CHAPTER X.

DEVELOPMENT OF MAXWELL’S THEORY.

We have endeavoured in the preceding pages to give some account of Maxwell’s contributions to electrical theory and the physics of the ether. We must now consider very briefly what evidence there is to support these views. At Maxwell’s death such evidence, though strong, was indirect. His supporters were limited to some few English-speaking pupils, young and enthusiastic, who were convinced, it may be, in no small measure, by the affection and reverence with which they regarded their master. Abroad his views had made very little way.

In the last words of his book he writes, speaking of various distinguished workers--

“There appears to be in the minds of these eminent men some prejudice, or _à priori_ objection, against the hypothesis of a medium in which the phenomena of radiation of light and heat, and the electric actions at a distance, take place. It is true that, at one time, those who speculated as to the causes of physical phenomena were in the habit of accounting for each kind of action at a distance by means of a special ætherial fluid, whose function and property it was to produce these actions. They filled all space three and four times over with æthers of different kinds, the properties of which were invented merely to ‘save appearances,’ so that more rational enquirers were willing rather to accept not only Newton’s definite law of attraction at a distance, but even the dogma of Cotes,[64] that action at a distance is one of the primary properties of matter, and that no explanation can be more intelligible than this fact. Hence the undulatory theory of light has met with much opposition, directed not against its failure to explain the phenomena, but against its assumption of the existence of a medium in which light is propagated.

“We have seen that the mathematical expression for electro-dynamic action led, in the mind of Gauss, to the conviction that a theory of the propagation of electric action in time would be found to be the very key-stone of electro-dynamics. Now we are unable to conceive of propagation in time, except either as the flight of a material substance through space, or as the propagation of a condition of motion, or stress, in a medium already existing in space.

“In the theory of Neumann, the mathematical conception called potential, which we are unable to conceive as a material substance, is supposed to be projected from one particle to another in a manner which is quite independent of a medium, and which, as Neumann has himself pointed out, is extremely different from that of the propagation of light.

“In the theories of Riemann and Betti it would appear that the action is supposed to be propagated in a manner somewhat more similar to that of light.

“But in all of these theories the question naturally occurs:--If something is transmitted from one particle to another at a distance, what is its condition after it has left one particle and before it has reached the other? If this something is the potential energy of the two particles, as in Neumann’s theory, how are we to conceive this energy as existing in a point of space, coinciding neither with the one particle nor with the other? In fact, whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other, for energy, as Torricelli[65] remarked, ‘is a quintessence of so subtle a nature that it cannot be contained in any vessel except the inmost substance of material things.’ Hence all these theories lead to a conception of a medium in which the propagation takes place, and if we admit this medium as an hypothesis, I think it ought to occupy a prominent place in our investigations, and that we ought to endeavour to construct a mental representation of all the details of its action, and this has been my constant aim in this treatise.”

Let us see, then, what were the experimental grounds in Maxwell’s day for accepting as true his views on electrical action, and how since then, by the genius of Heinrich Hertz and the labours of his followers, those grounds have been rendered so sure that nearly the whole progress of electrical science during the last twenty years has consisted in the development of ideas which are to be found in the “Treatise on Electricity and Magnetism.”

The purely electrical consequences of Maxwell’s theory were of course in accord with all known electrical observations. The equations of the field accounted for the electro-magnetic forces observed in various experiments, and from them the laws of electro-magnetic induction could be correctly deduced; but there was nothing very special in this. Similar equations had been obtained from the theory of action at a distance by various writers; in fact, Helmholtz’s theory, based on the most general form of expression for the force between two elements of current consistent with certain experiments of Ampère’s, was more general in its character than Maxwell’s. The destructive features of Maxwell’s theory were:

(1) The assumption that all currents flow in closed circuits.

(2) The idea of energy residing throughout the electro-magnetic field in consequence of the strains and stresses set up in the electro-magnetic medium by the actions to which it was subject.

