James Clerk Maxwell.

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an aiTangement in narrow rings which may retard the process."

Part of the work, dealing with the oscillatory waves set up in a ring of satellites,
was illustrated by an ingenious mechanical contrivance which was greatly admired when
exhibited before the Royal Society of Edinburgh.

This essay, besides securing the prize, obtained for its author great credit among
scientific men. It was characterized by Sir George Airy as one of the most remarkable
applications of Mathematics to Physics that he had ever seen.

The suggestion has been made that it was the irregular motions of the particles which
compose the Rings of Saturn resulting on the whole in apparent regularity and uni-
formity, which led Maxwell to the investigation of the Kinetic Theory of Gases, his first
contribution to which was read to the British Association in 1859. This is not unlikely,
but it must also be borne in mind that Bernoulli's Theory had recently been revived by
Herapath, Joule and Clausius whose writings may have drawn Maxwell's attention to the
subject.

In 1860 King's College and Marischal College were joined together as one institution,
now known as the University of Aberdeen. The new chair of Natural Philosophy thus
created was filled up by the appointment of David Thomson, formerly Professor at King's
College and Maxwell's senior. Professor Thomson, though not comparable to Maxwell as a
physicist, was nevertheless a remarkable man. He was distinguished by singular force of
character and great administrative faculty and he had been prominent in bringing about
the fusion of the Colleges. He was also an admirable lecturer and teacher and had done
much to raise the standard of scientific education in the north of Scotland. Thus the choice
made by the Commissioners, though almost inevitable, had the effect of making it appear
that Maxwell failed as a teacher. There seems however to be no evidence to support such
an inference. On the contrary, if we may judge from the number of voluntary students
attending his classes in his last College session, he would seem to have been as popular as a
professor as he was personally estimable.



XVI PREFACE.

This is also borne out by the fact that he was soon afterwards elected Professor of
Natural Philosophy and Astronomy in King's College, London. The new appointment had
the advantage of bringing him much more into contact with men in his own department
of science, especially with Faraday, with whose electrical work his own was so intimately
connected. In 1862 — 63 he took a prominent part in the experiments organised by a
Committee of the British Association for the determination of electrical resistance in
absolute measure and for placing electrical measurements on a satisfactory basis. In the
experiments which were conducted in the laboratory of King's College upon a plan due
to Sir W. Thomson, two long series of measurements were taken in successive years. In
the first year, the working members were Maxwell, Balfour Stewart and Fleeming Jenkin ; in
the second, Charles Hockin took the place of Balfour Stewart. The work of this Committee
was communicated in the form of reports to the British Association and was afterwards
republished in one volume by Fleeming Jenkin.

Maxwell was a professor in King's College from 1860 to 1865, and this period of his
life is distinguished by the production of his most important papers. The second memoir
on Colours made its appearance in 1860. In the same year his first papers on the Kinetic
Theory of Gases were published. In 1861 came his papers on Physical Lines of Force
and in 1864 his greatest memoii' on Electricity, — a Dynamical Theory of the Electro-
magnetic Field. He must have been occupied with the Dynamical Theory of Gases in 1865,
as two important papers appeared in the following year, first the Bakerian lecture on the
Viscosity of Gases, and next the memoir on the Dynamical Theory of Gases.

The mental strain involved in the production of so much valuable work, combined
with the duties of his professorship which required his attention during nine months of
the year, seems to have influenced him in a resolution which in 1865 he at length
adopted of resigning his chair and retiring to his country seat. Shortly after this he had
a severe illness. On his recovery he continued his work on the Dynamical Theory of
Gases, to which reference has just been made. For the next few years he led a quiet
and secluded life at Glenlair, varied by annual visits to London, attendances at the British
Association meetings and by a tour in Italy in 1867. He was also Moderator or Examiner
in the Mathematical Tripos at Cambridge on several occasions, ofiBces which entailed a few
weeks' residence at the University in winter. His chief employment during those years
was the prepai-ation of his now celebrated treatise on Electricity and Magnetism which,
however, was not published till 1873. He also wrote a treatise on Heat which was
published in 1871.

