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James Clerk Maxwell

The story of the life of James Clerk Maxwell has been told so recently

by the able pen of his lifelong friend, Professor Lewis Campbell, that

it is unnecessary, in the few pages which now remain to us, to attempt

to give a repetition of the tale which would not only fail to do

justice to its subject, but must of necessity fall far short of the

merits of the (confessedly imperfect) sketch which has recently been

ithin the reach of all. Looking back on the life of Clerk

Maxwell, he seems to have come amongst us as a light from another

world--to have but partly revealed his message to minds too often

incapable of grasping its full meaning, and all too soon to have

returned to the source from whence he came. There was scarcely any

branch of natural philosophy that he did not grapple with, and upon

which his vivid imagination and far-seeing intelligence did not throw

light. He was born a philosopher, and at every step Nature partly drew

aside the veil and revealed that which was hidden from a gaze less

prophetic. A very brief sketch of the principal incidents in his life

may, however, not be out of place.

James Clerk Maxwell was born in Edinburgh, on June 13, 1831. His

father, John Clerk Maxwell, was the second son of James Clerk, of

Penicuik, and took the name of Maxwell on inheriting the estate at

Middlesbie. His mother was the daughter of R. H. Cay, Esq., of North

Charlton, Northumberland. James was the only child who survived


Some years before his birth his parents had built a house at Glenlair,

which had been added to their Middlesbie estate, and resided there

during the greater part of the year, though they retained their house

in Edinburgh. Hence it was that James's boyish days were spent almost

entirely in the country, until he entered the Edinburgh Academy in

1841. As a child, he was never content until he had completely

investigated everything which attracted his attention, such as the

hidden courses of bell-wires, water-streams, and the like. His

constant question was "What's the go o' that?" and, if answered in

terms too general for his satisfaction, he would continue, "But what's

the particular go of it?" This desire for the thorough investigation

of every phenomenon was a characteristic of his mind through life.

From a child his knowledge of Scripture was extensive and accurate,

and when eight years old he could repeat the whole of the hundred and

nineteenth psalm. About this time his mother died, and thenceforward

he and his father became constant companions. Together they would

devise all sorts of ingenious mechanical contrivances. Young James was

essentially a child of nature, and free from all conventionality. He

loved every living thing, and took delight in petting young frogs, and

putting them into his mouth to see them jump out. One of his

attainments was to paddle on the duck-pond in a wash-tub, and to make

the vessel go "without spinning"--a recreation which had to be

relinquished on washing-days. He was never without the companionship

of one or two terriers, to whom he taught many tricks, and with whom

he seemed to have complete sympathy.