(3) The identification of this electro-magnetic medium with the luminiferous ether, and the consequent view that light is an electro-magnetic phenomena.

(4) The view that electro-magnetic forces arise entirely from strains and stresses set up in the ether; the electrostatic charge of an insulated conductor being one of the forms in which the ether strain is manifested to us.

(5) A dielectric under the action of electric force is said to become polarised, and, according to Maxwell (vol. i. p. 133), all electrification is the residual effect of the polarisation of the dielectric.

Now it must, I think, be admitted that in Maxwell’s day there was direct proof of very few of these propositions. No one has even yet so measured the displacement currents in a dielectric as to show that the total flow across every section of a circuit is at any given moment the same, though there are other experiments of an indirect character which have now completely justified Maxwell’s hypothesis. Experiments by Schiller and Von Helmholtz prove it is true that some action in the dielectric must be taken into consideration in any satisfactory theory; they therefore upset various theories based on direct action at a distance, “but they tell us nothing as to whether any special form of the dielectric theory, such as Maxwell’s or Helmholtz’s, is true or not.” (J. J. Thomson, “Report on Electrical Theories,” B.A. Report, 1885, p. 149.)

When Maxwell died there had been little if any experimental evidence as to the stresses set up in a body by electric force. Fontana, Govi, and Duter had all observed that changes take place in the volume of the dielectric of a condenser when it is charged. Quincke had taken up the work, and the first of his classic papers on this subject was published in 1880, the year following Maxwell’s death. Maxwell himself was fond of shewing an experiment in which a charged insulated sphere was brought near to the surface of paraffin; the stress on the surface causes a heaping up of the paraffin under the sphere.

Kerr had shewn in 1875 that many substances become doubly refracting under electric stress; his complete determination of the laws of this action was published at a later date.

As to direct measurements on electric waves, there were none; the value of the velocity with which, if Maxwell’s theory were true, they must travel had been determined from electrical observations of quite a different character. Weber and Kohlrausch had measured the value of K for air, for which μ is unity, and from their observations it follows that the value of the wave velocity for electro-magnetic waves is about 31 × 10⁹ centimetres per second. The velocity of light was known, from the experiments of Fizeau and Foucault, to have about this value, and it was the near coincidence of these two values which led Maxwell to write in 1864:--

“The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electro-magnetic disturbance propagated through the field according to electro-magnetic laws.”

By the time the first edition of the “Electricity and Magnetism” was published, Maxwell and Thomson (Lord Kelvin) had both made determinations of K, and had shewn that for air at least the resulting value for the velocity of electro-magnetic waves was very nearly that of light.

For other substances at that date the observations were fewer still. Gibson and Barclay had determined the specific inductive capacity of paraffin, and found that its square root was 1·405, while its refractive index for long waves is 1·422. Maxwell himself thought that if a similar agreement could be shewn to hold for a number of substances, we should be warranted in concluding that “the square root of K, though it may not be the complete expression for the index of refraction, is at least the most important term in it.”

Between this time and Maxwell’s death enough had been done to more than justify this statement. It was clear from the observations of Boltzmann, Silow, Hopkinson, and others that there were many substances for which the square root of the specific inductive capacity was very nearly indeed equal to the refractive index, and good reason had been given why in some cases there should be a considerable difference between the two.

Hopkinson found that in the case of glass the differences were very large, and they have since been found to be considerable for most solids examined, with the exception of paraffin and sulphur. For petroleum oil, benzine, toluene, carbon-bisulphide, and some other liquids the agreement between Maxwell’s theory and experiment is close. For the fatty oils, such as castor oil, olive oil, sperm oil, neatsfoot oil, and also for ether, the differences are considerable.

