REESE LIBRARY
UNIVERSITY OF CALIFORNIA.
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2-33 Class N:,.
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LECTURES ON PHYSICAL SCIENCE
LECTURES
ON SOME
RECENT ADVANCES
IN
PHYSICAL SCIENCE
WITH A SPECIAL LECTURE ON
FORCE
BY
P. G. TAIT, M.A.
FORMERLY FELLOW OF ST. PETER'S COLLEGE, CAMBRIDGE
PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY OF EDINBURGH
TJNIVEBSITY j
THIRD EDITION, REVISED
MACMILLAN AND CO
1885
lEainlmrgf) SRni&ersitg JGrcsc :
THOMAS AND ARCHIBALD CONSTABLE, PRINTERS TO HER MAJESTY.
WITH THIS WORK
I DESIRE TO ASSOCIATE THE NAMES
SOF
GEORGE BARCLAY AND THOMAS STEVENSON,
FELLOWS OF THE ROYAL SOCIETY OF EDINBURGH,
BY WHOSE EFFORTS THESE LECTURES WERE ORGANISED,
AND AT WHOSE WISH THEY ARE PUBLISHED AS DELIVERED.
P. G. T.
PREFACE TO THIRD EDITION.
IN preparing a Third Edition for the press, I have
adhered to my original plan of publishing these Lectures
just as they were taken down by the short-hand writers.
I have, however, altered here and there a mere word or
two, and in a few places, where it appeared to be called
for, I have added an explanatory sentence.
Other brief additions [enclosed in square brackets]
deal chiefly with facts which have been discovered since
the Second Edition (a very large one) was published.
I have not reprinted the polemical part of the Preface
to that edition. Professor Zollner's charges, there alluded
to, were withdrawn by himself : while those of Professor
Clausius were so fully met by me in the Philosophical
Magazine for May 1879 tnat his reply has not, so far
as I know, even yet appeared. And the reference to
Mohr's work has been amplified, and embodied in
the text of the book.
Here my Preface might have ended, had it not been
that a new critic has appeared on the scene, in the form
of Professor du Bois-Reymond, who, in his capacity of
Secretary to the Royal Academy of Sciences of Berlin,
considered himself justified in speaking as follows at
viii PREFACE TO THIRD EDITION.
a gala meeting of that Academy on March 28th,
' Foreign investigators, in their ignorance of the German lan-
guage, often discovered for the second time things long known to us.
' Not unfrequently, even when better informed, they took ad-
vantage of the presumed right of independent discovery to cite
their German predecessors only by the way or not at all. The
Germans, on the other hand, showed a perfect national impartiality
which was far more to their credit than their linguistic superiority.
Indeed they never even conceived the possibility of national
jealousy between learned men who seek nothing but the One Truth,
but live, ideally, with the investigators of all countries as with
their equals, without even imagining how little this . feeling is
reciprocated, chiefly because foreigners know so little of us.
* In other nations great pains were taken to find out among them-
selves the germs of new discoveries, and in one way or another
this always succeeded. The German man of science only wished
to find the true germ, whether it might be in a fellow-countryman
or in a foreigner, and he never hesitated to recognise, as probably
the first discoverer, a foreigner, if there was the slightest reason
for the supposition. He was far more pleased to do historical
justice than hurt to deprive Germany of a doubtful glory.
' In the same way it was far from the thought of German men
of science to exaggerate the importance of a first chance observa-
tion, in order out of it to add to Germany's scientific credit.
'What weight would others not have given to the fact, quite
unnoticed by us, that the first galvanic phenomenon, which besides
gave Volta the key to Galvani's researches, was observed here in
Berlin by one of our predecessors ?
' The national feeling does not blind German scientific men to
the fact that the seeking out of such Priority is a double-edged
weapon. For if an Irish physicist living in England and a
Scottish physicist (who need no such addition to their fame) had
Spectrum Analysis in their pocket ten years before Kirchhoff and
1 The obviously offensive intention which dictated this speech rendered
me anxious to avoid all suspicion of having heightened it in translation :
so, at my request, my colleague Dr. Crum Brown has kindly made the
subjoined version for me.
PREFACE TO THIRD EDITION.
IX
Bunsen, why did they not make out of it what Bunsen and Kirch-
hoff did ?
'Why? A Scottish man. of science, whose name has been
recently much before us, tells us in his Lectures on some Recent
Advances in Physical Science. The German investigator knows all
that is going on in Science, or at least has some one by him who does.
If a German comes on a new idea, he can at once see, or be told,
whether another has it or not, and in the latter case he can print
the idea, and so secure the priority : the poor Britons, on the other
hand, make the most splendid discoveries in the world without
ever guessing that they have struck on anything new like the
Bourgeois Gentilhomme, they speak prose without knowing it, and_^
let the priority slip them. The wily Germans ! who, instead of
contenting themselves like other innocent folks with their mother
tongue, sneak into foreign languages to spy out the discoveries ^
that are being made.
'The unpleasant impression produced by these statements in
the key of national antipathy is increased by other passages in these
Lectures. The author makes it his special business to elucidate
the history of the law of the conservation of energy, and tracks
this law back to Newton's third law of motion, the equality of
action and reaction. Newton's second explanation of his third law
is, he tells us, a nearly complete expression of the conservation of
energy.
'As the science of Mechanics depends on Newton's laws of
motion, of course the conservation of energy can be somehow read
out of them, or rather read into them. And we need not doubt
that a head like Newton's had, in private, as much knowledge of
the conservation of energy as could be had in his time. It is
another question what view he took of it, and what was his position
towards it as manifested in his works. Whoever is acquainted with
the history of this doctrine knows Descartes's original but un-
successful notions ; their correction by Leibniz : Leibniz's conception
of the material world substantially agreeing with that now held.
He knows that Newton in his Optics also disproved Descartes's
opinion, although without mentioning its correction by Leibniz,
and without himself undertaking this correction ; that the Cos-
mogony-speculator called in God to put the planetary system right
when it had gone wrong in consequence of accumulated perturba-
PREFACE TO THIRD EDITION.
tions, which scarcely accords with the conservation of energy. To
one who knows this epoch it will not seem impossible that the
dissensions between Leibniz and Newton disgusted the latter with
the subject, and formed the cause why the law of the conservation
of energy received then so little assent in England. Certain it is
that on the Continent, during the first half of last century, this law
in the form given to it by Leibniz was the common property of
scientifically educated persons, as it is now. This is no hidden
mystery : it is easy to make it out from the literature of the last
ten years. He who has all this before him can only shrug his
shoulders at the artificial attempts to put Newton at the head of
those to whom we owe the law of the conservation of energy.
Perhaps the author of the Lectures is not sufficiently acquainted
with the history on which he undertakes to throw light, and on the
later developments of which he passes such rough judgment, and
so only lays himself open to the suspicion, unfortunately not
weakened by his other writings, that the fiery Celtic blood of his
country sometimes runs away with him and makes him a scientific
Chauvin.
f ' Scientific Chauvinism, from which German men of science have
hitherto kept themselves free, is more hateful than political, inas-
much as one expects decent demeanour more from scientific men
than from politically excited masses. May it be far from us in
the future also ! Let us not be misled in our intellectual habits by
the present ebullition of national feeling in Europe. In spite of the
tone of irritation appearing, now here, now there, among other
nations, may we retain unlost the tradition of a scientific justice
exercised without respect of nation, and of the serious literary
work which this implies !
' May our Temple of the Muses remain a safe refuge for German
cosmopolitanism if the storms of the time tolerate it nowhere else ! '
Is not this conceived very much in the spirit of the
well-known passage : Ich danke dir, Gott, dass Ich
nicht bin wie andere Leute, Rauber, Ungerechte,
Ehebrecher ; oder auch wie dieser Zollner ?
To any one who reads the above extract from
Professor du Bois-Reymond's speech, it is obvious that
PREFACE TO THIRD EDITION. xi
the Chauvinism (surely Pharisaism would be the more
correct word) so freely denounced (in others) towards
the end, has been as freely practised (by the speaker
himself) from the beginning.
But this special form of accusation is most parti-
cularly unhappy as directed against my book. For the
book shows no Chauvinistic tendencies, properly so
called : its praise or blame may be deserved, or not,
but they are certainly awarded from considerations
altogether independent of nation or race ; they are used
throughout in favour of what I consider to be true
Science, and against quackery, knavery, bigotry, and
superstition, wherever found.
Fresnel and Carnot, Gauss and Riemann, Young and
Faraday, are names to be honoured to all time ; not
by any means because they belonged to Frenchmen,
Germans, or Britons ; but because they belonged to
men who have, each in his turn, led the van in the
intellectual struggles of his generation.
But when a false prophet arises, or is raised up by
others for the admiration of the unlearned multitude, it
is a duty (often, it may be, a pleasant duty) to expose
the hollowness of his pretensions ; and to do so with
sternly impartial relish whether he be French, German,
or British. Equally is it a duty to bring forward the
claims of a true prophet, be his nationality what it may ;
if these have suffered from his own modesty or care-
lessness, or from the neglect or disparagement of others.
My censor should have thought of the possible
application of some of his own phrases to himself.
xii PREFACE TO THIRD EDITION.
Was it not this fervent denouncer of Chauvinism who
apologised to his students for the too Gallic sound
of his own name ? What but an absolutely overmaster-
ing antipathy to everything Gallic could have led a
Professor of Physiology to speak of 'the fiery Celtic
blood ' of a Norseman ?
And the most recent authoritative text-book of
Spectrum Analysis, published a year or two ago in
Berlin, supplies a singular comment on the above
eulogy of German scientific men in general. Though
historical details are freely given in that work, the name
of Balfour Stewart is not even once mentioned! I take
this work as an example, because it is a high-class one.
But, even from my own reading, which has been mainly
confined to standard works (so far as German is con-
cerned), I could supply numerous equally striking
examples of exceptions to the sweeping statement so
confidently made by my censor.
My acquaintance with Leibnitz's works may not be
so profound as is that of Professor du Bois-Reymond ;
but, such as it is, it has led me to accept the opinion of
Huygens on him as a man, and that of Gauss on him
as a mathematician. Surely even Professor du Bois-
Reymond will allow that these (especially as neither
was Gallic) were competent judges.
P. G. TAIT.
COLLEGE, EDINBURGH,
Dec. 2tyh, 1884.
PREFACE TO FIRST EDITION.
THE following Lectures were given in the spring of
1874, at the desire of a number of my friends, mainly
professional men, who wished to obtain in this way a
notion of the chief advances made in Natural Philosophy
since their student days.
The only special requests made to me were, that I
should treat fully the modern history of Energy, and
that I should publish the Lectures verbatim.
The reader will judge for himself how far the first
request has been attended to. As to the second, it is
necessary to explain that, being very busy, I had not
time to do more than arrange a few notes for each
lecture ; so that the course was entirely extempore, and
was taken down by excellent short-hand writers.
Besides necessary corrections, only one large change
was made in the M.SS., viz., the excision of a great
many of those repetitions which are indispensable in
extempore lecturing, but are intolerable in a book.
Professors Clerk-Maxwell and Balfour Stewart have
been kind enough to read the proofs, and to suggest
several valuable improvements.
The work must, however, be regarded as in no sense
xiv PREFACE TO FIRST EDITION.
whatever a finished production, though I hope it will
be found not only accurate but also readable. In fact,
I could not possibly have found time to rewrite the whole
in the form in which I should like to have presented it
for publication ; so that the reader is requested to
remember, if he desires to find fault, that the non-
removal of many defects whose correction would have
required large changes, was the condition under which
alone the book could have appeared. Still, I should
not have allowed it to be published had I not been
assured by competent judges that in spite of its neces-
sary imperfections it is calculated to be useful.
P. G. TAIT.
COLLEGE, EDINBURGH,
February 1876.
CONTENTS.
LECTURE I.
INTRODUCTORY.
r
Classification of Recent Advances in Physical Science. General State-
ment of the Objects of Physics. Time and Space. Matter, Position,
Motion, and Force. Digression upon a priori reasoning. Instances
of modern or revived fallacies Uniformity of Earth's Rotation, Sta-
bility of Solar System, Heat developed the equivalent of work spent
in compressing a gas, Causa czqiiat effectum. Gilbert the true origi-
nator of Experimental Science. Test of the reality of Matter fails
when applied to Force not when applied to Energy. Conservation,
Transformation, and Dissipation of Energy. Ignorance and Inca-
pacity alike of Spiritualists and Materialists, ....
LECTURE II.
THE EARLY HISTORY OF ENERGY.
Newton's services to the subject only of late recognised. Second Law
There is no balancing of forces ; but only of the effects of forces
Geometrical composition of velocities. Third Law Its second in-
terpretation an all but complete statement of the Conservation of
Energy Arithmetical composition of the squares of velocities.
Experimental results of Rumford and Davy, filling up the lacuna
in Newton's statement. Their proofs that Heat is not matter.
Davy's statement of the true theory of Heat. Speculations of Sguin
and Mayer, . . . . 2 7
CONTENTS.
LECTURE III.
ESTABLISHMENT OF THE CONSERVATION OF ENERGY.
PAGE
Further inquiry into the asserted claims of Mayer. Opinions of Colding
and Joule on Mayer's first paper. [Insertion (1884) on the prior
claims of Mohr.] Colding's Experiments. Joule's Experiments.
Numerical value of the Dynamical Equivalent of Heat. Helmholtz's
argument from the Perpetual Motion. Transformation and Dissi-
pation of Energy. Illustrative experiments, . . . . 52
LECTURE IV.
TRANSFORMATION OF ENERGY.
Experimental Illustrations Heating of wires, and decomposition of
water, by a Galvanic current Electro-magnetic Engine Rotating
Disc Magneto-electric Machine Induction-Coil and Geissler Tube
Higher and Lower Forms of Energy. Work transformed wholly
into Heat Only a portion of the Heat can be reconverted into
Work. Carnot's Cycle of Operations and his Reversible Cycle.
Effect of pressure upon Ice, . . . . . .81
LECTURE V.
TRANSFORMATION OF HEAT INTO WORK.
Carnot's Cycle continued. Watt's Diagram of Energy. The Impossi-
bility of the Perpetual Motion is an experimental truth. Conditions
of Reversibility. Absolute definition of Temperature. Second Law
of Thermodynamics. Absolute zero of temperature, or temperature
of a body devoid of heat. Efficiency of the best steam-engine. Effect
of pressure on the freezing point of water. Mechanism of Glacier
motion, .... ... 107
LECTURE VI.
TRANSFORMATION OF ENERGY.
Further consequences of Carnot's ideas. Anomalous behaviour of water
and of india-rubber. Application to rock masses, and the state of
CONTENTS.
PAGE
the earth's interior. Availability of energy, and loss of availability.
To restore the availability of one portion of energy, another portion
must be degraded. Dissipation of energy. Sources of Terrestrial
and of Solar Energy. Energy of plants and animals. Measure of the
Sun's Radiant Energy. Energy now in the Solar System, . . 133
LECTURE VII.
SOURCES AND TRANSFERENCE OF ENERGY.
Available Sources of Energy on the Earth. Whence these have been
derived. Uniform itarian School of Geologists. Sir W. Thomson's
arguments as to the length of time during which life has been possible
on the earth. Transference of Energy through Solids, Fluids, and
through the Ether. Test of the Receptivity of a body or system for
energy in a vibratory form. Physical ' Analogies introductory to
Spectrum Analysis, ....... 162
LECTURE VIII.
RADIATION AND ABSORPTION.
History of the discovery of the Physical Basis of Spectrum Analysis. First
result of Spectrum Analysis applied to non-terrestrial bodies ; There
is Sodium gas in the Sun's Atmosphere. Elaborate experiments of
Stewart and Kirchhoff. Identity of Light and Radiant Heat. Dis-
tinctive characters of a particular ray. Application of Carnot's
principle to establish the equality of radiating and absorbing powers.
Black, transparent, and perfectly reflecting bodies, . . . 187
LECTURE IX.
SPECTRUM ANALYSIS.
Spectrum of incandescent black body ; of incandescent gas or vapour.
Absorption by vapour of parts of spectrum of incandescent black
body. Application to sunlight, and starlight. Solar spots and pro-
tuberances. Period of life of various stars. Fluorescence, . .214
xviii CONTENTS.
LECTURE X.
SPECTRUM ANALYSIS.
PAGE
Change of colour of Light by relative velocity of source and observer.
Analogy from sound. Causes of broadening of spectral lines.
Spectrum of Solar Corona ; of Double Stars ; of Comets. Probable
nature of Comets ; of Saturn's rings ; of the Zodiacal Light, . 237
LECTURE XL
CONDUCTION OF HEAT.
Fourier's Mathematical Theory. His Definition of Conducting Power.
Analogy between Thermal and Electric Conductivities. Forbes's
method and results. Angstrom's method. Penetration of Surface
temperature into the earth's crust. Analogy between conduction of
heat and conduction of electricity. Diffusion also analogous to these.
Diffusion of matter, of kinetic energy, and of momentum, . . 265
LECTURE XII.
STRUCTURE OF MATTER.
Limits of Divisibility of Matter. In physics the terms great and small
are merely relative. Various hypotheses as to structure of bodies
Hard Atom Centres of Force Continuous but Heterogeneous
Structure Vortex-atoms [Digression on Vortex- Motion.] Lesage's
Ultramundane Corpuscles. Proofs that matter has a grained struc-
ture. Approximation to its dimensions from the Dispersion of Light :
from the phenomena of Contact Electricity, . . . 287
LECTURE XIII.
STRUCTURE OF MATTER.
Approximation to dimensions of grained structure from capillary
phenomena from properties of gases. Mathematical consequences
CONTENTS. xix
of the supposition that a gas consists of constantly impinging
particles Gaseous Diffusion. Results of Maxwell's investigations.
Physical reason of Dissipation Andrews' results as to the continuity
of the liquid and gaseous states of matter. Conclusion, . . 317
LECTURE XIV.
FORCE.
Evening Address to the British Association, Sept. 8, 1876, . . 343
LECTURE I.
INTRODUCTORY.
Classification of Recent Advances in Physical Science. General Statement of
the Objects of Physics. Time and Space. Matter, Position, Motion, and
Force. Digression upon a priori reasoning. Instances of modern or
revived fallacies Uniformity of Earth's Rotation, Stability of Solar
System, Heat developed the equivalent of work spent in compressing a
gas, Causa <zquat effectum. Gilbert the true originator of Experimental
Science. Test of the reality of Matter fails when applied to Force not
when applied to Energy. Conservation, Transformation, and Dissipa-
tion of Energy. Ignorance and Incapacity alike of .Spiritualists and
Materialists.
IN considering what may be designated as * Recent
Advances in Physical Science,' it is well to remember
that many things which have become almost popularly
known within the last twenty-five years are much
older in the minds and writings of the foremost scien-
tific men. We cannot, however, treat them intelligibly
without reference, sometimes pretty full, to what was
known even earlier still : so that you must not be sur-
prised if I have a good deal to say of Davy and Rum-
ford, and even of Newton.
I shall, for the sake of clearness, attempt roughly to
classify these recent advances under five well-marked
heads ; but I shall do so very briefly, deferring expla-
nation even of new scientific terms till I have to treat
each of these heads in detail.
First and foremost, advances connected with the
A
INTRODUCTORY.
modern notion of Energy. Just as Gold, Lead, Oxygen,
etc., are different kinds of Matter, so Sound, Light,
Heat, etc., are now ranked as different forms of Energy,
which, as we shall presently see, has been shown to
have as much claim to objective reality as matter has.
This grand idea enables us to co-ordinate all the parts,
however apparently diverse, of the enormous subject
of Natural Philosophy. It has not only thus enabled
us to exhibit the science in a complete and connected
form, but it has also, specially by the application of the
laws of Thermo-dynamics (to which a large part of this
course will be devoted), enabled us to find those points
where rapid advance was most easily to be secured.
Secondly. The advances which have arisen, more or
less directly, from the requirements felt in practical
applications. To take but a single instance : think of
the immense improvements in instruments for the
measurement of electric charges and electric currents,
such as electrometers and galvanometers, which have
been effected because called for by the recent exten-
sions of submarine telegraphy. It is not too much to
say that the instruments now employed, and which
were primarily devised for practical telegraphic pur-
poses, are hundreds of times more sensitive, as well as
more exact, and therefore more useful for purely
scientific purposes, than the best of those which were
in use thirty years ago. Thus it is that a development
of science, in a practical direction, leads to the construc-
tion of instruments which have, as it were, a reflex
action on the development of the pure science itself.
Thirdly. Those which arise from the assistance ren-
dered to one another by pure sciences, such as astro-
nomy, chemistry, and physiology, where, in fact, the
INTRODUCTORY.
improvement of one branch has led, almost immedi-
ately, to important extensions of other branches.
Under this head we may also include those very great
advances which are due to improvements in our mathe-
matical methods.
Fourthly. What may be called casual discoveries,
though they are often of very great importance ; such
as, for instance, the discovery of fluorescence, with its
manifold consequences, and the invention of the pro-
cesses of photography. Such discoveries, instead of
being, as in old days, wondered at and left isolated, are
now at once attacked on all sides by numberless en-
thusiastic experimenters.
Fifthly. There is another class, very numerous but
more difficult to exactly describe. As a single ex-
ample of this class, I may mention the modern statis-
tical methods of treating certain problems of physical
science, especially those connected with the movements
of particles of gases and liquids, to which I shall advert
at considerable length in the course of these lectures.
I have now to consider how I should best commence
the analysis of these various heads ; and I think the
proper method will be first to sketch the subject as if
from a distance to point out a few of the principal
peaks which we have to ascend, and of the more formi-
dable abysses which we have to avoid ; striving all the
while to introduce as early as possible some of those
new technical terms which are absolutely indispensable
to accuracy and definiteness, and which, therefore, can
not be too soon mastered.
Natural Philosophy, as now regarded, treats generally
of the physical universe, and deals fearlessly alike with
quantities too great to be distinctly conceived, and with
INTRODUCTORY.
quantities almost infinitely too small to be perceived
even with the most powerful microscopes ; such as, for
instance, distances through which the light of stars or
nebulae, though moving at the rate of about 186,000
miles per second, takes many years to travel ; or the
size of the particles of water, whose number in a single
drop may, as we have reason to believe, amount to
somewhere about
io 26 , or 100,000,000,000,000,000,000,000,000.
Yet we successfully inquire not only into the composi-
tion of the atmospheres of these distant stars, but into
the number and properties of these water-particles, nay,
even into the laws by which they act upon one another.
The fundamental notions which occur to us when we
commence the study of physical science are those of
Time and Space. A measure of time may be obtained
by physical methods, as in fact is done incidentally in
Newton's First Law of Motion, wherein he asserts that
a mass left to itself moves uniformly. That is, equal
times are the times in which such a mass describes
equal spaces. Of space, we can ascertain by observa-
tion the properties. But we cannot inquire into the
actual nature of either space or time, except in the way
of a purely metaphysical, and therefore of necessity
absolutely barren, speculation. We have, however,
mathematical methods specially adapted to the treat-
ment of these two abstract ideas ; Algebra, which has
been called (by Sir W. R. Hamilton) the science of pure
time ; and Geometry, which may be designated the
science of pure space.
The common measurement of time primarily depends
upon the rotation of the earth about its axis. This,
however, as will be seen when we advance a little
INTRODUCTORY.
further, is by no means a uniform quantity, and there-
fore ultimately the measurement of time must be based
upon some motion depending on a physical property of
matter which we have every experimental reason for
believing to be unchangeable by time, and invariable
throughout the universe. Probably such an ultimate
standard for the measurement of time will be found in
one of the periods of vibration of the molecules of a
heated gas, such as hydrogen, under given conditions.
The properties of space, involving (we know not why)
the essential element of three dimensions, have recently
been subjected to a careful scrutiny by mathematicians
of the highest order, such as Riemann and Helmholtz j 1
and the result of their inquiries leaves it as yet un-
decided whether space may or may not have pre-
cisely the same properties throughout the universe.
To obtain an idea of what is meant by such a state-
ment, consider that in crumpling a leaf of paper, which
may be taken as representing space of two dimensions,
we may have some portions of it plane, and other
portions more or less cylindrically or conically curved.
But an inhabitant of such a sheet, though living in
space of two dimensions only, and therefore, we might
say beforehand, incapable of appretiating the third
dimension, would certainly feel some difference of
sensations in passing from portions of his space which
were less, to other portions which were more, curved.
So it is possible that in the rapid march of the solar
system through space, we may be gradually passing to
regions in which space has not precisely the same pro-
perties as we find here where it may have something
in three dimensions analogous to curvature in two
1 See Helmholtz' paper in Mind, No. III. 1876.
INTRODUCTORY.
dimensions something, in fact, which will necessarily
imply a fourth-dimension change of form in portions
of matter in order that they may adapt themselves to
their new locality. But for the full discussion of a
question like this it would be necessary to introduce
mathematical reasoning of a transcendental character.
In addition to these fundamental notions of time and
space, the next four which force themselves upon us in
the physical universe are those of Matter, Position,
Motion, and Force. As with these ideas commences
the study of physics proper, I leave them for a moment
to consider in what way or in what spirit we ought to
treat problems of physical science. Remember that
the subject of my lectures is the Advances of Physical
Science. It is well then to inquire briefly to what we
are indebted for such advances. And every one who
has with any attention studied the history of scientific
progress sees at once that
These advances come or not according as we remember
or forget that our science is to be based entirely upon ex-
periment or mathematical deductions from experiment.
There is nothing physical to be learned a priori. We
have no right whatever to ascertain a single physical
truth without seeking for it physically, unless it be a
necessary consequence of other truths already acquired
by experiment, in which case mathematical reasoning
is alone requisite.
Let us consider for a moment to what fearfully absurd
consequences a neglect of this self-evident principle has
led in former times, and too often even in modern days.
Men were told by the antients that the planets move in
circles because circular motion is perfect ! They were
told also in the middle ages that the sun cannot pos-
INTRODUCTORY.
sibly have spots ! They were told that the earth was
at rest ; that Nature abhors a vacuum, etc. etc. And
all these dogmas were enuntiated by otherwise reason-
able men. Within the last fifty years we have had
philosophers like Hegel saying that the motion of the
heavenly bodies is not a being pulled this way and
that : that they go along, as the antients said, like
blessed gods. Further, that pressure, gravity, etc., are
true only of terrestrial, not of celestial matter. Hegel
winds up this truly wonderful statement by saying
that both are matter, just as a good thought and a bad
one are both thoughts, but the bad is not therefore good
because the good one is a thought. 1
As instances of still more recent, in fact quite modern,
fallacies of a somewhat similar kind, I shall take but
four, two of which are in their very nature excusable,
the other two utterly unpardonable.
First, there is the assumption that the earth's rotation
is absolutely uniform. Now, to say nothing of the
effects of cooling and consequent shrinking, the effects
of volcanic disturbances and upheavals, the effects of
degradation of mountains, and various other causes
1 Naturphilosophie, 269. [The passage is so incredibly absurd that I
feel bound to quote it.] Die Bewegung der Himmelskorper ist nicht
em solches Hin- und Hergezogenseyn, sondern die freie Bewegung ; sie
gehen, wie die Alien sagten, als selige Cotter einher. Die himmlische
Korperlichkeit ist nicht eine solche, welche das Princip der Ruhe oder
Bewegung ausser ihr hatte. Weil der Stein trage ist, die ganze Erde
aber aus Steinen besteht, und die andera himmlischen Korper eben derglei-
chen sind ist ein Schluss, der die Eigenschaften des Ganzen denen des
Theils gleichsetzt. Stoss, Druck, Widerstand, Reibung, Ziehen und der-
gleichen gelten nur von einer andern Existenz der Materie, als die himm-
lische Korperlichkeit. Das Gemeinschaftliche Beider ist freilich die Ma-
terie, so wie ein guter Gedanke und ein schlechter beide Gedanken sind :
aber der sclilechte nicht darum gut, weil der gute ein Gedanke ist.
INTRODUCTORY.
which must tend more or less to affect the earth's rota-
tion (shrinking and degradation accelerating it, while
upheavals retard it, according to a mechanical principle
which is involved in Newton's Third Law of Motion),
there has been recently revived the study, first pointed
out by Kant, of the effect of tidal retardation upon the
length of the day. In fact, the earth with the tide-wave
upon it, pointing on the average almost axially towards
the moon, is virtually revolving in a friction-brake or
collar ; and so long as it moves with reference to this
tidal wave, so long must it move subject to friction, and
therefore of course with continually decreasing velocity.
Then, again, we had the confident assertion of the
absolute stability of the solar system ; that is to say,
grand arguments were founded by the Teleologists on
the assumption that the eccentricities and inclinations,
and so on, of the planetary orbits, though constantly
varying, fluctuated between certain definite, and in
general very narrow limits, and that after a by no
means long series of ages all bodies in the solar system
would return to almost precisely their former configura-
tion as to position and velocity. Now, in arriving at
this result, which of course they themselves under-
stood in its true sense, Laplace and Lagrange confess-
edly employed approximate methods of solution only.
They left out of account what are termed technically
the squares of disturbing forces ; that is to say, of two
planets, each of which has disturbed the other's position,
the effects of the first upon the second were calculated
by leaving out of account the disturbance of the posi-
tion of the first, and vice versd. In order to improve
upon this approximation, at least without enormous
labour, mathematical methods of a far more powerful
INTRODUCTORY.
order than have yet been invented are requisite, and
therefore it is not from this point of view that the solu-
tion can at present be improved ; nor can we well form
an idea of the nature of the modification which the
results of the approximate method would undergo. But
the idea which I have just mentioned with reference to
tidal friction, which has not yet been taken account of in
the solution of these planetary problems, shows at once
that so long as the parts of any moving integral portion
of the system are capable of being displaced relatively
to one another, and so moving relatively with friction,
so long must there be a cause tending constantly to the
degradation of the rates of motion in the system, and
therefore that stability of the planetary system is im-
possible under present conditions. Remember that it
was in the imagined interests of religion that the earth's
motion was denied. History repeats itself here. An
ill-informed Teleologist, however good his intentions, is
far more dangerous to the cause he has at heart than
the bitterest of its declared enemies.