As a boy, Maxwell was not one to profit much by the ordinary teaching

of the schools, and experience with a private tutor at home did not

lead to very satisfactory results. At the age of ten, therefore, he

was sent to the Edinburgh Academy, under the care of Archdeacon

Williams, who was then rector. On his first appearance in this

fashionable school, he was naturally a source of amusement to his

companions; but he held his ground, and soon gained more respect than

he had previously provoked ridicule. While at school in Edinburgh, he

resided with his father's sister, Mrs. Wedderburn, and devoted a very

considerable share of his time and attention to relieving the solitude

of the old man at Glenlair, by letters written in quaint styles,

sometimes backwards, sometimes in cypher, sometimes in different

colours, so arranged that the characters written in a particular

colour, when placed consecutively, formed another sentence. All the

details of his school and home life, and the special peculiarities of

the masters at the academy, were thus faithfully transmitted to his

father, by whom the letters were religiously preserved. At thirteen he

had evidently made progress in solid geometry, though he had not

commenced Euclid, for he writes to his father, "I have made a

tetrahedron, a dodecahedron, and two other hedrons whose names I don't

know." In these letters to Glenlair he generally signed himself, "Your

most obedient servant." Sometimes his fun found vent even upon the

envelope; for example:--

"Mr. John Clerk Maxwell,


"Kirkpatrick Durham,


Sometimes he would seal his letters with electrotypes of natural

objects (beetles, etc.), of his own making. In July, 1845, he


I have got the eleventh prize for scholarship, the first for

English, the prize for English verses, and the mathematical


When only fifteen a paper on oval curves was contributed by him to the

Proceedings of the Royal Society of Edinburgh. In the spring of 1847

he accompanied his uncle on a visit to Mr. Nicol, the inventor of the

Nicol prism, and on his return he made a polariscope with glass and a

lucifer-match box, and sketched in water-colours the chromatic

appearances presented by pieces of unannealed glass which he himself

prepared. These sketches he sent to Mr. Nicol, who presented him in

return with a pair of prisms of his own construction. The prisms are

now in the Cavendish Laboratory at Cambridge. Maxwell found that, for

unannealed glass, pieces of window-glass placed in bundles of eight or

nine, one on the other, answered the purpose very well. He cut the

figures, triangles, squares, etc., with a diamond, heated the pieces

of glass on an iron plate to redness in the kitchen fire, and then

dropped them into a plate of iron sparks (scales from the smithy) to


In 1847 Maxwell entered the University of Edinburgh, and during his

course of study there he contributed to the Royal Society of Edinburgh

papers upon rolling curves and on the equilibrium of elastic solids.

His attention was mostly devoted to mathematics, physics, chemistry,

and mental and moral philosophy. In 1850 he went to Cambridge,

entering Peterhouse, but at the end of a year he "migrated" to

Trinity; here he was soon surrounded with a circle of friends who

helped to render his Cambridge life a very happy one. His love of

experiment sometimes extended to his own mode of life, and once he

tried sleeping in the evening and working after midnight, but this was

soon given up at the request of his father. One of his friends writes,

"From 2 to 2.30 a.m. he took exercise by running along the upper

corridor, down the stairs, along the lower corridor, then up the

stairs, and so on until the inhabitants of the rooms along his track

got up and laid perdus behind their sporting-doors, to have shots at

him with boots, hair-brushes, etc., as he passed." His love of fun,

his sharp wit, his extensive knowledge, and above all, his complete

unselfishness, rendered him a universal favourite in spite of the

temporary inconveniences which his experiments may have occasionally

caused to his fellow-students.

An undergraduate friend writes, "Every one who knew him at Trinity can

recall some kindness or some act of his which has left an ineffaceable

impression of his goodness on the memory--for 'good' Maxwell was in

the best sense of the word." The same friend wrote in his diary in

1854, after meeting Maxwell at a social gathering, "Maxwell, as usual,

showing himself acquainted with every subject on which the

conversation turned. I never met a man like him. I do believe there is

not a single subject on which he cannot talk, and talk well too,

displaying always the most curious and out-of-the-way information."

His private tutor, the late well-known Mr. Hopkins, said of him, "It

is not possible for that man to think incorrectly on physical


In 1854 Maxwell took his degree at Cambridge as second wrangler, and

was bracketed with the senior wrangler (Mr. E. J. Routh) for the

Smith's prize. During his undergraduate course, he appears to have

done much of the work which formed the basis of his subsequent papers

on electricity, particularly that on Faraday's lines of force. The

colour-top and colour-box appear also to have been gradually

developing during this time, while the principle of the stereoscope

and the "art of squinting" received their due share of attention.

Shortly after his degree, he devoted a considerable amount of time to

the preparation of a manuscript on geometrical optics, which was

intended to form a university text-book, but was never completed. In

the autumn of 1855 he was elected Fellow of Trinity. About this time

the colour-top was in full swing, and he also constructed an

ophthalmoscope. In May, 1855, he writes:--

The colour trick came off on Monday, 7th. I had the proof-sheets

of my paper, and was going to read; but I changed my mind and

talked instead, which was more to the purpose. There were sundry

men who thought that blue and yellow make green, so I had to

undeceive them. I have got Hay's book of colours out of the

University Library, and am working through the specimens,

matching them with the top.

The "colour trick" came off before the Cambridge Philosophical Society.

While a Bachelor Fellow, Maxwell gave lectures to working men in

Barnwell, besides lecturing in college. His father died in April,

1856, and shortly afterwards he was appointed Professor of Natural

Philosophy in Marischal College, Aberdeen. This appointment he held

until the fusion of the college with King's College in 1860. These

four years were very productive of valuable work. During them the

dynamical top was constructed, which illustrates the motion of a rigid

body about its axis of greatest, least, or mean moment of inertia;

for, by the movement of certain screws, the axis of the top may be

made to coincide with any one at will. The Adams Prize Essay on the

stability of Saturn's rings belongs also to this period. In this essay

Maxwell showed that the phenomena presented by Saturn's rings can only

be explained on the supposition that they consist of innumerable small

bodies--"a flight of brickbats"--each independent of all the others,

and revolving round Saturn as a satellite. He compared them to a siege

of Sebastopol from a battery of guns measuring thirty thousand miles

in one direction, and a hundred miles in the other, the shots never

stopping, but revolving round a circle of a hundred and seventy

thousand miles radius. A solid ring of such dimensions would be

completely crushed by its own weight, though made of the strongest

material of which we have any knowledge. If revolving at such a rate

as to balance the attraction of the planet at one part, the stress in

other parts would be more than sufficient to crush or tear the ring.