In 1871 Maxwell was, with some reluctance, induced to quit his retreat in the
country and to enter upon a new career. The University of Cambridge had recently
resolved to found a professorship of physical science, especially for the cultivation and
teaching of the subjects of Heat, Electricity and Magnetism. In furtherance of this
object her Chancellor, the Duke of Devonshire, had most generously undertaken to build
a laboratory and furnish it with the necessary apparatus. Maxwell was invited to fill the



PREFACE. XVU

new chair thus formed and to superintend the erection of the laboratory. In October,
1871, he delivered his inaugural lecture.

The Cavendish Laboratory, so called after its founder, the present venerable chief of
the family which produced the great physicist of the same name, was not completed
for practical work until 1874. In June of that year it was formally presented to the
University by the Chancellor. The building itself and the fittings of the several rooms
were admirably contrived mainly by Maxwell himself, but the stock of apparatus was
smaller than accorded with the generous intentions of the Chancellor. This defect must
be attributed to the anxiety of the Professor to procure only instruments by the best
makers and with such improvements as he could himself suggest. Such a defect therefore
required time for its removal and afterwards in great measure disappeared, apparatus being
constantly added to the stock as occasion demanded.

One of the chief tasks which Maxwell undertook was that of superintending and
directing the energies of such young Bachelors of Arts as became his pupils after
having acquired good positions in the University examinations. Several pupils, who have
since acquired distinction, carried out valuable experiments under the guidance of the
Professor. It must be admitted, however, that the numbers were at first small, but perhaps
this was only to be expected from the traditions of so many years. The Professor was
singularly kind and helpful to these pupils. He would hold long conversations with them,
opening up to them the stores of his mind, giving them hints as to what they might try
and what avoid, and was always ready with some ingenious remedy for the experimental
troubles which beset them. These conversations, always delightful and instructive, were,
according to the account of one of his pupils, a liberal education in themselves, and were
repaid in the minds of the pupils by a grateful affection rarely accorded to any teacher.

Besides discharging the duties of his chair, Maxwell took an active part in conducting
the general business of the University and more particularly in regulating the courses of
study in Mathematics and Physics.

For some years previous to 1866 when Maxwell returned to Cambridge as Moderator
in the Mathematical Tripos, the studies in the University had lost touch with the great
scientific movements going on outside her walls. It was said that some of the subjects most
in vogue had but little interest for the present generation, and loud complaints began to
be heard that while such branches of knowledge as Heat, Electricity and Magnetism, were
left out of the Tripos examination, the candidates were wasting their time and energy
upon mathematical trifles barren of scientific interest and of practical results. Into the
movement for reform Maxwell entered warmly. By his questions in 1866 and subsequent
years he infused new life into the examination ; he took an active part in drafting the
new scheme introduced in 1873 ; but most of all by his writings he exerted a powerful
influence on the younger members of the University, and was largely instrumental in
bringing about the change which has been now effected.



XVIU PREFACE.

In the first few years at Cambridge Maxwell was busy in giving the final touches
to his great work on Electricity and Magnetism and in passing it through the press.
This work was published in 1873, and it seems to have occupied the most of his attention
for the two previous years, as the few papers published by him during that period relate
chiefly to subjects forming part of the contents. After this publication his contributions to
scientific journals became more numerous, those on the Dynamical Theory of Gases being
perhaps the most important. He also wrote a great many short articles and reviews
which made their appearance in Nature and the Encyclopcedia Britannica. Some of these
essays are charming expositions of scientific subjects, some are general criticisms of the
works of contemporary writers and others are brief and appreciative biographies of fellow
workers in the same fields of research.