Then let us take the question of the heat developed
by compressing a gas. You all know that a piece of
tinder can be set on fire when it is enclosed in a cylin-
der in which the air is suddenly compressed by pushing
in a tight-fitting piston. Great credit has recently been
claimed for two speculators, Seguin and Mayer, who
independently propounded the hypothesis that the heat
developed in such a case is the equivalent of the work
spent in compressing the air ; or its converse, that the
heat lost in expansion is the equivalent of the work done
by the expanding material. To make such hypotheses
without preliminary experimental measurements, is
simply to fall into the fatal error to which I have already
io INTRODUCTORY.
adverted, the a priori assertion of physical principles.
To see that it is so, we have only to consider that a
gas might (for all we can tell without experiment) have
the properties of a spiral spring. Suppose, in fact, in-
stead of air, the cylinder above spoken of to be filled
with a number of spiral springs so adjusted as not to
interfere with each other's motions. In compressing
such a set of springs, exactly the same amount of work
may be spent as in compressing air, and yet we may
find no trace whatever of heat generated. It therefore
appears obvious that until we know for certain the ulti-
mate nature of a gas, the only way (independent of mere
guessing) to discover the relation between the heat
developed by compression and the work spent in pro-
ducing it, is to experiment ; and that without experi-
ment it is impossible to lay down any general relation
between them. The modern view of the constitution of
a gas, in which its particles are supposed to be flying
about with great velocity in all directions, and constantly
impinging upon one another and upon the sides of the
vessel, leads us almost directly to many valuable conclu-
sions, among which I will refer for the moment only to
the result known as Boyle's law, where we contemplate
the compression of a gas whose temperature is kept con-
stant. Suppose, for instance, the particles to be moving
with a certain velocity in every direction, we find that if
the piston could be moved half way down the cylinder,
and the velocity of the particles not thereby increased, 1
the number of impacts per second upon the ends of the
cylinder must become twice as great as it was before,
1 This would be a violation of the principle of Dissipation of Energy, as
will be seen by the reader of Lecture VI. But that does not invalidate its
usefulness as an illustration of the present argument.
INTRODUCTORY. n
because the length of the cylinder is only half as great.
Also, the number of impacts per second per square inch
upon the curved sides of the cylinder must likewise
be doubled, simply because there is the same number
of particles as before, impinging with the same velo-
cities, but upon only one half of the surface. If we
could manage to advance the whole piston by infini-
tesimally small stages, so as at each such advance to
take advantage of the absence of all molecular pres-
sure upon the piston, or to advance at every instant
those parts of the piston upon which for the moment
no impact was impending, we should produce this dimi-
nution of bulk without altering in any respect the velo-
cities of the particles of gas ; and therefore, according
to Boyle's law, and according to the analysis just given,
we should have the case of a gas doubled in pressure,
and occupying exactly one half the bulk which it occu-
pied at first, but without increase of temperature. Here
then is another mode of contemplating the compression
of a gas without any production of heat. This question
is one of great importance, and I intend to treat it
pretty fully in the course of these lectures.
The only other fallacy which I shall mention for the
present, is that of basing physical results upon the old
dog-Latin dogma, causa <quai effectum. It is difficult to
decide whether the Latinity or the (semi-obscure) sense
is in this dogma the more incorrect. The fact is, that
we have not yet quite cast off that tendency to so-called
metaphysics which has often completely blasted the
already promising career of a physical inquirer. I say
'so-called' metaphysics, because there is a science of
metaphysics ; but from the very nature of the case, the
professed metaphysicians will never attain to it. In fact
1 2 IN TROD UCTOR Y.
if we once begin to argue upon such a dogma as the
above, the next step may very naturally be to inquire
whether cause and effect are simultaneous or succes-
sive : and then we shall have become so mystified
about the meaning of the word Cause that we may well
be ready to inquire (as many have already done) what
is the necessarily ever acting cause of the uniform
motion of a body upon which no forces act !
The originator of true experimental science seems
to have been Gilbert of Colchester, whose deservedly
celebrated treatise De Magnete was published 300 years
ago. After him came Galileo and Newton, each making
gigantic strides in the true direction, and by them this,
the ONLY way of attaining to a discovery of physical
laws, was permanently established. The proof of this
is, that the last two centuries and a half have achieved,
in purely physical science, million-fold what had been
accomplished before them. And it is not that we are
now more able, nor that we have more leisure cer-
tainly not :
' . . . for Romans now
Have thewes and limbs like to their ancestors'.'
It is rather that whenever the direction given to inquiry
is a proper one, the men come forward. This direction
was good in Britain at certain memorable times, as when
Newton and Hooke were contemporaries ; in the days
of Maclaurin and Cotes, and in those of Cavendish and
Watt. At intervals it broke down entirely as regards
mathematical physics, partly as regards experimental
physics, and once again it has become good ; and conse-
quently, since the ever-memorable days of Young and
Davy, we have had Green and Hamilton, Faraday and
Graham, and we can still rejoice in the possession of
INTRODUCTORY.
Stokes and Thomson, Adams and Clerk-Maxwell, Joule
and Andrews. This list is as good as either of the
others, and might be considerably increased. Other
countries have had their similar fluctuations, all I be-
lieve traceable to similar causes. Little more than
half a century ago, France had such mighty names as
Ampere, Laplace, Lagrange, Poisson, Fresnel, Fourier,
Carnot, Cauchy, etc. I name them just as they occur
to me. We cannot do much in the way of classifying
men like these. Germany now has Helmholtz, Weber,
Kirchhoff, and has but recently lost Gauss, Jacobi, Dir-
ichlet, Plucker, Riemann, and Magnus.
The sad fate of Newton's successors ought ever to
be a warning to us. Trusting to what he had done,
they allowed mathematical science almost to die out
in this country, at least as compared with its immense
progress in Germany and France. It required the
united exertions of the late Sir J. Herschel and many
others to render possible in these islands a Boole and
a Hamilton. If the successors of Davy and Faraday
pause to ponder even on their achievements, we shall
soon be again in the same state of ignominious in-
feriority. Who will then step in to save us ?
Even as it is, though we have among us many names
quite as justly great as any that our rivals can pro-
duce, we have also (even in our educated classes) such
an immense amount of ignorance and consequent cre-
dulity, that it seems matter for surprise that true sci-
ence is able to exist. Spiritualists, Circle-squarers,
Perpetual-motionists, Believers that the earth is flat
and that the moon has no rotation, swarm about us.
They certainly multiply much faster than do genuine
men of science. This is characteristic of all inferior
14 INTRODUCTORY.
races, but it is consolatory to remember that in spite of
it these soon become extinct. Your quack has his little
day, and disappears except to the antiquary. But in
science nothing of value can ever be lost ; it is certain
to become a stepping-stone on the way to further truth.
Still, when our stepping-stones are laid, we should not
wait till others employ them. ' Gentlemen of the Guard,
be kind enough to fire first/ is a courtesy entirely out
of date ; with the weapons of the present day it would
be simply suicide.
To come back to our second set of elementary ideas,
Matter, Position, Motion and Force. Of these, the
second (Position) is a purely space relation, or geo-
metrical conception, and must necessarily be relative,
unless something like the idea of Riemann already
referred to have an actual existence in the universe.
The third (Motion) is mere change of position, but as
that change may take place more or less rapidly, it
involves the idea of time as well as of space. But both
of these ideas are quite independent of the remaining
two (Matter and Force) ; and in fact their study forms
the subject of a special mixed science of Time and
Space, called Kinematics, which takes its place beside
the older sciences, Geometry and Algebra, which I have
already adverted to as the sciences of pure Space and
pure Time.
The grand test of the reality of what we call Matter,
the proof that it has an objective existence, is its in-
destructibility and uncreateability if the term may be
used by any process at the command of man. The
value of this test to modern chemistry can scarcely be
estimated. In fact we can barely believe that there
could have existed an exact science of chemistry had it
INTRODUCTORY.
not been for the early recognition of this property of
matter ; nor in fact would there be the possibility of
a chemical analysis, supposing that we had not the
assurance by enormously extended series of previous
experiments, that no portion of matter, however small,
goes out of existence or comes into existence in any
operation whatever. If the chemist were not certain
that at the end of his operations, provided he has taken
care to admit nothing and to let nothing escape, the
contents of his vessels must be precisely the same in
quantity as at the beginning of the experiment, there
could be no such thing as chemical analysis. Some
substance might suddenly appear, 1 or some substance
might suddenly vanish, and no reasoning whatever could
lead to a deduction from the results of experiments
under such conditions. This, then, is to be looked
upon as the great test of the objective reality of matter.
There remains to be treated Force, the last of the
fundamental four. The notion is suggested to us di-
rectly, by the so-called ' muscular sense,' which gives us
the feeling of pressure, as when we move a body with our
hand or foot. But we must be particularly cautious as
to the way in which we treat the evidence of our senses
in such matters. Think of Sound and Light, for in-
stance which, till they affect a special organ of sense,
are mere wave-motions. The sensation is as different
from the cause in such cases as are the bruise and the
1 Hegel believed in such possibilities. Witness, among others, the
following almost the raciest of the manifold absurdities of the Naturphilo-
sophu. It occurs in 332. Ebenso werden die kaustischen Kali wieder
milde ; man sagt dann, sie ziehen Kohlensaure aus der Luft ein. Das ist
aber eine Hypothese ; sie machen vielmehr aus der Luft erst Kohlensaure,
um sich abzustumpfen.
1 6 INTROD UCTOR Y.
pain produced by a cudgel or a cricket ball from the
mere motion of those portions of matter before impact
on a part of the human body. In all likelihood a
similar (probably a more sweeping) statement is true
of force. [This subject is treated in a special Lecture,
appended to the present work.]
The definition of force in physical science is implicitly
contained in Newton's First Law of Motion, and may
thus be given :
Force is any cause which alters a bodys natural state
of rest or of uniform motion in a straight line.
The only difficulty, and it is a serious one, which we
feel here, is as to the word 'cause ;' for this, amongst
material things, usually implies objective existence.
Now we have absolutely no proof of the objective ex-
istence of force in the sense just explained. In every
case in which force is said to act, what is really observed,
independent of the muscular sense (whose indications,
like those of the sense of touch in matters concerning
the temperatures of bodies, are apt to be excessively
misleading), is either a transference, or a tendency to
transference, of what is called energy from one portion
of matter to another. Whenever such a transference
takes place, there is relative motion of the portions of
matter concerned, and the so-called force in any direc-
tion is merely the rate of transference, or of trans-
formation, of energy per unit of length for displacement
in that direction. Force then has not necessarily
objective reality any more than has Velocity or Posi-
tion. The idea, however, is still a very useful one, as
it introduces a term which enables us to abbreviate
statements which would otherwise be long and tedious ;
but, as Science advances, it is in all probability destined
.
UK! VF.IU -:T
INTRODUCTORY. 17
to be relegated to that Limbo which has already
received the Crystal Spheres of the Planets, and the
Four Elements, along with Caloric and Phlogiston, the
Electric Fluid and the Odic or Psychic Force.
It is only, however, within comparatively recent years
that it has been generally recognised that there is some-
thing else in the physical universe which possesses to
the full as high a claim to objective reality as matter
possesses, though it is by no means so tangible, and
therefore the conception of it was much longer in forcing
itself upon the human mind. The so-called ' imponde-
rables,' things of old supposed to be matter such as
heat and light, et cetera^ are now known by the purely
experimental, and therefore the only safe, method to be
but varieties of what we call Energy, something which,
though not matter, has as much claim to recognition
on account of its objective existence as any portion of
matter. The grand principle of Conservation of Energy, 1
which asserts that no portion of energy can be put out
of existence, and no amount of energy can be brought
into existence by any process at our command, is sim-
ply a statement of the invariability of the quantity of
1 Great confusion has been introduced into many modern British works
by a double use of the word Force. It is employed, without qualification,
sometimes in the sense of force proper (as above defined), sometimes in the
sense of energy ! The two things (if force proper can be called a * thing, '
having probably no objective existence, and certainly no conservation,
except possibly in a highly refined sense, which Faraday in vain attempted
to realise experimentally, but which, even if it were proved, would have
no connection with conservation of energy) are of as different orders as
miles and square miles, though perhaps they are not quite so incomparable
as minutes and yards or pence. Even a mere want of precision in the
use of terms of such fundamental importance is altogether incompatible
with the existence of true scientific method. [See Lecture xiv. (on Force)
at the end of this volume.]
B
1 8 INTRODUCTORY,
energy in the universe, a companion statement to that
of the invariability of the quantity of matter.
The laws of energy differ from those of matter in one
most important respect, so far at least as we yet know
by experiment. Matter cannot, so far as we yet know,
be transmuted from one kind to another, though in
some cases it assumes what is called an allotropic form.
The great characteristic of energy, on the other hand,
is that in general we can readily transform it (in fact it
is of use to us solely because it can be transformed), but
in all its transformations the quantity present remains
precisely the same.
Energy may be defined as the power of doing work,
or, if we like to put it so, of doing mischief. I have
already pointed out to you that the notion of energy is
harder to seize than that of matter. Wherein, for in-
stance, consists the difference between a mass of snow
lying on the mountain side and the same mass when it
has fallen and rests in the valley below ? Obviously,
so far as the matter present is concerned, the two sub-
tances are identical, except in so far as molecular
changes, such as melting, may have altered the state
of some portions of the mass during or after its descent.
Yet the elevated mass possesses, in virtue of its eleva-
tion alone, a power of doing work or mischief, which it
has lost entirely when it has descended as far as it can.
By the mere fact, then, of its elevation, it possesses a
power which it does not possess when it has descended.
This is called energy of position, or Potential Energy.
Other examples of it are to be found in a wound-up
spring or weight, as in a clock, a bent bow ; or in gun-
powder ; and various others might easily be mentioned,
ferhaps the most striking of all instances that we can
INTRODUCTORY. 19
give is that of the food of animals, including as one of
the principal constituents the oxygen of the atmosphere.
But when the snow is detached from the mountain
side, in descending it acquires another form of energy,
depending entirely on its motion ; and thus we distin-
guish between energy of position and energy of motion
or Kinetic Energy. To those who have acquired the
intelligent use of the terms it is matter of common
observation that as the one of these quantities becomes
less, the other becomes greater. The velocity of the
falling snow increases constantly as it gradually de-
scends ; and exact calculation, according to physical
experiment, shows us that the amount of potential
energy lost in every stage of the operation is precisely
equal to the amount of Kinetic energy gained. The
process may be inverted if we consider Kinetic energy
to be originally communicated to a body, suppose, for
simplicity, in a vertically upward direction. We know
that a stone thrown into the air gradually loses velocity
as it ascends higher and higher ; for an instant, when it
has lost all velocity, it pauses, and then returns, gradually
regaining velocity, as it in turn loses its advantage of
position ; and calculation, applied to this case, shows
that at every stage, whether of the ascent or of the
descent, the sum of the Potential and the Kinetic
energies remains precisely the same, except in so far
as it is modified by the resistance of the air. This,
however, gives us no exception to the general truth of
the principle of conservation of energy, because any
energy lost by the stone is communicated without loss
of quantity to the surrounding air.
We contemplate, therefore, with reference to energy,
its conservation, which merely asserts its objective
20 IN TROD UCTOR Y.
reality ; its transformations, which render it indispens-
able to the existence of life and the physical changes in
the universe ; but it has in addition another and even
more curious property. We have seen that change is
essential to the existence of phenomena such as we
observe : and, that this change may take place, it is
necessary that there should be constant transformations
of energy. But some forms of energy are more capable
of being transformed than others ; and every time that
a transformation takes place, there is always a tendency
to pass, at least in part, from a higher or more easily trans-
formable to a lower or less easily transformable form.
Thus the energy of the universe is, on the whole,
constantly passing from higher to lower forms, and
therefore the possibility of transformation is becoming
smaller and smaller, so that after the lapse of sufficient
time all higher forms of energy must have passed from
the physical universe, and we can imagine nothing as
remaining, except those lower forms which are incapable,
so far as we yet know, of any further transformation.
The low form to which all transformations with which
we are at present acquainted seem inevitably to tend,
is that of uniformly diffused heat : or, more precisely,
heat so diffused as to produce uniform temperature.
We know, in fact, that in order to make any use of heat
to transform.it into mechanical power or into any
other form of energy it is absolutely necessary that we
should have bodies of different temperatures. We must,
as it were, have a source and a condenser. Now, when
all the energy of the universe has taken the final form
of heat so diffused as to produce uniform temperature,
it will obviously be impossible to make any use of this
heat for further transformation. Thus, so far as we can
INTRODUCTORY. 21
as yet determine, in the far distant future of the universe
the quantities of matter and energy will remain ab-
solutely as they now are the matter unchanged alike
in quantity and quality, but collected together under
the influence of its mutual gravitation, so that there
remains no potential energy of detached portions of
matter ; the energy also unchanged in quantity, but
entirely transformed in quality to the low form of heat
so diffused as to produce uniformity of temperature. 1
This, the Dissipation of Energy, 2 is by no means well
understood, and many of the results of its legitimate
application have been received with doubt, sometimes
even with attempted ridicule. Yet it appears to be at the
present moment by far the most promising and fertile
portion of Natural Philosophy, having obvious applica-
tions of which as yet only a small percentage appear to
have been made. Some, indeed, were made before the
enuntiation of the Principle, and have since been recog-
nised as instances of it. Of such we have good ex-
amples in Fourier's great work on Heat-conduction, in
.the optical theorem that an image can never be brighter
than the object, in Gauss's mode of investigating elec-
trical distribution, and in some of Thomson's theorems
as to the energy of an electromagnetic field. But its
discoverer has, so far as I know, as yet confined himself
in its explicit application to questions of Heat-conduc-
tion and Restoration of Energy, Geological Time, the
Earth's Rotation, and such like. Unfortunately his long-
expected Rede Lecture* has not yet been published, and
1 Thomson On a Universal Tendency in Nature to Dissipation ofEnei-gy.
Proc. R.S.E. 1852.
2 What follows is extracted from my address as President of Section A
at the British Association Meeting of 1871.
3 Delivered in the Senate House, Cambridge, in 1866.
22 INTRODUCTORY.
its contents (save to those who were fortunate enough
to hear it) are still almost entirely unknown.
But there can be little question that the Principle
contains implicitly the whole theory of Thermo-electri-
city, of Chemical Combination, of Allotropy, of Fluor-
escence, etc., and perhaps even of matters of a higher
order than common physics and chemistry. In Astro-
nomy it leads us to the grand question of the age, or
perhaps more correctly the phase of life, of a star or
nebula, shows us the material of potential suns, other
suns in the process of formation, in vigorous youth, and
in every stage of slowly protracted decay. It leads us to
look on each planet and satellite as having been at one
time a tiny sun, a member of some binary or multiple
group, and even now (when almost deprived, at least at
its surface, of its original energy) presenting an endless
variety of subjects for the application of its methods.
It leads us forward in thought to the far-distant time
when the materials of the present stellar systems shall
Jiave lost all but their mutual potential energy, but
shall in virtue of it form the materials of future larjger
suns with their attendant planets. Finally, as it alone
is able to lead us, by sure steps of deductive reasoning, to
the necessary future of the universe necessary, that is,
if physical laws for ever remain unchanged so it enables
us distinctly to say that the present order of things has
not been evolved through infinite past time by the
agency of laws now at work, but must have had a
distinctive beginning, a state beyond which we are
totally unable to penetrate ; a state, in fact, which
must have been produced by other than the now
[visibly] acting causes.
Thus also it is possible that in Physiology it may, ere
INTRODUCTORY. 23
long, lead to results of a different and much higher
order of novelty and interest than those yet obtained,
immensely valuable though these certainly are.
It was a grand step in science which showed that just
as the consumption of fuel is necessary to the working
of a steam-engine, or to the steady light of a candle,
so the living engine requires food to supply its expen-
diture in the forms of muscular work and animal heat.
Still grander was Rumford's early anticipation that the
animal is a more economic engine than any lifeless one
we can construct. Even in the explanation of this
there is involved a question of very great interest, still
unsolved, though Joule and many other philosophers of
the highest order have worked at it. Joule has given a
suggestion of great value, viz., that the animal resembles
an electromagnetic- rather than a heat-engine ; but this
throws us back again upon our difficulties as to the
nature of electricity. Still, even supposing this ques-
tion fully answered, there remains another perhaps
the highest which the human intellect is capable of
directly attacking, for it is simply preposterous to sup-
pose that we shall ever be able to understand scientifi-
cally the source of Consciousness and Volition, not to
speak of loftier things there remains the question of
Life. Now it may be startling to some of you, especi-
ally if you have not particularly considered the matter,
to hear it surmised that possibly we may, by the help
of physical principles, especially that of the Dissipation
of Energy, some time attain to a notion of what con-
stitutes Life mere Vitality, I repeat, nothing higher.
If you think for a moment of the vitality of a plant
or a zoophyte, the remark perhaps will not appear so
strange after all. But do not fancy that the Dissipation
24 INTRODUCTORY.
of Energy to which I refer is at all that of a watch or
suchlike piece of mere human mechanism, dissipating
the low and common form of energy of a single coiled
spring. It must be such that every little part of the
living organism has its own store of energy constantly
being dissipated, and as constantly replenished from
external sources drawn upon by the whole arrangement
in their harmonious working together. As an illustra-
tion of my meaning, though an extremely inadequate
one, suppose Vaucanson's Duck to have been made up
of excessively small parts, each microscopically con-
structed, as perfectly as was the comparatively coarse
whole, we should have had something barely distin-
guishable, save by want of instincts, from the living
model. But let no one imagine that, should we ever
penetrate this mystery, we shall thereby be enabled to
produce, except from life, even the lowest form of life.
Sir W. Thomson's splendid suggestion of Vortex-atoms,
if it be correct, will enable us thoroughly to understand
matter, and mathematically to investigate all its pro-
perties. Yet its very basis implies the absolute necessity
of an intervention of Creative Power to form or to de-
stroy one atom even of dead matter. The question
really stands thus : Is Life physical or no ? For if it
be in any sense, however slight or restricted, physical, it
is to that extent a subject for the Natural Philosopher,
and for him alone.
There must always be wide limits of uncertainty
(unless we choose to look upon Physics as a necessarily
finite Science) concerning the exact boundary between
the Attainable and the Unattainable. One herd of
ignorant people, with the sole prestige of rapidly in-
creasing numbers, and with the adhesion of a few fana-
INTRODUCTORY. 25
tical deserters from the ranks of Science, refuse to admit
that all the phenomena even of ordinary dead matter
are strictly and exclusively in the domain of physical
science. On the other hand, there is a numerous group,
not in the slightest degree entitled to rank as Physicists
(though in general they assume the proud title of Philo-
sophers), who assert that not merely Life, but even
Volition and Consciousness are merely physical mani-
festations. These opposite errors, into neither of which
it is possible for a genuine scientific man to fall, so long
at least as he retains his reason, are easily seen to be
very closely allied. They are both to be attributed to
that Credulity which is characteristic alike of Ignorance
and of Incapacity. Unfortunately there is no cure;
the case is hopeless, for great ignorance almost neces-
sarily presumes incapacity, whether it show itself in the
comparatively harmless folly of the Spiritualist or in
the pernicious nonsense of the Materialist.
Alike condemned and contemned, we leave them to
their proper fate oblivion ; but still we have to face
the question, where to draw the line between that which
is physical and that which is utterly beyond physics.
And, again, our answer is Experience alone can tell
us ; for experience is our only possible guide. If we
attend earnestly and honestly to its teachings, we shall
never go far astray. Man has been left to the resources
of his intellect for the discovery not merely of physical
laws, but of how far he is capable of comprehending
them. And our answer to those who denounce our
legitimate studies as heretical is simply this, A reve-
lation of anything which we can discover for ourselves,
by studying the ordinary course of nature, would be an
absurdity.
26 INTRODUCTORY.
A profound lesson may be learned from one of the
earliest little papers of Sir W. Thomson, published while
he was an undergraduate at Cambridge, where he shows
that Fourier's magnificent treatment of the Conduction
of Heat [in a solid body] leads to formula: for its distri-
bution which are intelligible (and of course capable of
being fully verified by experiment) for all time future,
but which, except in particular cases, when extended
to time past, remain intelligible for a finite period only,
and then indicate a state of things which could not
have resulted under known laws from any conceivable
previous distribution [of heat in the body]. So far as
heat is concerned, modern investigations have shown
that a previous distribution of the waiter involved may,
by its potential energy, be capable of producing such
a state of things at the moment of its aggregation ;
but the example is now adduced not for its bearing on
heat alone, but as a simple illustration of the fact that
all portions of our Science, and especially that beautiful
one, the Dissipation of Energy, point unanimously to a
beginning, to a state of things incapable of being
derived by present laws [of tangible matter and its
energy] from any conceivable previous arrangement.
I conclude by quoting some noble words used by
Stokes in his Address to the British Association at
Exeter: 'When from the phenomena of life we pass
on to those of mind, we enter a region still more pro-
foundly mysterious. . . . Science can be expected to
do but little to aid us here, since the instrument of re-
search is itself the object of investigation. It can but
enlighten us as to the depth of our ignorance, and lead
us to look to a higher aid for that which most nearly
concerns our wcllbcing.'
LECTURE II.
THE EARLY HISTORY ,OF ENERGY.
Newton's services to the subject only of late recognised. Second Law
There is no balancing of forces ; but only of the effects of forces Geome-
trical composition of velocities. Third Law Its second interpretation
an all but complete statement of the Conservation of Energy Arithme-
tical composition of the squares of velocities. Experimental results of
Rumford and Davy, filling up the lacuna in Newton's statement. Their
proofs that Heat is not matter. Davy's statement of the true theory of
Heat. Speculations of Se"guin and Mayer.
THOUGH the subject which has been proposed to
me is, ' The Advances of Physical Science within the
last thirty years/ we must look upon the calling atten-
tion to valuable though neglected or misunderstood
discoveries of old time, as being quite as much an
advance in the present age as anything that has been
done for the first time within the last few years. I
cannot commence better than with those two of the
great advances made by Newton, which were unfor-
tunately very little recognised during his life, but which
within the last ten or twelve years have been brought
prominently before the world, and have shown us how
enormously in advance of his time and perhaps in some
respects even of our time Newton was.
The first of these is contained in his simple state-
ment of the Second Law of Motion. I shall read it,
not in his own words, but in a translation. He says :
28 THE EARL Y HISTOR Y OF ENERG Y.
' CJtange of motion is proportional to force, and takes
place in the direction of the straight line in which the
force acts' Now, for the century and a half since
Newton's time, mathematicians and natural philo-
sophers have been puzzling themselves to invent
various proofs so-called statical proofs of the law
of composition of forces ; the law which informs us
how we are to find a single force which will produce
precisely the same effect upon a body as two simul-
taneously acting forces applied at one point. All these
different schemes have been, I may say, one more
complex than another ; and they have finally landed
the student in utter confusion. Out of that confusion
we have only recently escaped by coming back to the
simple, but extraordinarily complete, statement of
Newton's which I have just read.
Newton tells you, * Change of motion is proportional
to force.' He says nothing whatever as to what the
motion was to begin with. He says nothing whatever
as to the force being alone. There may be as many
forces acting as we please ; and of every one of them
he says the change of motion which it produces is pro-
portional to it, and takes place in its direction.
Moreover, in that statement Newton tells us that a
force, according to him, always produces an effect
There is no such thing as two or more forces balancing
one another preventing one another from acting, as
it were. Newton's notion is, if there is a force at all, it
is doing something ; and what it does is, it produces a
change of motion, or, in modern language, a change of
momentum, proportional to itself and in its own direc-
tion. So that, according to Newton, there is practi-
cally no such thing as Statics. There is no balancing
THE EARLY HISTORY OF ENERGY. 29
of forces. There is balancing of the effects of forces,
which is quite another thing. A force always produces
its effect, and if two forces or more produce effects
which balance one another, then we shall have perpetual
balancing ; but we have no balancing forces, merely
a balancing of the effects they produce. We have the
very simplest case of this where a weight is lying on a
table. Gravity is constantly acting : the weight is con-
stantly being pulled down by the attraction of the
earth, but it is as constantly being pressed upwards by
the resistance of the table ; and each of these is pro-
ducing in each second a certain quantity of momentum.
The one is producing momentum in a vertically down-
ward direction ; the other is producing momentum in
a vertically upward direction. These correspond to
equal velocities in an upward and a downward direc-
tion ; but it is the velocities, not the forces, which
balance or neutralise one another.
To extend this statement to the case of the funda-
mental proposition in statics, which tells us how to
compound two forces, and to find their resultant, all we
have to do is to consider the two forces as acting upon
a single particle of matter. If one of them acted alone,
for a certain time, it would give it a velocity of a certain
amount, and in a certain direction. If the other acted
alone, for the same period of time, it would equally
give a velocity definite in amount, and definite in direc-
tion ; but a particle cannot be moving in more than one
direction at a time, so that what we have to consider is
this : as Newton virtually tells us that the presence of
a second force in no way interferes with the action of
the first, we have to seek first what are the effects of the
two separately, and then what, in consequence of these
30 THE EARLY HISTORY OF ENERGY.
effects supposed simultaneous, will be the actual motion
of the particle. It comes then to be a question merely
of compounding velocities a purely geometrical (or,
more strictly, kinematical) question instead of a physical
one. The Second Law of Motion, therefore, enables us
to commence with the purely kinematical notion of
compounding two velocities, and thereafter to translate
that into the compounding of two forces.
But the law of composition deserves a word or two.
The compounding of two velocities is of course seen at
once to be equivalent to this : If one body, such as a
carriage, for instance, be moving in a certain direction
with a certain velocity, and if some object in the carriage
be simultaneously moving with reference to the carriage
in a certain other direction, and with a certain other
velocity, you can consider each of these separately
the motion of the carriage, or the motion of this body
relatively to the carriage ; but when you take the two
simultaneously, the result is that, with reference to the
ground supposed fixed, there is a perfectly definite
direction and velocity with which the body is moving.
