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which flows as if electricity were an incompressible fluid, and which determines external
electrodynamic actions. In this respect it differs from the theory of Helmholtz which
also takes into account the action of the dielectric. Professor J. J. Thomson » in his
Review of Electric Theories has entered into a full discussion of the points at issue



PREFACE. XXlll

between the two above mentioned theories, and the reader is referred to his paper for
further information *. Maxwell in the memoir before us has also applied his theory to
the passage of light through crystals, and gets rid at once of the wave of normal vibrations
which has hitherto proved the stumbling block in other theories of light.

The electromagnetic Theory of Light has received numerous developments at the hands
of Lord Rayleigh, Mr Glazebrook, Professor J. J. Thomson and others. These volumes
also contain various shorter papers on Electrical Science, though perhaps the most complete
record of Maxwell's work in this department is to be found in his Treatise on Electricity
and Magnetism in which they were afterwards embodied.

Another series of papers of hardly less importance than those on Electricity are the
various memoirs on the Dynamical Theory of Gases. The idea that the properties of
matter might be explained by the motions and impacts of their ultimate atoms is as
old as the time of the Greeks, and Maxwell has given in his paper on " Atoms " a full
sketch of the ancient controversies to which it gave rise. The mathematical difficulties of
the speculation however were so great that it made little real progress till it was taken
up by Clausius and shortly afterwards by Maxwell. The first paper by Maxwell on the
subject is entitled "Illustrations of the Dynamical Theory of Gases" and was published
in the Philosophical Magazine for January and July, 1860, having been read at a meeting
of the British Association of the previous year. Although the methods developed in this
paper were afterwards abandoned for others, the paper itself is most interesting, as it indicates
clearly the problems in the theory which Maxwell proposed to himself for solution, and so far
contains the germs of much that was treated of in his next memoir. It is also epoch-making,
inasmuch as it for the first time enumerates various propositions which ai-e characteristic
of Maxwell's work in this subject. It contains the first statement of the distribution of velo-
cities according to the law of errors. It also foreshadows the theorem that when two gases
are in thermal equilibrium the mean kinetic energy of the molecules of each system is the
same ; and for the first time the question of the viscosity of gases is treated dynamically.

In his great memoir "On the Dynamical Theory of Gases" published in the Philo-
sophical Transactions of the Royal Society and read before the Society in May, 1866, he
returns to this subject and lays down for the first time the general d3niamical methods
appropriate for its treatment. Though to some extent the same ground is traversed as in
his former paper, the methods are widely different. He here abandons his former h}^othesis
that the molecules are hard elastic spheres, and supposes them to repel each other with
forces varying inversely as the fifth power of the distance. His chief reason for assuming
this law of action appears to be that it simplifies considerably the calculation of the
collisions between the molecules, and it leads to the conclusion that the coefficient of
viscosity is directly proportional to the absolute temperature. He himself undertook an
experimental enquiry for the purpose of verifying this conclusion, and, in his paper on the
Viscosity of Gases, he satisfied himself of its correctness. A re-examination of the numerical

* British Association Report, 1885.



XXIV PREFACE.

reductions made in the course of his work discloses however an inaccuracy which materially
affects the values of the coefl&cient of viscosity obtained. Subsequent experiments also seem
to shew that the concise relation he endeavoured to establish is by no means so near
the truth as he supposed, and it is more than doubtful whether the action between two
molecules can be represented by any law of so simple a character.

