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THE SCIENTIFIC PAPERS OF

JAMES CLERK MAXWELL



Edited by W. D. NIVEN, M.A., F.R.S.



Two Volumes Bound As One



DOVER PUBLICATIONS, INC., NEW YORK



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ternational Copyright Conventions.



Published in Canada by General Publishing Com-
pany, Ltd., 30 Lesmill Road, Don Mills, Toronto,
Ontario.

Published in the United Kingdom by Constable
and Company, Ltd., 10 Orange Street, London
W. C. 2.



This Dover edition, first published in 1965, is an
unabridged and unaltered republication of the work
first pubhshed by Cambridge University Press in
1890. This edition is published by special arrange-
ment with Cambridge University Press.

The work was originally pubhshed in two separate
volumes, but is now published in two volumes
bound as one.



Library of Congress Catalog Card Number: A53 -9813



Manufactured in the United States of America

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THE SCIENTIFIC PAPERS OF

JAMES CLERK MAXWELL



Edited by W. D. NIVEN, M.A., F.R.S,



Volume One



TO HIS GRACE

THE DUKE OF DEVONSHIRE K.G.

CHANCELLOR OF THE UNIVERSITY OF CAMBRIDGE

FOUNDER OF THE CAVENDISH LABORATORY

THIS MEMORIAL EDITION

OF

THE SCIENTIFIC PAPERS

OF

THE FIRST CAVENDISH PROFESSOR OF EXPERIMENTAL PHYSICS

IS

BY HIS GRACE'S PERMISSION

RESPECTFULLY AND GRATEFULLY DEDICATED



SHORTLY after the death of Professor James Clerk Maxwell a Committee was
formed, consisting of graduate members of the University of Cambridge and
of other friends and admirers, for the purpose of securing a fitting memorial of
him.

The Committee had in view two objects : to obtain a likeness of Professor
Clerk Maxwell, which should be placed in some public building of the Uni-
versity ; and to collect and publish his scattered scientific writings, copies of
which, so far as the funds at the disposal of the Committee would allow,
should be presented to learned Societies and Libraries at home and abroad.

It was decided that the likeness should take the form of a marble bust.
This was executed by Sir J. E. Boehm, R.A., and is now placed in the
apparatus room of the Cavendish Laboratory.

In carrying out the second part of their programme the Committee
obtained the cordial assistance of the Syndics of the University Press, who
willingly consented to publish the present work. At the request of the Syndics,
Mr W. D. Niven, M.A., Fellow and Assistant Tutor of Trinity College and
now Director of Studies at the Royal Naval College, Greenwich, undertook the
duties of Editor.

The Committee and the Syndics desire to take this opportunity of
acknowledging their obligation to Messrs Adam and Charles Black, Publishers
of the ninth Edition of the EiicyclopcEdia Biitannica, to Messrs Taylor and
Francis, Publishers of the London, Edinburgh, and Dublin Philosophical Maga-
zine and Journal of Science, to Messrs Macmillan and Co., Publishers of
Nature and of the Cambridge and Dublin Mathematical Joui-nal, to Messrs
Metcalfe and Co., Publishers of the Quarterly Journal of Pure and Applied
Mathematics, and to the Lords of the Conmiittee of Council on Education,
Proprietors of the Handbooks of the South Kensington Museum, for their
courteous consent to allow the articles which Clerk Maxwell had contributed to
these publications to be included in the present work ; to Mr Norman Lockyer
for the assistance which he rendered in the selection of the articles re-printed
from Nature; and their further obligation to Messrs Macmillan and Co. for
permission to use in this work the steel engravings of Faraday, Clerk Maxwell,
and Helmholtz from the Nature Series of Portraits.



Numerous and important Papers, contributed by Clerk Maxwell to the
Transactions or Proceedings of the Royal Societies of London and of Edinburgh,
of the Cambridge Philosophical Society, of the Royal Scottish Society of Arts,
and of the London Mathematical Society; Lectures delivered by Clerk Maxwell
at the Royal Institution of Great Britain pubHshed in its Proceedings; as well
as Communications and Addresses to the British Association published in its
Reports, are also included in the present work with the sanction of the above
mentioned learned bodies.