This is an obvious truth ; and the geometrical result is
that, If we represent in magnitude and direction one
of the two velocities by a line AB, and the second
velocity by another line BC, drawn from the extremity
of the first, then the single velocity, which is equivalent
to the simultaneous existence of these two velocities, is
found by drawing the third side AC of the hitherto
uncompleted triangle. It follows then that (turning
to the forces which produce these motions) as AB
multiplied by the mass of the body is the change
of motion produced by one of the forces, and BC
multiplied by the same mass represents the change of
THE EARLY HISTORY OF ENERGY. 31
motion produced by the second force, the change of
motion produced by the two forces acting simultane-
ously is the product of the mass moved into the third
side A C of the triangle. But Newton's Law tells us
that changes of motion are proportional to the forces
which produce them. Therefore if AB be now taken
to represent on a certain scale one of the forces, and
BC the other, the single force which is represented on
the same scale by the third side of the triangle will
produce precisely the same effect upon the body as
would be produced by the simultaneous action of the
two separate forces. And you will see at once how it
is that this law of geometrical composition of forces
(what is called the triangle of forces), is merely a slightly
different mode of expressing what you may be more
familiar with under the designation of the parallelogram
of forces, the so-called fundamental principle of statics.
There, then, is the law of the geometrical composition
of forces, and also of velocities. We have in this case
two sides of a triangle (taken consecutively and in the
same way round), which may be said in a sense to be
geometrically equivalent to the third side (taken the op-
posite way round), but the sum of their lengths is not
equal to the length of the third side. This is the law of
composition of what Sir W. R. Hamilton called vectors,
and it is obviously generalisable into a similar construe-
32 THE EARL Y HIS TOR Y OF ENERG Y.
tion for the composition of any number of velocities or
forces in any directions in space. I leave it, without
further comment for the moment, until I have made
some remarks on Newton's Third Law, and then you
will see how there is a physical sense in which we must
take the sum, not of two sides themselves, but of the
squares of two sides ; how, in fact, the 47th proposition
of the first book of Euclid comes in as part of the inter-
pretation of Newton's Third Law of Motion.
Newton's Third Law of Motion, to which I have just
referred, is expressed in very simple words : ' To every
action there is always an equal and contrary reaction?
These terms, ' action ' and * reaction,' Newton proceeds
to explain. He tells us that there are two senses, quite
different from one another, in which you may interpret
each of these words ; and yet that this same simple
statement of the equality of action and reaction holds
for each of these two perfectly distinct meanings.
The first form of action is that of an ordinary force
or pressure ; and Newton's statement then is equivalent
simply to this : that if a weight presses upon a table,
the table must react upon the weight with an equal and
opposite pressure, and this whether the table is moving
or not. Even supposing I were to lay so large a mass
upon a table that the table were to give way, still while
it was giving way, in the act of moving, if there were
pressure at all between them, the load would press
at every instant upon the table with an exactly equal
and opposite force to that with which the table presses
upon the load, and the same will hold however you
may connect two bodies together. If you connect
them either by mere contact, or by strings, or chains,
or rods, or girders, anything wherever there is a con-
THE EARL Y HISTOR Y OF ENERG Y. 33
nection between two bodies if there be any action
whatever along that connecting link, there always is an
equal and opposite reaction. And a visible or tangible
link is not necessary. The same law is true of gravita-
tion-attraction, and of electric and magnetic attractions.
So far, then, this is merely a question of forces ; but
it seems to have entirely escaped the notice, not only
of Newton's contemporaries, but of those who have
succeeded him during the last 150 or 200 years, until
quite lately, that Newton's second explanation, his second
mode of interpreting his Third Law, is something per-
fectly different from this, and leads us into a new order
or range of phenomena. This second interpretation is"" 1
so important that I must bestow considerable time upon
it, because in reality it shows Newton to have been in
possession of many of the principal facts of the conser-
vation and transformation of energy. One or two of
these facts escaped him, simply because he did not
know what heat is, but he was very, very near attaining
even that. He has given us all the mathematical mate-
rials that are required for the treatment of it ; but he
missed one great point, simply because experiment had
not gone far enough in his time. Of course I need
not say that he knew nothing (not even the name) of
electro-magnetism and other recently discovered phy-
sical agents, all of which we can now classify under
energy ; but for everything that was known in his time,
with the exception of heat, light, and electric energy, he
gave us a complete statement. That complete state-
ment, strange to say, has only been found in his great
work within the last few years. It is this, literally
translated : ' If the activity of an agent be measured [not
by the agent itself, as in the case of a force, but] by the
C
34 THE EA RL Y HIS TOR Y OF EN ERG Y.
^ product of its force into its velocity, and if similarly the
counter-activity of the resistance be measured by the veloci-
ties of its several parts multiplied into their several forces,
whether these arise from friction, cohesion, weight, or
acceleration ; activity and counter-activity in all combina-
^tions of machines will be equal and opposite' Now, in
order to see the full force of this statement, let us con-
sider what is meant by the product of a force into its
velocity. Newton, as he has shown in a previous defini-
tion, understands, by the velocity of a force, not the
whole velocity of the point to which it is applied, but
the component of that velocity which is in the direction
of the force. If, for instance, a horse is dragging a canal
boat along, you are not to multiply the force of tension
of the rope by the velocity of the canal boat, because
the canal boat moves in one direction, and the tension
of the rope is in general in a different direction. What
you must do then is this : you must find out how much
of the velocity of the boat is in the direction of the action
of the force ; resolve it, as it is called, multiplying the
amount of the velocity of the boat by the cosine of the
angle between its direction and the direction of the
force which is applied by the rope. Then, what Newton
says is this : if you so treat it multiply each force by
the velocity (in this sense) of its point of application
you will find that the sum of the activities will be equal
to the sum of the counter-activities.
A word or two more about this before I consider the
very admirable statement of various cases which Newton
gives, Let us see what we mean now-a-days by what
Newton calls here ' the action of the agent' It is the
product of the force into the resolved part of the velo-
city in the direction of the force. Therefore it is the
THE EARL Y HISTOR V OF EJSTERG Y. 35
product of the force into the rate at which the point of
application moves in the direction of the force. The
product of a force into the space through which it
moves its point of application in its own direction is
what we now call the amount of Work done by the
force. But in Newton's statement it is not the amount
of work done, but the rate at which work is being done,
so that what he contemplates is really what we now-a-
days measure, after Watt, by the unit called a horse-
power the rate at which an agent works when doing
33,000 foot-pounds of work per minute.
Now, you will particularly notice that he says the
several parts of the resistance, ' whether these arise from
friction, cohesion, weight, or acceleration.'
I shall take, first, cohesion and weight. You can
easily see how a resistance may arise from cohesion,
which simply means what we now call molecular forces
in general, as, for instance, when work is spent in
changing the shape of a body when it is employed
in producing a shear, for instance. There you have
the elastic forces of the body worked against ; and what
Newton says is, that the amount of work spent, or the
rate of spending work in distorting the body, is equal
to the amount of work done or the rate of doing work
against the elastic forces. It is thus stored up in the
distorted body as Potential Energy.
Then he says 'weight :' the rate at which an agent
works in lifting a mass is exactly equal to the rate
at which work is done against gravity : and the work
so done is stored up as Potential energy of the raised
mass.
Then he says ' acceleration ; ' and that is by far the
most important of those I have yet mentioned. When
36 THE EARL Y HISTOR V OF ENERG Y.
work is spent on a body where there is no resistance
from friction or from weight, or from cohesion, Newton
says that work will always be spent against a resistance
due to acceleration ; that is, work is spent in overcoming
the inertia of a body and increasing its velocity. This
is a statement of very great importance ; and when we
interpret it according to Newton's previously laid down
definitions, we find that his Third Law here asserts that
the rate at which the agent works is the rate at which
the kinetic energy of the body increases. For it is an
immediate consequence of Newton's words that the rate
at which work is spent is measured by the product of
the momentum into the acceleration in the direction of
motion. Hence the Kinetic Energy (which is half the
product of the mass into the square of its velocity) is
increased by an amount equal to the work spent. Work
spent against resistance to acceleration is thus stored up
in the body in the form of an increase in the kinetic
energy.
That is very important ; but there is a still more
important point, which Newton takes account of, and
that is, work spent against friction. Whenever work is
spent against friction, we all know now-a-days that
heat is produced, and it has been proved by elaborate
experiments, which I shall presently discuss, that the
amount of heat produced is precisely proportional to
the amount of work spent in producing it. If Newton
had known that such is the case, he could have had no
difficulty whatever, after this extremely lucid statement
of his, in passing to the general modern statement of
the conservation of energy. So near had he arrived at
it, that it wanted only experiments like those I am
presently to describe, to have enabled him at once to
THE EARL Y HIS TOR Y OF ENERG Y. 37
take a full grasp of the subject, at least so far as we
know it in the present day.
Before I leave this matter, however, I must say a
word or two as to the result of compounding two
amounts of Kinetic energy. Suppose we have a
southward velocity amounting, let us- say, to 3 feet
per second, and simultaneously an eastward velocity
amounting to 4 feet per second, then we know by
Kinematics, how to construct the single velocity, which
is the resultant of these two. All we have to do is
to draw a line of length 3 southwards, and from its
extremity a line of length 4 to the eastward, and
then complete the triangle. In a geometrical sense,
therefore, a velocity of 3 southwards and a velocity
of 4 eastwards will be equivalent to a velocity which,
if you calculate what the third side of that triangle will
be, is represented by 5 on the same scale. It will
then be a velocity of 5 in a direction which makes
an angle, whose sine is |, with the south line. So
far the geometrical conception of composition is
perfectly definite. But now let us see what this in-
volves in the case of Kinetic energy. If a mass were
moving with a velocity of 3 southwards, and simultane-
ously with a velocity of 4 eastwards : its Kinetic
energy, being proportional to the square of the velocity,
is in the southward direction proportional to 9, the
square of 3, while in the eastward direction it is pro-
portional to 1 6. But the same mass moving with the
resultant of these velocities has Kinetic energy pro-
portional (on the same scale) to 25 the arithmetical
sum of the other two. So that there are two ways of
compounding these combinations of the velocity and
mass of a body. When it is a question of Momenta
38 THE EARL Y HISTOR Y OF ENERG Y.
that is to say, when it is a question of the application
of Newton's first meaning of the word actio when the
actio means a simple force or its time-integral, then you
are to compound geometrically, and two sides of a
triangle are in that sense equal to the third ; but when
it comes to compounding Kinetic energies which are
proportional to the square of the velocity, then you are
limited to right-angled triangles, and having to add the
squares of the two sides, you obtain the square of the
third side. The difference then between the geometrical
composition and the simple arithmetical addition is a
difference depending upon the use of the first or second
power of the velocity. When, as in momentum, the
first power is involved, the magnitude is essentially a
directed one, and two directed magnitudes must be
compounded geometrically. But Kinetic energy, de-
pending as it does upon the square of the velocity, is
essentially non-directional, and its various parts, when
independent of one another (as they are when they
depend upon motions in directions perpendicular to
one another), are to be compounded by simple addition.
These two things, then, Momentum and Kinetic Energy,
perfectly distinct from one another, having no reference
to one another that we can trace at present, are both
included in the simple form of statement of Newton's
Third Law, only with a corresponding difference of
meaning to be attached to two of the words involved.
What Newton really wanted then was to know what
becomes of work which is spent in friction. Now, the
first successful answerer of that question was un-
doubtedly Count Rumford, and from his paper of 1798
I shall read some extracts, because it is one of the
most valuable experimental papers that perhaps ever
THE EARL Y HISTOR Y OF ENERG Y. 39
was published. It is most admirably philosophical in
its mode of experimenting, and it is throughout entirely
opposed to that d priori style of reasoning which (as I
showed you in my last lecture) is so fatal to progress
in natural philosophy. Count Rumford says :
1 It frequently happens, that in the ordinary affairs and occupa-
tions of life, opportunities present themselves of contemplating
some of the most curious operations of Nature ; and very interest-
ing philosophical experiments might often be made, almost with-
out trouble or expense, by means of machinery contrived for the
mere mechanical purposes of the arts and manufactures.
4 1 have frequently had occasion to make this observation ; and
am persuaded, that a habit of keeping the eyes open to everything
that is going on in the ordinary course of the business of life has
oftener led, as it were by accident, or in the playful excursions of
the imagination, put into action by contemplating the most common
appearances, to useful doubts, and sensible schemes for investiga-
tion and improvement, than all the more intense meditations of
philosophers, in the hours expressly set apart for study.'
Then again he says :
* Being engaged, lately, in superintending the boring of cannon,
in the workshops of the military arsenal at Munich, I was struck
with the very considerable degree of Heat which a brass gun
acquires, in a short time, in being bored ; and with the still more
intense Heat (much greater than that of boiling water, as I found
by experiment) of the metallic chips separated from it by the borer.
'The more I meditated on these phenomena, the more they
appeared to me to be curious and interesting. A thorough investi-
gation of them seemed even to bid fair to give a further insight
into the hidden nature of Heat ; and to enable us to form some
reasonable conjectures respecting the existence, or non-existence,
of an igneous fluid; a subject on which the opinions of philoso-
phers have, in all ages, been much divided.
* From whence comes the Heat actually produced in the mechani-
cal operation above mentioned ?
4 Is it furnished by the metallic chips which are separated by the
borer from the solid mass of metal ?
40 THE EARL Y HISTOR Y OF ENERG Y.
1 If this were the case, then, according to the modern doctrines
of latent Heat, and of caloric, the capacity for Heat of the parts of
the metal, so reduced to chips, ought not only to be changed, but
the change undergone by them should be sufficiently great to
account for all the Heat produced.'
He sees the difficulty : he catches at once really what
is wanted the true method of upsetting the old notion
that heat is matter. The explanation which was
given of the heat produced by friction by those who
believed that heat is matter was simply this : The
body in its solid state, or rather in its massive state,
before you began to abrade filings from it, possessed
in that state a certain quantity of heat. It had a
certain capacity for heat at a certain temperature ;
in other words, it required so much heat to be mixed
up with its particles in order to make the tempera-
ture of the whole that which was observed. But if
you could make it more capacious if you could give it
greater capacity for heat then it would hold more
heat without becoming of a higher temperature. On
the other hand, if by any process whatever you could
diminish its capacity for heat, then, of course, it would
become hotter itself, and even give out heat to sur-
rounding bodies, so that, according to the notion of the
supporters of the caloric theory (as it was called), the
production of heat by friction or abrasion is due to the
fact that you make the capacity of a body for heat
smaller by reducing it to powder. For of course, when
its capacity for heat is thus made smaller, it must part
with some of the heat it had at first ; or if it retains it,
it must necessarily show the effect of the heat more than
it did before, and must therefore rise in temperature.
Now, this reasoning is, so far, perfectly philosophical.
iv K
C/I.Cf
77/ ^tfZ Y HISTOR Y OF ENERG Y. 41
We can say nothing against a mode of reasoning of
that kind. The only fallacy in it was the assumption
that heat is a substance. Now, see how well Rumford
laid hold of that point, and how he proceeds by ex-
periment to try if possible to satisfy his doubts about it.
He says :
' If this were the case, then, according to the modern doctrines
of latent Heat, and of caloric, the capacity for Heat of the parts
of the metal so reduced to chips, ought not only to be changed,
but the change undergone by them should be sufficiently great to
account for all the Heat produced.'
Rumford found no difference, so far as his form of
experiment enabled him to test it, between the capacity
for heat of the abraded metal and the metal before
the abrasion had taken place ; so that if this experiment
had been only a satisfactory one and Rumford did
not see how to make it thoroughly satisfactory the
fact that heat is not matter would have been con-
clusively established. What Rumford really did want
was this : he wanted a process by which to bring the
abraded metal and the non-abraded metal, if possible,
to the same final state. He tried to do this by throwing
them into water equal quantities of the lumps and of
the filings, equally hot, into equal quantities of water
at the same lower temperature to see whether they
would produce different changes of temperature, each
in its own vessel of water. But then they were not in
the same final state. The filings, remember, were in
a distorted state ; they might have been very con-
siderably compressed, or they might have been distorted
in shape by shearing or something of that kind, in virtue
of which they might have had a certain quantity of latent
heat which he could not discover by this process. The
42 THE EARL Y HISTOR Y OF ENERG Y.
only legitimate and practicable process which we know
of for completely answering that question, which was
Rumford's sole difficulty, is a chemical process. Dissolve
your lumps and an equal weight of your filings in equal
quantities of the same acid. At the end of the operation,
of course, there can be no doubt that the chemical sub-
stances produced will be precisely the same, whether
you begin with lumps or with filings. You will have
the same chemical substance ; but if there be any
mysterious difference as to the capacity for heat in
them, that will be shown during the process of solution.
In general, in dissolving a metal in an acid, there is a
development of heat ; but if there were any difference
in the quantity of heat which the lumps and an equal
weight of filings contained that is to say, if heat could
by any possibility be matter then there would neces-
sarily have been an escape of heat more in one vessel
than the other. If Rumford had tried that one additional
experiment, he would have had the sole credit of having
established the non-materiality of heat.
The details of Rumford's experiments are given in
full, but I shall not describe them to you. I merely
mention that they show extraordinary skill and care in
experimenting, and wonderful precaution in trying to
avoid, as far as possible, the necessary losses in the
experiments. When losses were unavoidable and of a
large amount, the same skill is shown in making separ-
ate side experiments, in order to enable the operator
to allow for them in the main experiments. The
whole work itself is a model of experimental science.
I shall now pass on to the final reasoning, merely
mentioning in passing that Rumford actually managed
to boil a large quantity of water, though an immense
THE EARL Y HISTOR Y OF ENERG Y. 43
amount of heat was lost in spite of all his precautions.
Still the work of a single horse for two hours and twenty
minutes was found sufficient to boil about 19 Ibs. of
water, besides heating a large casting of the cannon,
and all the machinery that was engaged in the process.
He says :
* It would be difficult to describe the surprise and astonishment
expressed in the countenances of the by-standers, on seeing so
large a quantity of cold water heated, and actually made to boil,
without any fire.
' Though there was, in fact, nothing that could justly be con-
sidered as surprising in this event, yet I acknowledge fairly that it
afforded me a degree of childish pleasure which, were I ambitious
of the reputation of a grave philosopher, I ought most certainly
rather to hide than to discover. 3
Here is his final reasoning :
A
' In reasoning on this subject, we must not forget to consider
that most remarkable circumstance, that the source of the Heat
generated by friction in these experiments, appeared evidently to
be inexhaustible.
' It is hardly necessary to add, that anything which any insu-
/atedbody or system of bodies can continue to furnish without limi-
tation^ cannot possibly be a material substance. It appears to me
to be extremely difficult, if not quite impossible, to form any dis-
tinct idea of anything capable of being excited and communicated
in the manner in which the heat was excited and communicated in
these experiments, except it be motion. I am very far from pre-
tending to know how or by what means or mechanical contrivance
that particular kind of motion in bodies which has been supposed
to constitute Heat is excited, continued, and propagated ;'
and then he proceeds to apologise for the minutiae
given in his paper.
Now, when we make a calculation from the data fur-
nished by Rumford's paper, we find this : that, supposing
heat to be a form of energy, and taking 30,000 foot-
44 THE EARL Y HISTOR Y OF ENERG Y.
pounds per minute as the work of a horse (that is
something like an ordinary estimate), the mechanical
equivalent of heat is 940 foot-pounds. The meaning of
that statement is, that if you were to expend the
amount of work designated as 940 foot-pounds in stirring
a single pound of water, then that pound of water when
brought to rest at the end of the operation would be one
degree Fahrenheit hotter than before you commenced.
[Rumford throughout uses Fahrenheit's degrees.] We
can put it in another form, which is perhaps still more
striking. If you had a cascade or waterfall 940 feet
high, then, in the fall of the water down that cascade,
there would be 940 foot-pounds of work done by gravity
upon each pound of water ; and therefore if all the
energy which the moving water has, as it reaches the
bottom of the fall, were spent simply in heating the
water, the result would be that the water in the pool at
the bottom of the fall would be I deg. Fahrenheit hotter
than the water at the top of the fall.
I may remind you here, that Rumford's experiments
were published in 1798, so that they are of considerably
old date ; but, like those which I am just going to
advert to, they were barely noticed, or noticed only to
be laughed at, until somewhere about the year 1840.
Now, in the very year after the experiments of Rum-
ford were published, we had the experiments of Davy.
I need not go into minute details about them, because
they were not by any means such models of careful
experimental work as Rumford's. But, for all that,
Davy gave conclusive proof (if he had only at the time
seen it himself) that heat is not matter. His proofs
were of this kind. He first showed that by rubbing
two pieces of ice together by simply expending work in
THE EARL Y HISTOR Y OF ENERG Y. 45
the friction of two pieces of ice you could melt the ice.
Now, supposing heat had been matter, this is the sort
of argument that a believer in the caloric theory would
have used : two pieces of ice when rubbed together
cannot possibly melt one another, because in order to
melt them you will have to furnish heat to them. But
the heat can only come from themselves when they are
rubbed together ; it cannot come from surrounding
bodies, and therefore they cannot possibly melt to-
gether, because to melt one another, they would have
first to part with some of their heat in order to produce
the melting. Davy showed, however, that the mere
rubbing together of two pieces of ice by proper
mechanical processes was sufficient to melt the surface
layer of each. There still was this possible objection,
that the heat might have come from some external
source, so that his second experiment was of this kind.
He rubbed two pieces of metal together, keeping them
surrounded by ice, and in the exhausted receiver of an
air-pump, so as if possible to avoid radiant heat, heat
carried by convection-currents of air, and so on, and to
remove every possible disturbing cause, or even source
of suspicion, from his experiment ; and still he found
that these two pieces of metal, when rubbed together
thus, constantly produced heat and melted the ice, every
precaution having been taken to prevent heat from
getting at them from every side. It is curious that his
reasoning upon the subject is extremely inconclusive,
although his experiments themselves completely settle
the question. He says :
' From this experiment it is evident that ice by friction is con-
verted into water, and according to the supposition its capacity is
diminished ; but it is a well-known fact that the capacity of water
46 THE EARL Y HISTOR Y OF ENERG Y.
for heat is much greater than that of ice ; and ice must have an
absolute quantity of heat added to it before it can be converted
into water. Friction, consequently, does not diminish the capa-
I cities of bodies for heat ;'
and there he stops. [Sir W. Thomson remarks on
this passage (Encyc. Brit., last edition, art. Heat), as
follows : Delete from ' and according to the supposi-
tion,' to 'greater than that of ice,' inclusive; and
delete the lame and impotent conclusion stated in the
last eleven words. The residue constitutes an unanswer-
able demonstration of Davy's negative proposition that
heat is not matter.] But some years afterwards he came
to this conclusion from these experiments :
' Heat, then, or that power which prevents the actual contact of
the corpuscles of bodies, and which is the cause of our own sensa-
tions of heat and cold, may be defined as a peculiar motion, pro-
bably a vibration of the corpuscles of bodies tending to separate
them. It may with propriety be called the repulsive motion.
Bodies exist in different states, and these states depend upon the
action of attraction and of the repulsive power on their corpuscles,
or, in other words, on their different quantities of repulsion and
attraction.'
Now, we see at a glance how he explains by these
experiments what is the difference between a solid and
a liquid, and the difference again between a liquid and
a gas. In general, the melting of a solid is produced
by communicating heat to it. In other words, accord-
ing to Davy's explanation, the particles of the solid
are set in vibration, and thus, in consequence of the
repeated impacts upon one another, they push one
another side. And, as he also says, you may consider
this repulsive motion to have a complete analogy to
the so-called centrifugal force in a planetary orbit, for
the faster one particle is moving about another, the
THE EARL Y HISTOR Y OF ENERG Y. 47
larger necessarily is the orbit into which it will be forced.
The particles of a solid then are forced from one another
by this repulsive action of heat, and the action of the
heat upon it puts it into a liquid state. When you
increase still further the amount of heat communicated
to the body, you at length overcome altogether the
cohesive forces, and you have free particles, as in a gas,
flying about and impinging upon one another, but only
for very brief periods coming near enough in the course
of their gyrations to bring into play the molecular
forces again. Whenever, however, the molecular forces
do come into play for a moment, you may have two
particles adhering together, but they are soon knocked
asunder by a blow from a third particle.
There is one other sentence, however, which I must
quote from Davy, and then I shall have finished my
account of his contributions, which were later than
1799, when his first paper was published. In fact, in
1812 he enounces this proposition :
{ The immediate cause of the phenomenon of heat, then, is motion, i\\
and the laws of its communication are precisely the same as the
laws of the communication of motion.'
Now, we see at a glance to what an immense extent
the science had been advanced in Davy's time. When
Davy was in a position to make that statement, one
had only to take it in addition to the second interpreta-
tion of Newton's Third Law, and the dynamical theory
of heat was in his possession. Still, that publication
of Davy's in 1812, like the earlier ones of Rumford and
of Davy himself, remained almost unnoticed looked
upon, perhaps, as an ingenious guess, or something of
that sort, but as something which it was not worth the
trouble of philosophers to consider; and it was not
48 THE EARL Y HISTOR Y OF ENERG Y.
until Joule's time, somewhere about 1840, that the
subject was fairly taken up, and that justice was
rendered to their real value. Notice how distinctly
these two great leaders were men who based their work
directly upon experiment. There is no a priori guess-
ing, or anything of that kind, about either Rumford's or
Davy's work. They simply set to work to find out what
heat is. They did not speculate on what it might be.
But both before and after their time, there have been
numbers of philosophers who have, without trying a
single experiment, or at best trying only the roughest
forms of experiment, endeavoured to discover by a
priori reasoning what heat is. The list is a very long
one, and includes names such as Locke and Bacon, which
are distinguished in very different subjects, as well as
to some extent in physics. These both express their
complete conviction that heat consists in a brisk agita-
tion of the particles of matter ; but then, as this was
based upon no experiment whatever, it can simply be
looked upon as a happy guess. In the present day
when a philosopher comes forward and makes similar
statements, without any experiment, we simply put
him in the same category as Locke and Bacon, we
justly refuse to give him any credit for a matter of that
kind.
There was one man of this class, however, M.
Seguin, a nephew of the celebrated Montgolfier, who
all but redeemed himself from being so classified.
Seguin himself says he got from his uncle his idea that
heat is certainly not matter, but corresponds to a
certain kind of energy ; and he says that he had made
various experiments with a steam-engine, in order to
test whether the same quantity of heat reached the
THE EARL Y HIS TOR Y OF EN ERG Y. 49
condenser as had left the boiler. He was, unfortunately,
unsuccessful in all his experiments. He was certainly j
on the right track, and had he succeeded there he
would have been entitled to be considered as an inde-
pendent discoverer of the non-materiality of heat. For
it is obvious that if we can show by any experiment
whatever that heat is put out of existence, or that fresh
heat is brought into existence, either of these at once
destroys all possibility of its being material. Now, if
Seguin could have proved, by his actual measurements,
that less heat in any case reaches the condenser than
left the boiler, he would have completely settled the
question. From that point of view experiments have
been made, and made very carefully, in recent times,
by Him. Hirn has actually measured, in an ordinary")
working steam-engine, by most careful experimental
methods, the quantity of heat which leaves the boiler
and the quantity which reaches the condenser. He has
measured also the quantity which is lost by radiation,
conduction, and currents of air over all parts of the
machine, and he has found, as a final result, that when
the engine is at work, as, for instance, when a number
of spindles are being turned, there is a greater difference
between the quantity of heat which leaves the boiler
and the quantity which reaches the condenser than when
the steam is simply blown through the engine without,,
doing any work. In the latter case the greater part of
it reaches the condenser ; in the former case there was
less of it that reached the condenser more of it, in
fact, was put out of existence, or, to speak more cor-
rectly, more of it was converted into work done by the
engine during the operation.
But what I chiefly wish to impress upon you is that
D
50 THE EA RL Y HIS TOR Y OF EN ERG Y.
Seguin, although he went to work in a correct manner,
reasoned from an utterly unsound basis. His reason-
ing was of this kind, that when a body expands and
thereby becomes colder, it loses heat, and that the heat
so lost is necessarily the equivalent of the work done
during the expansion.
Another of the speculators on the dynamical theory
of heat, but who did not publish till 1842, three years
after Seguin, was Mayer, who in very many quarters
still gets the credit of being the real author of the
whole science of Energy, including Thermo-dynamics.
Mayer's speculation was based on precisely the con-
Averse of that of Seguin. Seguin said the amount of
work done by an expanding heated body is the equi-
valent of the heat which it loses. Mayer said the
amount of heat which is produced by compressing
a gas or any other body is the equivalent of the work
u spent in compressing it. You will see at once that these
two statements are precisely the same, only the one is
the converse of the other. If the one be true, the other
necessarily will be true also ; but both are a priori
assumptions, and we now know by experiment that
neither of them is true under any realisable circum-
stances whatever ; though in certain cases they are ap-
proximately true. Each of the two speculators, Seguin
and Mayer, tried to apply his hypothesis by calculation
to the properties of a particular substance. Seguin tried
steam, because he was more familiar with steam ; Mayer
tried air, because he had some physical data for it.
Seguin's calculations were very far wrong on the one side
of the truth ; Mayer's were very far wrong on the other
side of the truth ; but Mayer's substance, namely, air,
has been since experimentally proved by Joule to be
THE EARL Y HISTOR Y OF EN ERG Y. 5 1
capable of giving an almost exact result. Mayer by
chance, then, in the middle of his a priori speculations,
lit upon a method although he got it from a false
principle which Joule afterwards proved to be a good
one, and used as one of his modes of obtaining the
value of the dynamical equivalent of heat. Still, we
must give Mayer no credit for that, for although he laid
down his law quite generally, air was the only substance
he had data for, and he chose it on that account. But
even with this, his data were so bad that he got a result
as far from the truth as the one obtained by Seguin.