Laplace had shown that a narrow ring might revolve about the planet

and be stable if so loaded that its centre of gravity was at a

considerable distance from its centre, and thought that Saturn's

rings might consist of a number of such unsymmetrical rings--a theory

to which some support was given by the many small divisions observable

in the bright rings. Maxwell showed that, for stability, the mass

required to load each of Laplace's rings must be four and a half times

that of the rest of the ring; and the system would then be far too

artificially balanced to be proof against the action of one ring on

another. He further showed that, in liquid rings, waves would be

produced by the mutual action of the rings, and that before long some

of these waves would be sure to acquire such an amplitude as would

cause the rings to break up into small portions. Finally, he concluded

that the only admissible theory is that of the independent satellites,

and that the average density of the rings so found cannot be much

greater than that of air at ordinary pressure and temperature.

While he remained at Aberdeen, Maxwell lectured to working men in the

evenings, on the principles of mechanics. On the whole, it is doubtful

whether Aberdeen society was as congenial to him as that of Cambridge

or Edinburgh. He seems not to have been understood even by his

colleagues. On one occasion he wrote:--

Gaiety is just beginning here again.... No jokes of any kind are

understood here. I have not made one for two months, and if I

feel one coming I shall bite my tongue.

But every cloud has its bright side, and, however Maxwell may have

been regarded by his colleagues, he was not long without congenial

companionships. An honoured guest at the home of the Principal, "in

February, 1858, he announced his betrothal to Katherine Mary Dewar,

and they were married early in the following June." Professor Campbell

speaks of his married life as one of unexampled devotion, and those

who enjoyed the great privilege of seeing him at home could more than

endorse the description.

In 1860 Maxwell accepted the chair of Natural Philosophy at King's

College, London. Here he continued his lectures to working men, and

even kept them up for one session after resigning the chair in 1865.

On May 17, 1861, he gave his first lecture at the Royal Institution,

on "The Theory of the Three Primary Colours." This lecture embodies

many of the results of his work with the colour-top and colour-box, to

be again referred to presently. While at King's College, he was placed

on the Electrical Standards Committee of the British Association, and

most of the work of the committee was carried out in his laboratory.

Here, too, he compared the electro-static repulsion between two discs

of brass with the electro-magnetic attraction of two coils of wire

surrounding them, through which a current of electricity was allowed

to flow, and obtained a result which he afterwards applied to the

electro-magnetic theory of light. The colour-box was perfected, and

his experiments on the viscosity of gases were concluded during his

residence in London. These last were described by him in the Bakerian

Lecture for 1866.

After resigning the professorship at King's College, Maxwell spent

most of his time at Glenlair, having enlarged the house, in accordance

with his father's original plans. Here he completed his great work on

"Electricity and Magnetism," as well as his "Theory of Heat," an

elementary text-book which may be said to be without a parallel.

On March 8, 1871, he accepted the chair of Experimental Physics in the

University of Cambridge. This chair was founded in consequence of an

offer made by the Duke of Devonshire, the Chancellor of the

University, to build and equip a physical laboratory for the use of

the university. In this capacity Maxwell's first duty was to prepare

plans for the laboratory. With this view, he inspected the

laboratories of Sir William Thomson at Glasgow, and of Professor

Clifton at Oxford, and endeavoured to embody the best points of both

in the new building. The result was that, in conjunction with Mr. W.

M. Fawcett, the architect, he secured for the university a laboratory

noble in its exterior, and admirably adapted to the purposes for which

it is required. The ground-floor comprises a large battery-room, which

is also used as a storeroom for chemicals; a workshop; a room for

receiving goods, communicating by a lift with the apparatus-room; a

room for experiments on heat; balance-rooms; a room for pendulum

experiments, and other investigations requiring great stability; and a

magnetic observatory. The last two rooms are furnished with stone

supports for instruments, erected on foundations independent of those

of the building, and preserved from contact with the floor. On the

first floor is a handsome lecture-theatre, capable of accommodating

nearly two hundred students. The lecture-table is carried on a wall,

which passes up through the floor without touching it, the joists

being borne by separate brick piers. The lecture-theatre occupies the

height of the first and second floors; its ceiling is of wood, the

panels of which can be removed, thus affording access to the

roof-principals, from which a load of half a ton or more may be safely

suspended over the lecture-table. The panels of the ceiling, adjoining

the wall which is behind the lecturer, can also be readily removed,

and a "window" in this wall communicates with the large

electrical-room on the second floor. Access to the space above the

ceiling of the lecture-theatre is readily obtained from the tower.