The Essay which gained the Adams Prize for the year 1856 in the
University of Cambridge, the introductory Lecture on the Study of Experimental
Physics delivered in the Cavendish Laboratory, and the Rede Lecture delivered
before the University in 1878, complete this collection of Clerk Maxwell's scientific
writings.

The diagrams in this work have been re-produced by a photographic
process from the original diagrams in Clerk Maxwell's Papers by the Cambridge
Scientific Instrument Company.

It only remams to add that the footnotes inserted by the Editor are
enclosed between square brackets.

Cambridge, Augv^t, 1890.



PEEFACE.



CLERK MAXWELL'S biography has been written by Professors Lewis Campbell and
Wm. Garnett with so much skill and appreciation of their subject that nothing further
remains to be told. It would therefore be presumption on the part of the editor of his
papers to attempt any lengthened narrative of a biographical character. At the same time
a memorial edition of an author's collected writings would hardly be complete without
some account however slight of his life and works. Accordingly the principal events of
Clerk Maxwell's career will be recounted in the following brief sketch, and the reader
who wishes to obtain further and more detailed information or to study his character in
its social relations may consult the interesting work to which reference has been made.

James Clerk Maxwell was descended from the Clerks of Penicuick in Midlothian,
a well-known Scottish family whose history can be traced back to the IGth century. The
first baronet served in the parliament of Scotland. His eldest son, a man of learning,
was a Baron of the Exchequer in Scotland. In later times John Clerk of Eldin a
member of the family claimed the credit of having invented a new method of breaking
the enemy's line in naval warfare, an invention said to have been adopted by Lord
Rodney in the battle which he gained over the French in 1782. Another John Clerk,
son of the naval tactitian, was a lawyer of much acumen and became a Lord of the
Court of Session. He was distinguished among his Edinburgh contemporaries by his ready
and sarcastic wit.

The father of the subject of this memoir was John, brother to Sir George Clerk of
Penicuick. He adopted the surname of Maxwell on succeeding to an estate in Kirkcud-
brightshire which came into the Clerk family through marriage with a Miss Maxwell. It
cannot be said that he was possessed of the energy and activity of mind which lead
to distinction. He was in truth a somewhat easy-going but shrewd and intelligent
man, whose most notable characteristics were his perfect sincerity and extreme benevolence.
He took an enlightened interest in mechanical and scientific pursuits and was of an
essentially practical turn of mind. On leaving the University he had devoted himself
to law and was called to the Scottish Bar. It does not appear however that he met
mth any great success in that profession. At all events, a quiet life in the country



X PREFACE.

presented so many attractions to his wife as well as to himself that he was easily induced
to relinquish his prospects at the bar. He had been married to Frances, daughter of
Robert Cay of N. Charlton, Northumberland, a lady of strong good sense and resolute
character.

The country house which was their home after they left Edinburgh was designed
by John Clerk Maxwell himself and was built on his estate. The house, which was named
Glenlair, was surrounded by fine scenery, of which the water of Urr with its rocky and
wooded banks formed the principal charm.

James was bom at Edinburgh on the 13th of June, 1831, but it was at Glenlair
that the greater part of his childhood was passed. In that pleasant spot under healthful
influences of all kinds the child developed into a hardy and ccirageous boy. Not
precociously clever at books he was yet not without some signs of future intellectual
strength, being remarkable for a spirit of inquiry into the caupjs and connections of the
phenomena around him. It was remembered afterwards when he had become distinguished,
that the questions he put as a child shewed an amount of thoughtfulness which for his
years was very unusual.

At the age of ten, James, who had lost his mother, was placed under the charge of
relatives in Edinburgh that he might attend the Edinburgh Academy. A charming account
of his school days is given in the narrative of Professor Campbell who was Maxwell's
schoolfellow and in after life an intimate friend and constant correspondent. The child is
father to the man, and those who were privileged to know the man Maxwell will easily
recognise Mr Campbell's picture of the boy on his first appearance at school, — the home-
made garments more serviceable than fashionable, the rustic speech and curiously quaint
but often humorous manner of conveying his meaning, his bewilderment on first undergoing
the routine of schoolwork, and his Spartan conduct under various trials at the hands of
his schoolfellows. They will further feel how accurate is the sketch of the boy become
accustomed to his surroundings and rapidly assuming the place at school to which his
mental powers entitled him, while his superfluous energy finds vent privately in carrying
out mechanical contrivances and geometrical constructions, in reading and even trying his
hand at composing ballads, and in sending to his father letters richly embellished with
grotesquely elaborate borders and drawings.