Only Seguin has this great credit, to which Mayer has
no claim, that, seeing that if heat be not matter, some
of it must disappear in the working of an engine, he
tried to measure the quantity of heat coming to the
condenser, in order to show that it was less than that
which left the boiler.
I find that I have now exhausted my time, and there-
fore I shall merely mention that, in my next lecture, I
shall take up the history of the theory of energy, as it
was developed by the sound methods of Colding and
Joule in papers published about 1843 \ an< ^ I shall then
endeavour, with the facilities which this room affords
me, to illustrate my explanation by a few experiments.
\Note to J^hird Edition. The last three or four pages have been left in
their original form, as expressing what was well known in 1874. But, of
late, attention has been called to the services of Mohr, whose date is prior
to that of Seguin, and still more so to that of Mayer. In the next lecture,
a notice of these services will be inserted. ]
LECTURE III.
ESTABLISHMENT OF THE CONSERVATION OF ENERGY.
Further inquiry into the asserted claims of Mayer. Opinions of Colding and
Joule on Mayer's first paper. [Insertion (1884) on the prior claims
of Mohr.] Colding's Experiments. Joule's Experiments. Numerical
value of the Dynamical Equivalent of Heat. Helmholtz's argument
from the Perpetual Motion. Transformation and Dissipation of
Energy. Illustrative experiments.
IN my last lecture I showed you in what state Newton
left the grand question of conservation of energy, what
an enormous step he took, and what was the sole great
difficulty remaining in his way. Then I showed you
how, in regard to the particular branch of it which we
call the dynamical theory of heat, Rumford and Davy
had, at the very end of last century, almost completely
settled the question that heat is not matter. A little
was wanting in the work ot each. Rumford wanted
only one small chemical experiment in addition to his
grand physical experiments. Davy wanted a little more
conclusive reasoning than he showed at the time. Had
one or other of these been furnished before the end of
the last century, it would have been to the last century
that we should have been indebted entirely for the
dynamical theory of heat. It was not, however, until
1812 that Davy applied correct reasoning to his experi-
ments, and obtained the correct deductions from them ;
and then he stated in a distinct form the important
THE CONSER VA T1ON OF EN ERG Y. 53
propositions that heat is motion, and that the laws of its
communication are precisely the same as the laws of
communication of motion. Then I showed you that
Seguin, although he was altogether wrong in his d priori
idea, had a true sense of what was really wanted to this
question, and that he made a correct, but unhappily
unsuccessful, experimental attempt to supply it. Then
we came to Mayer, a man who has, especially of late,
been persistently held up as the discoverer, not merely
of the dynamical theory of heat, but of the whole sub-
ject of conservation of energy. Of him, I may remark
because the question is one of importance though
at the present day we are hardly perhaps far enough
advanced in time calmly and dispassionately to consider
the relative claims of these authors ; still, I may remark
that a great deal of the eulogy which has been bestowed
upon Mayer is altogether undeserved, and that Joule
has even yet received far too little credit for the enor-
mous advances he made. In the first place, Mayer
was altogether wrong in his a priori idea. On that Sir
William Thomson and I made, in 1862, the following
remarks, which no one has ventured directly to challenge
in the slightest particular :
* Mayer's method is founded on the supposition that diminution
of the volume of a body implies an evolution or generation of heat ;
and it involves essentially a false analogy between the natural fall
of a body to the earth, and the condensation produced in an elastic
fluid by the application of external force. The hypothesis on which
he thus grounds a definite numerical estimate of the relation be-
tween the agencies here involved, is that the heat evolved when an
elastic fluid is compressed and kept cool, is simply the dynamical
equivalent of the work employed in compressing it. The experi-
mental investigations of subsequent naturalists have shown that
this hypothesis is altogether false for the generality of fluids, espe-
54 THE CONSER VA TION OF EN ERG Y.
cially liquids, and is at best only approximately true for air ;
whereas Mayer's statements imply its indiscriminate application
to all bodies in nature, whether gaseous, liquid, or solid, and show
no reason for choosing air for the application of the supposed prin-
ciple to calculation ; but that at the time he wrote, air was the only
body for which the requisite numerical data were known with any
approximation to accuracy.'
Then, in addition to these two absolute errors which
are mentioned in this passage, I may call attention to
the preposterous a priori principles upon which he
reasons. There are two of them ; the one is causa
cequat effectum, to which I have never been able to attach
any meaning, and the other ex nihilo nihil fit. These
may be a basis for scholastic disquisitions, such as the
celebrated old question of the number of angels that
can simultaneously dance on the point of a needle, but
they are altogether unfit for introduction in any shape
whatever into physical reasoning. Then, again, Mayer's
work was altogether destitute of experiment. He sug-
gests, no doubt, the carrying out, on a larger scale, an
experiment which he says he tried, namely, shaking
a little phial of water for a considerable time, to find
it at the end of the time warmer than it was at the com-
mencement : merely, I may say in passing, a bad sub-
stitute for a hint due to Rumford, that the churning of
water would be a good experimental method, I daresay
most of you will see that such an experiment as Mayer's,
unless proper precautions were taken to prevent con-
duction of heat from the hand to the bottle of water,
would very probably have resulted in the heating of the
water considerably, even without the shaking : so that,
in order to prove that the heat was due to the shaking,
we should have required at all events a statement
on Mayer's part of the precautions he had taken to
THE CONSER VA T1ON OF EN ERG Y. 5 5
prevent one known source of heat from affecting the
water. 1
But, in addition to this, Mayer did not even believe
that heat depends on motion ; and this is perhaps the
most wonderful comment that can be made upon the
consistency of those who, while constantly speaking of
heat as a ' mode of motion/ call him the discoverer of
the modern theory of heat. To effect this must surely
have involved (to use the vigorous and expressive
language of one of the most prominent popularisers of
science) the necessity of * wrangling resolutely with the
facts !' Mayer himself says, in his very earliest paper, and
he never afterwards to my knowledge modified this state-
ment (I translate freely), ' We might much rather assert
the opposite, that motion, whether it be a simple one or
a vibratory one like light, like radiant heat, and so
on must, in order to become heat, cease to be motion.'
He actually says it must cease to be motion in order to
become heat! Then he makes another and a very
curious statement, the absolute erroneousness of which
you will see in the course of another lecture. He says,
sneeringly : ' Let any one try to melt ice by pressure,
however enormous.' I shall show you that, as a con-
sequence of the second law of thermo-dynamics, the
melting of ice by pressure was predicted beforehand,
and was verified afterwards by actual experiment.
It is time, then, I say, that Mayer, even with our as
yet imperfect means of judging, should be ranged, so
far as we can, in his true place. He has been injudi-
ciously praised, and he has been an unfortunate man,
1 Even this experiment, but carried out with something like philo-
sophical precautions, was long before described.by Reade in Nicholson's
Journal, 1808, p. 113.
56 THE CONSER VA TION OF EN ERG Y.
and therefore, of course, there will be an outcry against
any one who undertakes the necessary task of pointing
out his real demerits. However, there is no such thing
in scientific history as the argumentum ad misericor-
diam. The blame, if any there be in such a matter, is
due to those who preposterously gave him credit for
what he did not do. The real merits of Mayer, how-
ever, which are extremely great, but which are in
danger of being forgotten or ignored in consequence of
the unwarrantable claims made for him, depend upon
his having, after getting a true theory by false reason-
ing from inadequate and sometimes inadmissible pre-
mises, reasoned rightly upon it, and developed it widely
in its applications. Language has lost all meaning,
however, if this can be called a claim to establishment
of the theory itself. The fact is that in 1839 Faraday,
and in 1841 Liebig, and about the same time others
of the great philosophers who have lately died, made
close approaches to the true theory by methods far
more sound than those of either Mayer or Seguin ; and
yet, curiously enough, they have scarcely at any hand
got the slightest recognition. 1
The true modern originators and experimental demon-
strators of the conservation of energy in its generality
were undoubtedly Colding of Copenhagen and Joule of
Manchester. It is interesting to see in what light these
men regard Mayer and some others of those who pre-
ceded them. I shall presently give you a quotation or
two bearing on that point.
In the meantime I may say, with regard to Colding, 2
that he began by being metaphysical, but saw at once,
1 See Phil. Mag. 1864, II. p. 474; 1865, I. p. 217 ; and 1876, II. p. no.
a See his very interesting letter, Phil. Mag. Jan. 1864.
THE CONSERVATION OF ENERGY. 57
or very soon, that metaphysics was not the proper
basis on which to found a search for physical facts.
His metaphysics led him to form certain opinions, but
before publishing one of them he set to work and
laboriously brought it to the test of fact. Joule, on the
other hand, seems to have begun by experimenting
with the view of determining certain physical constants.
He does not tell us whether he had any metaphysical
opinion about their relations or not. He set to work
experimenting, and it was only after a great and varied
series of his experiments had been fully carried out, and
valuable results obtained, that he began to make cer-
tain applications of metaphysical reasoning to the con-
nections which he had discovered. He did not apply
metaphysics to discover anything, but to try and
co-ordinate with other things the discoveries he had
already made. Colding's work is by no means so exten-
sive as Joule's. It is very nearly simultaneous with
it, but it is neither so exact nor so extensive. Still,
although Colding is hardly to be compared with Joule,
he stands enormously high in comparison with any of
the others who had experimented up to that time upon
the conservation of energy. I will read you one or two
extracts from Colding, and you will see from them how
properly he went to work. He says :
' It was in accordance with this idea that I twenty years ago pre-
sented to the Royal Society of Science here in Copenhagen, a trea-
tise in which I explained my idea that force is imperishable and
immortal ; and, therefore, when and wherever force seems to vanish
in performing certain mechanical, chemical, or other work, the force
then merely undergoes a transformation and reappears in a new
form, but of the original amount as an active force.
* In the year 1843 tms idea, which completely constitutes the new
principle of the perpetuity of energy, was distinctly given by me,
58 THE CONSER VA TION OF EN ERG Y.
the idea itself having been clear to my own mind nearly four years
before, when it arose at once in my mind by studying LfAlemberfs
celebrated and successful enunciation of the principle of active and
lost forces j but of course the new principle was not as clear to me
from the beginning as it was when I wrote my treatise in
1843-'
I may here parenthetically observe that Colding
speaks of D'Alembert's celebrated and successful enun-
tiation of a certain principle. This is nothing more or
less than a particular case of that principle of Newton,
which I gave you in a former lecture j 1 so that you see
Colding really got his idea suggested to him by New-
ton's work :
r ' According to the view which led me to this principle, its future
importance, in case it were really true, was perfectly clear to me
from the first instant. But this made me very anxious not to pub-
lish it as a new law of nature until I should be able to give experi-
mental proof of its truth ; and scientific men to whom I explained
my idea, and especially our celebrated professor, H. C. (Ersted,
agreed with me and advised me to be safe in this respect before I
wrote ; and it was for this reason that I departed from my original
intention of explaining it to a meeting of Natural Philosophers held
>,_in Copenhagen in 1840.
' In my first treatise, of 1843, the title of which is " Theses con-
cerning Force " (Nogle S&tninger om Krcefterne\ I therefore not
only presented my idea to the Royal Society (of Copenhagen) as a
thing that most likely would hereafter be found to be a general law
of nature, but, after stating that the only trustworthy decision of
the question was to be got from the experimental investigation of
nature itself, I went on to call attention to several old experi-
ments made previously to my time, the first of which was Dulong's
celebrated discovery respecting the heat disengaged or absorbed
during the compression or expansion of a great number of different
airs and gases, and I then showed how perfectly these experi-
ments proved the truth of the said principle for bodies of that
d.'
Ante, p. 33. See Thomson and Tail's Natural Philosophy, 264.
THE CONSER VA TION OF EN ERG Y. 59
Then he goes on to say that having established the
proposition for elastic fluids, he proceeded to try ex-
periments in conjunction with QErsted upon the com-
pression of water ; and that next he advanced, just as
Joule did about the same time, to experiments upon
the compression of solids. He also says :
' I closed my discussion by showing that the discovery of a
perpetuum mobile would be possible if my principle was wrong.'
This shows that, to a certain extent at least, he had
anticipated Helmholtz, of whose great services to this
branch of science I shall presently speak.
The remarks he makes about Mayer deserve to be
quoted. He desires the republication, in an English
journal, of his first paper, in order that it might be com-
pared, as he says, with the paper of Mayer, which
was most loudly vaunted in England at the time when
his letter was written :
' I need scarcely say that such a comparison would be of great
interest to me, as I believe it would convince your readers of the
fact that M. Mayer wrote his remarks in 1842, before he was able
to support them by a single experiment or by anything like a proof
of their exactness, whilst I thought it to be my duty, before I wrote,
to prove that my suppositions concerning the forces were confirmed
by nature itself, as a law of nature. 3
He also says of his own experimental approximation
to the dynamical equivalent of heat, that it is
'very near the proportion that M. Mayer in 1842 supposed, but
did not prove, to be right.'
Joule's remarks 1 upon the subject of Seguin and Mayer
are also deserving of quotation :
' Seguin gives data from which the mechanical equivalent of heat
may be readily deduced on his hypothesis, the result being too
1 Phil. Mag. 1864, II. p. 151 ; see also 1862, II. p. 121.
60 THE CONSER VA TION OF EN ERG Y.
great in consequence of the thermal effect of the compression of
vapour being understated. Neither in Se"guin's writings of 1839,
nor in Mayer's paper of 1842, were there such proofs of the hypo-
thesis advanced as were sufficient to cause it to be admitted into
science without further inquiry. I believe that the experiment
attributed to Gay-Lussac was not referred to by Mayer previously
H:o the year 1845. Mayer appears to have hastened to publish his
views for the express purpose of securing priority. He did not
wait until he had the opportunity of supporting them by facts.
My course, on the contrary, was to publish only such theories as
I had established by experiments calculated to commend them to
the scientific public, being well convinced of the truth of Sir
J. Herschel's remark, that "hasty generalisation is the bane of
i science."'
To these it would be easy to add several even more
telling passages to the same effect.
[In 1876 my attention was called to a paper by
Mohr (Journal fur Pharmacie), of which I published a
translation in the Phil. Mag. for August of that year.
The date of the paper is 1837, or ^ ve years before
Mayer, and it contains, in a considerably superior form,
almost all that is correct in Mayer's paper. Though it
contains many mistakes, it avoids some of the worst
errors of Mayer, especially his false analogy and his
a priori reasoning. The very process (for determining
the mechanical equivalent of heat from the two specific
heats of air) for which Mayer has been so extravagantly
lauded : although it is in principle, albeit not in
practice, utterly erroneous : is here stated much more
! clearly than it was stated five years later by Mayer.
In December 1877, I received by post a copy of a
work Allgemeine Theorie der Bewegung imd Kraft, etc.
(Braunschweig 1869), with the inscription, in a bold hand,
' dedicated by the author, Dr. Mohr.' This work is con-
clusive against Mayer's first paper. It leaves absolutely
THE CONSER VA TION OF EN ERG Y. 6 1
nothing to him save his blunders. For it contains a
reprint of an article by Mohr, published in 1837 in
Baumgartner* s und v. Holger's Zeitschrift fiir Physik (of
which the paper above alluded to was, it seems, a mere
resume). One sentence, only, need be extracted from
this article (which ought certainly to be translated into
English verbatim) to show how definitely in 1837 Mohr
put into words a clear statement of the truth which
Mayer vainly attempted to express clearly five years
later.
'Ausser den bekannten 54 chemischen Elementen
gibt es in der Natur der Dinge nur noch ein Agens, und
dieses heisst Kraft: es kann unter den passenden
Verhaltnissen als Bewegung, chemische Affinitat, Co-
hasion, Electricitat, Licht, Warme und Magnetismus
hervortreten, und aus jeder dieser Erscheinungsarten
konnen alle ubrigen hervorgebracht werden. Dieselbe
Kraft, welche den Hammer hebt, kann, wenn sie anders
angewendet wird, jede der ubrigen Erscheinungen her-
vorbringen.'
This notable article did not obtain insertion in
Poggendorff's Annalen, to which it was first sent. One
of the earliest and most valuable of Joule's papers met
a similar fate at the hands of the Royal Society]
Having said this much with regard to the relative
merits of these men, and having shown you that Joule
is far the foremost, while Colding is the only one who
deserves mention in comparison with him, so far as the
present part of our subject is concerned, I proceed to give
a rough general statement of what Joule really did, and
then you will see what enormous advances he made
within a few years from 1840. Joule, in 1840, published" 1
his first paper, which was with reference to the heat
62 THE CONSERVATION OF ENERGY.
produced by electric currents under various circum-
stances. He was led by these experiments to see that
there must be some relation between the heat produced
and the quantity of zinc consumed in the battery ; thus,
as it were, eliminating the mysterious agent, electricity,
altogether from the final result. The novelty and value
of this idea can hardly now be realised by us. Then,
again, Faraday's grand discovery of induced currents
suggested to Joule the measurement of the amount of
mechanical work we require to spend in order to pro-
duce a given amount of electric current, which in its
turn shall be frittered down into a given amount of heat.
We should thereby have, as it were, not an immediate
conversion of work into heat, as in the case of friction
(which appears at least at first sight to give an imme-
diate transformation from work into heat), but we should
have a mediate transformation by induction of currents
we should transform the work of driving the mag-
neto-electric machine into the energy of so much
electric current, and then let that again turn itself
into heat You have first the work, then the electric
currents, and finally the heat. Now, Joule seems to
have observed that the same amount of heat was
produced from this amount of work, whether the
work was first employed in producing electricity, and
then the electricity employed in producing heat, or
whether the work was simply spent directly in produc-
ing heat by friction ; and from that time he began to
experiment, with the view of determining exactly what
is the mechanical equivalent of heat, because he saw
that unless it were certain, experimentally, that in all
cases of friction, where there is nothing but heat to show
for the work that has been spent unless there could
THE CONSERVATION OF ENERGY. 63
always be found the same amount of heat for the same
amount of work, whatever were the bodies which were
made to rub against each other unless something of
that kind could be established, it would be vain to seek
for any such thing as conservation of energy, or even for
the much lower and in fact mere particular case of the
equivalence between heat and work. If work and heat
be equivalent in any sense, and if you spend work
wholly in producing heat, you must get always the same
amount of heat for the same amount of work, whatever
be the nature of the engine which you employ. I may
parenthetically remark (as it gives an inkling of what is
to follow) that it is quite another question when you
come to the conversion of heat into work ; when it comes
to be a question of beginning with the heat, and con-
verting that into work, the conversion cannot be wholly
accomplished. Begin with work, and you can convert it
all into heat. Begin with heat, and you cannot convert
it all into work. The one case is perfectly definite, and
therefore Joule, reasoning upon it, virtually said : ' If
there be nothing but heat to show for a certain amount
of work spent, then unless we always get, with every
apparatus, the same amount of heat for the same amount
of work, conservation cannot possibly hold.' He proved
that this equivalence does subsist ; and his determination,
finally published with all his latest improvements in
1849, was 772 foot-pounds for a unit of heat ; that is to
say, a pound of water which has fallen 772 feet, and had
the whole of the energy of its fall, or the whole excess of
potential energy which it had before falling, converted
into heat, will simply be I deg. Fahr. hotter than it was
before it fell. As I pointed out to you in my last lec-
ture, Rumford's estimate was considerably above that ;
64 THE CONSER VA TION OF EN ERG Y.
but it was confessedly only an estimate, while Joule's
was the final result of an extended and laborious series
of experiments. This leads us then to the statement
of what is called the First Law of Thermo-dynamics.
It may be put in very many forms, but I shall take the
form which seems to be the most effective. The first
law of thermo-dynamics, then, really established by
Davy and Rumford, but altogether neglected and for-
gotten, re-established by Joule and supplied by him
with a definite numerical datum, for the purpose of cal-
culation, may be put in this form :
When equal quantities of mechanical effect are pro-
duced by any means whatever, from purely thermal
sources, or lost in purely thermal effects, then equal quan-
tities of heat are put out of existence or are generated :
and for every unit of heat measured by the raising of a
pound of water I deg. Fahr. in temperature, you have to
expend 772 foot-pounds of work.
It is possible that that last figure of the 772, which is
for the latitude of Manchester, may be wrong. The
true number may be, for instance, 771*5 or 772^5, or
something of that kind, but there is little doubt that
Joule's determination is at all events considerably within
one per cent, of the truth. It is particularly noteworthy
that in 1843, from the heat developed by the friction of
water in narrow tubes, Joule had given 770 foot-pounds
as the mechanical equivalent. 1
In addition to all this, Joule gave an experimental
extension of the principle of conservation to other forms
of energy, that is to say, in addition to heat he enabled
us to take current electricity, electro-magnetism, etc.,
into the same category. In fact, even in 1840, before
i Phil. Mag. 1843, II.
THE CONSERVATION OF ENERGY. 65
he had come to definite conclusions as to the generality
of the principle of conservation, he had established ex-
perimentally a grand series of particular cases of it ; and
one of the most remarkable was this :
When any voltaic arrangement, whether simple or compound,
passes a current of electricity through any substance, whether an
electrolyte or not, the total voltaic heat which is generated in any
time, is proportional to the number of atoms which are electro-
lysed in each cell of the circuit, multiplied by the virtual intensity
of the battery. l
Therefore, even at that -early time, his experiments (and
his reasoning was entirely based ^jpon experiment)
had led him to this conclusion, that 'whenever some-
thing that was imponderable disappeared, and there
appeared some other imponderable which could have
no other origin, then the quantity of the one was
directly proportional to the quantity of the other, and
the ratio between these two had only to be determined
by accurate measurement in order that you might
know the mechanical equivalent of so much current
electricity, or of so much heat, or even of the poten-
tial energy of so much zinc and dihite sulphuric acid,
or of any other substances in a state fit for chemical
combination.
Another most valuable experimental research of
Joule's bears on the question of the mechanical value
of Light?' He compared the heat evolved in the wire
conducting a galvanic current, when the wire was ignited
by the passage of the current, with that evolved when
(with an equal current, suppose) it was kept cool by im-
1 Phil. Mag. 1841, II. p. 275. Paper read before the Royal Society,
December 17, 1840.
z Phil. Mag. 1843, I. p. 207.
E
66 THE CONSER VA TION OF ENERG Y.
mersion in water. These experiments showed a small,
but unmistakeable, diminution of the heat when light
also was given out. However, all that was necessary
in order to extend the principle of conservation to light
was to show that light, like heat, electric currents, and
so on, is a form of energy and not a form of matter ; in
other words, to establish what is called the undulatory
theory instead of the corpuscular theory.
I may digress for a little to say a word or two as to
how that was done. It is one of the important advances
made within the period to which my lectures chiefly
refer. 1 It was established in France by Fizeau and
Foucault, working originally by independent processes,
but afterwards working together. The proposition then
to be decided upon is : Does light, as it comes to us from
the sun, for instance, consist in the transference of par-
ticles of something luminiferous ? Is it matter, in fact,
which is shot out from the sun ? or is it a propagation
of disturbance of some kind or other which may be
assimilated, for purposes of illustration, to wave-motion ?
Is it, in short, a propagation of energy in some form
or other, whether wave-motion or not, or is it a
propagation of matter ? Now, Newton and Huyghens
had, long ago, each from his own point of view, assigned
1 I am aware that many excellent authorities attribute the establishment
of the undulatory theory to Young and Fresnel saying that interference
as in the phenomena of diffraction, etc. , had, in their hands, completely
upset the corpuscular theory. But, as a fact, some of the more noted
supporters of that theory (including Biot) were not convinced by these
experiments, but were led to make further modifications of their favourite
theory, while there can be little doubt that they would have accepted
Fizeau and Foucault's results as decisive against them. Of course, such
a statement as this in no way impugns the value of the magnificent work
done by Young and by Fresnel.
THE CONSER VA TION OF ENERG Y. 67
the means of perfectly settling this question. Newton,
in fact, had shown that if light be matter, then, on
being refracted into a dense body, it will move more
nearly in a direction perpendicular to the surface,
provided it move faster in the dense body than in the
rare one outside. That is to say, that, since we know
that an oblique ray of light falling upon the surface of
water, for instance, which is denser than the air, is
refracted more nearly to the vertical, Newton had
mathematically demonstrated that if light consist of
particles, it must move faster in water than in air.
Huyghens, on the other hand, showed that if light consist
of wave-motion, and be refracted towards the vertical,
at the horizontal surface of a dense body such as water,
then its velocity in the dense body must be less than its
velocity in the rare body. Thus there was a distinc-
tion of the most marked character between the two
theories. If therefore you can discover by experiment
whether the velocity of light is greater or less in water
than in air, you settle for ever the question whether
light consists in the propagation of matter or in the
propagation of motion or energy. Now the experiments
separately made by Fizeau and Foucault both gave the
result, that in water light moves slower than in air, and
therefore it necessarily followed that light is a form of
energy.
So far, then, we have come to the complete establish-
ment experimentally of the classification of the impon-
derables under the head of energy, and we have arrived
at a general notion of relations of equivalence between
them. The mere fact of conservation, of course, at once
establishes that there must be relations of equivalence.
So much of the one is equivalent to so much of the
68 THE CONSERVATION OF ENERGY.
other, provided you can effect the conversion of the one
into the other. Of course it will always, or at least for
a very long time, remain an extremely difficult problem
to measure the equivalent of an amount of light. Still,
it has been approximated to, and, among other processes,
in this way : Light, when absorbed by an opaque body,
is found to make the opaque body hotter. Here is an
example of the principle of conservation. The energy
of the light is not destroyed, but its vibratory motion
cannot pass through this opaque body as light. It is
employed in agitating the particles of the opaque body,
and that body becomes hotter in consequence. We can
measure, then, the quantity of light in terms of the heat
which it produces, or to which it is equivalent, and then
we can measure that quantity of heat in terms of
mechanical work, so that, as Sir William Thomson did
many years ago, shortly after Joule's discoveries appeared
in print, we can calculate what he calls the mechanical
value of a cubic mile of sunlight ; we can calculate how
many foot-pounds of work are equivalent to the sunlight
which a cubic mile of the earth's atmosphere, filled with
direct sunlight, has in consequence of that luminous
energy which is passing through it at the instant.
Before I leave for the moment the subject of the con-
servation of energy, I must .speak of one additional
name in connection with its discovery and early develop-
ment, that of Helmholtz, the great physiologist of Berlin,
who has now, at least nominally, ceased to be a physio-
logist, but who remains one of the foremost of living
mathematicians and natural philosophers. One of his
early works was published in 1847, shortly after Joule
and Colding had published their discoveries. It seems,
however, that he was barely acquainted with the writings
THE CONSERVATION OF ENERGY. 69
of either, but had set to work himself, from a mathe-
matical point of view, to settle the principle of conserva-
tion of energy. In fact, the German title of his book is
precisely an equivalent to our English phrase ' conserva-
tion of energy.' He based the principle upon one or
other of two propositions, and it is interesting in the
highest degree to consider what these propositions are,
and to see how a man who was fully acquainted with the
whole science of the time looked at a subject of this sort,
and pointed out in what direction experiment ought to
be turned in order to verify the conclusions of theory.
He says, in effect, that if you take Newton's principle
the principle you have already heard [p. 33]- i -and if you
combine it with one or other of the two following postu-
lates, you will establish completely the conservation of
energy. The first postulate is : Let us suppose matter
to consist of ultimate particles which exert on each other
forces whose directions are those of the lines joining each
pair of particles, and whose amounts depend simply on
the distances between the particles. Suppose, in fact,
that something akin to gravitation-force exists amongst
all the particles of matter in the universe, that each
particle attracts every other particle with a force which
depends only upon the distance between them, not in
any way upon the sides which are turned to one another,
so that if you know the distance between them you
know the amount of the attraction, and that the attrac-
tion shall also be (in accordance with Newton's Third
Law of Motion) in the direction of the line joining them.
If you make that assumption, then it is a mere con-
sequence of the ordinary laws of motion of gross matter
that, if all forms of energy depend upon motion or
position of such particles, the conservation of energy
70 THE CONSER VA TION OF ENERG Y.
must hold, and also that the so-called perpetual motion
would be impossible under any circumstances.
As an alternative, Helmholtz shows that we may take
as our postulate this consequence of the first postulate.
Take the impossibility of the so-called perpetual motion
as a postulate, and take along with it Newton's grand
statement of his second interpretation of the Third Law
of Motion, these two together would, by themselves,
enable you to prove the principle of conservation of
energy. Now it had for many years back been an
accepted matter among men of science (as typified by
the long-since announced determination of the French
Academy to consider as not having readied it, any paper
whatever upon the perpetual motion), it had been
accepted by men of science, I say, almost universally
that experiment had conclusively demonstrated the
perpetual motion to be impossible. So Helmholtz, by
showing that if you simply begin with that experimental
fact, and take in addition to it Newton's statement,
you can establish the conservation of energy, had
made, independently of Joule and Colding, a dis-
covery of this great principle for himself. You will
notice that he did, almost as distinctly as either Joule
or Colding, insist upon the necessity of experiment for
the establishment of such a principle, but he brought in
his experiment in the form of an universally accepted
result of the experiments of others, namely, the im-
possibility of the perpetual motion, while they preferred
to make perhaps more direct experiments for themselves.
I shall have occasion to say a word or two more about
the so-called perpetual motion, because it has really
been for natural philosophy and it remains even to
this day as important in its influences, especially in
S)
THE CONSER VA TION OF EN ERG Y. 7 1
aiding us to simple proofs of important theorems, as, for
instance, the notion of alchemy has been in chemistry.
We all know that if there had not been a pursuit after
the philosopher's stone, chemistry could not yet have
been anything like the gigantic science it now is. In
the same way, we can say that modern physics could
not yet have covered the ground it now occupies had
it not been for this experimental seeking for the so-
called perpetual motion, and the consequent establish-
ment of a definite and scientifically useful negative.