Adjoining the lecture-room is the preparation-room, and communicating

with the latter is the apparatus-room. This room is fitted with

mahogany and plate-glass wall and central cases, and at present

contains, besides the more valuable portions of the apparatus

belonging to the laboratory, the marble bust of James Clerk Maxwell,

and many of the home-made pieces of apparatus and other relics of his

early work. The rest of the first floor is occupied by the

professor's private room and the general students' laboratory.

Throughout the building the brick walls have been left bare for

convenience in attaching slats or shelves for the support of

instruments. The second floor contains a large room for electrical

experiments, a dark room for photography, and a number of private

rooms for original work. Water is laid on to every room, including a

small room in the top of the tower, and all the windows are provided

with broad stone ledges without and within the window, the two

portions being in the same horizontal plane, for the support of

heliostats or other instruments. The building is heated with hot

water, but in the magnetic observatory the pipes are all of copper and

the fittings of gun-metal. Open fireplaces for basket fires are also

provided. Over the principal entrance of the laboratory is placed a

stone statue of the present Duke of Devonshire, together with the arms

of the university and of the Cavendish family, and the Cavendish

motto, "Cavendo Tutus." Maxwell presented to the laboratory, in 1874,

all the apparatus in his possession. He usually gave a course of

lectures on heat and the constitution of bodies in the Michaelmas

term; on electricity in the Lent term; and on electro-magnetism in the

Easter term. The following extract from his inaugural lecture,

delivered in October, 1871, is worthy of the attention of all students

of science:--

Science appears to us with a very different aspect after we

have found out that it is not in lecture-rooms only, and by

means of the electric light projected on a screen, that we may

witness physical phenomena, but that we may find illustrations

of the highest doctrines of science in games and gymnastics, in

travelling by land and by water, in storms of the air and of the

sea, and wherever there is matter in motion.

The habit of recognizing principles amid the endless variety of

their action can never degrade our sense of the sublimity of

nature, or mar our enjoyment of its beauty. On the contrary, it

tends to rescue our scientific ideas from that vague condition

in which we too often leave them, buried among the other

products of a lazy credulity, and to raise them into their

proper position among the doctrines in which our faith is so

assured that we are ready at all times to act on them.

Experiments of illustration may be of very different kinds. Some

may be adaptations of the commonest operations of ordinary life;

others may be carefully arranged exhibitions of some phenomenon

which occurs only under peculiar conditions. They all, however,

agree in this, that their aim is to present some phenomenon to

the senses of the student in such a way that he may associate

with it some appropriate scientific idea. When he has grasped

this idea, the experiment which illustrates it has served its


In an experiment of research, on the other hand, this is not the

principal aim.... Experiments of this class--those in which

measurement of some kind is involved--are the proper work of a

physical laboratory. In every experiment we have first to make

our senses familiar with the phenomenon; but we must not stop

here--we must find out which of its features are capable of

measurement, and what measurements are required in order to make

a complete specification of the phenomenon. We must then make

these measurements, and deduce from them the result which we

require to find.

This characteristic of modern experiments--that they consist

principally of measurements--is so prominent that the opinion

seems to have got abroad that, in a few years, all the great

physical constants will have been approximately estimated, and

that the only occupation which will then be left to men of

science will be to carry these measurements to another place of


If this is really the state of things to which we are

approaching, our laboratory may, perhaps, become celebrated as a

place of conscientious labour and consummate skill; but it will

be out of place in the university, and ought rather to be

classed with the other great workshops of our country, where

equal ability is directed to more useful ends.

But we have no right to think thus of the unsearchable riches of

creation, or of the untried fertility of those fresh minds into

which these riches will continually be poured.... The history

of Science shows that, even during that phase of her progress

in which she devotes herself to improving the accuracy of the

numerical measurement of quantities with which she has long been

familiar, she is preparing the materials for the subjugation of

new regions, which would have remained unknown if she had been

contented with the rough methods of her early pioneers.