An event of his school-days, worth recording, was his invention of a mechanical method
of drawing certain classes of Ovals. An account of this method was printed in the
Proceedings of the Royal Society of Edinburgh and forms the first of his writings
collected in the present work. The subject was introduced to the notice of the Society
by the celebrated Professor James Forbes, who from the first took the greatest possible
interest in Maxwell's progress. Professor Tait, another schoolfellow, mentions that at the
time when the paper on the Ovals was written. Maxwell had received no instruction in
Mathematics beyond a little Euclid and Algebra.



PREFACE. aa

In 1847 Maxwell entered the University of Edinburgh where he remained for three
sessions. He attended the lectures of Kelland in Mathematics, Forbes in Natural Philosophy,
Gregory in Chemistry, Sir W. Hamilton in Mental Philosophy, Wilson (Christopher North)
in Moral Philosophy. The lectures of Sir W. Hamilton made a strong impression upon
him, in stimulating the love of speculation to which his mind was prone, but, as might
have been expected, it was the Professor of Natural Philosophy who obtained the chief share
of his devotion. The enthusiasm which so distinguished a man as Forbes naturally inspired
in young and ardent disciples, evoked a feeling of personal attachment, and the Professor, on
his part, took special interest in his pupil and gave to him the altogether unusual
privilege of working with his fine apparatus.

What was the nature of this experimental work we may conjecture from a perusal of
his paper on Elastic Solids, written at that time, in which he describes some experiments
made with the view of verifying the deductions of his theory in its application to Optics.
Maxwell would seem to have been led to the study of this subject by the following cir-
cumstance. He was taken by his uncle John Cay to see William Nicol, the inventor of
the polarising prism which bears his name, and was shewn by Nicol the colours of unan-
nealed glass in the polariscope. This incited Maxwell to study the laws of polarised light
and to construct a rough polariscope in which the polariser and analyser were simple glass
reflectors. By means of this instrument he was able to obtain the colour bands of unannealed
glass. These he copied on paper in water colours and sent to Nicol. It is gratifpng to
find that this spirited attempt at experimenting on the part of a mere boy was duly
appreciated by Nicol, who at once encouraged and delighted him by a present of a couple of
his prisms.

The paper alluded to, viz. that entitled "On the Equilibrium of Elastic Solids," was
read to the Royal Society of Edinburgh in 1850. It forms the third paper which Maxwell
addressed to that Society. The first in 1846 on Ovals has been abready mentioned. The
second, under the title "The Theory of Rolling Curves," was presented by Kelland in 1849.

It is obvious that a youth of nineteen years who had been capable of these efforts
must have been gifted with rare originality and with great power of sustained exertion.
But his singular self-concentration led him into habits of solitude and seclusion, the tendency
of which was to confirm his peculiarities of speech and of manner. He was shy and
reserved with strangers, and his utterances were often obscure both in substance and in
his manner of expressing himself, so many remote and unexpected allusions perpetually
obtruding themselves. Though really most sociable and even fond of society he was
essentially reticent and reserved. Mr Campbell thinks it is to be regretted that Maxwell
did not begin his Cambridge career eai'lier for the sake of the social intercourse which
he would have found it difficult to avoid there. It is a question, however, whether in
losing the opportunity of using Professor Forbes' apparatus he would not thereby have lost
what was perhaps the most valuable part of his early scientific training.



XU PREFACE.

It was originally intended that Maxwell should follow his father's profession of advocate,
but this intention was abandoned as soon as it became obvious that his tastes lay in a
direction so decidedly scientific. It was at length determined to send him to Cambridge
and accordingly in October, 1850, he commenced residence in Peterhouse, where however he
resided during the Michaelmas Term only. On December 14 of the same year he migrated
to Trinity College.