We notice, then, as a deduction from what I have just
explained about the work of these three independent dis-
coverers of conservation of energy, that all physical phe-
nomena are necessarily transformations of energy of some
kind or other ; and we may carry our deduction so far as
to say that even that mysterious thing, whatever it may
be, the life of plants and animals, is, so far as it is
physical, entirely an exhibition of transformations of
energy. There are things connected even with life
which may not be purely physical. There are other
things associated with living beings which, of course, no
one in his senses can regard as physical. Even such
things as Consciousness and Volition we have abso-
lutely no reason, however vague, for classifying, even in
the smallest degree, under the head of physics. But
everything which is really physical in life and we are
beginning to find many things that are so is merely
an example of some form of transformation of energy.
Having said so much, it will be obvious to you that
our proper course now will be to consider the principle
of transformations, and then inquire in what direction we
must seek for more light. We shall find that the ques-
tion which is suggested by all these tentative experi-
72 THE CONSERVATION OF ENERGY.
ments is, What is the law of transformation of energy ?
From a given quantity of a given kind of energy, how
much of another assigned kind of energy can be pro-
duced by a given process ?
This question breaks up into two. The first is,
How much of a given kind of energy can be trans-
formed into some other given kind ? And then there
is a second question : When you have got so much of
it transformed, to how much of the other kind will it
correspond ? That is the question of equivalence again.
I have already discussed that, so I confine myself now
to the first question. The first question fully stated
is : Given a certain quantity of energy in one form and
under given conditions, how much of it can you, by
means of a given kind of apparatus, convert into some
other definitely assigned form, the rest being either
untransformed, or transformed in whole or in part into
some third form ? Now, you will see at a glance that
there is something very important under this. Just think
for a moment of the enormous amount of waste which
is known to take place in an, ordinary steam-engine.
In the very best engine, even if it were theoretically per-
fect, and working at ordinary ranges of temperature, it
has been satisfactorily demonstrated that only some-
where about one-fourth very rarely so much as that,
but at the best about one-fourth of the heat which is
actually employed is converted into work ; that is to say,
three-fourths of the coals, or three-fourths of the heat
employed, are absolutely wasted under the most favour-
able circumstances. Now, what is it that determines
this ? Why is it that if I have a quantity of work or
potential energy I can convert the whole of it, if I
please, into heat ; but when I have got it converted into
THE CONSER VA TION OF ENERG Y. 73
heat, I cannot convert the heat back again, except in
part, into the higher form of work or potential energy ?
The answer is included entirely in that word ' higher!
which I have just used. When you are converting energy
from the high form into the low, you can carry out
the process in its entirety, but when it comes to be a
question of the reversal going up-hill as it were then
it is only a fraction, in general (even under the most
favourable circumstances) only a small fraction, of the
lower kind of energy which can be raised up again into
the higher form. All the rest sinks down still lower in
the process. When you have got it low already, and
when you are to elevate part of it and transform it into
a higher order, you must inevitably still further degrade
a large part of it ; in general the larger part of it.
This, as we shall find later, is one of the most impor-
tant scientific discoveries ever made : having most
stupendous bearing on the future of the whole visible
Universe.
I shall conclude this lecture by showing some
examples of conservation of energy with the apparatus
before me. I shall necessarily at the same time give
some illustrations of transformation of energy, inde-
pendent altogether of the particular physical experi-
ments which are employed for the purpose. I am
merely giving you these experiments as illustrating
conservation of energy, and incidentally, in addition,
transformation and dissipation 'of energy, so that we
are not concerning ourselves with what is the branch
of physical science to which any particular experiments
belong, but simply with how far the experimental results
help to illustrate the transformation.
Take, then, first of all, the simplest form the case of
74 THE CONSER VA TION OF ENERG Y.
an ordinary pendulum. When the pendulum is vibrating,
there is constantly going on transformation of energy of
the very simplest kind transformation from the poten-
tial form which I give it by drawing it aside (and there-
fore lifting it), and which it gradually loses as it falls
back, getting more and more kinetic energy instead, until
at the middle of its course, when it is moving fastest,
it has its greatest amount of kinetic energy, having lost
for an instant all its potential energy. Then it gra-
dually loses the kinetic energy as it is climbing up
again, and regaining potential energy, then the energy
is all potential, then it becomes kinetic again, and so on.
Of course if there were no air-resistance, and if the stand
itself were absolutely rigid, and the cord supporting the
mass flexible and inextensible, this process would go on
absolutely for ever. It would be perpetual motion, but
it would not be the perpetual motion. Remember the
distinction there. Perpetual motion is simply a state-
ment of Newton's First Law of Motion. All motion
is perpetual until force interferes to alter or modify it.
But this is not the perpetual motion, because, although
under the favourable circumstances I spoke of just now,
the pendulum would remain for ever moving with the
same quantity of energy it has at present, yet it could
not help you to drive machinery, except at the expense
of that energy. It cannot drive anything else without
losing part of its own energy, and when that occurs, the
case does not come under the head of what is called the
perpetual motion, although, when there is no drain upon
it, it may be a perpetual motion.
Now, as we know by experience that this vibration
will not go on for ever, let us consider why it is that its
energy is gradually being lost. What becomes and,
THE CONSERVATION OF ENERGY. 75
according to the principle of conservation of energy, we
ought to be able to trace it what becomes of all the
energy I gave it at first ? Well, we see in a short time
that it is communicating motion to the air around it ;
every time that it vibrates backwards and forwards
it sends alternately a wave of compression and one of
dilatation through the air of the room. These waves do
not sufficiently rapidly succeed one another to produce
an impression upon our sense of hearing, but they are
sufficient to agitate the air of the room. They are pro-
pagated through the air of the room with the velocity of
sound, and they are gradually frittered down into heat
because air is not a perfect fluid. Because then there
is something producing effects akin to those of friction
amongst its particles, these waves are gradually rubbed
down into heat, and if we had a sufficient number of
such pendulums set into vibration to begin with, and
all sufficiently resisted by the air, we should be able to
warm the air of the room, no doubt to an extremely
small extent, but still so that the quantity of heat
produced should be precisely equivalent to the quantity
of energy which you had communicated to the pen-
dulums at starting. But then this suggests another
question. At present the pendulum, hanging at rest,
has no potential energy, that is, if the string cannot be
cut. It has at present potential energy if you can cut
the string, because it will drop on the table, or at least
it will have the power of falling. But suppose the
string is absolutely inextensible, and cannot be cut, then
we must consider it in this position as having no poten-
tial energy at all, because it cannot get down any lower
than it is at present. How is it, then, that I can give it
energy ? because if there be conservation of energy, and
76 THE CONSERVATION OF ENERGY.
if we so put it that it has none to begin with, and it gets
some, there must be some other energy spent in com-
municating it. Now, that leads us to the grand con-
sideration of the source of animal energy, because, by
pressing the pendulum with my hand, and thus elevat-
ing it, I must have done work, for I have exerted a
pressure through a certain space. Work has been done,
and therefore something has been expended in my body
for the purpose of producing it. This raises the ques-
tion of how the animal supplies the work ; and the
further one, in what form does the animal get the work
supplied to it, which it is constantly giving out even
when in repose ? Of course you can at once see that it
must be in some way or other connected with food.
That, then, will lead us, in another lecture, back to the
consideration of whence the food derives its energy, and
so on in succession. So you see that even so simple an
experiment as setting this pendulum in vibration leads
us to a train of consequences, both back and forward,
in reasoning, which might well occupy us for a whole
series of lectures. Nothing is better calculated to show
at once the profundity of Nature's secrets, and the firm
grasp we have already taken of some of them, than an
example like this so simple and yet so complex.
Instead of taking the case where the motion of the
air is not capable of being perceived by the ear, let us
take a case in which we use a special instrument for the
purpose of communicating vibrations to the air in such
a form that the ear can seize them. If I were to take
this tuning-fork and strike it against the table, or start
it in any of the ordinary ways, and it were not provided
with this sounding-board, the amount of surface which
it presents to the air is so slight that the amount of
THE CONSER VA TION OF EN ERG Y. 77
energy which it would spend in a given time in the form
of sound would be exceedingly small ; and therefore
the sound would be hardly audible at any considerable
distance. But when we furnish it with a resonant
cavity, as it is called, such as this, every part of which
is set in vibration by the motion of the fork in exactly
the same period as the fork ; and when, moreover, the
dimensions of this cavity containing air are exactly
adjusted, so that when it is set in vibration, it tends to
vibrate in exactly the same time as the fork, then we
have got a sensitive apparatus which enables us, as it
were, to lay hold^of the air, and to dissipate or spend at
a very great rate the energy which we give to the fork.
The pendulum here spends it at a very slow rate, but in
this fork we have applied our knowledge of physics
so to construct an apparatus as to make it spend its
energy or communicate it to the air as rapidly as pos-
sible. We have it now in the form of sound affecting
our ears, but you will notice that the sound gradually
dies away. The vibrations of the tuning-fork die away
far faster than those of the pendulum, because if you
will give out the energy at a great rate, the original
stock can last only for a short time. The greater the
rate at which you give it out, the shorter the time for
which it will last. But there is another cause in this
case for the very speedy cessation of the sound. The
greater part of the energy which I gave to the tuning-
fork by muscular work done in forcing these prongs
asunder for a moment, the greater part of that energy
is spent in heating the body of the fork itself. Steel-
however startling this may appear to some of you is
exceedingly imperfect in its elasticity. When a steel
bar, such as this, is rapidly changing its form, there is
78 THE CONSER VA TION OF ENERG Y.
an enormous amount of internal friction, and thus is
consumed a great part of the energy which is given to
it, so that only a part of the energy originally communi-
cated is given back in the form of sound, even with the
help of the resonant cavity.
To take another instance. I have got a galvanic
battery under the table, and it is connected with a
certain electrical apparatus. Now, whenever I allow
the electric current to pass through this apparatus,
there is for the moment a certain quantity of zinc con-
sumed, or, as we may put it, a certain quantity of
potential energy in the battery has been converted into
the kinetic energy of a current of electricity. That
current of electricity passes round some yards of copper
wire, coiled round a bar of iron or a number of fine
iron wires which are standing vertically inside this
apparatus. The moment the current passes, these iron
wires are converted into magnets, but, in consequence
of the conservation of energy, while this is going on
they weaken the current. The current of electricity
becomes weaker in the act of making the magnet,
but the moment the magnet springs into existence it
again is weakened, because, from the necessities of
its position, its mere coming into existence necessitates
the passage of a new current of electricity in another
coil of wire which surrounds this externally. So that
here are a number of transformations : First, we have
a certain amount of zinc dissolved, i.e. a certain amount
of potential energy lost ; then a certain current of
electricity produced in consequence ; then that current
of electricity weakened by producing magnetism in
certain iron wires ; then the magnetism of these iron
wires re-acted upon to produce a new current in
THE CONSER VA TION OF EN ERG Y. 79
another set of wires ; and finally, we can use that
induced current, as it is called, to produce heat, or light,
or sound. Let us try it, for instance, in such a form as to
produce heat. Every time you hear that click [of the
contact-breaker], a fresh amount of zinc has been dis-
solved, and in consequence that series of transforma-
tions I have just described has taken place. You will
notice that the zinc is burning, though without almost
any development of heat, in the battery, but we can
have the fire wherever we please. We have no heat, at
least nothing to speak of, in the battery. The heat that
would be produced by the dissolving of the zinc is not
developed inside the battery at all ; if we had a couple
of Atlantic cables here, between the battery and this
apparatus, we should be able to produce it at a distance
of 3000 miles from the place where the fire burned. In
order to show that heat is produced largely in such a
case as this, my assistant will hold a piece of paper
between the poles. [You see it is at once ignited.]
You will notice that the burning of the zinc is below
the table, but it might have taken place 3000 miles off
if we had had good enough conductors. There you see
it has at once produced a development of heat sufficient
to inflame the paper. Now, I may easily alter this in
a striking manner. Use the same amount of zinc as
before, or as nearly as possible the same amount of zinc,
but instead of the spark being a quiet one, make it
noisy and luminous, as you see is easily done by attach-
ing the coatings of a Leyden jar to the ends of the
secondary coil. Then we shall find that it is not so hot
as before (at least so far as the paper test can inform
us). Of course it could not be expected to be so hot,
because, if conservation of energy be there, and if there
8o THE CONSERVATION OF ENERGY.
is a certain quantity only of energy that the spark can
have, and if it be made to spend the greater part of
that energy as sound and light, you cannot expect it to
have as much heat as before. You see it now im-
mensely brighter than before, and accompanied by a
sharp crack, but we might go on with the experiment
indefinitely, and never set the paper on fire.
This is a very excellent instance of multifold trans-
formations, and furnishes also, as you have seen, a rough
illustration of conservation.
LECTURE IV.
TRANSFORMATION OF ENERGY.
Experimental Illustrations Heating of wires, and decomposition of water, by
a Galvanic current Electro-magnetic Engine Rotating Disc Magneto-
electric Machine Induction-Coil and Geissler Tube Higher and Lower
Forms of Energy. Work transformed wholly into Heat Only a portion
of the Heat can be reconverted into Work. Carnot's Cycle of Operations
and his Reversible Cycle. Effect of pressure upon Ice.
IN my last lecture I showed you how, mainly by
Joule's grand experiments, it had been conclusively
demonstrated that conservation holds for every form of
energy, and therefore that all physical phenomena con-
sist in mere transformations of energy. There cannot
be a destruction or creation of energy. All that we
can have is a modification or transformation of it ; and
therefore we must to-day consider more fully the laws
of such transformation. I shall begin the consideration
of them by taking one or two experiments, and point-
ing out in each of them the various forms in which the
energy appears, how it was first introduced into the
apparatus, under what successive forms it passed through
the various parts of the apparatus, and in what final
forms it was thrown out.
Galvanic Battery with stout copper terminals. The
first and simplest experiment of this kind is the pro-
duction of heat directly by chemical combination. As
in all or most of the experiments I am about to show,
F
82 TRA NSFORMA TION OF ENERG Y.
I intend to begin with a galvanic battery, I may say a
word or two as to the form in which its energy appears.
The energy in the battery consists mainly in the fact
that we have zinc which is capable of being burned,
as it were, by being dissolved in dilute sulphuric acid.
Now, if we were to burn the zinc, as can easily be done
by simply allowing it to dissolve (that is, by not taking
the precautions we have here taken against its dissolv-
ing without permission in the sulphuric acid), we should,
simply in consequence of the potential energy which is
lost by the zinc and the acid when they combine, have
a certain amount of heat generated by their combina-
tion, and this would be developed in the cell of the
battery. But instead of permitting this, we can cause
the combination to take place without almost any
development of heat. We can have practically all of
it in the form of some other manifestation of energy.
We can have it in the form, for instance, of current elec-
tricity ; and we can employ the kinetic energy of that
current for the purpose of producing various other forms
of energy by suitable transformations. In consequence
of the amalgamation of the zinc, and the other precau-
tions taken in the cells of the battery, very little com-
bination goes on in this battery until the circuit is
closed, as it is called ; but as soon as we close the
circuit, by joining together the terminal wires, a current
of electricity passes. A current of electricity is now
passing through the circuit, and chemical action (both
decomposition and combination) is going on to exactly
the same extent in every one of the cells. But the
chemical action now going on is attended with the
development of a large quantity of heat in the cells,
almost precisely the same amount of heat as would have
TRANSFORMA TION OF ENERG Y. 83
been developed if we had dissolved the same quantity
of zinc in the sulphuric acid without any production of
electricity at all ; the reason being that the conducting
power of this wire which I have for the moment used to
close or complete the circuit is so great that the small
resistance it offers to the electricity scarcely fritters any of
the electricity down into heat. The heat which is equi-
valent to what would be produced by the direct burn-
ing of the zinc, is all or almost all produced in the cells
themselves, because it is in them that the current suffers
resistance. But if I interpose in the path of the elec-
tricity an imperfect conductor, which shall resist a great
deal more than the copper wire, or even than the cells
themselves (as I do by inserting in the circuit a long
fine iron wire), then you notice that we get the heat (which
is really due to the chemical action taking place in the
cells), we get that heat produced in another locality
altogether, and we could have transferred that locality
as far away as we pleased, if we had simply made our
copper wires thick enough and long enough. By simply
making them Jhiqk enough, so as to waste as little as
possible~6Tthe kinetic energy of the current electricity,
by friction" on" tHe way, we should have kept it all or
nearly all for the purpose of developing as far as we
please from the battery the heat really due to the com-
bustion there.
Voltameter introduced in circuit. Instead of using
the current electricity for the purpose of producing
heat, let us endeavour to ascend again from the kinetic
energy of the current to potential energy of combus-
tibles. Remember that it was the chemical potential
energy of combustibles which we had in the battery to
begin with. By allowing the zinc to dissolve, we got
84 TRANSFORMA TION OF ENERG Y.
our current electricity, and now we shall use that cur-
rent for pulling asunder two substances in chemical
combination. We shall use it simply for the purpose
of decomposing water. By causing the current to pass
through a vessel of water, you notice that we cause
bubbles of gas in large quantities to ascend from the
ends of the conducting wires ; and we have the kinetic
energy of the current spent entirely, or almost entirely,
in pulling asunder, against their chemical attraction, the
particles of oxygen and hydrogen which form the water.
You see that a quantity of the water is being decom-
posed, for you see how the gas is bubbling up through
the water from the end of this collecting tube. Now,
supposing there to have been no loss during the opera-
tion no frittering down of the electricity into heat
but that the whole energy of the electric current has
been spent in decomposing the water, then the potential
energy of the separated oxygen and hydrogen which I
collect in this way should be precisely equivalent to the
amount of potential energy which was consumed in the
battery, or rather was there transformed into the energy
of the current. In order to show (with as little risk as
possible) that there is a large amount of potential energy
in these mixed gases, all we have to do is to employ
them to produce froth in the form of a multitude of
small soap-bubbles blown with the mixture. By apply-
ing a lighted match, we shall be able to produce from the
potential energy of the mixed gases a violent explosion,
which of course represents a certain amount of energy.
That explosion gives you light, heat, and a very loud
sound. The sum of all these energies taken together,
provided nothing has been lost during the process
that nothing has been frittered away (by breakage of
TRANSFORMA TION OF ENERG Y. 85
the mortar, for instance) will represent precisely the
amount of energy corresponding to the amount of zinc
which has been dissolved during the operation. You
notice that here we have now in another form and a
form which affects the air more than any of the other
forms of energy we have used the energy which ought
to have been developed in the form of heat by the
combustion of the zinc, but was not, because we had
electricity in the place of it ; then, in place of that elec-
tricity, we had work done in overcoming the chemical
attraction of oxygen for hydrogen ; then we had the
mixed gases, which as soon as we pulled the trigger, as
it were, by applying the lighted match, gave us back
our energy in another kinetic form, or as a mixture of
several kinetic forms.
Electro-magnetic Engine. You had in the voltameter
current electricity produced by the battery, and em-
ployed for the purpose of producing potential energy, by
separating the particles of a chemical compound. But
we can produce potential energy by the help of a battery
by another and somewhat simpler method. Suppose
we employ the current of electricity produced by the
same battery, for the purpose of setting an electro-mag-
netic engine at work. (We are not at present concerned
with the details of construction of the engine.) For this
purpose we do not (at least with the engine before you)
require anything like so powerful a battery as we used
for the rapid decomposition of water. Two, or at most
three, cells will be sufficient for our present purpose.
You notice that the current is now producing motion of
machinery, and has actually raised a weight not by
any means a great one, but still the fact remains that a
certain mass has been raised against the earth's attrac-
86 TRANSFORMA TION OF EN ERG Y.
tion to a certain height above its surface ; and you can
easily see that, if the experiment succeeds through a
space of three or four feet, as it has- now done, it would
equally succeed (if we kept the engine working long
enough) in enabling us to raise the weight, by proper
mechanical adjustments, to any height whatever. Now,
let us consider what transformation of energy took place
as the current of electricity passed round these electro-
magnets, being shunted now into one of them and then
off it and into the next ; into each when its becoming a
magnet will aid the desired effect ; off it when it would
tend to hinder it. This is a mere detail of mechanical
arrangement, and is effected by different combinations
of machinery in different electro-magnetic engines. But
we are not concerned with details of machinery ; we
confine ourselves to the transformations of energy which
are going on during the working of the engine. But
from this point of view what takes place here ? The
energy of the current is to a certain extent converted
into the raising of weights ; that is to say, potential
energy is produced in place of the kinetic energy
which was supplied from the battery ; but if the current
not only drives this machinery but keeps it doing work,
then there would not be conservation of energy unless
the current itself were kept at a reduced strength, at
least while it is in the act of doing work. Now, that is
what is found to take place. It is found that while the
engine is working, the current is considerably feebler
than it is if we were simply to stop the engine, and
allow the current to pass without doing any work. This
is quite analogous to the case I pointed out to you in
a former lecture. When a given quantity of steam is
blown through the engine from the boiler into the con-
TRANSFORMA TION OF ENERG Y. 87
denser without doing any work, we find that the quan-
tity of heat which goes into the condenser is larger than
the quantity of heat which goes into it while the engine
is doing work. In precisely the same way, then, while
the current of electricity is employed in actually lifting
a weight, or in driving an electro-magnetic engine, the
current which is passing along the wire is feebler than
before, and corresponds, according to a great discovery
of Faraday's, to a less amount of chemical combination
(that is, a less rapid consumption of zinc) in the battery.
The battery has really less hard work, while driving this
electro-magnetic engine, than it would have if we were
simply to stop the engine and allow the current to pass
and develop heat in the conducting wires and cells. It
must do something. The current of electricity always
fritters itself down into heat in time, unless you utilise
it and change it into a form of energy more useful than
heat. But what we find is this, that, though there must
of course always be a current passing : or else these
iron horse-shoes would not successively become electro-
magnets the current is very much weaker when the
engine is doing work than when it is not. And it is also
found that the weaker the current becomes (the more
the current is checked by reflex action, as it were, by
the resistance it meets with in doing work), the greater
is the percentage of the amount of energy really spent in
the battery which is finally converted into useful work.
Thus, in order to get an electro-magnetic engine of this
kind to do work on a large scale and at a profitable
rate, it would be necessary to drive it with enormous
rapidity ; for the faster it is driven the greater is the
reaction upon the current, and therefore the more is
the current enfeebled, and the greater the percentage
TRANSFORMATION OF ENERGY.
of the driving power which is utilised. And the laws
discovered by Faraday and Joule respectively viz.,
that the strength of the current is directly as the quantity
of zinc dissolved per second, and that the heat developed
is directly as the square of the strength of the current,
show that the efficiency of the engine is directly pro-
portional to the weakening of the current. The more
the engine weakens the current by reaction, the greater
is the fraction of the whole amount of fuel spent which
is converted into useful work.
Many of you are doubtless practically much better
acquainted with the subject I am now to mention than
I am, and therefore I shall only briefly state that, even
if we could succeed in making an engine of this kind
work at a very great speed, and thereby obtain the
highest efficiency possible ; and if we could, for the
purpose of keeping up such a speed, almost wholly
get over the difficulties of ordinary friction, which of
course become far greater and more serious as the
rapidity of the working of the engine increases, even
if all this could be done, still, if we calculate the cost of
the fuel here, we shall find that such an engine could
never economically compete with an ordinary steam-
engine, because of the fact that in order to smelt a quan-
tity of zinc, an expenditure of about sixty times its
weight in coal is required ; while, weight for weight, the
coal is far the more powerful fuel, i.e. loses far more
potential energy in being burned ; and therefore of
course there can be no comparison between the prices
of the fuel in the two cases, if the same ultimate amount
of work is done.
Copper disc with multiplying gear. The next case I
take is a very curious one. I have got here an arrange-
TRANSFORM A TION OF ENERG Y, 89
ment (never mind the details) consisting of a driving
wheel and multiplying gear, by which I can communi-
cate an extremely great velocity of rotation to this
copper disc, which is mounted as freely as possible upon
well-oiled and well-supported axles. It is, in fact, easily
driven at a rate of somewhere about a couple of hun-
dred turns per second, if we work the driving handle at
the rate of about two turns per second. The disc con-
sists of a highly conducting material copper, and it is
placed between two pieces of iron which do not touch
it, but come very near it. These pieces of iron form
part of the armature of a small electro-magnet. Now,
the coils of this electro-magnet have at present no
current passing through them, and I find that, as you
see, there is nothing more easy than to set the disc in
very rapid motion indeed. You notice that when I
remove my hand, the inertia of the wheel-work is such
that the whole goes on turning for a very considerable
time. Now notice what the effect will be if, while I am
driving it, my assistant suddenly throws the current,
even from three cells of a battery, round the electro-
magnet. Then I shall be endeavouring to drive the
copper disc in the immediate neighbourhood of a strong
north pole on the one side of it, and an equally strong
south pole on the other. Although there is no contact
nothing of what we ordinarily call friction you will
see that this acts exactly like a friction brake of very
great power. There ; you observe the instantaneous
stoppage, and you also see that, strive as I may, I can
scarcely move' the driving handle. With such battery
power as that, it is utterly impossible for any one man
to drive the disc fast ; it would require perhaps four or
five persons to force it to rotate at even a very moderate
90 TRANSFORMA TION OF ENERG Y.
speed. If I put on a single cell instead of three, you see
that by great exertions I manage to keep the disc
rotating at a slow rate for a short time ; but it is only
by the expenditure of a very considerable amount of
labour. I could keep it going perhaps for a few minutes,
but there is no necessity for pushing the trial further.
Now comes the question, What have we to show for
this ? What necessitates the extraordinary amount of
effort that is required in order to keep the disc turning
in the magnetic field ? In order that you may see this
experiment in another and perhaps a clearer light, I
shall take advantage of the fact that, as you saw a little
ago, the machinery is capable by its inertia, if once set
rapidly in motion, of going on for a considerable time
before the motion finally dies out. I start it again, with
the same rapidity as before, and you see the almost in-
stantaneous collapse as soon as the circuit is closed.
We have in fact a friction brake acting without contact,
and to force that disc to move rapidly in the neighbour-
hood of the magnet requires an enormous expenditure
of work. Now comes the question, Where does this
work go to ? Suppose that in spite of this enormous
resistance to the motion of the disc, we were to expend
work in turning it. The answer must simply be this, that
the whole, or almost the whole of the work so spent
goes to heat the disc : and that, simply by persistently
turning it under these circumstances, you can make the
copper absolutely red-hot, and, in fact, melt it, if the
experiment is carried on far enough, without any con-
tact whatever with the iron of the electro-magnet. The
mode in which this heat is produced is also very inter-
esting. It depends upon induced currents, one of Fara-
day's great discoveries. Faraday discovered, as I daresay
TRANSFORMA TION OF EN ERG Y. 9 1
you are all aware, so long ago as 1831, that when a con-
ducting body is made to move in the neighbourhood
of a magnet, the relative motion of the two produces
currents of electricity in the conductor. Now, when a
current of electricity is once produced, we have seen
that unless it be diverted to produce work, or potential
energy, or some other form of energy, it always in time
fritters itself down into heat. If, then, you keep this
copper disc moving in the neighbourhood of the magnet,
the faster it moves the stronger are the currents pro-
duced in it ; and as there is no appliance here to collect
these currents, so as to utilise them for any other pur-
pose, the currents must fritter themselves away into
heat in the copper disc itself. A permanent magnet
would have precisely the same effect as our electro-
magnet the only reason for using an electro-magnet
being that it is so easy to magnetise and demagnetise
the soft iron, i.e. virtually to present or withdraw the
magnet by the mere making or breaking of contact of
two wires. The currents which are generated in the
disc, are in such a direction as always to be attracted
by the magnet ; or, as it may be more scientifically
put, in the words of Lenz, the mutual action between
the magnet, and the currents generated by the relative
motion of the conductor, always tends to diminish that
relative motion. Hence the work constantly required
to maintain the rotation of the disc.
Magneto-electric Machine. Now, still further to illus-
trate this part of the subject, I may refer to this magneto-
electric engine, which was devised to take advantage of
Faraday's discovery just mentioned. Here are a couple
of coils of wire with iron cores, which are to be made to
move in presence of a bundle of steel magnets. Here
92 - TRANSFORMATION OF ENERGY.
we have, in a somewhat different shape, the essential
features of the engine I have just been using. We apply
a certain amount of mechanical work, in order to move
these coils in the presence of the poles of the magnets ;
and thus have currents developed in them as we had
them developed a little ago in the simple copper disc.
I am now about to collect these currents for the pur-
pose of producing light, instead of allowing them to be
frittered down into heat, as in the former apparatus ;
and you see that we produce a brilliant spark by
simply expending mechanical power or work upon the
driving handle, without any battery, without any electro-
magnet, or anything of that kind. By simply forcing
the conductor to move in presence of the steel magnets,
we can develop currents strong enough to produce that
brilliant spark. Of course with this little machine the
light is on a very small scale, but the engine is acting
on precisely the same principle as the magneto-electric
machines, driven by steam-power, which have been
recently employed with great effect for the purpose of
lighthouse illumination.
Induction Coil with Geissler-tube containing highly
rarefied Carbonic Acid. There is only one other illus-
trative experiment connected with these to which I
shall now advert, and that is another mode of convert-
ing work or potential energy into light ; that is, by
means of an induction coil, as it is called. I am using
with it the battery I have hitherto been employing.
We produce a current of electricity by means of it ; we
magnetise a bundle of iron wires by the help of that
current ; then we break the circuit and stop the current,
and the iron wires cease to be magnets. At the instant
that they cease to be magnetic they are virtually, as it
TRANSFORMATION OF ENERGY. 93
were, suddenly pulled away to an infinite distance. Now,
this coil (consisting of a very long conducting wirf^ is in
the immediate neighbourhood of the bundle of iron wires.
When they become magnetic, it is as if a powerful magnet
were suddenly inserted in the coil. When they cease to
be magnetic, it is as if the magnet were instantaneously
withdrawn. In either of these cases, we have the
development of an electric current in the conducting
coil. Now, instead of driving that current through a
very small space of common air, as I did in the case of
the magneto-electric machine, I will drive it through a
considerable length of the contents of a highly exhausted
receiver. I do this for a particular reason, which will
appear as soon as we have got the room darkened.