Maxwell's "Electricity and Magnetism" was published in 1873. Shortly

afterwards there were placed in his hands, by the Duke of Devonshire,

the Cavendish Manuscripts on Electricity, already alluded to. To these

he devoted much of his spare time for several years, and many of

Cavendish's experiments were repeated in the laboratory by Maxwell

himself, or under his direction by his students. The introductory

matter and notes embodied in "The Electrical Researches of the

Honourable Henry Cavendish, F.R.S.," afford sufficient evidence of the

amount of labour he expended over this work. The volume was published

only a few weeks before his death. Another of Maxwell's publications,

which, as a text-book, is unique and beyond praise, is the little book

on "Matter and Motion," published by the S.P.C.K.

In 1878 Maxwell, at the request of the Vice-Chancellor, delivered the

Rede Lecture in the Senate-House. His subject was the telephone, which

was just then absorbing a considerable amount of public attention.

This was the last lecture which he ever gave to a large public


It was during his tenure of the Cambridge chair that one of the

cottages on the Glenlair estate was struck by lightning. The discharge

passed down the damp soot and blew out several stones from the base of

the chimney, apparently making its way to some water in a ditch a few

yards distant. The cottage was built on a granite rock, and this event

set Maxwell thinking about the best way to protect, from lightning,

buildings which are erected on granite or other non-conducting

foundations. He decided that the proper course was to place a strip of

metal upon the ground all round the building, to carry another strip

along the ridge-stay, from which one or more pointed rods should

project upwards, and to unite this strip with that upon the ground by

copper strips passing down each corner of the building, which is thus,

as it were, enclosed in a metal cage.

After a brief illness, Maxwell passed away on November 5, 1879. His

intellect and memory remained perfect to the last, and his love of fun

scarcely diminished. During his illness he would frequently repeat

hymns, especially some of George Herbert's, and Richard Baxter's hymn


"Lord, it belongs not to my care."

"No man ever met his death more consciously or more calmly."

It has been stated that Thomas Young propounded a theory of

colour-vision which assumes that there exist three separate

colour-sensations, corresponding to red, green, and violet, each

having its own special organs, the excitement of which causes the

perception of the corresponding colour, other colours being due to the

excitement of two or more of these simple sensations in different

proportions. Maxwell adopted blue instead of violet for the third

sensation, and showed that if a particular red, green, and blue were

selected and placed at the angular points of an equilateral triangle,

the colours formed by mixing them being arranged as in Young's

diagram, all the shades of the spectrum would be ranged along the

sides of this triangle, the centre being neutral grey. For the mixing

of coloured lights, he at first employed the colour-top, but, instead

of painting circles with coloured sectors, the angles of which could

not be changed, he used circular discs of coloured paper slit along

one radius. Any number of such discs can be combined so that each

shows a sector at the top, and the angle of each sector can be varied

at will by sliding the corresponding disc between the others. Maxwell

used discs of two different sizes, the small discs being placed above

the larger on the same pivot, so that one set formed a central circle,

and the other set a ring surrounding it. He found that, with discs of

five different colours, of which one might be white and another black,

it was always possible to combine them so that the inner circle and

the outer ring exactly matched. From this he showed that there could

be only three conditions to be satisfied in the eye, for two

conditions were necessitated by the nature of the top, since the

smaller sectors must exactly fill the circle and so must the larger.