In the same memoir he gives a fresh demonstration of the law of distribution of
velocities, but though the method is of permanent value, it labours under the defect of
assuming that the distribution of velocities in the neighbourhood of a point is the same
in every direction, whatever actions may be taking place within the gas. This flaw in
the argument, first pointed out by Boltzmann, seems to have been recognised by Maxwell,
who in his next paper "On the Stresses in Rarefied Gases arising from inequalities of
Temperature," published in the Philosophical Transactions for 1879, Part I., adopts a form
of the distribution function of a somewhat different shape. The object of this paper was
to arrive at a theory of the effects observed in Crookes's Radiometer. The results of the
investigation are stated by Maxwell in the introduction to the paper, from which it would
appear that the observed motion cannot be explained on the Dynamical Theory, unless it
be supposed that the gas in contact with a solid can slide along the surface with a finite
velocity between places whose temperatures are different. In an appendix to the paper
he shews that on certain assumptions regarding the nature of the contact of the solid
and gas, there will be, when the pressure is constant, a flow of gas along the surface
from the colder to the hotter parts. The last of his longer papers on this subject is
one on Boltzmann's Theorem. Throughout these volumes will be found numerous shorter
essays on kindred subjects, published chiefly in Nature and in the Encyclopcedia Britannica.
Some of these contain more or less popular expositions of this subject which Maxwell
bad himself in great part created, while others deal with the work of other writers in
the same field. They are profoundly suggestive in almost every page, and abound in acute
criticisms of speculations which he could not accept. They are always interesting; for
although the larger papers are sometimes difficult to follow, Maxwell's more popular writings
are characterized by extreme lucidity and simplicity of style.

The first of Maxwell's papers on Colour Perception is taken from the Transactions of
the Royal Scottish Society of Arts and is in the form of a letter to Dr G. Wilson dated
Jan. 4, 1855. It was followed directly afterwards by a communication to the Royal Society
of Edinburgh, and the subject occupied his attention for some years. The most important
of his subsequent work is to be found in the papers entitled "An account of Experiments
on the Perception of Colour " published in the Philosophical Magazine, Vol xiv. and " On
the Theory of Compound Colours and its relation to the colours of the spectrum " in the
Philosophical Transactions for the year 1860. We may also refer to two lectures delivered
at the Royal Institution, in which he recapitulates and enforces his main positions in his
usual luminous style. Maxwell from the first adopts Young's Theory of Colour Sensation,
according to which all colours may ultimately be reduced to three, a red, a green and



PREFACE. XXV

a violet. This theory had been revived by Helmholtz who endeavoured to find for it a
physiological basis. Maxwell however devoted himself chiefly to the invention of accurate
methods for combining and recording mixtures of colours. His first method of obtaining
mixtures, that of the Colour Top, is an adaptation of one formerly employed, but in
Maxwell's hands it became an instrument capable of giving precise numerical results by
means which he added of varying and measuring the amounts of colour which were
blended in the eye. In the representation of colours diagrammatical ly he followed Young
in employing an equilateral triangle at the angles of which the fundamental colours were
placed. All colours, white included, which may be obtained by mixing the fundamental
colours in any proportions will then be represented by points lying within the triangle.
Points without the triangle represent colours which must be mixed with one of the funda-
mental tints to produce a mixture of the other two, or with which two of them must be
mixed to produce the third.

In his later papers, notably in that printed in the Philosophical Transactions, he
adopts the method of the Colour Box, by which different parts of the spectrum may be
mixed in different proportions and matched with white, the intensity of which has been
suitably diminished. In this way a series of colour equations are obtained which can be
used to evaluate any colour in terms of the three fundamental colours. These observations
on which Maxwell expended great care and labour, constitute by far the most important
data regarding the combinations of colour sensations which have been yet obtained, and
are of permanent value whatever theory may ultimately be adopted of the physiology of the
perception of colour.

In connection with these researches into the sensations of the normal eye, may be
mentioned the subject of colour-blindness, which also engaged Maxwell's attention, and is
discussed at considerable length in several of his papers.

Geometrical Optics was another subject in which Maxwell took much interest. At an early
period of his career he commenced a treatise on Optics, which however was never completed.
His first paper "On the general laws of optical instruments," appeared in 1858, but a brief
account of the first part of it had been previously communicated to the Cambridge Philosophical
Society. He therein lays down the conditions which a perfect optical instrument must fulfil,
and shews that if an instrument produce perfect images of an object, i.e. images free from
astigmatism, curvature and distortion, for two different positions of the object, it will give
perfect images at all distances. On this result as a basis, he finds the relations between
the foci of the incident and emergent pencils, the magnifying power and other characteristic
quantities. The subject of refraction through optical combinations was afterwards treated
by him in a different manner, in three papers communicated to the London Mathematical
Society. In the first (1873), "On the focal lines of a refracted pencil," he applies Hamilton's
characteristic function to determine the focal lines of a thin pencil refracted from one
isotropic medium into another at any surface of separation. In the second (1874), "On



XXVI PREFACE.