An undertaking in which he was long engaged and which, though it proved exceedingly
interesting, entailed much labour, was the editing of the "Electrical Researches" of the Hon.
Henry Cavendish. This work, published in 1879, has had the eflfect of increasing the
reputation of Cavendish, disclosing as it does the unsuspected advances which that acute
physicist had made in the Theory of Electricity, especially in the measurement of electrical
quantities. The work is enriched by a variety of valuable notes in which Cavendish's
views and results are examined by the light of modern theory and methods. Especially
valuable are the methods applied to the determination of the electrical capacities of con-
ductors and condensers, a subject in which Cavendish himself shewed considerable skill
both of a mathematical and experimental character.

The importance of the task undertaken by Maxwell in connection with Cavendish's
papers will be understood from the following extract from his introduction to them.

"It is somewhat difficult to account for the fact that though Cavendish had
prepared a complete description of his experiments on the charges of bodies, and had
even taken the trouble to write out a fair copy, and though all this seems to have
been done before 1774 and he continued to make experiments in Electricity till 1781
and lived on till 1810, he kept his manuscript by him and never published it."

"Cavendish cared more for investigation than for publication. He would under-
take the most laborious researches in order to clear up a difficulty which no one
but himself could appreciate or was even aware of, and we cannot doubt that the
result of his enquiries, when successful, gave him a certain degree of satisfaction.
But it did not excite in him that desire to communicate the discovery to others
which in the case of ordinary men of science, generally ensures the publication of
their results. How completely these researches of Cavendish remained unknown to
other men of science is shewn by the external history of electricity."

It will probably be thought a matter of some difficulty to place oneself in the
position of a physicist of a century ago and to ascertain the exact bearing of his
experiments. But Maxwell entered upon this undertaking with the utmost enthusiasm and



PREFACE. XIX

succeeded in completely identifying himself with Cavendish's methods. He shewed that
Cavendish had really anticipated several of the discoveries in electrical science which have been
made since his time. Cavendish was the first to form the conception of and to measure
Electrostatic Capacity and Specific Inductive Capacity; he also anticipated Ohm's law.

The Cavendish papers were no sooner disposed of than Maxwell set about preparing
a new edition of his work on Electricity and Magnetism; but unhappily in the summer
term of 1879 his health gave way. Hopes were however entertained that when he returned
to the bracing air of his country home he would soon recover. But he lingered through
the summer months with no signs of improvement and his spirits gradually sank He was
finally informed by his old fellow-student, Professor Sanders, that he could not live more
than a few weeks. As a last resort he was brought back to Cambridge in October that he
might be under the charge of his favourite physician, Dr Paget*. Nothing however could
be done for • his malady, and, after a painful illness, he died on the 5th of November, 1879,
in his 49th year.

Maxwell was thus cut oflf in the prime of his powers, and at a time when the depart-
ments of science, which he had contributed so much to develop, were being every day
extended by fresh discoveries. His death was deplored as an irreparable loss to science and
to the University, in which his amiable disposition was as universally esteemed as his genius
was admired.

It is not intended in this preface to enter at length into a discussion of the relation
which Maxwell's work bears historically to that of his predecessors, or to attempt to estimate
the effect which it has had on the scientific thought of the present day. In some of his
papers he has given more than usually copious references to the works of those by whom
he had been influenced; and in his later papers, especially those of a more popular nature
which appeared in the Encyclopoedia Britannica, he has given full historical outlines of some
of the most prominent fields in which he laboured. Nor does it appear to the present
editor that the time has yet arrived when the quickening influence of Maxwell's mind on
modem scientific thought can be duly estimated. He therefore proposes to himself the duty
of recalling briefly, according to subjects, the most important speculations in which Maxwell
engaged.

His works have been arranged as far as possible in chronological order but they fall
naturally under a few leading heads; and perhaps we shall not be far wrong if we place
first in importance his work in Electricity.