It seems probable that the reason for this difference lies in the fact that, in the light waves, we are dealing with the wave velocity of a disturbance of an extremely short period. Now, we know that the substances mentioned shew optical dispersion, and we have at present no completely satisfactory theory from which we can calculate, from experiments on very short waves, what the velocity for very long waves will be. In most cases Cauchy’s formula has been used to obtain the numbers given. The value of K, however, as found by experiment, corresponds to these infinitely long waves, and to quote Professor J. J. Thomson’s words, “the marvel is not that there should not be substances for which the relation K = μ² does not hold, but that there should be any for which it does.”[66]

It has been shewn, moreover, both by Professor J. J. Thomson himself and by Blondlot, that when the value of K is measured under very rapidly varying electrifications, changing at the rate of about 25,000,000 to the second, the value of the inductive capacity for glass is reduced from about 6·8 or 7 to about 2·7; the square root of this is 1·6, which does not differ much from its refractive index. The values of the inductive capacity of paraffin and sulphur, which it will be remembered agree fairly with Maxwell’s theory, were found to be not greatly different in the steady and in the rapidly varying field.

On the other hand, some experiments of Arons and Rubens in rapidly varying fields lead to values which do not differ greatly from those given by other methods. The theory, however, of these experiments seems open to criticism.

To attempt anything like a complete account of modern verifications of Maxwell’s views and modern developments of his theory is a task beyond our limits, but an account of Maxwell written in 1895 would be incomplete without a reference to the work of Heinrich Hertz.

Maxwell told us what the properties of electro-magnetic waves in air must be. Hertz[67] in 1887 enabled us to measure those properties, and the measurements have verified completely Maxwell’s views.

The method of producing electrical oscillations in a conductor had long been known. Thomson and Von Helmholtz had both pointed it out. Schiller had examined such oscillations in 1874, and had determined the inductive capacity of glass by their means, using oscillations whose period varied from ·000056 to ·00012 of a second.

These oscillations were produced by discharging a condenser through a coil of wire having self-induction. If the electrical resistance of the coil be not too great, the charge oscillates backwards and forwards between the plates of the condenser until its energy is dissipated in the heat produced in the wire, and in the electro-magnetic radiations which leave it.

The period of these oscillations under proper conditions is given by the formula T = 2π√(CL) where L, the coefficient of self induction, and _C_ the capacity of the condenser. These quantities can be calculated, and hence the time of an oscillation is known. From such an arrangement waves radiate out into space. If we could measure by any method the length of such a wave we could determine its velocity by dividing the wave length by the period. But it is clear that since the velocity is comparable with that of light the wave length will be enormous, unless the period is very short. Thus, a wave, travelling with the velocity of light, whose period was ·0001 second, such as the waves Schiller worked with, would have a length of ·0001 × 30,000,000,000 or 3,000,000 centimetres, and would be quite unmeasurable. Before measurements on electric waves could be made it was necessary (1) to produce waves of sufficiently rapid period, (2) to devise means to detect them. This is what Hertz did.

The wave length of the electrical oscillations can be reduced by reducing either the electrical capacity of the system, or the coefficient of self-induction of the wire. Hertz adopted both these expedients. His vibrator, in some of his more important experiments, consisted of two square brass plates 40 cm. in the side. To each of these is attached a piece of copper wire about 30 cm. in length, and each wire ends in a small highly-polished brass ball. The plates are placed so that the wires lie in the same straight line, the brass balls being separated by a very small air gap. The two plates are then charged, the one positively the other negatively, until the insulation resistance of the air gap breaks down and a discharge passes across. Under these conditions the discharge is oscillatory. It does not consist of a single spark, but of a series of sparks, which pass and repass in opposite directions, until the energy of the original charge is radiated into space or dissipated as heat; the plates are then recharged and the process repeated. In Hertz’s experiments the oscillator was charged by being connected to the secondary terminals of an induction coil.

In 1883 Professor Fitzgerald had called attention to this method of producing electric waves in air, and had given two metres as the minimum wave length which might be attained. In 1870 Herr von Bezold had actually made observations on the propagation and reflection of electrical oscillations, but his work, published as a preliminary communication, had attracted little notice. Hertz was the first to undertake in 1887 in a systematic manner the investigation of the electric waves in air which proceed from such an oscillator with a view to testing various theories of electro-magnetic action.