It may readily be supposed that his preparatory training for the Cambridge course
was far removed from the ordinary type. There had indeed for some time been practically
no restraint upon his plan of study and his mind had been allowed to follow its natural
bent towards science, though not to an extent so absorbing as to withdraw him from
other pursuits. Though he was not a sportsman, — indeed sport so called was always repugnant
to him — he was yet exceedingly fond of a country life. He was a good horseman and a
good swimmer. Whence however he derived his chief enjoyment may be gathered from the
account which Mr Campbell gives of the zest with which he quoted on one occasion the
lines of Bums which describe the poet finding inspiration while wandering along the banks
of a stream in the free indulgence of his fancies. Maxwell was not only a lover of poetry
but himself a poet, as the fine pieces gathered together by Mr Campbell abundantly testify.
He saw however that his true calling was Science and never regarded these poetical
efforts as other than mere pastime. Devotion to science, already stimulated by successful
endeavour, a tendency to ponder over philosophical problems and an attachment to English
literature, particularly to English poetry, — these tastes, implanted in a mind of singular
strength and purity, may be said to have been the endowments with which young Maxwell
began his Cambridge career. Besides this, his scientific reading, as we may gather from his
papers to the Royal Society of Edinburgh referred to above, was already extensive and
varied. He brought with him, says Professor Tait, a mass of knowledge which was really
immense for so young a man but in a state of disorder appalling to his methodical
private tutor.

Maxwell's undergraduate career was not marked by any specially notable feature. His
private speculations had in some measure to be laid aside in favour of more systematic
study. Yet his mind was steadily ripening for the work of his later years. Among those
with whom he was brought into daily contact by his position, as a Scholar of Trinity
College, were some of the brightest and most cultivated young men in the University. In
the genial fellowship of the Scholars' table Maxwell's kindly humour found ready play, while
in the more select coterie of the Apostle Club, formed for mutual cultivation, he found a field
for the exercise of his love of speculation in essays on subjects beyond the lines of the
ordinary University course. The composition of these essays doubtless laid the foundation
of that literary finish which is one of the characteristics of Maxwell's scientific writings.
His biographers have preserved several extracts on a variety of subjects chiefly of a specu-
lative character. They are remarkable mainly for the weight of thought contained in them
but occasionally also for smart epigrams and for a vein of dry and sarcastic humour.



PREFACE.



These glimpses into Maxwell's character may prepare us to believe that, with all his
shyness, he was not without confidence in his own powers, as also appears from the account
which was given by the late Master of Trinity College, Dr Thompson, who was Tutor when
Maxwell personally applied to him for permission to migrate to that College. He appeared
to be a shy and diffident youth, but presently surprised Dr Thompson by producing a
bundle of papers, doubtless copies of those we have already mentioned, remarking " Perhaps
these may shew you that I am not unfit to enter at your College."

He became a pupil of the celebrated William Hopkins of Peterhouse, under whom his
course of study became more systematic. One striking characteristic was remarked by his
contemporaries. Whenever the subject admitted of it he had recourse to diagrams, though
his fellow students might solve the question more easily by a train of analysis. Many
illustrations of this manner of proceeding might be taken from his writings, but in
truth it was only one phase of his mental attitude towards scientific questions, which
led him to proceed from one distinct idea to another instead of trusting to symbols and
equations.

Maxwell's published contributions to Mathematical Science during his undergraduate career
were few and of no great importance. He found time however to carry his investigations
into regions outside the prescribed Cambridge course. At the lectures of Professor Stokes*
he was regular in his attendance. Indeed it appears from the paper on Elastic Solids,
mentioned above, that he was acquainted with some of the writings of Stokes before he
entered Cambridge. Before 1850, Stokes had published some of his most important contri-
butions to Hydromechanics and Optics ; and Sir W. Thomson, who was nine years' Maxwell's
senior in University standing, had, among other remarkable investigations, called special
attention to the mathematical analogy between Heat-conduction and Statical Electricity.
There is no doubt that these authors as well as Faraday, of whose experimental researches
he had made a careful study, exercised a powerful directive influence on his mind.

In January, 1854, Maxwell's undergraduate career closed. He was second wrangler, but
shared with Dr Routh, who was senior wrangler, the honours of the First Smith's Prize.
In due course he was elected Fellow of Trinity and placed on the staff of College Lecturers.