Hamilton's characteristic function for a narrow beam of light," he considers the more general
question of the passage of a ray from one isotropic medium into another, the two media
being separated by a third which may be of a heterogeneous character. He finds the most
general form of Hamilton's characteristic function from one point to another, the first being
in the medium in which the pencil is incident and the second in the medium in which
it is emergent, and both points near the principal ray of the pencil. This result is then
applied in two particular cases, viz. to determine the emergent pencil (1) from a spectroscope,
(2) from an optical instrument symmetrical about its axis. In the third paper (1875) he
resumes the last-mentioned application, discussing this case more fully under a somewhat
simplified analysis.

It may be remarked that all these papers are connected by the same idea, which was —
first to study the optical efiects of the entire instrument without examining the mechanism
by which these effects are produced, and then, as in the paper in 1858, to supply whatever
data may be necessary by experiments upon the instrument itself.

Connected to some extent with the above papers is an investigation which was published
in 1868 " On the cyclide." As the name imports, this paper deals chiefly with the geometrical
properties of the surface named, but other matters are touched on, such as its conjugate
isothermal functions. Primarily however the investigation is on the orthogonal surfaces to
a system of rays passing accurately through two lines. In a footnote to this paper Maxwell
describes the stereoscope which he invented and which is now in the Cavendish Laboratory.

In 1868 was also published a short but important article entitled " On the best arrange-
ment for producing a pure spectrum on a screen."

The various papers relating to the stresses experienced by a system of pieces joined
together so as to form a frame and acted on by forces form an important group connected
with one another. The first in order was "On reciprocal figures and diagrams of forces,"
published in 1864. It was immediately followed by a paper on a kindred subject, "On
the calculation of the equilibrium and stiffness of frames." In the first of these Maxwell
demonstrates certain reciprocal properties in the geometry of two polygons which are related
to one another in a particular way, and establishes his well-known theorem in Graphical
Statics on the stresses in frames. In the second he employs the principle of work to
problems connected with the stresses in frames and structures and with the deflections
arising from extensions in any of the connecting pieces.

A third paper " On the equilibrium of a spherical envelope," published in 1867, may
here be referred to. The author therein considers the stresses set up in the envelope by
a system of forces applied at its surface, and ultimately solves the problem for two normal
forces applied at any two points. The solution, in which he makes use of the principle
of inversion as it is applied in various electrical questions, turns ultimately on the deter-
mination of a certain function first introduced by Sir George Airy, and called by Maxwell



PREFACE. XXvii

Airy's Function of Stress. The methods which in this paper were attended with so much
success, seem to have suggested to Maxwell a reconsideration of his former work, with the
view of extending the character of the reciprocity therein established. Accordingly in 1870
there appeared his fourth contribution to the subject, "On reciprocal figures, frames and
diagrams of forces." This important memoir was published in the Transactions of the Royal
Society of Edinburgh, and its author received for it the Keith Prize. He begins with a
remarkably beautiful construction for drawing plane reciprocal diagrams, and then proceeds
to discuss the geometry and the degrees of freedom and constraint of polyhedral frames,
his object being to lead up to the limiting case when the faces of the polyhedron become
infinitely small and form parts of a continuous surface. In the course of this work he
obtains certain results of a general character relating to inextensible surfaces and certain
otjiers of practical utility relating to loaded frames. He then attacks the general problem of
representing graphically the internal stress of a body and by an extension of the meaning
of "Diagram of Stress," he gives a construction for finding a diagram which has mechanical
as well as geometrical reciprocal properties with the figure supposed to be under stress. It
is impossible with brevity to give an account of this reciprocity, the development of which
in Maxwell's hands forms a very beautiful example of analysis. It will be suflScient to
state that under restricted conditions this diagram of stress leads to a solution for the
components of stress in terms of a single function analogous to Airy's Function of Stress.
In the remaining parts of the memoir there is a discussion of the equations of stress, and
it is shewn that the general solution may be expressed in terms of three functions analogous
to Airy's single function in two dimensions. These results are then applied to special
cases, and in particular the stresses in a horizontal beam with a uniform load on its upper
surface are fully investigated.