Maxwell's experiments, therefore, confirmed, in general, Young's

theory. They showed, however, that the relative delicacy of the

several colour-sensations is different in different eyes, for the

arrangement which produced an exact match in the case of one observer,

had to be modified for another; but this difference of delicacy proved

to be very conspicuous in colour-blind persons, for in most of the

cases of colour-blindness examined by Maxwell the red sensation was

completely absent, so that only two conditions were required by

colour-blind eyes, and a match could therefore always be made in such

cases with four discs only. Holmgren has since discovered cases of

colour-blindness in which the violet sensation is absent. He agrees

with Young in making the third sensation correspond to violet rather

than blue. Maxwell explained the fact that persons colour-blind to the

red divide colours into blues and yellows by the consideration that,

although yellow is a complex sensation corresponding to a mixture of

red and green, yet in nature yellow tints are so much brighter than

greens that they excite the green sensation more than green objects

themselves can do, and hence greens and yellows are called yellow by

such colour-blind persons, though their perception of yellow is really

the same as perception of green by normal eyes. Later on, by a

combination of adjustable slits, prisms, and lenses arranged in a

"colour-box," Maxwell succeeded in mixing, in any desired proportions,

the light from any three portions of the spectrum, so that he could

deal with pure spectral colours instead of the complex combinations of

differently coloured lights afforded by coloured papers. From these

experiments it appears that no ray of the solar spectrum can affect

one colour-sensation alone, so that there are no colours in nature so

pure as to correspond to the pure simple sensations, and the colours

occupying the angular points of Maxwell's diagram affect all three

colour-sensations, though they influence two of them to a much smaller

extent than the third. A particular colour in the spectrum corresponds

to light which, according to the undulatory theory, physically

consists of waves all of the same period, but it may affect all three

of the colour-sensations of a normal eye, though in different

proportions. Thus, yellow light of a given wave-length affects the red

and green sensations considerably and the blue (or violet) slightly,

and the same effect may be produced by various mixtures of red or

orange and green. For his researches on the perception of colour, the

Royal Society awarded to Clerk Maxwell the Rumford Medal in 1860.

Another optical contrivance of Maxwell's was a wheel of life, in which

the usual slits were replaced by concave lenses of such focal length

that the picture on the opposite side of the cylinder appeared, when

seen through a lens, at the centre, and thus remained apparently

fixed in position while the cylinder revolved. The same result has

since been secured by a different contrivance in the praxinoscope.

Another ingenious optical apparatus was a real-image stereoscope, in

which two lenses were placed side by side at a distance apart equal to

half the distance between the pictures on the stereoscopic slide.

These lenses were placed in front of the pictures at a distance equal

to twice their focal length. The real images of the two pictures were

then superposed in front of the lenses at the same distance from them

as the pictures, and these combined images were looked at through a

large convex lens.

The great difference in the sensibility to different colours of the

eyes of dark and fair persons when the light fell upon the fovea

centralis, led Maxwell to the discovery of the extreme want of

sensibility of this portion of the retina to blue light. This he made

manifest by looking through a bottle containing solution of chrome

alum, when the central portion of the field of view appears of a light

red colour for the first second or two.

A more important discovery was that of double refraction temporarily

produced in viscous liquids. Maxwell found that a quantity of Canada

balsam, if stirred, acquired double-refracting powers, which it

retained for a short period, until the stress temporarily induced had


But Maxwell's investigations in optics must be regarded as his play;

his real work lay in the domains of electricity and of molecular


In 1738 Daniel Bernouilli published an explanation of atmospheric

pressure on the hypothesis that air consists of a number of minute

particles moving in all directions, and impinging on any surface

exposed to their action. In 1847 Herapath explained the diffusion of

gases on the hypothesis that they consisted of perfectly hard

molecules impinging on one another and on surfaces exposed to them,

and pointed out the relation between their motion and the temperature

and pressure of a gas. The present condition of the molecular theory

of gases, and of molecular science generally, is due almost entirely

to the work of Joule, Clausius, Boltzmann, and Maxwell. To Maxwell is

due the general method of solving all problems connected with vast

numbers of individuals--a method which he called the statistical

method, and which consists, in the first place, in separating the

individuals into groups, each fulfilling a particular condition, but

paying no attention to the history of any individual, which may pass

from one group to another in any way and as often as it pleases

without attracting attention. Maxwell was the first to estimate the

average distance through which a particle of gas passes without coming

into collision with another particle. He found that, in the case of

hydrogen, at standard pressure and temperature, it is about 1/250000

of an inch; for air, about 1/389000 of an inch. These results he

deduced from his experiments on viscosity, and he gave a complete

explanation of the viscosity of gases, showing it to be due to the

"diffusion of momentum" accompanying the diffusion of material

particles between the passing streams of gas.