His first paper on this subject bearing the title "On Faraday's Lines of Force" was
read before the Cambridge Philosophical Society on Dec. 11th, 1855. He had been previously
attracted by Faraday's method of expressing electrical laws, and he here set before himself
the task of shewing that the ideas which had guided Faraday's researches were not incon-
sistent with the mathematical formulae in which Poisson and others had cast the laws of
♦ Now Sir George Edward Paget, K.C.B.



PREFACE.



Electricity. His object, he says, is to find a physical analogy which shall help the mind
to grasp the results of previous investigations "without being committed to any theory
founded on the physical science from which that conception is borrowed, so that it is neither
draw aside from the subject in the pursuit of analytical subtleties nor carried beyond the
truth by a favorite hypothesis."

The laws of electricity are therefore compared with the properties of an incompressible
fluid the motion of which is retarded by a force proportional to the velocity, and the fluid
is supposed to possess no inertia. He shews the analogy which the lines of flow of such
a fluid would have with the lines of force, and deduces not merely the laws of Statical
Electricity in a single medium but also a method of representing what takes place when the
action passes from one dielectric into another.

In the latter part of the paper he proceeds to consider the phenomena of Electro-
magnetism and shews how the laws discovered by Ampere lead to conclusions identical with
those of Faraday. In this paper three expressions are introduced which he identifies with
the components of Faraday's electrotonic state, though the author admits that he has not
been able to frame a physical theory which would give a clear mental picture of the
various connections expressed by the equations.

Altogether this paper is most important for the light which it throws on the principles
which guided Maxwell at the outset of his electrical work. The idea of the electrotonic
state had afready taken a firm hold of his mind though as yet he had formed no physical
explanation of it. In the paper "On Physical Lines of Force" printed in the Philosophical
Magazine, Vol. xxi. he resumes his speculations. He explains that in his former paper he
had found the geometrical significance of the Electrotonic state but that he now proposes
"to examine magnetic phenomena from a mechanical point of view." Accordingly he propounds
his remarkable speculation as to the magnetic field being occupied by molecular vortices,
the axes of which coincide with the lines of force. The cells within which these vortices
rotate are supposed to be separated by layers of particles which serve the double purpose
of transmitting motion from one cell to another and by their own motions constituting an
electric current. This theory, the parent of several working models which have been devised
to represent the motions of the dielectric, is remarkable for the detail vnth which it is
worked out and made to explain the various laws not only of magnetic and electromagnetic
action, but also the various forms of electrostatic action. As Maxwell subsequently gave a
more general theory of the Electromagnetic Field, it may be inferred that he did not desire
it to be supposed that he adhered to the views set forth in this paper in every particular;
but there is no doubt that in some of its main features, especially the existence of
rotation round the lines of magnetic force, it expressed his permanent convictions. In his
treatise on "Electricity and Magnetism," Vol. ii. p. 416, (2nd edition 427) after quoting from
Sir W. Thomson on the explanation of the magnetic rotation of the plane of the polarisation
of light, he goes on to say of the present paper,



PREFACE. XXI

"A theory of molecular vortices which T worked out at considerable length was
published in the Phil. Mag. for March, April and May, 1861, Jan. and Feb. 1862."

- " I think we have good evidence for the opinion that some phenomenon of rotation
is going on in the magnetic field, that this rotation is performed by a great number
of very small portions of matter, each rotating on its own axis, that axis being parallel
to the direction of the magnetic force, and that the rotations of these various vortices
are made to depend on one another by means of some mechanism between them."

"The attempt which I then made to imagine a working model of this mechanism

must be taken for no more than it really is, a demonstration that mechanism may

be imagined capable of producing a connection mechanically equivalent to the actual

connection of the parts of the Electromagnetic Field."