It remained, however, necessary to devise an apparatus for detecting the waves. When the waves are incident on a conductor, electric surgings are set up in the conductor, and may, under proper conditions, be observed as tiny sparks. Hertz used as his detector a loop of wire, the ends of which terminated in two small brass balls. The wire was bent so that the balls were very close together, and the sparks could be seen passing across the tiny air gap which separated them. Such a wire will have a definite period of its own for oscillations of electricity with which it may be charged, and if the frequency of the electric waves which fall on it agrees with that of the waves which it can itself emit, the oscillations which are set up in the wire will be stronger than under other conditions, the sparks seen will be more brilliant.[68] Hertz’s resonator was a circle of wire thirty-five centimetres in radius, the period for such a resonator would, he calculated, be the same as that of his vibrator.

There is, however, very considerable difficulty in determining the period of an electric oscillator from its dimensions, and the value obtained from calculation for that of Hertz’s radiator is not very trustworthy. The complete period is, however, comparable with two one hundredth millionths of a second; in his original papers, Hertz, through an error, gave a value greater than this.

With these arrangements Hertz was able to detect the presence of electrical radiation at considerable distances from the radiator; he was also able to measure its wave length. In the case of sound waves the existence of nodes and loops formed under proper conditions is well known. When waves are directly reflected from a flat surface, interference takes place between the incident and reflected waves, stationary vibrations are set up, and nodes and loops--places, that is, of minimum and of maximum motion respectively--are formed. The position of these nodes and loops can be determined by the aid of suitable apparatus, and it can be shewn that the distance between two consecutive nodes is half the wave length.

Similarly when electrical vibrations fall on a reflector, a large flat surface of metal, for example, stationary vibrations due to the interference between the incident and reflected waves are produced, and these give rise to electrical nodes and loops. The position of such nodes and loops can be found by the use of Hertz’s apparatus, or in other ways, and hence the length of the electrical waves can be found. The existence of the nodes and loops shews that the electric effects are propagated by wave motion. The length of the waves is found to be definite, since the nodes and loops recur at equal intervals apart.

If it be assumed that the frequency is known, the velocity of wave propagation can be determined. Hertz found from his experiments that in air the waves travelled with the velocity of light. It appears, however, that there were two errors in the calculation which happened to correct each other, so that neither the value of the frequency given in Hertz’s paper nor the wave length observed is correct.

By modifying the apparatus it was possible to measure the wave length of the waves transmitted along a copper wire, and hence, again assuming the period of oscillation, to calculate the velocity of wave propagation along the wire. Hertz made the experiment, and found from his first observations that the waves were propagated along the wire with a finite velocity, but that the velocity differed from that in air. The half-wave length in the wire was only about 2·8 metres; that in air was about 4·5 metres.

Now, this experiment afforded a crucial test between the theories of Maxwell and Von Helmholtz. According to the former, the waves do not travel in the wire at all; they travel through the air alongside the wire, and the wave length observed by Hertz ought to have been the same as in air. According to Von Helmholtz, the two velocities observed by Hertz should have been different, as, indeed, they were, and the experiment appeared to prove that Maxwell’s theory was insufficient and that a more general one, such as that of Von Helmholtz, was necessary. But other experiments have not led to the same result. Hertz himself, using more rapid oscillations in some later measurements, found that the wave length of the electric waves from a given oscillator was the same whether they were transmitted through free space or conducted along a wire.[69] Lecher and J. J. Thomson have arrived at the same result; but the most complete experiments on this point are those of Sarasin and De la Rive.

It may be taken, then, as established that Maxwell’s theory is sufficient, and that the greater generality of Von Helmholtz is unnecessary.