You now notice the exquisite luminous effect produced
by resistance : but observe especially this peculiarity
about it, that it remains persistent for a certain time
after the discharge has been interrupted. You see at
once that the discharge has ceased, by the disappearance
of the purple and the blue light near the ends of the
tube ; while the olive green light which is in the wider
parts of the apparatus remains for a time visible, and
gradually dies away. It has scarcely yet, as it were,
cooled. It presents, except as to colour, exactly the
appearance of a heated body cooling. This remark-
able effect then, though due primarily of course to the
current, gives us a curious instance of a body which,
when agitated by the passage of the current, can convert
its energy into light, and part with it in that form. There
is in fact scarcely any radiation of dark heat from that
glowing and cooling body. I interpolated that experi-
ment just now, not because it has any direct connection
(except as to the exciting cause, the battery) with what
94 TRANSFORMA TION OF ENERG Y.
we have had before, and shall have immediately after it ;
but because I had the apparatus ready, and it was as
well to show the experiment while it was at hand.
In all these cases you will have noticed that there
has been a transformation sometimes many transfor-
mations in succession ; but there is one law of nature
which we notice in the case of all these transformations.
Some kinds of energy are of a higher order than others,
and if you begin with one of the higher orders, you can
get from it any of the others, and in general you can
transform almost the whole of it into any of the others
you please ; but when you begin with one of the lower
forms, the reversal of the process is attended by extra-
ordinary difficulties. The lines
. . . facilis descensus Averno ;
noctes atque dies patet atri janua Ditis :
sed revocare gradum, superasque evadere ad auras,
hoc opus, hie labor . . .
seem almost to have been written by one who antici-
pated our knowledge of the laws of the transformation
of energy.
We come then to the question of the raising of
energy from lower to higher forms, which is the only
one which presents much difficulty ; and if we thoroughly
understand upon what conditions the utmost transforma-
tion of heat into work depends, and how it is that at best
only a small fraction of a given quantity of heat can,
under the most favourable circumstances, be converted
into work, then we shall have no difficulty whatever in
seeing that laws of a similar kind, although not perhaps
precisely the same, must hold for every other transfor-
mation from one form of energy to a second, espe-
cially if the second be the higher form of the two. Now,
TRANSFORMATION OF ENERGY. 95
the ordinary conversion of work into heat you may see
illustrated in the most direct form in manifold ways.
Savages, for instance, procure a light by rubbing two
pieces of dry wood together, or still better by using a
piece of hard wood to bore a hole in a soft piece. Any
of us can effect that operation, and set the pieces of
wood on fire, by applying long enough and with suffi-
cient rapidity and pressure a sort of drilling motion. It
is quite easy, by the expenditure of a little mechanical
energy, to set fire to both pieces of wood. That is
merely of course an improvement upon the apparatus
used by the savage. When we stir or churn, or any-
how rapidly agitate a mass of water, we find that
the amount of work we spend upon it is at first con-
verted into actual or kinetic energy of the moving water.
You see it rotating round as you stir the vessel ; but if
you leave it to itself, you see that its rotation gradually
slackens until it comes finally to rest. In such a case, it
is found that the whole of the work spent upon the
water has been ultimately converted into heat. When-
ever you apply work to the production of heat by
friction, you have an apparatus perfect enough to get
the whole of the work transformed into heat. It may be
that part of the energy is originally not in the form of
motion, as when part of the surface of. rotating water
is raised above its mean level, but this potential energy
also gets frittered down into heat by degrees. It may
be also that, even in ordinary friction, even in such a case
as the friction of sand-paper against a piece of wood, the
first thing produced by the friction, or rather by the work
spent in friction, consists of electric currents in the im-
mediate neighbourhood of the place where the rubbing
is effected. We have something very similar to that,
96 TRANSFORMATION OF ENERGY.
although on a more delicate scale, in the case of an
ordinary friction electrical machine. There is no doubt
that the electricity there is produced by something very
closely resembling ordinary friction, although it may be
something intermediate between it and contact ; but this
leads us to the supposition that it may be possible that
in many cases of what appears to us to be downright
friction, perhaps even (as Sir W. Thomson says) when
actually carried to the extent of abrasion of particles of
the two bodies which are rubbed on one another, there
may be, first of all, the production of electric currents
to a certain extent, and that these currents may be
almost immediately frittered down into heat by the
resistance or bad conducting power of the two rubbing
bodies ; so that in such cases work spent in friction
may not immediately produce heat But there is no
question whatever that whether heat be immediately
produced or whether it is produced mediately, through
electric currents, we can convert the whole of the amount
of work spent in friction into heat.
Then in the same way we know that, by hammering
a horse-shoe or other small piece of iron on an anvil, a
skilful smith can without much trouble raise it to a dark
red heat. The work spent in producing these im-
pacts is almost entirely converted into heat, and this
mainly in the piece of iron to which he applies his
blows. And you will see something of the same kind,
though on a grander scale, in artillery practice. When-
ever the huge projectiles of the modern great guns have
been employed for the purpose of penetrating armour
plates, though a great part of their energy has no doubt
been spent in actually penetrating the thick iron plate,
yet at the same time there is an immense flash of light,
TRANSFORMA TION OF ENERG Y. 97
accompanied by heat and various gases produced from
the two metals by actual fusion and evaporation, all
taking place at the instant of the impact, and corre-
sponding to portions of the work transformed. In these
cases, then, there is no difficulty whatever in getting the
work converted directly into heat.
But we now come to the question how to get heatj ;
converted into work, and here our difficulties begin.
Even in the best steam-engine, we cannot convert into
useful forms more than between one-fourth and one-third
of the heat which is employed.
In treating of this subject, I must introduce an ad-
vance in scientific method which was not known to men
of science till within the last thirty years, although it
was published in 1824; the great work of Sadi Carnot,
a work of which it is impossible to speak in suffi-
ciently high terms in such a series of lectures as I am
giving. I need only say that without this work of Car-
not's, the modern theory of energy, and especially that
branch of it, which is at present by far the most im-
portant in practice, the dynamical theory of heat, could
never have attained in so few years its now enormous
development. Carnot's claims to recognition are of an
exceedingly high order, because they depend not merely
upon his method : which is one of startling novelty and
originality, and is not confined to the subject of heat
alone : but upon the fundamental principle on which he
based his mode of comparing the heat employed with
the work procured from it. Every reasoner (who has
applied himself to the subject of heat since Carnot) has
gone right, so far as he attended to Carnot's principle,
but has inevitably gone wrong, when he forgot or did
not attend to it. The fundamental blunders of Seguin
G
98 TRANSFORM A TION OF ENERG Y.
and Mayer and various others whose admitted claims
I have pointed out in a former lecture are almost
entirely due to their ignoring the great principle laid
down by Carnot so early as 1824.
Carnot's work is upon the Motive Power of Heat. It
forms no inconsiderable portion of Sir W. Thomson's
many scientific claims that he recognised at the right
moment the full merits of this all but forgotten volume,
and recalled the attention of scientific men to it in 1848 ;
pointing out, among other things, that it enabled us to
give, for the first time, an absolute definition of Tempera-
ture. Although Carnot (seemingly against his own con-
victions) 1 reasons on the assumption that heat is matter,
and therefore indestructible ; and although, in conse-
quence, some of his investigations are not quite exact,
his work is of inestimable value, because it has fur-
nished us, not only with a correct basis on which to
reason but, with a physical method of extraordinary
novelty and power, which enables us at once to apply
mathematical reasoning to all questions of this kind.
These then are his two great claims, first, the setting
thermo-dynamics upon a proper physical and experi-
mental basis ; and, second, in the furnishing us with a
means of reasoning upon it which was absolutely new in
mathematical physics, and which has been, not merely
in Carnot's hands, but in the hands of a great many of
his successors, as fruitful in new discoveries as the idea
of the conservation of energy itself.
1 [Note to Third Edition. Since the publication of the last edition of
this work Carnot's posthumous papers have been issued, along with a
reprint of his great work. They indicate an amount of insight into the
true theory, and the proper modes of experiment, truly marvellous even
in comparison with the grand advances made in that work itself.]
TRANSFORMA TION OF ENERG Y. 99
Now, these two grand things which Carnot intro-
duced, which were entirely originated by him, and
which left him in an almost perfect form, were the
idea of a Cycle of Operations, and the further idea of a
Reversible Cycle.
In order to reason upon the working of a heat-engine
(suppose it for simplicity a steam-engine), you must
imagine a set of operations, such that at the end of the
series you bring the steam or water back to the exact
state in which you had it at starting. That is what
Carnot calls a cycle of operations, and of it Carnot says,
then, and only then, i.e. at the conclusion of the cycle,
are you entitled to reason upon the relation between
the work which you have acquired, and the heat which
you have spent in acquiring it. If you were to take,
as Seguin proposed, a quantity of steam, and merely
allow it to expand, giving out heat in the process and
doing work, you have no right whatever to say that
the quantity of heat which has disappeared is the
equivalent of the work which you have got, because at
the end of the operation the steam is in a different state
as to pressure and temperature from that in which it
was at the beginning. It was saturated steam at a
certain temperature, let us say, to start with, but at the
end of the operation it may still, if you make proper
adjustments, be saturated steam, but it is necessarily at
a different temperature, and therefore you cannot tell
whether or not it possesses intrinsically the same amount
of energy as it did in its former state. You have no
right whatever to reason upon the quantity of heat
which appears to have gone, as compared with the work
which has been done, when your working substance
begins in one state and ends in another. But if you
ioo TRANSFORMA TION OF ENERG Y.
can by any process bring your working substance back
to its initial state, then you are entitled to assert that, as
it has returned to its initial state, it must contain neither
more nor less energy than it did at first, and therefore
of course you are also entitled to reason upon all the
external things that have taken place during the
operation, and to determine the condition of equivalence
among them. You now see how completely unscientific
was Seguin's reasoning, though his work was published
fifteen years after that of Carnot. A similar remark of
course applies to Mayer, who was the greater, because
the later, sinner in this matter.
The other grand point with reference to Carnot is
this, that he started the notion of a Reversible Engine,
reversible not in the ordinary technical sense of work-
ing its parts backwards, not in the mere sense of back-
ing, but reversible in the sense that, instead of using heat
and getting work from it, you can drive your engine
through your cycle the other way round, and by taking
in work, pump back heat (as it were) from the condenser
to the boiler again, a reversing of the whole process,
not a mere reversing of the direction in which the engine
is driving. Now, Carnot introduced that notion, and
he showed by perfectly conclusive reasoning that if you
can obtain a reversible engine, it is the perfect engine,
i.e. that it is impossible to get an engine more perfect
than a reversible one reversible being taken in the sense
in which I have just explained it. We see at once what
an enormous step is gained, supposing we can establish
that second principle, because, as you will presently find,
we can settle the conditions of reversibility altogether
independently of the nature of the working substance in
our engine. You see then that we are not now bound
TRANSFORMA TION OF ENERG Y. 101
down to a steam-engine, or any one working substance.
We are enabled now to state our conclusions in terms,
not of the particular engine but, of the circumstances
in which the engine works. All perfect engines that
is, all reversible engines will do exactly the same
amount of work with the same amount of heat, pro-
vided their boilers and their condensers be at the same
temperatures, and therefore you can define the relation
between the whole amount of heat which enters the
engine and the utmost amount of it which can be con-
verted into work, and this altogether independently of
the particular engine, but solely and simply in terms of
the temperature of the boiler and the temperature of
the condenser. These, then, are the grand claims which
Carnot has in Thermodynamic Science.
Now, in order to make it intelligible how we can
have a reversible engine at all, in this sense, it will
be necessary for me to go through a series of ima-
ginary operations explanatory of the nature of Carnot's
reasoning. Besides, if you once thoroughly understand
this, it gives the key to an enormous number of new
physical facts and properties of matter which, before
we learned from Carnot the correct method of rea-
soning, we might well have despaired of ever being
able to understand, at least in their true physical inter-
dependency.
Digression. Beam of ice, supported horizontally at the
ends, with a fine wire, stretched by weights, hung over it.
Before I go into a description of it, however, I may call
your attention to an experiment which has been going on
for some time in your presence, and whose result, in one
of its many forms, was first predicted from those very
principles of Carnot's. What is its direct connection
102 TRANSFORMA TION OF ENERG Y.
with them I shall explain in another lecture. In the
meantime, the experiment is nothing more than this :
Take a block or bar of ice, supported horizontally : lay
over it a fine wire, and append equal weights to the two
ends of the wire. The wire, as you notice, has gradu-
ally, by the action of the weights, sliced through the
bar of ice, and there are two such slices of which you
can see the planes through the slab by the distortion of
the air bubbles. The wire has actually passed through
the ice in two planes parallel to one another, and yet
the ice is now probably stronger at these two places
where it has been cut than at any other place through-
out the block. The statement of observed fact is, that
as the wire was forced by the weights into the ice, the
pressure melted the ice, making it colder, so that the
water produced, passing round the chilled wire, and
being thus relieved from pressure, froze again. Still the
ice goes on melting in front of the wire, in consequence
of the pressure, and the water formed continually trickles
round it and freezes again. In that way the ice-block
is reunited, and you would see no trace whatever of this
interruption of it were it not for the fact that this
particular mass of ice was originally full of air bubbles,
and some of these bubbles having been permitted to
escape during the passage of the wire, have left a trans-
parent stratum which shows you where each section has
been cut. Ice, in fact, being a substance which melts
under sufficient pressure, behaves absolutely like a
viscous or plastic substance, for it melts (and contracts)
wherever the pressure is sufficiently great, thereby
handing on the pressure to another part, and in so
doing becoming solid again in its new form. Thus
Forbes' Viscous Theory of Glacier-Motion, propounded
TRANSFORMA TION OF ENERG Y. 103
in 1843 as a statement of observed facts, is seen to be
but the necessary consequence of a remarkable physical
property of ice.
Now, come to the consideration of this method of
Carnot's. I take an ideal engine, because that is quite
sufficient for the purpose of our reasoning. If our rea-
soning be correct, it is only a question of greater com-
plexity to apply it to an engine of a more elaborate
character. Suppose then we have the cylinder of a steam-
engine we shall dispense with the boiler altogether,
because we shall, for the sake of simplicity, always
make the cylinder its own boiler. Let us have in the
cylinder a small quantity of water, and the piston pressed
down so as to be nearly in contact with it. Suppose,
then, that our piston and the sides of our cylinder are
absolutely impervious to heat. That is another thing
we cannot realise, but it will have important bearings
when we come to consider what are the conditions of
the reversibility of an engine. We shall find in fact
that any loss of heat by conduction through the sides
of the cylinder is fatal to the reversibility of the engine ;
but for all that, in our theoretical reasoning we assume
that the sides of the cylinder and the piston itself are
perfect non-conductors of heat. We also assume that the
bottom of the cylinder is a perfect conductor of heat.
These of course are all suppositions which cannot be
realised in practice, but they serve to give us a conceiv-
able and extremely simple engine to theorise upon.
Suppose, then, we have three stands, on any one of which
I may place this cylinder. The first of them I call A,
the second B, and the middle one C. Now, suppose A
to be a body which has a certain defined temperature,
S, which is to be the temperature of the boiler. This
104 . TRANSFORMA TION OF ENERG Y.
body A is supposed to be constantly supplied with heat,
so as always to be kept up (whatever happens) to that
particular temperature. Then, B, which is to be used
as the condenser, is to be kept constantly at a definite
temperature T, lower than the temperature, S, of A.
The third body is to be used merely for the theory of
the operation ; it has really no effect itself. It is simply
a non-conductor of heat ; it is in fact a sort of second
bottom to be put upon the cylinder when it is not
placed either upon the boiler or the condenser. Now,
we can commence our operations in any order with this
apparatus. The way in which Carnot did it is perhaps
not the simplest, but it is historically the more im-
portant. We will commence, then, by setting the whole
of this apparatus upon the hot body. The effect of
this, as the bottom of the cylinder is a perfect con-
ductor, is that the hot body begins at once to part with
heat to the water inside, under the piston. The water
then rises to the temperature 5, and steam begins to
form above it. This steam is limited in quantity by
the space which is afforded for it, and by the tempera-
ture of the body. When as much steam has been
formed as is consistent with these conditions, it is called
saturated steam corresponding to the temperature S.
Now suppose that, when things are in that condition,
we allow the steam to expand or the piston to rise
(the atmospheric pressure above the piston being easily
neutralised by a counterpoise, especially in an imaginary
engine), we could employ it to raise weights or do work
of some kind or other externally. As it rises notice
what takes place. The temperature remains the same
as before, but more space is afforded for the formation
of steam, and therefore more steam is formed, so that
TRANSFORMA TION OF EN ERG Y. 1 05
you go on keeping up saturated steam at the pressure
corresponding to the temperature, S, of the boiler. As >
more steam is formed, more work is done, and more
heat is absorbed from the boiler, because latent heat
is required for the new steam as it is formed. Then,
while things are in that condition the piston having
risen say midway up the cylinder put the whole upon
the body C. No heat can get into the cylinder now,
nor can any escape, for the contents are now completely
surrounded by non-conducting bodies. Ih that state,
however, the contents have still the temperature of the
boiler. Let them still further expand, they will still do
work, because fresh steam is formed, but the contents
will become colder because of the latent heat required.
Let them go on expanding and doing work until they
cool down to the temperature, T> of the condenser, and
then, while they are in that state, shift the whole to the
condenser. There will obviously be no transference of
heat. While things are in that condition, suppose we
spend work in forcing down the piston a certain way.
In doing so we compress the steam, and the contents
tend to become hotter, but cannot^ do so, because this
body of temperature T is in contact with them ; so that
part of the steam condenses, and the latent heat which it
gives out is transferred to the cold body.
With regard to the amount by which you must push
down the piston during this part of the operation, Carnot
said : Push it so far that you give out to the condenser
exactly the same amount of heat as you had taken from
the boiler during the first stage of the expansion. That
statement, however, is incorrect, and requires modifica-
tion, because Carnot argued on the assumption that
heat is indestructible.
1 06 TRA NSFORMA TION OF EN ERG V.
Bearing in mind Carnot's notion of a cycle, we
see that the amount by which the piston is to be
depressed while the whole stands on the condenser, is
to be determined by the condition that when the
whole is finally placed on the impervious stand, and
the piston pressed home, the temperature of the con-
tents shall be raised to 5, the temperature of the
boiler. [This complete rectification of Carnot's cycle
was given by James Thomson in 1849.] If this be
effected, we can transfer the cylinder to the body A,
and everything is in the condition from which we
started, so that the operation may be repeated as often
as we please.
LECTURE V.
TRANSFORMATION OF HEAT INTO WORK.
Carnot's Cycle continued. Watt's Diagram of Energy. The Impossibility
of the Perpetual Motion is an experimental truth. Conditions of Reversi-
bility. Absolute definition of Temperature. Second Law of Thermo-
dynamics. Absolute zero of temperature, or temperature of a body
devoid of heat. Efficiency of the best steam-engine. Effect of pressure
on the freezing point of water. Mechanism of Glacier motion.
You will remember that at the close of my last
lecture I had just given a sketch of the first part of the
reasoning of Carnot the most important reasoning that
has ever been introduced into the treatment of any part
of the dynamical theory of heat. I may briefly recapi-
tulate (but in a somewhat improved form) what I then
said, in order that there may be no break of continuity.
The nature of the hypothetical operation which Car-
not introduced for the purpose of reasoning on this
subject, and only for that purpose, is of this kind. He
said Let us have a hot body which is constantly
maintained at a certain temperature. Let us have a
cold body which is also constantly maintained at a
definite temperature lower than the first. Then let us
suppose that in addition to these we have a body which,
as regards other bodies, is neither cold nor hot, for the
simple reason that it is incapable of absorbing heat or
of giving it out, a body which is a non-conductor of
heat. Then commence your series of operations, not
as I did (after Carnot) in my last lecture, but with the
io8 TRANSFORMATION OF HEAT INTO WORK.
non-conductor. Suppose your cylinder and your piston
to be non-conductors, but the bottom of the cylinder
a perfect conductor. If you have a quantity of water
and steam in the cylinder, both at the temperature of
(u the cold body, and expend work in pressing down the
piston, the contents will become warmer, and some
steam will be liquefied. 1 Continue this process till the
temperature rises to that of the hot body then transfer
the cylinder to it!~ONow allow the piston to rise, the
contents remaining at the temperature of the hot body,
fresh steam is generated, and work is done. Arrest
this process at any stage and transfer the cylinder to
the non-conducting body. .- If we now allow the contents
further to expand, more work is done, but the tempera-
ture gradually sinks. Continue this till the temperature
falls to that of the cold body, to which, therefore, with-
out loss or gain of heat, it may now be transferred.
y Next apply work to compress it at the constant tem-
perature of the cold body till (by condensation) the
contents have become exactly as they were at starting.
The cylinder may now be transferred to the non-con-
ducting stand, and everything is as it was at first save
that some heat was taken from the hot body in the
second operation, and heat was given to the cold body
during the fourth. Also it is evident that more work
has been done during the second and third operations
than was spent in the first and fourth, for the tempera-
ture, and therefore the pressure, of the contents were
1 \Note to Third Edition. This statement requires limitation, in order
to avoid complications not alluded to in the text. If there be too small a
quantity of water, as compared with the steam, pressure will vaporise some
of the water, instead of, as is assumed in the text, condensing some of the'
steam. See Tait's HEAT, 391.]
TRANSFORMA TION OF HE A T INTO WORK. 109
greater during the expansion than during the com-
pression. Of course you can go over this operation as
many times as you please.
Notice particularly what the peculiarity of the opera-
tion is. You must always have the steam or expanding
substance, whatever it is, for air or anything else would
do equally well, in contact with bodies at its own
temperature, or else with non-conducting bodies. If it
were in contact with a body which was not at its own
temperature, there would be a waste of heat. Heat
would pass by conduction from the cylinder to external
bodies, and would of course be wasted as regards work.
The same would happen if we were to take it from,
let us say, the non-conducting body and place it upon
the cold body, before we had let it expand far enough
to cool down to the temperature of the cold body : we
should have some heat conducted away at once without
having any good from it. So, throughout the whole of
Carnot's operation, it is essential that there should be
no direct transfer of heat at all except while heat is
being taken in from the hot body or given out to the
cold body : the temperature of the contents of the
cylinder being in each of these cases the same as that
of the body with which they are at the time in contact.
A remark of great importance must now be made,
though it involves somewhat of a digression. You must
have noticed how much more easily we managed in
to-day's than in yesterday's lecture to lay down the
limits for the range of volume of the working substance
during each of the four operations included in Carnot's
cycle. Yet the only difference in our proceedings con-
sisted in the fact that yesterday, following Carnot him-
self, we began with expansion at the higher temperature
1 10 TRANSFORMA TION OF HE A T INTO WORK.
while to-day we have preferred to commence with
compression on the non-conducting stand. With the
help of a device due to Watt it may be possible to make
this point much more easily intelligible. The device I
allude to is called the Indicator Diagram, and is even
now constantly employed for the purpose of ascertaining
the work actually done by an engine, especially that of
a steam-ship.
It is not my business to enter into purely mechanical
details, and therefore I shall only say that this diagram
is traced out by a pencil attached to the piston-rod of
the engine, and therefore sharing its to-and-fro motion ;
while it has also a motion in a direction perpendicular
to the piston-rod, such that the displacement at any in-
stant is proportional to the pressure in the cylinder at
that instant. To fix the ideas, suppose the cylinder to
be horizontal, and the just-mentioned transverse motion
vertical. Then any re-entrant line whatever (lying wholly
TRANSFORMA TION OF HE A T INTO WORK. 1 1 1
between Op and Ov) may be supposed to be traced, once
over in each cycle of the engine, by the pencil P. For
reasons to be afterwards explained, I take the curvilinear
quadrilateral PP'QQ. Let Ov be the axis of the
cylinder, Op perpendicular to it ; and let PM be perpen-
dicular to Ov. Then, by our conditions, OM represents
the distance of the piston from the bottom of the
cylinder ; i.e. the volume of the working substance, while
MP represents its pressure, each upon a definite scale.
It follows from this, by a mathematical investigation
which, though very simple, I must not give in such a
lecture as this, that if P be any other position of the
pencil, and P' M be perpendicular to Ov, the area of the
figure PP M' M is proportional to the amount of work
done by the expanding substance while the pencil passes
from P to P '. Hence you easily see that the area of
the figure PP Q'Q is the excess of the work done by, over
that spent on, the working substance ; i.e. the equivalent
of the heat which disappears during the cycle.
Now, by properly regulating the temperature during
the cycle, it is obvious that we may make the pressure
what we please at each stage of the expansion and con-
traction. Hence any closed curve whatever might, by
proper arrangement, be made the diagram of energy
for a heat-engine. But now note particularly that in
Carnot's ideal engine we are carefully restricted to two
kinds of operations (direct or reversed), and to two only.
Hence the parts of the indicator-curve for each of the
four operations in Carnot's cycle belong to two classes
of curves, each of which is known, or at least can be
experimentally determined, so soon as we know what
is the working substance.
One of these is the curve representing the relation of
1 1 2 TRANSFORMA TION OF HE A T INTO WORK.
pressure to volume when the working substance ex-
pands or contracts without change of temperature. Call
this a line of constant temperature PP or Q Q in the
diagram.
The other, PQ or P Q , represents the corresponding
relation when the substance expands or contracts in a
vessel impervious to heat. This is called, after Ran-
kine, an Adiabatic Line. We might conceive Watt's
graphical process actually applied to trace out these
curves. And it is obvious that we can have one, and
only one, of each kind, passing through each given point
P in the plane of the indicator diagram. For that point
specifies a particular volume and pressure of the work-
ing substance (treated as constant in quantity), from
which we are to start by one or other of the two pro-
cesses I have just mentioned. Also it is obvious that
as, in general, the pressure of the working substance
will fall off faster as it expands when no heat is com-
municated to it, than when its temperature is kept con-
stant, of the two lines passing through the point P,
that corresponding to constant temperature PP tends
less quickly to fall to the line of no pressure Ov, than
does the adiabatic line PQ, for equal increments of
volume of the working substance.
You now see that Carnot's process essentially involves
a cycle whose boundary (in Watt's diagram) is formed
by two lines of equal temperature and two adiabatic
lines. But, while these lines of equal temperature were
at once specified by the numbers S and T, we had no
such definite nomenclature for the adiabatic lines.
Hence (so far as an elementary lecture is concerned)
the greater simplicity of the method I have to-day used
over that originally given by Carnot. To-day's method
TRANSFORMA TION OF HE A T INTO WORK. 1 1 3
in fact began by taking any point Q in the line of
temperature T, thence P was found by an adiabatic
line : then P' may be any point in the other given line
of equal temperature, and from this the adiabatic gives
Q '. The difficulty in yesterday's method arose in speci-
fying Q in the third operation, so that we should arrive
at a given point P, in the fourth.
We now come to another point, also perfectly novel,
and of importance at least proportional to its novelty.
If you think again of the various steps of the opera-
tions in Carnot's cycle, you will easily see that it is
possible to consider them as performed in exactly the
reverse order. Begin, for instance, with the hot body,
but do not allow the piston to rise there. Take the
cylinder from the hot body when the water and the
little quantity of steam above it have acquired the
higher temperature. Lift it to the non-conducting
body, and then allow the piston to rise. Let it rise till
the temperature sinks to that of the cold body ; place
the whole on the cold body ; allow it to expand still
further, it will be in that case giving out work but
absorbing heat : then when it has risen to its former
highest point, place it back again on the non-conducting
body, force the piston back to the same extent as that
to which it rose when (in Carnot's direct set of opera-
tions) it was first placed on that body. Everything has
taken place in precisely the reverse order to that in
which it took place before. Finish then upon the hot
body, and press home. From Carnot's point of view
you give to the hot body in that final operation precisely
the quantity of heat you took from the cold body ; but
during the two last operations you are forcing down the
piston, while during the two first operations the piston
H
ii4 TRANSFORMATION OF HEAT INTO WORK.
was being forced up, but it was always being forced up
at.a lower temperature, and therefore at a lower pressure
than the temperature and pressure you had to overcome
in forcing it home again. And, therefore, in the reverse
method of working this engine, you take heat from the
cold body and deposit it in the hot body, exactly to the
same amount as in the direct operation ; and, on the
whole, you now spend as much work as you formerly
gained.
These are the grand ideas which Carnot introduced.
Their two distinctive features are, first, the idea of a
complete cycle of operations, at the end of which the
working substance, whatever it is, is brought back to
precisely its primary condition ; a cycle which can be
repeated over and over again indefinitely. Secondly,
The notion of making the cycle a reversible one, so that
you can perform all the operations in it in the reverse
order, and instead of taking in heat at any place it may
be made to give out that amount of heat, instead of
the engine doing work at any place that amount of work
can be spent upon it. With these changes in each opera-
tion, the whole cycle can be gone over the reverse way.
Now, Carnot proceeds to reason upon this. Consider-
ing heat as a material substance, he says that obvi-
ously it has done work in the direct series of operations
by being let down from the higher temperature to the
lower, just as water does work by being let down through
a turbine or other water-engine, in proportion to the
quantity that comes down and the height through which
it is allowed to descend. We now know that this
notion of the nature of heat is erroneous, 1 but still
1 Carnot, as is now ascertained, had long ago found this out for himself.
See note to p. 98.
TRANSFORMATION OF HEAT INTO WORK. 115
Carnot's reasoning is of the highest value, because it
wants only the change of a word or two to render it per-
fectly applicable to our modern knowledge of the subject.
You see at a glance one point which appears conclu-
sively to show that Carnot's assumption was wrong,
because nothing is easier than to let the heat down at
once without the performance of any work. If you put
the hot body into direct communication with the cold
body, the same quantity of heat might be allowed to
go down from one to the other, and yet give you no
work at all. There must be, then, something wrong in
that statement of Carnot. We now know what it is ;
but let us follow Carnot a little further, and see how
much more of what is eminently useful and true he
attained even with his false assumption. He carried it
further in this way. He said If an engine be reversible
(as this cycle of operations has been shown to be), it does
as much work as can be got out of a given quantity of
heat under the same given circumstances. So that, no
matter what you make your engine of, no matter what
be the substance which is expanding and contracting,
if a certain quantity of heat be let down from a source
at a certain temperature through your reversible engine
to a sink at another temperature, then the quantity of
useful work which can be got from that heat will be
absolutely the same. Reversibility is the sole necessary
condition of equivalence between two such engines. You
will see in an instant what an enormous step this is in
physical science. The reasoning here is independent
altogether of the properties of any particular substance.