On the subjects in which Maxwell's investigations were the most numerous it has
been thought necessary, in the observations which have been made, to sketch out briefly
the connections of the various papers on each subject with one another. It is not how-
ever intended to enter into an account of the contents of his other contributions to science,
and this is the less necessary as the reader may readily obtain the information he may
require in Maxwell's own language. It was usually his habit to explain by way of
introduction to any paper his exact position with regard to the subject matter and to
give a brief account of the nature of the work he was contributing. There are however
several memoirs which though unconnected with others are exceedingly interesting in them-
selves. Of these the essay on Saturn's Rings will probably be thought the most important
as containing the solution of a diflScult cosmical problem ; there are also various papers on
Dynamics, Hydromechanics and subjects of pure mathematics, which are most useful con-
tributions on the subjects of which they treat.

The remaining miscellaneous papers may be classified under the following heads: (a)
Lectures and Addresses, (b) Essays or Short Treatises, (c) Biographical Sketches, (d) Criticisms
and Reviews.



XXVIU PREFACE.

Class (a) comprises his addresses to the British Association, to the London Mathematical
Society, the Rede Lecture at Cambridge, his address at the opening of the Cavendish
Laboratory and his Lectures at the Royal Institution and to the Chemical Society.

Class (6) includes all but one of the articles which he contributed to the Encyclo-
pcedia Britanrdca and several others of a kindred character to Nature.

Class (c) contains such articles as " Fai-aday " in the Encyclopcedia Britannica and
" Helmholtz " in Nature.

Class (d) is chiefly occupied with the reviews of scientific books as they were pub-
lished. These appeared in Nature and the most important have been reprinted in these
pages.

In some of these writings, particularly those in class (b), the author allowed himself a
gi-eater latitude in the use of mathematical symbols and processes than in others, as
for instance in the article " Capillary Attraction," which is in fact a treatise on that subject
treated mathematically. The lectures were upon one or other of the three departments
of Physics with which he had mainly occupied himself; — Colour Perception, Action through
a Medium, Molecular Physics; and on this account they are the more valuable. In the
whole series of these more popular sketches we find the same clear, graceful delineation of
principles, the same beauty in arrangement of subject, the same force and precision in
expounding proofs and illustrations. The style is simple and singularly free fi-om any kind
of haze or obscurity, rising occasionally, as in his lectures, to a strain of subdued eloquence
when the emotional aspects of the subject overcome the purely speculative.

The books which were written or edited by Maxwell and published in his lifetime but
which are not included in this collection were the "Theory of Heat" (1st edition, 1871);
"Electricity and Magnetism" (1st edition, 1873); "The Electrical Researches of the Hon-
ourable Henry Cavendish, F.R.S., written between 1771 and 1781, edited from the original
manuscripts in the possession of the Duke of Devonshire, K.G." (1879). To these may be
added a graceful little introductory treatise on Dynamics entitled "Matter and Motion"
(published in 1876 by the Society for promoting Christian Knowledge). Maxwell also
contributed part of the British Association Report on Electrical Units which was afterwards
published in book form by Fleeming Jenkin.

The "Theory of Heat" appeai-ed in the Text Books of Science series published by
Longmans, Green and Co., and was at once hailed as a beautiful exposition of a subject,
part of which, and that the most interesting part, the mechanical theory, had as yet but
commenced the existence which it owed to the genius and laboui-s of Rankine, Thomson and
Clausius. There is a certain charm in Maxwell's treatise, due to the freshness and originality
of its expositions which has rendered it a great favourite with students of Heat.