In a later paper Hertz showed that electric waves could be reflected and refracted, polarised and analysed, just like light waves. In his introduction to his “Collected Papers” he writes (p. 19):--

“Casting now a glance backwards, we see that by the experiments above sketched the propagation in time of a supposed action at a distance is for the first time proved. This fact forms the philosophic result of the experiments, and indeed, in a certain sense, the most important result. The proof includes a recognition of the fact that the electric forces can disentangle themselves from material bodies, and can continue to subsist as conditions or changes in the state of space. The details of the experiments further prove that the particular manner in which the electric force is propagated exhibits the closest analogy[70] with the propagation of light; indeed, that it corresponds almost completely to it. The hypothesis that light is an electrical phenomenon is thus made highly probable. To give a strict proof of this hypothesis would logically require experiments upon light itself.

“What we here indicate as having been accomplished by the experiments is accomplished independently of the correctness of particular theories. Nevertheless, there is an obvious connection between the experiments and the theory in connection with which they were really undertaken. Since the year 1861 science has been in possession of a theory which Maxwell constructed upon Faraday’s views, and which we therefore call the Faraday-Maxwell theory. This theory affirms the possibility of the class of phenomena here discovered just as positively as the remaining electrical theories are compelled to deny it. From the outset Maxwell’s theory excelled all others in elegance and in the abundance of the relations between the various phenomena which it included.

“The probability of this theory, and therefore the number of its adherents, increased from year to year. But as long as Maxwell’s theory depended solely upon the probability of its results, and not on the certainty of its hypotheses, it could not completely displace the theories which were opposed to it.

“The fundamental hypotheses of Maxwell’s theory contradicted the usual views, and did not rest upon the evidence of decisive experiments. In this connection we can best characterise the object and the result of our experiments by saying: The object of these experiments was to test the fundamental hypotheses of the Faraday-Maxwell theory, and the result of the experiments is to confirm the fundamental hypotheses of the theory.”

Since Maxwell’s death volumes have been written on electrical questions, which have all been inspired by his work. The standpoint from which electrical theory is regarded has been entirely changed. The greatest masters of mathematical physics have found, in the development of Maxwell’s views, a task that called for all their powers, and the harvest of new truths which has been garnered has proved most rich. But while this is so, the question is still often asked, What is Maxwell’s theory? Hertz himself concludes the introduction just referred to with his most interesting answer to this question. Prof. Boltzmann has made the theory the subject of an important course of lectures. Poincaré, in the introduction to his “Lectures on Maxwell’s Theories and the Electro-magnetic Theory of Light,” expresses the difficulty, which many feel, in understanding what the theory is. “The first time,” he says, “that a French reader opens Maxwell’s book a feeling of uneasiness, often even of distrust, is mingled with his admiration. It is only after prolonged study, and at the cost of many efforts, that this feeling is dissipated. Some great minds retain it always.” And again he writes: “A French _savant_, one of those who have most completely fathomed Maxwell’s meaning, said to me once, ‘I understand everything in the book except what is meant by a body charged with electricity.’”

In considering this question, Poincaré’s own remark--“Maxwell does not give a mechanical explanation of electricity and magnetism, he is only concerned to show that such an explanation is possible”--is most important.

We cannot find in the “Electricity” an answer to the question--What is an electric charge? Maxwell did not pretend to know, and the attempt to give too great definiteness to his views on this point is apt to lead to a misconception of what those views were.

On the old theories of action at a distance and of electric and magnetic fluids attracting according to known laws, it was easy to be mechanical. It was only necessary to investigate the manner in which such fluids could distribute themselves so as to be in equilibrium, and to calculate the forces arising from the distribution. The problem of assigning such a mechanical structure to the ether as will permit of its exerting the action which occurs in an electro-magnetic field is a harder one to solve, and till it is solved the question--What is an electric charge?--must remain unanswered. Still, in order to grasp Maxwell’s theory this knowledge is not necessary.

The properties of ether in dielectrics and in conductors must be quite different. In a dielectric the ether has the power of storing energy by some change in its configuration or its structure; in a conductor this power is absent, owing probably to the action of the matter of which the conductor is composed.