We are not dealing with steam, or air, or ether, or any
one working substance in particular ; yet we have a
crucial test of the perfection of an engine which is abso-
ii6 TRANSFORMATION OF HEAT INTO WORK.
lutely the same when applied to any working substance
and any heat-engine whatever. That test is, if a heat-
engine is reversible it is perfect, not perfect in the popular
sense, but in a scientific sense ; that is to say in the sense
that it is as good as it is possible physically to make it.
Now the proof that it is so is very easily given, but
before I give it I may say a word or two upon a similar
but somewhat simpler sort of proof which will prepare
you for the reasoning employed, and which bears directly
upon the ordinary notion of the perpetual motion.
We know (of course only by experiment) that in all
cases of natural laws, such as the laws of gravitation, and
of magnetic attraction, whatever work is spent in moving
a body through a certain course in one direction, you
get back exactly by letting it return along the same
track, always on the supposition that friction is avoided.
The reason of this is that these forces depend upon
relative position only, and therefore undo, at each stage
of an exactly reversed path, precisely the amount of
work which they did at the same stage of the direct path.
A
Suppose then that there could be two courses,
from A to B, by the one of which more work would
be spent on the mass than by the other. Let these
amounts of work be W and w. I say that if such
were the case you would be able at once to pro-
duce the perpetual motion. All you have to do is
TRANSFORMA TION OF HE A T INTO WORK. 1 1 7
to apply frictionless constraint to guide the mass, so
that in its ascent it shall travel along the course AwB,
and in its descent along BWA. From A to B you
have to spend the amount w of work against the
forces of the system from B to A these forces refund
the amount W. On the whole, after a complete cycle,
the mass is restored to A with an amount W-w of
energy additional to what it possessed at starting.
Well, we have gained something by that, and every
time the mass goes round the double course in the
direction I have indicated, it gains the difference be-
tween the larger quantity and the smaller one, and
therefore you can, at the end of each complete cycle,
drain that amount off to turn some machine ; to do
useful work. If, therefore, there were one way of doing
a thing at less cost than another, and if the more costly
operation were reversible (in the strict scientific sense
above explained), then it would be possible for you
under such circumstances to get unlimited amounts of
useful work from nothing. Now we know that, so far
as experience extends, this is impossible. The multi-
plied experiments of some of the most ingenious men
who ever lived, Vaucanson and others, were directed to
this question. Yet these men, who constructed automata
which mimicked, and often copied, the motions and
physical functions of living animals, these men were
entirely baffled in attempting to get at anything like
the perpetual motion. We may say distinctly that all
really scientific experiment has led to the conclusion
that the perpetual motion in the old sense is absolutely
unattainable.
Well, let us see how this reasoning applies to Carnot's
engine. He demonstrates its property by almost the
1 1 8 TRANSFORMA TION OF HE A T INTO WORK.
same application of reasoning as that which I have just
given you for a similar but very simple case. He says
that a reversible heat-engine is a perfect one; for, if
not, let us suppose there could be one more perfect.
Well, you can always use these two engines in conjunc-
tion. Let the more perfect engine (i.e. the less costly
one) be employed in taking a quantity of heat, conveying
it down to the condenser from the boiler, and giving you
from it a larger quantity of work than the reversible
engine could do. You can now use the reversible engine
to pump that heat back again. Every time the heat
goes down, it is through the more perfect engine ; every
time it is coming up, it is through the worse engine, and
therefore it does more work going down than requires
to be spent on bringing it up, and thus every time the
compound engine makes a complete stroke, or passes
through the double cycle of operations, you have an
excess of work given by the one part over what has to
be spent on the other. Therefore, this is not merely an
engine which will go for ever, but an engine which can
go on for ever, and besides steadily do work on external
bodies.
That, however, as we have seen, is inconsistent with
all our experimental results, and therefore we must at
once pronounce the supposition which led us to this con-
clusion, viz., that there can be a more perfect engine
than a reversible one, to be false. This is Carnot's
final proof that (on the assumption that heat is matter)
a reversible heat-engine is a perfect engine. It requires
very little indeed, as a moment's reflection will show
you, to make this reasoning consistent with our modern
knowledge of heat.
We have now to consider the cycle in the light of
TRANSFORMA TION OF HE A T INTO WORK. 1 19
the conservation of energy, so that if you get work from
heat at all, some of that heat must have disappeared in
its production, and that, therefore, under no circum-
stances if the engine is doing external work at all
can the quantity of heat which reaches the condenser
ever be equal to that which leaves the boiler. The
difference between them, if none has been wasted by
conduction or in other unprofitable ways, the differ-
ence between the quantity which leaves the source and
the quantity which reaches the condenser during a
complete cycle must be precisely the equivalent of the
external work which has been done. Taking that into
account, let us suppose we could make an engine more
perfect than a reversible one. Work the two together,
as before. Make the reversible engine continually pump
up just as much as the other lets down. Then, as it is
less perfect, it will require less work to be employed on
it, when reversed, to restore to the source or boiler that
quantity of heat than the other engine will do in letting
it down ; and therefore, on the whole, while you have a
pumping up of heat and letting it down which will
exactly compensate one another, or appear to do so, at
least so far as the source is concerned, you will have a
gain of work. There is the one point where the difficulty
is to be found, if there is any. The compound engine
will do work ; no question of that. The more perfect
engine lets down a certain quantity of heat to the con-
denser. The other engine pumps up heat from the con-
denser, and deposits in the boiler precisely the same
quantity as the other takes out from it. How is it then,
that, though we know heat is not matter, this double
system can do work ? It can only work in one possible
way, and that is by expenditure of heat it must
120 TRANSFORMA TION OF HE A T INTO WORK.
ultimately work, therefore, not by letting down heat
from the boiler, but by cooling the condenser. That is to
say : If there can be a more perfect engine than a
reversible one, then, with our present knowledge of heat,
and taking Carnot's cycle, modified so as to make it com-
patible with our modern knowledge, these two engines,
working together, the one restoring to the boiler pre-
cisely what the other took from it, can only do work,
on the whole, on external bodies by cooling and further
cooling the condenser. Hence, our result amounts to this,
that by taking, as the condenser for our compound engine,
any limited portion of the available universe, we could go
on getting work from that by making it constantly colder
and colder, till we removed all heat from it. Now, we
may safely assume it to be axiomatic that we cannot do
this ; all experimental laws are against it ; and as we see
that the supposition that a more perfect engine than a
reversible one can exist has led us to this absurdity,
we have it ex absurdo that there can be no engine
more perfect than a reversible one. What I have just
given you is, in a much amplified form, the gist of some
of Sir W. Thomson's remarks of 1851 on this point.
Clausius, in the preceding year, had endeavoured
to supply this defect in Carnot's work by an appeal to
the general behaviour of heat, i.e. its always striving to
pass from a warmer body to a colder one. I have else-
where given reasons which seem to show this proof to
be inadmissible. 1
However complete and satisfactory the demonstra-
tion just given may appear to be, you must now be told
1 See the correspondence in full in the Phil. Mag. 1872, I. pp. 106, 338,
443, 516, and II. 117, 240. Also 1879, I. p. 344. The last of these
is referred to in the Preface.
TRANSFORMATION OF HEAT INTO WORK. 121
that it is possible, but possible only in a very curious
way, and to an extremely limited extent, to get round
this apparent difficulty, to make a body colder than
surrounding objects, and to get work from it in con-
sequence. This (which, alone, is absolutely fatal to
Clausius' reasoning, even with his later modification of
it) was first pointed out by Clerk-Maxwell not long ago,
and he showed that the mode of escape from the
difficulty is, that it would require the intervention of
beings, still finite, but infinitely more acute and able
than any human beings (or even than the utmost ideal
a human being can well conceive), to effect the object
on a finite scale, and thus upset the basis on which
Carnot's results have been re-established by Thomson.
Clerk-Maxwell's reasoning depends upon the mole-
cular theory of gases, an essential feature of which is
that even in a mass of gas undisturbed by currents, and
of uniform temperature, the particles have not all the
same velocity. He points out that if such imaginary
beings, whom Sir W. Thomson provisionally calls
demons small creatures without inertia, of extremely
acute senses and intelligence, and marvellous agility
were to watch the particles of a gas contained in a
vessel with a partition full of trap-doors, also devoid of
inertia ; prepared to open and close these doors so as
to let the quicker particles get out of the first compart-
ment into the second, and to let an equal number of
the slower ones escape from the second compartment
into the first, they could, without doing any work them-
selves, give to the system the power of doing a certain
amount of work without help from external bodies.
You must be careful, however, not to fancy that there
is here any gain or creation of energy not
UNIVERj
evejjK
f U
v
122 TRANSFORMATION OF HEAT INTO WORK.
demon could effect that there is a gain of transforma-
bility, a slight rise in the scale of availability zw7 tout.
As you will be told in another lecture, this restoration
of energy is constantly going on, but on a very limited
scale, in every mass of gas. If there were only a few
hundred particles in a small vessel of gas, the chances
would be that if we suddenly cut off half the vessel
there would be a sensible difference of temperature
between the two parts. But, in consequence of the
enormous number of particles in a cubic inch, of even
the most rarefied gas, the amended form of Carnot's
reasoning just given must be taken as holding good for
every heat-engine. For, alas ! we are not demons (in
Maxwell's sense), and therefore, so far as experiment
goes, and practical application goes, we may take this
improved form of Carnot's demonstration as being abso-
lutely decisive of the important result, that nojigat-
engine can be more perfect than a reversible one. This
is, virtually, the Second Law of Thermodynamics, the
First Law being that of the Equivalence of Heat and
Work.
The consideration that follows immediately upon this
is : If all reversible engines are perfect, they must all be of
equal efficiency. They must all be able to give you pre-
cisely the same amount of work, from the same quantity
of heat, under the same conditions. Therefore it follows
that it is these CONDITIONS alone which determine how
much work can be produced by a perfect engine, from
a given quantity of heat. Now, what are the condi-
tions ? I have mentioned no conditions whatever but
the temperatures of the boiler and condenser. The tem-
peratures of the boiler and condenser were the only
things this set of perfect engines had in common. Sup-
TRANSFORMATION OF HEAT INTO WORK. 123
pose they were all worked for such a period of time
that they would all employ equal quantities of heat,
then all would do the same amount of work. Therefore,
having established Carnot's result, independently of
Carnot's erroneous assumption, we are entitled to con-
clude that the perfect heat-engine converts into work a
fraction of the heat it uses, the value of which fraction
depends only upon the temperatures employed. Hence
follows immediately one of the most important conse-
quences of Carnot's method. It was given, as I have
already said, by Sir William Thomson in 1848, when he
first recalled attention to Carnot's work. He pointed
out that here we have an absolute method of measuring
temperature. All previous methods had depended on
the properties of some particular substance. It is no
matter what your zero and your Newtonian fixed points
may be, let us suppose them defined by melting ice
and boiling water. Take a number of carefully made
and calibrated thermometers ; fill one with mercury, one
with sulphuric acid, and so on, and one with water. All
of these, if properly adjusted, will agree at the zero or
freezing point and at the boiling point, but no two will,
in general, agree at any intermediate point. In fact, the
water thermometer would be an extremely curious
thing, because for a few degrees from the freezing point
upwards the water contracts instead of expanding. The
water, heated from the freezing point, would at first go
downwards on the scale, and then rise with increasing
rapidity towards the boiling point. The mercury, on the
other hand, would go pretty uniformly up, and so on.
Thus, in employing such instruments you must, in addi-
tion to noting the degrees on the scale, also note the
particular liquid employed. The temperature, then, of a
124 TRANSFORMATION OF HEAT INTO WORK.
body measured by thermometers filled with different sub-
stances, would give generally as many different readings
as there are thermometers ; and, therefore, unless you
state what is the particular liquid employed, and even
what is the particular kind of glass employed, your reader
cannot be sure of the particular temperature which is
meant. But Sir William Thomson pointed out that the
reversible cycle gives us the means of defining tempera-
ture absolutely; that is, with complete independence of
the properties of any particular substance, because Car-
not's engine, if only reversible, is perfect. We do not need
to inquire what is the working substance air, water,
chloroform, or ether, or whatever it is the engines are all
equivalent to one another, and the fraction of the heat
they take in, which is converted into useful work, depends
solely on the two temperatures. And we have seen that
for a reversible engine it is only necessary that the working
substance should never be in contact with a body of a
temperature different from its own, unless indeed it be an
absolute non-conductor of heat. Now, suppose we could
keep a body at the temperature of boiling water, under
certain conditions, such as that the barometer shall be at
a height of 760 m.m., or, roughly, 30 inches. Suppose we
keep another body at the temperature of melting ice,
with the barometer at the same height. Suppose we can
measurewhat amountof heat is taken in and what amount
given out by a perfect engine working between these two
temperatures, we should find that they are as nearly
as possible in the proportion of 374 to 274. I make
this statement just now simply as an assertion ; we shall
see afterwards by what process these numbers have been
approximately obtained. In the ordinary Centigrade
scale we call the freezing temperature zero, and we call
TRANSFORMATION OF HEAT INTO WORK. 125
the temperature of boiling water, under the 30 inches of
pressure of the atmosphere, 100. The experimental
numbers have been so taken that their difference is
100, for a reason which will immediately appear. It is
obvious now that we may define the temperatures of
the boiler and condenser of a perfect engine by any
functions of the relative quantities of heat taken in
and given out. Sir William Thomson's first suggestion
was not that which he finally adopted. To give as
slight a dislocation as possible from the common modes
of measuring temperature, it was found best, as it is also
simplest, to define as follows : When a perfect engine
takes in heat at one temperature and gives it out at an-
other temperature, then the temperatures of the source
and of the refrigerator are in proportion to the quan-
tities of heat taken in and given out, so that, as we see
by experiment in the case above mentioned, that for
374 taken in, 274 are given out, the temperature of boil-
ing water will on this scale be represented by 374, and
of freezing water or melting ice by 274, the range be-
tween these being the ordinary 100 of the Centigrade
thermometer. Therefore we have this curious result, that
if you could get a body cooled down far enough under
the freezing point we have many artificial processes
for such cooling : we can go nearly 140 degrees
Centigrade below the freezing point, if we could go
twice as far, or 274 degrees below zero, we should have
taken all the heat out of the body, we should have re-
duced it to the absolute zero of temperature. It would
be impossible to make it any colder than the absolute
zero of temperature just stated as 274 C. under the freez-
ing point of water. Otherwise an engine could be con-
structed which would give more work from a quantity
126 TRANSFORMATION OF HEAT INTO WORK.
of heat than its dynamical equivalent And this engine
would work by taking heat from a body already more
than totally deprived of heat !
In passing, I may say a word or two illustrative, per-
haps even to be regarded as corroborative, of that con-
clusion. It has been long known that the pressure of a
gas, such as air, in a closed vessel, becomes greater as you
make it hotter. Take a vessel enclosing a quantity of
gas, and shut off the connection between the interior and
the exterior, and then apply heat to it. We know that
the gas presses more strongly on the containing vessel.
On the other hand, if, instead of applying heat to it, we
immerse the vessel in a freezing mixture, we know that
the pressure becomes less. Now, the amount of increase
of pressure per degree of increase of temperature, and
also the amount of diminution of pressure per degree of
diminution of temperature, have been carefully measured,
and it has been found that almost exactly not quite
exactly, for a reason afterwards to be assigned, but quite
nearly enough for our present purpose if you were to
suppose the gas cooled down to a temperature of 274 C.
under freezing point, and calculate, by assuming the ex-
perimental results I have mentioned to hold throughout
that whole range of temperature, the pressure thus de-
duced would be almost exactly nothing. So that on the
assumption that the formula for its dilatation (found
experimentally for small ranges of temperature) holds
for great ranges also, a gas would cease to exert any
pressure upon its containing vessel if you could cool it
down to 274 under ordinary freezing point, the degrees
between the freezing and boiling points being, as in the
Centigrade scale, 100. This, taken in connection with
Carnot's result, appears conclusively to show that the
TRANSFORMATION OF HEAT INTO WORK. 127
pressure of a gas is due to motion of its particles. The
application of heat produces this motion of its particles,
in virtue of which they fly about and impinge upon
the walls of the vessel ; the energy of their motion is the
heat contained by the gas. Go on cooling, and their
motion becomes slower ; and finally, when you have got
the gas to the absolute zero of temperature, their motion
will have ceased, and therefore we should find no pres-
sure upon the retaining vessel.
I may now mention, in connection with the produc-
tion of work from heat, and as a practical illustration of it,
that suppose we could get a steam-engine made to fulfil
Carnot's condition of reversibility that is to say, that
we could prevent the steam from ever being in contact
with bodies at other than its own temperature for the
time being, prevent loss by conduction, etc., in other
words, suppose we had a perfect engine, the fraction of
the whole heat employed which would be converted
into work would not be a large one. Using data, which
I take from a statement of Joule, as fairly representing
a practical case ; suppose the engine to be a high-pres-
sure one, working at 3^ atmospheres, or something
about 53 Ibs. pressure on the square inch, it would
require in the boiler a temperature of very nearly 300
Fahrenheit. Joule says that while working such an
engine at an ordinary rate of speed it is next to impos-
sible to keep the condenser colder than about 1 10 Fah-
renheit. Now the question is, what fraction of the heat
spent upon that engine would be converted into useful
work ? The answer is remembering Carnot's cycle
again the quantity of heat taken in is to the quantity
given out in the proportion of the absolute temperature
of the boiler to the absolute temperature of the con-
128 TRANSFORMATION OF HEAT INTO WORK,
denser ; so it comes to be a question simply of arith-
metic. Two hundred and seventy-four degrees under
zero Centigrade is the point of absolute cold ; what cor-
responds to that upon Fahrenheit's scale ? This is
easily found to be 461 '2 under the Fahrenheit zero.
And, therefore, 76i*2 is the absolute temperature of the
boiler; and S7 l ' 2 will De the absolute temperature of
the condenser. Therefore of 761*2 units of heat which
go in, only 571*2 units go out; and as the engine is
perfect, all the rest, that is, 190 units, amounting almost
exactly to one-fourth, is converted into work. So our
engine, under these conditions, which are about as
favourable as any occurring in practice, and even with
the additional assumption that it is a perfect engine
a thing quite unrealisable in practice converts only
one-fourth of the heat from the boiler into useful work.
The other three-fourths are sent to the condenser, and
in general wholly and absolutely wasted.
I come now to the consideration of various important
advances in the pure science of natural philosophy, which
have been made possible, or have at all events been
brought forward sooner than they otherwise would have
been, in consequence of the recognition of this great dis-
covery of Carnot. One of the first of these, and cer-
tainly one of the most important, is that made by James
Thomson, with regard to the effect of pressure upon the
freezing point of water. As you will find immediately,
the whole effect is, even for great pressures, an extremely
small one, and yet, in all probability it has fitted ice
to be one of the most important agents in modifying
physical geography.
Let us consider for a moment that when water freezes
there is very considerable expansion. With a very
[( TJKJVJ-: s
TRANSFORMA TION OF HE A T INztimRK. 1 29
slight change of temperature of water near the freezing
point you have a very considerable change of bulk.
Taking Carnot's engine again : Suppose that instead of
putting into our cylinder a quantity of hot water with
a little steam above it, we put a quantity of cold water
with some ice in it, which went through the same set of
operations ; then and this was almost precisely the way
in which James Thomson regarded it it is easy to show
that, taking account of the expansion in the act of
freezing, you could get, without any expenditure of heat
whatever, any amount of work you pleased from such
an ice-water engine. The only way in which you could
get out of this inadmissible difficulty is by assuming
that the freezing point of water depends upon the pres-
sure. If this be allowed, everything can be explained ;
but if not, then unquestionably an ice-engine would
enable us to get work from no expenditure. Thus, ,
by simply applying Carnot's process with the change of
a word or two, and availing himself of the experiment-
ally demonstrated impossibility of the perpetual motion,
James Thomson made out the result, that the freez-
ing point of water is necessarily lowered by pressure.
Well, one can calculate, suppose it were not lowered,
how much work could be done in one stroke of this
compound engine. One can compare that with the work
done by expansion of water when converted into ice
and the amount of latent heat set free, and from these
one can calculate conversely by how much the pressure
must be increased in order to lower the freezing point
one degree, or how much the freezing point would
be altered by a change of one additional atmosphere
of pressure. Thomson made both these calculations.
The result was extremely small, namely this fraction
I
130 TRANSFORMATION OF HEAT INTO WORK.
O'OO75 C. The freezing point of water is lower by this
small fraction of a degree Centigrade for every addi-
tional atmosphere of pressure. You can calculate from
this that it would require 133 additional atmospheres
of pressure, that is to say, 133 times 15 Ibs., or about
2000 Ibs. weight on the square inch, to be applied to a
quantity of ice which has a temperature one degree
Centigrade lower than the freezing point, in order that
the ice should melt. So that ice can always be melted
by applying pressure great enough ; but if you make the
ice very much colder than the freezing point, the amount
of pressure required to melt it is so great that we can
hardly conceive of its ever being applied. It is only
when ice is moderately near its melting point that you
can apply sufficient pressure to get its present tempera-
ture to represent its melting point ; and if its present
temperature represents its melting point, of course it
melts. I showed you in my last lecture one beautiful
method of exhibiting the melting of ice under pressure,
which was described last year in Nature by Mr. Bot-
tomley. It consisted in cutting through a bar of ice
with a wire, as you would cut soap or cheese. But
the ice behaves in a totally different way from that
in which soap or cheese would have behaved under
the same circumstances. If the ice had been one or two
degrees colder than the freezing point, the wire would
have hung inactive. It is only when the ice is near
the freezing point that the wire, with moderate weights
at its ends, is capable of melting it. As the ice melts,
it passes round behind the wire, and, thus escaping
the pressure, sets into ice again. Thus, as fresh ice
has pressure applied to it by the advancing wire, there
is a constant melting of the ice before the wire, and a
TRANSFORMA TION OF HE A T INTO WORK. 131
constant re-freezing behind it; and the block of ice
remains practically continuous, except just at the place
where the wire is cutting it. Now, this property of ice
was known in some of its effects at all events to every
one who had seen a glacier for hundreds of years ; but
it was only within comparatively recent times that atten-
tion was directly called to it. The first who seems to
have done so was Dollfuss-Ausset, in his experiments
upon the Swiss glaciers, where he showed that by com-
pressing a number of fragments of ice in a Bramah press,
it was possible to melt them ; and when pressure was
taken off them, to allow them to revert again into a solid
block. But he found that with very cold ice the experi-
ment did not succeed. In fact, as we now see, even with
his Bramah press, he could not apply pressure enough.
Another form in which it must have been well known
for hundreds of years is the form in which we try the
same experiment every time we make a snowball.
Schoolboys know well that after a very frosty night the
snow will not 'make:' their hands cannot apply
sufficient pressure. But if the snow be held long enough
in the hands to be warmed nearly to its melting point
it recovers the power of 'making,' or rather of 'being
made.' Every time we see a wheel-track in snow we see
the snow is crushed, and even after one loaded cart has
passed over it, certainly after two or three have passed,
the snow has been crushed into clear transparent ice.
The same thing takes place by degrees after people
enough have walked over a snow-covered pavement ;
and in all these cases this minute lowering of the freez-
ing point has led to the result. And now we see how
it is that the enormous mass of a glacier moves slowly
on like a viscous body, because in consequence of this
132 TRANSFORMATION OF HEAT INTO WORK.
most extraordinary property it behaves under great
pressure precisely as if it were a viscous body. The
pressure down the mass of a glacier must of course be
very great, and as the mass is especially in summer
freely percolated through by water, its temperature can
never (except on special occasions, and then near the
free surface) fall notably below the freezing point. Now,
in the motion of the mass on its journey, there will
be at every instant places at which the pressure' is
greatest, where in fact a viscous body, if it were placed
in the position of the glacier ice, would give way. The
ice, however, has no such power of yielding ; but it has
what produces quite a similar result wherever there is
concentration of pressure at one particular place it
melts, and as water occupies less bulk than the ice from
which it is formed, there is immediate relief, and the
pressure is handed on to some other place or part of
the mass. The water is thus relieved from the pressure
by the yielding caused by its own diminution of bulk
on melting. The pressure is handed on ; but the water
still remains colder than the freezing point, and there-
fore instantly becomes ice again. The only effect is
that the glacier is melted for an instant at the place
where there is the greatest pressure, and gives way there
precisely as a viscous body would have done. But the
instant it has given way and shifted off the pressure
from itself it becomes ice again, and that process goes
on continually throughout the whole mass ; and thus
it behaves, though for special reasons of its own, precisely
as a viscous fluid would do under the same external
circumstances.
LECTURE VI.
TRANSFORMATION OF ENERGY.
Further consequences of Carnot's ideas. Anomalous behaviour of water and
of india-rubber. Application to rock masses, and the state of the earth's
interior. Availability of energy, and loss of availability. To restore the
availability of one portion of energy, another portion must be degraded.
Dissipation of energy. Sources of Terrestrial and of Solar Energy.
Energy of plants and animals. Measure of the Sun's Radiant Energy.
Energy now in the Solar System.
I SHALL commence this afternoon by taking a few
further consequences of the grand ideas of Carnot, which
I developed at full length in my last lecture. Where-
ever, in fact, we meet with any one anomalous physical
result, we almost invariably find that it is associated
with other anomalous results ; and perhaps it is in this
respect that Carnot's ideas have been of the greatest
use in giving us new information.
Let us take, for instance, what I incidentally men-
tioned in connection with thermometers in my last
lecture, the fact that water would be an exceedingly
bad substance to employ for the purpose of filling a
thermometer bulb, because, even supposing that it did
not burst the bulb when it froze, supposing that we
were using it from zero of Centigrade scale up to 100,
it would begin to contract when first heated, and would
continue to do so up to the temperature of 4 C, and
then it would expand like most other liquids. Now,
here is a substance, which, when heated, becomes less
134 TRANSFORMA TION OF ENERG Y.
in bulk : it contracts instead of expanding. We should
expect, therefore, to find that water exhibits some other
anomaly, really the same thing if we could understand
exactly all about the physical question involved, but
appearing very startling to us when presented as some-
thing apparently quite new and different.
Let us look closely into the circumstances of this
question. We are applying heat to water, and in con-
sequence the water is contracting instead of expanding.
Suppose, then, that we take water at a temperature
between zero and 4 C., and apply pressure to it, what
should we expect ? Pressure applied to water at any
temperature above 4 C., and to most other liquids at
any temperature whatever, develops heat. Now Car-
not's reasoning shows that just for the same reason that
pressure produces a development of heat in a liquid
which expands by heating, so in a liquid such as water
between zero and 4 C., a liquid which contracts on being
heated, pressure produces cooling, so that water taken
at any temperature between these narrow limits and
squeezed in a Bramah press becomes colder in conse-
quence of the forced contraction in bulk.
Another very startling result is derived from the
anomalous behaviour, which I daresay is familiar to
most of you, of an india-rubber band. I daresay you
all know that an india-rubber band suddenly stretched
and applied to the lip feels warmer than before. Most
bodies when extended become colder, as air does when
it expands. If you pull out a steel spring it becomes
colder, as Joule showed by direct experiment; but
india-rubber is an exception : it not only becomes
warmer when it is pulled out, but if, keeping it still
pulled out you allow it to cool to the temperature of
TRANSFORMA TION OF ENERG Y. 1 35
the air, and then suddenly allow it to contract again, it
is very much colder than before, as you feel by apply-
ing it again to your lip.
Now these other bodies, such as air and the steel
spring, when heat is applied to them, expand. A
steel spring supporting a weight, and with heat applied
to it, will expand, and allow the weight to descend.
On the contrary, as I hope to be able to show you by
a simple arrangement, when you apply heat to stretched
india-rubber, instead of expanding it contracts, and
perfectly in accordance with the theoretical prediction
of Sir William Thomson from Carnot's reasoning
applied to this case.
I suppose the 'spot of light crossed by a sharp hori-
zontal dark line is visible to all of you near the top of
the scale. The light from an incandescent lime-ball
passes through a lens, and (after reflection from a plane
mirror) is brought to a focus on the scale. The hori-
zontal dark line is the image of a wire stretched in
front of the lime-ball. This is our index, not the
vaguely-defined spot of light. I have here suspended
a piece of vulcanised india-rubber gas-tubing, with the
spiral wire-core removed from it. Its lower end has a
scale-pan attached, and is also fastened to a lever which
moves the plane mirror. In order to show you what
the movements of the apparatus indicate, my assistant
will put one or two additional weights into the scale-
pan hanging from the tube, and you will notice that
the effect of the additional weights, which is of course
to extend the india-rubber, produces a movement of
the reflected light up the scale. Hence, if this india-
rubber were to expand further by the application of
heat, we should see the spot of light on the scale move
TRANSFORMATION OF ENERGY.
farther up ; but, on the contrary, as soon as heat is
applied by a spirit-lamp to the india-rubber, the spot
of light you see moves downwards upon the scale,
showing that the india-rubber is contracting instead of
expanding. India-rubber is a very bad conductor of
heat, so that it will require some time to cool ; but if
we 'were to allow it time to do so, we should find it
return almost exactly to its original length ; so that
while being heated under tension it contracts, and while
cooling under tension it expands.
TRANSFORMA TION OF ENERG Y. 1 37
[Clerk-Maxwell has recently improved this experi-
ment in a most marked manner, by heating the india-
rubber tube by the passage of a current of steam
through it. The shortening produced can now easily
be made visible directly to a large audience.]