This paper is also important as containing the first hint of the Electromagnetic Theory

of Light which was to be more fully developed afterwards in his third great memoir

" On the Dynamical Theory of the Electromagnetic Field." This memoir, which was presented

to the Royal Society on the 27th October, 1864, contains Maxwell's mature thoughts on a

subject which had so long occupied his mind. It was afterwards reproduced in his Treatise

with trifling modifications in the treatment of its parts, but without substantial changes

in its main features. In this paper Maxwell reverses the mode of treating electrical

phenomena adopted by previous mathematical writers; for while they had sought to build

up the laws of the subject by starting from the principles discovered by Ampere, and

deducing the induction of currents from the conservation of energy, Maxwell adopts the

method of first arriving at the laws of induction and then deducing the mechanical

attractions and repulsions.

After recalling the general phenomena of the mutual action of cuiTents and magnets
and the induction produced in a circuit by any variation of the strength of the field m
which it lies, the propagation of light through a luminiferous medium, the properties of
dielectrics and other phenomena which point to a medium capable of transmittmg force
and motio^i, he proceeds. —

"Thus then we are led to the conception of a complicated mechanism capable

of a vast variety of motions but at the same time so connected that the motion of

one part depends, according to definite relations, on the motion of other parts, these

teotions being communicated by forces arising from the relative displacement of their

connected parts, in virtue of their elasticity. Such a mechanism must be subject

to the laws of Dynamics."

On applying dynamical principles to such a connected system he attains certain general

propositions which, on being compared with the laws of induced currents, enable him to

identify certain features of the mechanism with properties of currents. The induction of

currehts and their electromagnetic attraction are thus explained and connected.



XXll PREFACE.

In a subsequent part of the memoir he proceeds to establish from these premises
the general equations of the Field and obtains the usual formulae for the mechanical
force on currents, magnets and bodies possessing an electrostatic charge.

He also returns to and elaborates more fully the electromagnetic Theory of Light.
His equations shew that dielectrics can transmit only transverse vibrations, the speed of
propagation of which in air as deduced from electrical data comes out practically identical
with the known velocity of light. For other dielectrics the index of refraction is equal
to the square root of the product of the specific inductive capacity by the coefficient of
magnetic induction, which last factor is for most bodies practically unity. Various comparisons
have been made with the view of testing this deduction. In the case of paraffin wax and
some of the hydrocarbons, theory and experiment agree, but this is not the case with
glass and some other substances. Maxwell has also applied his theory to media which
are not perfect insulators, and finds an expression for the loss of light in passing through
a stratum of given thickness. He remarks in confirmation of his result that most good
conductors are opaque while insulators are transparent, but he also adds that electrolytes
which transmit a current freely are often transparent, while a piece of gold leaf whose
resistance was determined by Mr Hockin allowed far too great an amount of light to
pass. He observes however that it is possible "there is less loss of energy when the
electromotive forces are reversed with the rapidity of light than when they act for sensible
times as in our experiments." A similar explanation may be given of the discordance
between the calculated and observed values of the specific inductive capacity. Prof. J. J,
Thomson in the Proceedings of the Royal Society, Vol. 46, has described an experiment by
which he has obtained the specific inductive capacities of various dielectrics when acted
on by alternating electric forces whose frequency is 25,000,000 per second. He finds that
under these conditions the specific inductive capacity of glass is very nearly the same as
the square of the refractive index, and very much less than the value for slow rates of
reversals. In illustration of these remarks may be quoted the observations of Prof. Hertz who
has shewn that vulcanite and pitch are transparent for waves, whose periods of vibration are
about three hundred millionths of a second. The investigations of Hertz have shewn that
electro-dynamic radiations are transmitted in waves with a velocity, which, if not equal to, is
comparable with that of light, and have thus given conclusive proof that a satisfactory
theory of Electricity must take into account in some form or other the action of the
dielectric. But this does not prove that Maxwell's theory is to be accepted in every
particular. A peculiarity of his theory is, as he himself points out in his treatise, that
the variation of the electric displacement is to be treated as part of the current as well
as the current of conduction, and that it is the total amount due to the sum of these



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