators.

EXPERIMENT III.

Positive and Negative Electrification.

3.] Take another tray and insulate it as before, then after discharging the first tray remove the electrified sheet from it and place it on the second tray. It will be found that both trays are now electrified. If a small ball of elder pith suspended by a white silk thread b be made to touch the first tray, it will be immediately repelled from it but attracted towards the second. If it is now allowed to touch the second tray it will be repelled from it but attracted towards the first. The electrifications of the two trays are therefore of opposite kinds, since each attracts what the other repels. If a metal wire, attached to an ebonite rod, be made to touch both trays at once, both trays will be completely discharged. If two pith balls be used, then if both have been made to touch the same tray and then hung up near each other they are found to repel each other, but if they have been made to touch different trays they attract each other. Hence bodies when electrified in the same way are repelled from each other, but when they are electrified in opposite ways they are attracted to each other.

If we distinguish one kind of electrification by calling it positive, we must call the other kind of electrification negative. We have no physical reason for assigning the name of positive to one kind of electrification rather than to the other. All scientific men, however, are in the habit of calling that kind of electrification positive which the surface of polished glass exhibits after having been rubbed with zinc amalgam spread on leather. This is a matter of mere convention, but the convention is a useful one, provided we remember that it is a convention as arbitrary as that adopted in the diagrams of analytical geometry of calling horizontal distances positive or negative according as they are measured towards the right or towards the left of the point of reference.

In our experiment with a sheet of gutta-percha excited by flannel, the electrification of the sheet and of the tray on which it is placed is negative; that of the flannel and of the tray from which the gutta-percha has been removed is positive.

In whatever way electrification is produced it is one or other of these two kinds.

EXPERIMENT IV.

The Electrophorus of Volta.

4.] This instrument is very convenient for electrical experiments and is much more compact than any other electrifying apparatus. It consists of two disks, and an insulating handle which can be screwed to the back of either plate. One of these disks consists of resin or of ebonite in front supported by a metal back. In the centre of the disk is a metal pin c, which is in connection with the metal back, and just reaches to the level of the surface of the ebonite. The surface of the ebonite is electrified by striking it with a piece of flannel or cat’s fur. The other disk, which is entirely of metal, is then brought near the ebonite disk by means of the insulating handle. When it comes within a certain distance of the metal pin, a spark passes, and if the disks are now separated the metal disk is found to be charged positively, and the disk of ebonite and metal to be charged negatively.

In using the instrument one of the disks is kept in connection with one conductor while the other is applied alternately to the first disk and to the other conductor. By this process the two conductors will become charged with equal quantities of electricity, that to which the ebonite disk was applied becoming negative, while that to which the plain metal disk was applied becomes positive.

ELECTROMOTIVE FORCE.

5.] Definition.—Whatever produces or tends to produce a transfer of Electrification is called Electromotive Force.

Thus when two electrified conductors are connected by a wire, and when electrification is transferred along the wire from one body to the other, the tendency to this transfer, which existed before the introduction of the wire, and which, when the wire is introduced, produces this transfer, is called the Electromotive Force from the one body to the other along the path marked out by the wire.

To define completely the electromotive force from one point to another, it is necessary, in general, to specify a particular path from the one point to the other along which the electromotive force is to be reckoned. In many cases, some of which will be described when we come to electrolytic, thermoelectric, and electromagnetic phenomena, the electromotive force from one point to another may be different along different paths. If we restrict our attention, however, as we must do in this part of our subject, to the theory of the equilibrium of electricity at rest, we shall find that the electromotive force from one point