When we are said to charge an insulated conductor we really act on the ether in the neighbourhood of the body so as to store it with energy; if there be another conductor in the field we cannot store energy in the ether it contains. As, then, we pass from the outside of this conductor to its interior there is a sudden change in some mechanical quantity connected with the ether, and this change shows itself as a force of attraction between the two conductors. Maxwell called the change in structure, or in property, which occurs when a dielectric is thus stored with electrostatic energy, _Electric Displacement_; if we denote it by D, then the electric force R is equal to 4πD/K, and hence the energy in a unit of volume is 2πD²/K, where K is a quantity depending on the insulator.

Now, D, the electric displacement, is a quantity which has direction as well as magnitude. Its value, therefore, at any point can be represented by a straight line in the usual way; inside a conductor it is zero. The total change in D, which takes place all over the surface of a conductor as we enter it from the outside measures, according to Maxwell, the total charge on the conductor. At points at which the lines representing D enter the conductor the charge is negative; at points at which they leave it the charge is positive; along the lines of the displacement there exists throughout the ether a tension measured by 2πD²/K; at right angles to these lines there is a pressure of the same amount.

In addition to the above the components of the displacement D must satisfy certain relations which can only be expressed in mathematical form, the physical meaning of which it is difficult to state in non-mathematical language.

When these relations are so expressed the problem of finding the value of the displacement at all points of space becomes determinate, and the forces acting on the conductors can be obtained. Moreover, the total change of displacement on entering or leaving a conductor can be calculated, and this gives the quantity which is known as the total electrical charge on the conductor. The forces obtained by the above method are exactly the same as those which would exist if we supposed each conductor to be charged in the ordinary sense with the quantities just found, and to attract or repel according to the ordinary laws.

If, then, we define electric displacement as that change which takes place in a dielectric when it becomes the seat of electrostatic energy, and if, further, we suppose that the change, whatever it be mechanically, satisfies certain well-known laws, and that in consequence certain pressures and tensions exist in the dielectric, electrostatic problems can be solved without reference to a charge of electricity residing on the conductors.

Something such as this, it appears to me, is Maxwell’s theory of electricity as applied to electrostatics. It is not necessary, in order to understand it, to know what change in the ether constitutes electric displacement, or what is an electric charge, though, of course, such knowledge would render our views more definite, and would make the theory a mechanical one.

When we turn to magnetism and electro-magnetism, Maxwell’s theory develops itself naturally. Experiment proves that magnetic induction is connected with the rate of change of electric displacement, according to the laws already given. If, then, we knew the nature of the change to which the name “electric displacement” has been given, the nature of magnetic induction would be known. The difficulties in the way of any mechanical explanation are, it is true, very great; assuming, however, that some mechanical conception of “electric displacement” is possible, Maxwell’s theory gives a consistent account of the other phenomena of electro-magnetism.

Again, we have, it is true, an electro-magnetic theory of light, but we do not know the nature of the change in the ether which affects our eyes with the sensation of light. Is it the same as electric displacement, or as magnetic induction, or since, when electric displacement is varying, magnetic induction always accompanies it, is the sensation of light due to the combined effect of the two?

These questions remain unanswered. It may be that light is neither electric displacement nor magnetic induction, but some quite different periodic change of structure of the ether, which travels through the ether at the same rate as these quantities, and obeys many of the same laws.

In this respect there is a material difference between the ordinary theory of light and the electro-magnetic theory. The former is a mechanical theory; it starts from the assumption that the periodic change which constitutes light is the ordinary linear displacement of a medium--the ether--having certain mechanical properties, and from those properties it deduces the laws of optics with more or less success.

Lord Kelvin, in his labile ether, has devised a medium which could exist and which has the necessary mechanical properties. The periodic linear displacements of the labile ether would obey the laws of light, and from the fundamental hypotheses of the theory, a mechanical explanation, reasonably satisfactory in its main features, can be given of most purely optical phenomena. The relations between light and electricity, or light and magnetism, are not, however, touched by this theory; indeed, they cannot be touched without making some assumption as to what electric displacement is.