One portion of the theory of electricity had been considerably

developed by Cavendish; the application of mathematics to the theory

of attractions, and hence to that of electricity, had been carried to

a great degree of perfection by Laplace, Lagrange, Poisson, Green, and

others. Faraday, however, could not satisfy himself with a

mathematical theory based upon direct action at a distance, and he

filled space, as we have seen, with tubes of force passing from one

body to another whenever there existed any electrical action between

them. These conceptions of Faraday were regarded with suspicion by

mathematicians. Sir William Thomson was the first to look upon them

with favour; and in 1846 he showed that electro-static force might be

treated mathematically in the same way as the flow of heat; so that

there are, at any rate, two methods by which the fundamental formulae

of electro-statics can be deduced. But it is to Maxwell that

mathematicians are indebted for a complete exposition of Faraday's

views in their own language, and this was given in a paper wherein the

phenomena of electro-statics were deduced as results of a stress in a

medium which, as suggested by Newton and believed by Faraday, might

well be that same medium which serves for the propagation of light;

and "the lines of force" were shown to correspond to an actual

condition of the medium when under electrical stress. Maxwell, in

fact, showed, not only that Faraday's lines formed a consistent system

which would bear the most stringent mathematical analysis, but were

more than a conventional system, and might correspond to a state of

stress actually existing in the medium through which they passed, and

that a tension along these lines, accompanied by an equal pressure in

every direction at right angles to them, would be consistent with the

equilibrium of the medium, and explain, on mechanical principles, the

observed phenomena. The greater part of this work he accomplished

while an undergraduate at Cambridge. He showed, too, that Faraday's

conceptions were equally applicable to the case of electro-magnetism,

and that all the laws of the induction of currents might be concisely

expressed in Faraday's language. Defining the positive direction

through a circuit in which a current flows as the direction in which a

right-handed screw would advance if rotating with the current, and the

positive direction around a wire conveying a current as the direction

in which a right-handed screw would rotate if advancing with the

current, Maxwell pointed out that the lines of magnetic force due to

an electric current always pass round it, or through its circuit, in

the positive direction, and that, whenever the number of lines of

magnetic force passing through a closed circuit is changed, there is

an electro-motive force round the circuit represented by the rate of

diminution of the number of lines of force which pass through the

circuit in the positive direction.

The words in italics form a complete statement of the laws regulating

the production of currents by the motion of magnets or of other

currents, or by the variation of other currents in the neighbourhood.

Maxwell showed, too, that Faraday's electro-tonic state, on the

variation of which induced currents depend, corresponds completely

with the number of lines of magnetic force passing through the


He also showed that, when a conductor conveying a current is free to

move in a magnetic field, or magnets are free to move in the

neighbourhood of such a conductor, the system will assume that

condition in which the greatest possible number of lines of magnetic

force pass through the circuit in the positive direction.

But Maxwell was not content with showing that Faraday's conceptions

were consistent, and had their mathematical equivalents,--he proceeded

to point out how a medium could be imagined so constituted as to be

able to perform all the various duties which were thus thrown upon it.

Assuming a medium to be made up of spherical, or nearly spherical,

cells, and that, when magnetic force is transmitted, these cells are

made to rotate about diameters coinciding in direction with the lines

of force, the tension along those lines, and the pressure at right

angles to them, are accounted for by the tendency of a rotating

elastic sphere to contract along its polar axis and expand

equatorially so as to form an oblate spheroid. By supposing minute

spherical particles to exist between the rotating cells, the motion of

one may be transmitted in the same direction to the next, and these

particles may be supposed to constitute electricity, and roll as

perfectly rough bodies on the cells in contact with them. Maxwell

further imagined the rotating cells, and therefore, a fortiori, the

electrical particles, to be extremely small compared with molecules of

matter; and that, in conductors, the electrical particles could pass

from molecule to molecule, though opposed by friction, but that in

insulators no such transference was possible. The machinery was then

complete. If the electric particles were made to flow in a conductor

in one direction, passing between the cells, or molecular vortices,

they compelled them to rotate, and the rotation was communicated from

cell to cell in expanding circles by the electric particles, acting as

idle wheels, between them. Thus rings of magnetic force were made to

surround the current, and to continue as long as the current lasted.

If an attempt were made to displace the electric particles in a

dielectric, they would move only within the substance of each

molecule, and not from molecule to molecule, and thus the cells would

be deformed, though no continuous motion would result. The deformation

of the cells would involve elastic stress in the medium. Again, if a

stream of electric particles were started into motion, and if there

were another stream of particles in the neighbourhood free to flow,

though resisted by friction, these particles, instead of at once

transmitting the rotary motion of the cells on one side of them to the

cells on the other side, would at first, on account of the inertia of

the cells, begin to move themselves with a motion of translation

opposite to that of the primary current, and the motion would only

gradually be destroyed by the frictional resistance and the molecular

vortices on the other side made to revolve with their full velocity. A

similar effect, but in the opposite direction, would take place if the

primary current ceased, the vortices not stopping all at once if there

were any possibility of their continuing in motion. The imaginary

medium thus serves for the production of induced currents.