No sooner was he released from the restraints imposed by the Trinity Fellowship
Examination than he plunged headlong into original work. There were several questions
he was anxious to deal with, and first of all he completed an investigation on the Trans-
formation of Surfaces by Bending, a purely geometrical problem. This memoir he presentel
to the Cambridge Philosophical Society in the following March. At this period he also
set about an enquiry into the quantitative measurement of mixtures of colours and the
causes of colour-blindness. During his undergraduateship he had, as we have seen, found
time for the study of Electricity. This had already borne fruit and now resulted in the
first of his important memoirs on that subject,— the memoir on Faraday's Lines of Force.
• Now Sir George Gabriel Stokes, Bart., M.P. for the University.



Xiv PREFACE.

The number and importance of his papers, published in 1855—6, bear witness to his
assiduity during this period. With these labours, and in the preparation of his College
lectures, on which he entered with much enthusiasm, his mind was fully occupied and the
work was congenial. He had formed a number of valued friendships, and he had a variety of
interests, scientific and literary, attaching him to the University. Nevertheless, when the chair
of Natural Philosophy in Marischal College, Aberdeen, fell vacant, Maxwell became a candidate.
This step was probably taken in deference to his father's wishes, as the long summer
vacation of the Scottish College would enable him to reside with his father at Glenlair for
half the year continuously. He obtained the professorship, but unhappily the kind intentions
which prompted him to apply for it were frustrated by the death of his father, which took
place in April, 1856.

It is doubtful whether the change from the Trinity lectureship to the Aberdeen
professorship was altogether prudent. The advantages were the possession of a laboratory and
the long uninterrupted summer vacation. But the labour of drilling classes composed chiefly
of comparatively young and untrained lads, in the elements of mechanics and physics, was
not the work for which Maxwell was specially fitted. On the other hand, in a large college
like Trinity there could not fail to have been among its undergraduate members, some of the
most promising young mathematicians of the University, capable of appreciating his original
genius and immense knowledge, by instructing whom he would himself have derived ad-
vantage.

In 1856 Maxwell entered upon his duties as Professor of Natural Philosophy at Marischal
College, and two years afterwards he married Katharine Mary Dewar, daughter of the
Principal of the College. He in consequence ceased to be a Fellow of Tiinity College,
but was afterwards elected an honorary Fellow, at the same time as Professor Cayley.

During the yeai*s 1856 — 60 he was still actively employed upon the subject of colour
sensation, to which he contributed a new method of measurement in the ingenious instru-
ment known as the colour-box. The most serious demands upon his powers and upon his
time were made by his investigations on the Stability of Saturn's Rings. This was the
subject chosen by the Examiners for the Adams Prize Essay to be adjudged in 1857, and
was advertised in the following terms: —

"The Problem may be treated on the supposition that the system of Rings is
exactly or very approximately concentric with Saturn and symmetrically disposed about
the plane of his equator and different hypotheses may be made respecting the physical
constitution of the Rings. It may be supposed (1) that they are rigid; (2) that they
are fluid and in part aeriform ; (3) that they consist of masses of matter not materially
coherent. The question will be considered to be answered by ascertaining on these
hypotheses severally whether the conditions of mechanical stability are satisfied by the
mutual attractions and motions of the Planet and the Rings."



PREFACE. XV

"It is desirable that an attempt should also be made to determine on which of

the above hypotheses the appearances both of the bright rings and the recently

discovered dark ring may be most satisfactorily explained; and to indicate any causes

to which a change of form such as is supposed from a comparison of modem with the

earlier observations to have taken place, may be attributed."

It is sufficient to mention here that Maxwell bestowed an immense amount of labour

in working out the theory as proposed, and that he arrived at the conclusion that "the

only system of rings which can exist is one composed of an indefinite number of unconnected

particles revolving round the planet with different velocities according to their respective

distances. These particles may be arranged in a series of narrow rings, or they may move

about through each other irregularly. In the first case the destruction of the system will be

very slow, in the second case it will be more rapid, but there may be a tendency towards



Online LibraryJames Clerk MaxwellThe scientific papers of James Clerk Maxwell (Volume 1) → online text (page 1 of 50)