In recent years various suggestions have been made as to the nature of the change which constitutes electric displacement. One theory, due to Von Helmholtz, supposes that the electro-kinetic momentum, or vector potential of Maxwell, is actually the momentum of the moving ether; according to another, suggested, it would appear originally in a crude form by Challis, and developed within the last few months in very satisfactory detail by Larmor, the velocity of the ether is magnetic force; others have been devised, but we are still waiting for a second Newton to give us a theory of the ether which shall include the facts of electricity and magnetism, luminous radiation, and it may be gravitation.[71]

Meanwhile we believe that Maxwell has taken the first steps towards this discovery, and has pointed out the lines along which the future discoverer must direct his search, and hence we claim for him a foremost place among the leaders of this century of science.

FOOTNOTES

[1] A full biographical account of the Clerk and Maxwell families is given in a note by Miss Isabella Clerk in the “Life of James Clerk Maxwell,” and from this the above brief statement has been taken.

[2] “Life of J. C. Maxwell,” p. 26.

[3] “Life of J. C. Maxwell,” p. 27.

[4] “Life of J. C. Maxwell,” p. 49.

[5] “Life of J. C. Maxwell,” p. 52.

[6] “Life of J. C. Maxwell,” p. 56.

[7] “Life of J. C. Maxwell,” p. 67.

[8] “Life of J. C. Maxwell,” p. 75.

[9] Professor Garnett in _Nature_, November 13th, 1879.

[10] “Life of J. C. Maxwell,” p. 105.

[11] “Life of J. C. Maxwell,” p. 116.

[12] “Life of J. C. Maxwell,” pp. 123–129.

[13] “Life of J. C. Maxwell,” p. 190.

[14] Dean of Canterbury.

[15] Master of Trinity.

[16] “Life of J. C. Maxwell,” p. 174.

[17] “Life of J. C. Maxwell,” p. 195.

[18] “Life of J. C. Maxwell,” p. 207.

[19] “Life of J. C. Maxwell,” p. 208.

[20] “Life of J. C. Maxwell,” p. 210.

[21] “Life of J. C. Maxwell,” p. 211.

[22] “Life of J. C. Maxwell,” p. 216.

[23] “Life of J. C. Maxwell,” p. 256.

[24] “Life of J. C. Maxwell,” p. 267.

[25] “Life of J. C. Maxwell,” p. 269.

[26] “Life of J. C. Maxwell,” p. 278.

[27] “Life of J. C. Maxwell,” p. 292.

[28] “Life of J. C. Maxwell,” p. 303.

[29] “Life of J. C. Maxwell,” p. 259.

[30] B.A. Report, Newcastle, 1863.

[31] “Life of J. C. Maxwell,” p. 340.

[32] “Life of J. C. Maxwell,” p. 332.

[33] “Life of J. C. Maxwell,” p. 336.

[34] The Professors who were consulted were Challis, Willis, Stokes, Cayley, Adams, and Liveing.

[35] “Life of J. C. Maxwell,” p. 349.

[36] “Life of J. C. Maxwell,” p. 381.

[37] “Life of J. C. Maxwell,” p. 379.

[38] An account of the laboratory is given in _Nature_, vol. x., p. 139.

[39] The Chancellor continued to take to the end of his life a warm interest in the work at the laboratory. In 1887, the Jubilee year, as Proctor--at the same time I held the office of Demonstrator--it was my duty to accompany the Chancellor and other officers to Windsor to present an address from the University to Her Majesty. I was introduced to the Chancellor at Paddington, and he at once began to question me closely about the progress of the laboratory, the number of students, and the work being done there, showing himself fully acquainted with recent progress.

[40] In 1894 the list contained, in Part II., sixteen names, and in