The mechanical forces between currents and magnets and between

currents and currents, as well as between magnets and currents, were

accounted for by the tension and pressure produced by the molecular

vortices. When currents are flowing in the same direction in

neighbouring conductors, the vortices in the space between them are

urged in opposite directions by the two currents, and remain almost at

rest; the lateral pressure exerted by those on the outside of the

conductors is thus unbalanced, and the conductors are pushed together

as though they attracted each other. When the currents flow in

opposite directions in parallel conductors, they conspire to give a

greater velocity to the vortices in the space between them, than to

those outside them, and are thus pushed apart by the pressure due to

the rotation of the vortices, as though they repelled each other. In a

similar way, the actions of magnets on conductors conveying currents

may be explained. The motion of a conductor across a series of lines

of magnetic force may squeeze together and lengthen the threads of

vortices in front, and thus increase their speed of rotation, while

the vortices behind will move more slowly because allowed to contract

axially and expand transversely. The velocity of the vortices thus

being greater on one side of the wire than the other, a current must

be induced in the wire. Thus the current induced by the motion of a

conductor in a magnetic field may be accounted for.

This conception of a medium was given by Maxwell, not as a theory, but

to show that it was possible to devise a mechanism capable, in

imagination at least, of producing all the phenomena of electricity

and magnetism. "According to our theory, the particles which form the

partitions between the cells constitute the matter of electricity. The

motion of these particles constitutes an electric current; the

tangential force with which the particles are pressed by the matter of

the cells is electro-motive force; and the pressure of the particles

on each other corresponds to the tension or potential of the


When a current is maintained in a wire, the molecular vortices in the

surrounding space are kept in uniform motion; but if an attempt be

made to stop the current, since this would necessitate the stoppage of

the vortices, it is clear that it cannot take place suddenly, but the

energy of the vortices must be in some way used up. For the same

reason it is impossible for a current to be suddenly started by a

finite force. Thus the phenomena of self-induction are accounted for

by the supposed medium.

The magnetic permeability of a medium Maxwell identified with the

density of the substance composing the rotating cells, and the

specific inductive capacity he showed to be inversely proportional to

its elasticity. He then proved that the ratio of the electro-magnetic

unit to the electro-static unit must be equal to the velocity of

transmission of a transverse vibration in the medium, and consequently

proportional to the square root of the elasticity, and inversely

proportional to the square root of the density. If the medium is the

same as that engaged in the propagation of light, then this ratio

ought to be equal to the velocity of light, and, moreover, in

non-magnetic media, the refractive index should be proportional to the

square root of the specific inductive capacity. The different

measurements which had been made of the ratio of the electrical units

gave a mean very nearly coinciding with the best determinations of the

velocity of light, and thus the truth underlying Maxwell's speculation

was strikingly confirmed, for the velocity of light was determined by

purely electrical measurements. In the case also of bodies whose

chemical structure was not very complicated, the refractive index was

found to agree fairly well with the square root of the specific

inductive capacity; but the phenomenon of "residual charge" rendered

the accurate measurement of the latter quantity a matter of great

difficulty. It therefore appeared highly probable that light is an

electro-magnetic disturbance due to a motion of the electric particles

in an insulating medium producing a strain in the medium, which

becomes propagated from particle to particle to an indefinite

distance. In the case of a conductor, the electric particles so

displaced would pass from molecule to molecule against a frictional

resistance, and thus dissipate the energy of the disturbance, so that

true (i.e. metallic) conductors must be nearly impervious to light;

and this also agrees with experience.

Maxwell thus furnished a complete theory of electrical and

electro-magnetic action in which all the effects are due to actions

propagated in a medium, and direct action at a distance is dispensed

with, and exposed his theory successfully to most severe tests. In his

great work on electricity and magnetism, he gives the mathematical

theory of all the above actions, without, however, committing himself

to any particular form of mechanism to represent the constitution of

the medium. "This part of that book," Professor Tait says, "is one of

the most splendid monuments ever raised by the genius of a single

individual.... There seems to be no longer any possibility of doubt

that Maxwell has taken the first grand step towards the discovery of

the true nature of electrical phenomena. Had he done nothing but this,

his fame would have been secured for all time. But, striking as it is,

this forms only one small part of the contents of this marvellous