After his death an " Elementary Treatise on Electricity," the greater part of which he
had written, was completed by Professor Garnett and published in 1881. The aim of this



PREFACE. XXIX

treatise and its position relatively to his larger work may be gathered from the following
extract from Maxwell's preface.

" In this smaller book I have endeavoured to present, in as compact a form as I
can, those phenomena which appear to throw light on the theory of electricity and to
use them, each in its place, for the development of electrical ideas in the mind of
the reader."

"In the larger treatise I sometimes made use of methods which I do not think
the best in themselves, but without which the student cannot follow the investigations
of the founders of the Mathematical Theory of Electricity. I have since become more
convinced of the superiority of methods akic to those of Faraday, and have therefore
adopted them from the first."

Of the "Electricity and Magnetism" it is difficult to predict the future, but there is
no doubt that since its publication it has given direction and colour to the study of
Electrical Science. It was the master's last word upon a subject to which he had devoted
several years of his life, and most of what he wrote found its proper place in the treatise.
Several of the chapters, notably those on Electromagnetism, are practically reproductions of
his memoirs in a modified or improved form. The treatise is also remarkable for the handling
of the mathematical details no less than for the exposition of physical principles, and is
enriched incidentally by chapters of much originality on mathematical subjects touched on
in the course of the work. Among these may be mentioned the dissertations on Spherical
Harmonics and Lagrange's Equations in Dj-namics.

The origin and growth of Maxwell's ideas and conceptions of electrical action, cul-
minating in his treatise where all these ideas are arranged in due connection, form an
interesting chapter not only in the history of an individual mind but in the history of
electrical science. The importance of Faraday's discoveries and speculations can hardly be
overrated in their influence on Maxwell, who tells us that before he began the study of
electricity he resolved to read none of the mathematics of the subject till he had first
mastered the "Experimental Researches." He was also at first under deep obligations to
the ideas contained in the exceedingly important papers of Sir W. Thomson on the analogy
between Heat-Conduction and Statical Electricity and on the Mathematical Theory of
Electricity in Equilibrium. In his subsequent efforts we must perceive in Maxwell, possessed
of Faraday's views and embued with his spirit, a vigorous intellect bringing to bear on a
subject still full of obscurity the steady light of patient thought and expending upon it
all the resources of a never failing ingenuity.

Royal Navax College,
Greenwich,

August, 1890.



TABLE OF CONTENTS.



II.
Ill

IV.

V.

VI.

VII.

IX.

X.
XI.

XII.
XIII.

XIV.
XV.




On the Description of Oval Curves and those having a plurality of Foci; with

remarks by Professor Forbes

On the Theory of Rolling Curves ■*

On the Equilibrium of Elastic Solids ^^

Solutions of Problems

On the Transformation of Surfaces by Bending 80

On a paHicular case of the descent of a heavy body in a resisting medium . 115

On the Theory of Colours in relation to Colour- Blindness 119

Experiments on Colour as perceived by the Eye, with remarks on Colour -Blindness 126

On Faraday's Lines of Force ^"^^

Description of a New Form of the Platometer, an Instrument for measuring the

areas of Plane Figures drawn on paper 230

On the elementary theory of Optical Instruments 238

On a method of drawing the Theoretical Form3 of Faraday's Lines of Force

without calculation

On the unequal sensibility of the Foramen Centrale to Light of different Colours 242
On the Theory of Compound Colours with reference to mixtures of Blue and

Yellow Light ^^'^

On an instrument to illustrate Poimot's TJieory of Rotation . . • .246
On a Dynamical Top, for exhibiting the phenomena of the motions of a body of
invariable form about a fixed point, with s&ine suggestions as to the Earth's

motion

Account of Experiments on the Perception of Colour 263

97 1
On the general laius of Optical Instruments

On Theories of the Constitution of Saturn's Rings 286



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