There are a great many other substances which
present anomalous properties of the same kind ; but we
will now go back to cases which are not anomalous, and
there we shall see that the application of Carnot's prin-
ciples leads, in these as in other cases, to results which
may be of the very greatest importance. Take, for
instance, a piece of wax. We know that when wax
solidifies it contracts very considerably. Paraffin and
many other bodies do the same ; and, therefore, in exact
accordance with Carnot's reasoning, their melting points
are raised by pressure instead of being lowered, as the
melting point of ice is, so that in order to melt paraffin
under a very great pressure, you require to heat it very
much above its ordinary melting point.
This is exactly analogous to the case of the conver-
sion of water into steam. When water is converted
into steam, there is an enormous increase in the bulk,
and we know that the temperature of the boiling point
of water is greatly heightened by increased pressure. In
a high-pressure steam-engine, and wherever we insist
on having steam at a high pressure, the boiler requires
to be raised to a correspondingly high temperature
above the ordinary boiling point. We all know that
Papin's Digester was formed upon that principle, for the
purpose of heating water to a very much higher temper-
ature than the ordinary boiling point, and therefore to
confer upon it solvent powers for dissolving bones and
such like, which it does not possess at the ordinary boil-
1 38 TRANSFORMA TION OF ENERG 1 '.
ing point. And, in the same way, Alpine travellers have
told us of their difficulties in cooking tea and other
food on the top of a high mountain, because it is im-
possible at such altitudes, without enclosing the water
in a boiler with a closed lid, to heat it up to the tem-
perature of 1 00 C, the ordinary boiling point Water
boils in an open vessel at about 85 C. on the top of
Mont Blanc.
Now, consider the application of this on a far more
gigantic scale. Think of its application to the (originally
fluid) substances which now form the whole mass of the
earth. There can be no doubt whatever, from various
physical and geological proofs, that the interior of the
earth, at all events for a very considerable depth under
the surface, must, at some long time ago, have been in a
viscous or even a perfectly liquid state. Now, when that
mass first cooled, which it certainly would do most rapidly
at the surface, then if the substance were such as to con-
tract on cooling, so that the solid crust became denser
than the liquid below it, there would be an exceedingly
precarious state of equilibrium, as gradually the crust
formed, and, shrinking in, increased the pressure on
the liquid below, and thus produced a powerful hori-
zontal tension throughout its own substance. In all
probability the crust must have broken up by the
surface-tension necessary to balance this internal pres-
sure (as the tension of a soap-bubble balances the extra
pressure due to the compressed air it contains), and
tumbled in (and sunk) in pieces, and then solidifica-
tion commenced on the fresh exposed liquid surface,
and so on. But through the whole globe, there
may be, at depths even of so little as 500 miles
under the earth's surface, portions still left of the
TRANSFORMA TION OF ENERG Y. 1 39
originally liquid mass at temperatures equivalent to a
red heat ; or (it may be) even a white heat at tem-
peratures at all events far above their melting point
under ordinary pressures ; and yet, as Sir William
Thomson has shown by means of precession, and by
other astronomical determinations, still solid. The
whole mass of the earth is virtually solid ; more rigid
in fact than if it had been of glass throughout very
nearly as rigid as if it had been a solid mass of
steel ; still, I say there may be portions of the interior,
even not so much as 500 miles under the surface, which
are still at a white heat, and yet solid, because in conse-
quence of the immense superincumbent pressure their
melting points have been raised so high that even a white
heat is insufficient to liquefy them.
The illustrations of this lecture have been mainly
devoted to the law of transformation of energy from
one form to another, and all the examples I have given
have been simply applications of Carnot's great result,
as modified slightly so as to make it agree with modern
knowledge as to the nature of heat. But there are other
reflections which we must make on the same subject,
and especially with reference to the necessity in Carnot's
process of a large portion, by far the greater portion, of
the heat which even a perfect engine employs, being let
down, without undergoing transformation, from a high
temperature, where it has a great deal of available
energy, to a lower temperature, where it has a less
amount of available energy.
There is, of course, the same amount of energy in a
given quantity of heat in whatever body and at whatever
temperature you have it ; for a quantity of heat, what-
ever its temperature, represents its equivalent of work.
140 TRANSFORM A TION OF ENERG Y.
But though there is a definite mechanical equivalent
for so much heat, there are vast variations in its utility
under different circumstances. If you have the heat in
a very hot body, you can get a great deal of its value
out of it. On the contrary, if you have it in a com-
paratively cold body, you can get very little out of it ;
and therefore we are led to speak of the availability of
an amount of heat-energy. Availability of energy
simply means its capability of being transformed into
something more useful, i.e. of being raised higher in
the scale of energy ; and depends in the case of heat
entirely upon the temperature at which we have it.
We have seen that even a perfect engine, when it is
using heat, necessarily converts only a part of the heat
into work. We get the full benefit of that part of the
heat ; but the remainder is not left in the boiler, but is
degraded, is let down, through the range of temperature
corresponding to that between the boiler and the con-
denser ; and there, although even yet it is equivalent
as much as ever to work, it cannot be converted into
useful work ; for, in order that such a conversion should
take place, we must have a new engine working down
to a temperature lower than that of the original con-
denser. Therefore this heat, although quite as high
as the rest in its equivalent of mechanical energy, is
not so useful, because we have not the means of trans-
forming it. It has lost its standing, as it were ; it has
lost its availability ; and thus there is a constant ten-
dency, even with a perfect engine, and we cannot get
a perfect engine in any of our operations, to a degrada-
tion of the greater part of the heat employed.
This leads us, then, to the consideration of why it is
that such a degradation must take place. Perhaps the
TRANSFORMA TION OF ENERG Y. 141
best way of studying such a question will be to take
as another illustration of the perfect engine, and Car-
not's cycle the case of compressed air, or some other
such source of power which does not necessarily involve
the direct application of heat.
The case of compressed air is a very instructive one,
and at the same time a very simple one. It was first
thoroughly worked out by Joule, and in this way. He
took a strong vessel containing compressed air, and
connected it with another equal vessel which was ex-
hausted of air. These two vessels were immersed each
in a tank of water. After the water in the tanks had
been stirred carefully so as to bring everything to a
perfectly uniform state of temperature, a stop-cock in the
pipe connecting the two vessels was suddenly opened.
The compressed air immediately began to rush violently
into the empty vessel, and continued to do so till the
pressure became the same in both ; and the result
was, as every one might have expected, that the vessel
from which the air had been forcibly extruded fell in
temperature in consequence of that operation. It had
expended some of its energy on forcing the air into
the other vessel. But that air, being violently forced
into the other vessel, impinged against the sides of that
vessel, and thus the energy with which it was forced in
through the tap was again converted into heat. Thus
the air which was forced into the vacuum became hotter
than before, while the air which was left behind became
colder than before. But, on stirring the water round
these vessels, after the transmission of air had been
completed, and the stop-cock closed, Joule found that
the number of units of heat lost by the vessel and the
water on the one side, was almost precisely equal to
142 TRANSFORMA TION OF ENERG Y.
the quantity of additional heat which had been gained
on the other side.
He then repeated the experiment, putting instead
of two tanks of water, each holding one of the two
strong vessels, one larger tank also filled with water,
with both vessels buried side by side in it, then, on
allowing part of the air to escape, as before, from the
one into the other, and stirring till everything had ac-
quired exactly the same temperature, he found that there
was scarcely any measurable change in temperature.
These experimental methods, then, proved indisput-
ably that the quantity of heat lost by the one part of
the air was at least as nearly as that kind of experi-
ment enabled him to test it equal to the quantity of
heat gained by the other. Now, think of this for a
moment, and you will see that the compressed air had
at first a certain capability of doing work. You might
have used it to drive a compressed-air engine, or you
might have used it for propelling air-gun bullets, or
anything of that sort ; but in its final state, when it had
expanded to double its original bulk, it had not any-
thing like such an amount of available working power
stored up in it as it had before. There was, therefore,
dissipation of the energy, or of part of the energy, origin-
ally present ; and yet, as you have seen, the apparatus
and its contents had not lost any heat.
There was, on the whole, no heat lost, because what
was lost to the one vessel was gained by the other.
No heat was given out to external bodies, and no avail-
able work was done. The air was simply allowed to
expand to change its bulk without driving out
pistons, or doing anything by which it could convey
work to external bodies. It had, therefore, at last
TRANSFORMA TION OF ENERG Y. 143
precisely the same amount of energy as at first ; and
yet of that not nearly so much was available. The air
had seized at once the chance given it of dissipating
part of its energy, and did dissipate it, as far as was
compatible with the circumstances of the arrangement.
Now the really curious point about this is, that in
order to restore the lost availability to the energy of the
air, to get that air back into its former condition, so as
to be capable of doing as much work as it was capable
of doing at first, it would be necessary to spend work
upon it, pumping it back from the double vessel into
the single one ; but the amount of work which is so
spent in pumping it back goes to heat the whole mass
of air ; and when you have expended work enough to
force back the air into the first vessel from the second,
you find that the amount of heat which is given out
during that process and which can be measured with
great exactness is almost precisely equivalent to the
work which is spent in forcing the air back.
Thus to restore to the energy its former availability,
you do not need to spend any energy, you have only to
degrade some. You have spent work and got instead
its less useful heat-equivalent. You must waste a cer-
tain amount of energy, or rather get a bad form of
energy in place of it, in order to restore to the mass
of air the availability of the energy which it possessed
originally, and which had been allowed to be lost by
gradual expansion.
I can illustrate this in another and very instructive
way by taking an experiment belonging to the domain
of electricity. The experiment is, I daresay, a well-
enough known one, so far as the mere exhibition of an
experiment goes, but its really important feature, its
144 TRANSFORMA TION OF ENERG Y.
explanation as bearing upon the principles of energy,
and especially upon Carnot's results, does not appear to
be, at all events, very generally known. I have got here
a couple of Leyden jars, and, contrary to the usual
practice, their exterior and interior coatings are both
insulated. The jars are supported upon varnished glass
stems. Now, I am going to charge from the electric
machine only one of those two jars. First of all, we
shall charge and discharge it ; and you will be enabled
to judge roughly the amount of work which corresponds
to its full charge by the sound and light of the spark.
After that I shall charge it again as nearly as possible
to the same amount, and then share the charge of
electricity between the two jars, by putting first their
outer coatings together, and then their inner coatings ;
so that the charge shall be divided equally (because of
their equality) between the two. You now obtain
(showing) from the sound and light of that discharge-
TRANSFORMATION OF ENERGY. 145
spark an idea of the amount of work stored up in the
jar when charged. Now, the jar being charged again,
I simply place a chain over the two outer coatings, and
then I connect the interior coatings by means of the
discharging-rod. But you will notice that a spark
passes during that process. (Shows) Now, no elec-
tricity has disappeared, for the jars and discharging-
rod are, all of them, insulated. But by separating the
two jars from one another, and discharging them separ-
ately, you find there is a charge in each (shows), and
that these are as nearly as possible equal, so far as can
be judged by the appearance and sound of the discharges.
But you must have noticed, also, that of the four sparks
which you have just heard and seen, the first was very
much the stronger ; it made by far the greater noise, and
it was also the longer and more brilliant. The second
spark was the next in order of magnitude, and the two
final sparks, as we should have expected, were about
equal, but not at all comparable in intensity, even to
the second one, which was weaker than the first.
Now, this is a beautiful illustration of exactly, or
almost exactly, the same principle as that I have just
explained. When I had the full charge of electricity
in the one jar, there was a certain definite quantity of
what, for want of precise knowledge, we provisionally
call positive electricity, in the inner coating, and an
equal quantity of negative electricity was in the outer
coating. Then, when I connected the outer coatings of
the charged and the uncharged jar by means of this
chain, they formed, as it were, the outer coating of a
single jar ; but in order to make the two inner coatings
correspond in electric condition, I had to put the dis-
charging-rod between them, and you noticed that I
K
146 TRANSFORMA TION OF ENERG Y.
could not do so without allowing a spark to pass. A
spark necessarily passed during that operation, at least
it did so when a short stout metallic discharging-rod
was used.
Now, that spark represented a portion of energy
which was wasted a certain amount of work done in
producing sound, light, and heat. Therefore, obviously,
from the mere fact that such a spark passed when I
completed the connection between the two jars, you
saw that energy must have been wasted. But how
could the energy be wasted when there was no free
electricity lost? The quantity of positive electricity
originally in the inside of one jar was simply divided
between two jars ; there was just one-half the original
quantity of positive and one-half the quantity of negative
in each. The quantity of electricity remained the same,
and yet there was a quantity of energy dissipated during
the process. Now the answer is simply this (it was
originally made out as a very particular case of grand
general theorems, given first by Green and afterwards
interpreted and applied by Helmholtz and Sir William
Thomson), that the work due to a charge of electricity,
or the work which must be spent upon an electric
machine (suppose it wholly goes to producing electrical
charge of a conductor), depends upon the square of the
quantity of electricity. No matter what the form of
the conductor or jar is, the energy of the charge, or the
amount of work which it will do, depends upon the
square of the quantity of electricity. Now we can
understand perfectly our experimental result. Sup-
pose we call the quantity that the first jar had when it
was charged, one ; then, when I discharged it by itself
on the first occasion, you had a spark which corresponded
TRANSFORMA TION OF ENERG Y. 147
to the quantity of energy, the square of one, or one
itself. But when I put the two jars together, and thus
divided the charge, so that there was only one-half
the quantity of positive, and one-half the quantity of
negative in each jar, then the whole discharge of each
separate jar, or the energy of it, was proportional to
the square of one-half, that is, to one-fourth. Each of
these, when the charge had been divided between them,
contained a quantity of energy equal to one-fourth of
the original store, and therefore the two together corre-
sponded only to one-half of that store. Now we can see
what it was that produced the spark when I was dividing
the charge : that spark was the equivalent of the other
half of the energy, the half which necessarily went to
waste. You wasted the whole quantity by discharging
the charged jar itself; but in merely putting the two
together, so as to divide the charge, you wasted one-
half the energy, and then the quantities that you had
remaining corresponded to the two remaining quarters. 1
Now, in all these illustrations that I have shown you
whether they correspond to dissipation of ordinary
energy, or to dissipation by sound or friction, or even to
the production of heat, light, and so on, by electrical
discharges, in all these cases, you notice that there is a
tendency for the useful energy, whenever a transforma-
tion takes place, to run down in the scale, that, the
quantity being unaltered, the quality becomes deterior-
ated, or the availability becomes less ; and from similar
1 If instead of the stout, short, discharging-rod I had used a very long,
fine wire or other conductor of great resistance, such as, for instance, a
number of persons joining hands, the second spark might have been
reduced indefinitely ; but then the inevitably wasted half of the energy
would have appeared as heat in the wire, or in the physiological effects
of the shock.
1 48 TRANSFORMA TION OF ENERG Y.
results in all branches of physics we are entitled to
enuntiate, as Sir William Thomson did very early after
the new ideas were brought into full development, the
principle of Dissipation of Energy in nature.
The principle of dissipation, or degradation, as I
should prefer to call it, is simply this, that as every
operation going on in nature involves a transformation
of energy, and every transformation involves a certain
amount of degradation (degraded energy meaning
energy less capable of being transformed than before),
energy is continually becoming less and less trans-
formable.
As long as there are changes going on in nature, the
energy of the universe is getting lower and lower in the
scale, and you can see at once what its ultimate form
must be, so far at all events as our knowledge yet
extends. Its ultimate form must be that of heat so
diffused as to give all bodies the same temperature.
Whether it be a high temperature or a low temperature
does not matter, because whenever heat is so diffused
as to produce uniformity of temperature, it is in a con-
dition from which it cannot raise itself again. In order
to get any work out of heat, it is absolutely necessary
to have a hotter body and a colder one ; but if all the
energy in the universe be transformed into heat, and if
it be all in bodies at the same temperature, then it is
impossible at all events by any process that we know
of as yet to raise the smallest part of that energy into
a more available form.
Having seen then that this must be the ultimate end
of all the energy in the universe ; that so long at all
events as those I have just been explaining remain
physical laws this is the consequence to which they
TRANSFORMA TION OF ENERG Y. 149
must lead, it becomes a very necessary inquiry Whence
is it that the enormous quantities of energy which are
made use of, even on the surface of our diminutive
planet, are supplied to us ? What are our principal
sources of energy, and how do we transform the supplies
they afford us so as to make them useful for various
practical purposes, especially the most practical of all,
the practical one of living, which, so far as mere
vitality is concerned, is certainly a purely physical
process ?
Well, the muscular work which an animal does, and
the animal heat which it gives out (in much larger
equivalents than it does muscular work), these of course
we all know are due mainly to food. In such a term
as food, I include not merely solid and liquid food, but
also (and this is very important) the gaseous food which
we inhale. All these may be classed under the general
title of food. These being taken in, we have certain
other things which are got rid of, such as carbonic acid,
water, and so on. These you may call the ashes of our
food. These have, in their chemical relations, part of
the degraded energy of the food which was taken in.
The non-degraded part of the energy corresponds of
course to the muscular work done, and the store of
muscle, etc., laid up in the system.
Now, if this process were going on continuously
there would be constant using up of the oxygen of the
atmosphere by its combination with part of the food,
and production of the (to the animal) useless, or rather
pernicious, gas, carbonic acid. Leave this part of the
question as a difficulty for the moment, that we should
have the oxygen of the air gradually taken up, and its
place supplied, at all events to a great extent, with car-
1 50 TRANSFORM A TION OF ENERG Y.
bonic acid gas, in which an animal could not live :
still we have this further difficulty : Although animals
may live to a great extent upon animal food, yet if you
go on from man, who consumes a certain kind of
animal, while that animal also consumes animals, and
so on, there must be either a cycle in which the last
animal consumes man, or an infinite range as it were of
animals, so that all could live on animal food !
We know that it is not so, that there is a large class of
animals which consume only vegetable food. Now, it is
to the wonderful difference between the application of the
laws and processes of energy to the nutrition of animals,
and to that of vegetables, that we are indebted for the ex-
planation of the difficulty which I have just pointed out
to you what becomes of this large quantity of carbonic
acid gas, which in time would, if not got rid of, kill off
all animals, either by direct poisoning, or by depriving
them of their oxygen. The explanation is simply this,
that the animal takes in the oxygen, and with it animal
or vegetable food, giving out the objectionable carbonic
acid gas ; but, on the other hand, the plant takes the
carbonic acid gas, with water and other things, and
works it up again, gives back the oxygen to the air,
and stores up the carbon, etc., in the form of vegetable
food, upon which many animals live, and in their turn
become man's food.
Now, it is quite obvious that if plants were not assisted
by some external supply of energy, here would be some-
thing equivalent to the perpetual motion on the grandest
conceivable scale. If the plant were capable, merely by
its own peculiar organisation, of taking the ashes as it
were of the fuel burnt in the animal engine, and work-
ing them up again into fit and proper food, without
TRANSFORMA TION OF ENERG Y. 151
external assistance, then that process might go on
indefinitely, the animal all the time, remember, giving
out animal heat and doing muscular work.
This would be the perpetual motion on a scale never
contemplated even by the perpetual-motionists. It is
obvious then that in order to escape from our difficulty
no less than a contradiction in terms of what we
know to be a physical law there must be some source
of energy which the plant draws upon in order to help
it to work up that carbonic acid, etc., and store up the
available part of it as food for the animal.
It was long ago recognised, but first, perhaps, in a
nearly definite form, by Stephenson, that it was by
energy supplied in a radiant form from the sun, that
plants were enabled to decompose carbonic acid ; and it
is a very wonderful thing that those so-called actinic or
chemical radiations from the sun, which are most effec-
tive in promoting the decomposition of carbonic acid by
the leaves of plants, are the very rays which are most
absorbed by the green leaves. The green leaves are
particularly absorbent of them, and any of you may
convince himself of the fact by comparing the photo-
graph of a tree in full leaf with that of almost anything
else. In fact, the photographs of foliage (at all events
with the chemicals usually employed) are almost in-
variably exceedingly dull, even black, showing that the
chemically active rays, except those which have been
reflected from the surfaces of polished leaves, have been
absorbed at once by the green leaves, and in this act
have been performing their function of decomposing
carbonic acid and water.
In fact, we may make a rough comparison it is hot
by any means an exact one, but it is close enough to be
152 TRANSFORMA TION OF ENERG K
sufficient for our present purpose we may compare
roughly the animal to the cell of a galvanic battery,
where you have the virtual food supplied in the shape
of zinc and dilute sulphuric acid ; and the cell, by means
of the electric current it produces, driving an electro-
magnetic engine or producing heat in a wire, just as
the animal produces muscular work or animal heat.
On the other hand, you may roughly, with about the
same degree of approximate accuracy, compare the
plant to a cell in which energy, in the form of a current
of electricity, furnished from an external source, is
employed in decomposing water, let us say : separating
it into its oxygen and hydrogen, and producing that
high form of potential energy which I exhibited to you
experimentally in a former lecture ; so that fresh
materials, as it were, for the battery cell are being
actually separated, and getting their potential energy
given back to them in the decomposing cell. That
corresponds to the plant. You supply these materials
again to the cell of the battery, and it again produces
electric currents, and so on in succession.
But it is quite obvious that a process of that kind
cannot go on without a supply of energy from
without. The raising of energy from the lower form
to the higher always requires external application of
some fresh energy, which is itself degraded in the pro-
cess. This idea originated with Joule at a very early
period of his investigations ; and he pointed out that
not only does an animal much more nearly resemble
in its functions an electro-magnetic engine than it
resembles a steam-engine, but he also pointed out that
it is a much more efficient engine, that is to say, an
animal, for the same amount of potential energy of food
TRANSFORMA TION OF ENERG Y. 1 53
or fuel supplied to it (call it fuel, to compare it with the
other engines), gives you a larger amount converted
into work than any engine which we can construct
physically.
To use the vernacular of engineers on the subject, the
' duty ' of an animal engine is much larger than the
duty of any other engine, steam, or electro-magnetic,
or otherwise, which we can construct to employ fuel,
the duty simply meaning the percentage of the
energy of the fuel supplied to the engine which it can
convert into the useful or desired form. Carefully
observe here that this does not necessarily hold true
if we contemplate water-mills, etc., for there the energy
supplied is in general of a higher order than that of
food or fuel.
Now, from what I have said, you will see that the
supply which the plant requires comes from the sun.
That leads us then to the question what is the source
of the sun's energy ? Now, when, with the view of
answering that question, we make a few calculations,
we find that they at once upset the first ideas that we
are likely to form for ourselves on the subject. Of
course, the old notion that the sun is a huge fire, or
something of that kind, is one which will only occur to
those thinking of the matter for the first time ; but with
our modern chemical knowledge, assisting the more
ordinary physical reasoning which I have just given you,
we are enabled to say, that, massive as the sun is, if its
materials had consisted even of the very best materials
for giving out heat by what we understand on the ter-
restrial surface as combustion,- that enormous mass of
some 400,000 miles in radius could have supplied us
with only about 5000 years of its present radiation. A
1 54 TRANSFORM A TION OF ENERG Y.
mass of coal of that size would have produced very
much less than that amount of heat. Take (in mass
equal to the sun's mass) the most energetic chemicals
known to us, and in the proper proportion for giving
the greatest amount of heat by actual chemical combi-
nation ; and, so far as we yet know their properties,
we cannot see the means of supplying the sun's present
waste for even 5000 years.
Therefore, as we all know that geological facts, if
there were no others, point to at least as high -a radiation
from the sun as the present, for at all events a few
hundreds of thousands of years back, perhaps, as we
shall find later, even a few millions of years back,
and perhaps also indicate even a higher rate of
radiation from the sun in old time than at present
it is quite obvious to you that the heat of the sun
cannot possibly be supplied by any chemical process
of which we have the slightest conception.
Now, if we can find, on the other hand, any physical
explanation of this, consistent with our present know-
ledge, we are bound to take it and use it as far as we
can, rather than say This question is totally unanswer-
able unless there be chemical agencies at work in the
sun of a far more powerful order than anything that
we meet with on the earth's surface. If we can find a
thoroughly intelligible source of heat, which, though
depending upon a different physical cause from the
usual one, combustion, is amply sufficient to have
supplied the sun with such an amount of heat as to
enable it to have radiated for perhaps the last hundred
millions of years at the same rate as it is now radiating,
then I say we are bound to try that hypothesis first, and
argue upon it until we find it inconsistent with something
TRANSFORMA TION OF ENERG Y. 155
known. And if we do not find it inconsistent with
anything that is known, while we find it completely
capable of explaining our difficulty, then it is not only
philosophic to say that it is most probably the origin of
the sun's energy, but we feel ourselves constrained to
admit it. Newton long ago told us this obligation in
his Rides of Philosophising.
The shortest and easiest way in which I can illustrate
this simple though tremendously important step is by
stating that if we were to take a mass of the most per-
fect combustibles which we know, those combustibles
which give the greatest amount of energy when
burned together, and let it fall upon the sun merely
from the earth's distance, then the work done upon
it by the sun's attraction during its fall would give it
so large an amount of kinetic energy when it reached
the sun's surface as to produce an impact which
would represent 6000 times the amount of energy which
could be produced by its mere burning. It is, in fact,
capable of perfectly easy and simple demonstration,
that a mass which would produce the utmost known
energy by burning, would give 6000 times more energy
by a simple fall from the earth's distance upon the sur-
face of the sim.
It appears, then, that until it is shown that there is,
or has been, in the physical universe, at some time or
other, a greater amount of kinetic energy than can be
accounted for by the falling together of the masses
which compose the sun and stars, our natural and only
trustworthy mode of explaining the sun's heat at present,
in time past, and for time to come, must be something
closely analogous to, but not identical with, what was
called the nebular hypothesis of Laplace very eagerly
156 TRANSFORMA TION OF ENERG Y.
accepted when it was first proposed the hypothesis of
the falling together (from widely scattered distribution
in space) of the matter which now forms the various
suns and planets. We find, by calculations in which
there is no possibility of large error, that this hypothesis
is thoroughly competent to explain 100 millions of years'
solar radiation at the present rate, perhaps more ;
and it is capable of showing us how it is that the sun,
for thousands of years together, can part with energy
at the enormous rate at which it does still part with it,
and yet not apparently cool by perhaps any measurable
quantity.
Now, in confirmation of this it is well to state here,
that not only is the hypothesis itself capable of ex-
plaining the amounts of energy which are in question,
but also recent investigations, aided by the spectroscope,
of which I shall have a good deal to say in another
lecture, have shown us that there are gigantic nebular
systems at great distances from our solar system, in
the process of (physical) degradation in that very way,
by the falling together of scattered masses, and with
immense consequent developments of heat by impacts.
What are called temporary stars form another splendid
and still more striking instance of it, as where a star
suddenly appears of the first magnitude, or even brighter
than the first, outshining all the planets for a month or
two at a time, and then, after a little time, becomes
invisible in the most powerful telescope. Things of that
kind are constantly occurring on a larger or smaller
scale, and they can all be easily explained on this sup-
position of the impact of gravitating masses.
Now, holding that such may be the cause of the
enormous amount of radiation from the sun, let us
TRANSFORMA TION OF ENERG Y. 157
inquire what fraction of that whole radiation reaches our
own little globe. We know what an enormous quantity
of solar heat reaches the earth, reaches even our own
small corner of the earth. That is of course a very
small part of what reaches the earth's whole surface ;
but still, if you recollect that the earth, as seen from the
sun, appears very much less than the planet Jupiter, or
even Mars, as seen by us, that is, that it would present
no visible disc to the naked eye, and that to an observer
at such a distance as that of the sun it would require a
telescope of some little magnifying power to show it as
a disc at all, considering also that the sun is radiating
very nearly uniformly in all directions, how much of
the sun's entire radiations can reach this little speck at
such a distance as ninety millions of miles ? A circular
disc of four thousand miles radius, at a distance of
ninety-one million miles, appears to occupy less than
one two-thousand-millionth part of the celestial sphere.
You see, then, that the quantity of heat which the
whole earth gets from the sun is of the order of some-
thing less than the two-thousand-millionth part of that
which the sun gives out. Now, experiments have been
made, and fairly satisfactory ones, to determine what
amount of heat we do receive what amount of energy
does fall upon the earth's surface in a given time. Of
course, they are interfered with to a considerable extent
by absorption of the radiation as it passes through the
various and varying constituents of the earth's atmo-
sphere in each region of the globe ; and therefore the
most trustworthy experimental results have been such
as were obtained at considerable elevations in balloons,
or on the tops of very high mountains, where there is
comparatively little absorption.
1 5 8
TRANSFORMATION OF ENERGY.
This instrument, the pyrheliometer, is constructed
for the purpose of measuring the amount of radiation
from the sun. It is made of silver polished on the
cylindrical part, and on the back, because this is an
exceedingly bad radiator of heat, so that the instru-
TRANSFORMA TION OF ENERG K 1 59
ment loses by those sides very little of the heat which
it collects by the blackened side, which is a good
absorber and is turned directly to the sun. This little
silver vessel is filled with water, and all the radiant
heat and light, everything in the form of radiation that
falls upon this lampblack, is absorbed by it, and is
degraded into the form of heat and so communicated
to the water. In the middle of the water is the bulb of
the thermometer, whose stem runs down through the
axis of the apparatus. We can adjust it so that the
blackened disc shall receive the sun's rays perpendicu-
larly, by a very simple contrivance : a disc of metal at
the other end of the thermometer tube, of exactly the
same size as the first disc : then the whole being so set
that the shadows of the two discs coincide, we know
that it is turned directly to the sun. Take off the cap
of the instrument for a measured period, put it on again,
and after the whole has been thoroughly shaken up, so
that the temperature of the water is the same through-
out, read off the rise of temperature as shown by the
thermometer. Correct that for the loss of heat by
radiation during the performance of the experiment.
That can be done at once by simply watching how it
gradually loses heat when it is turned to the sky, but
screened from the sun's radiation. With this instru-
ment we can make a fairly approximate estimate of the
amount of heat which is received from the sun by the
blackened surface in a given time ; and by comparing
the surface of this disc with the surface of the whole
earth which is exposed to the sun, we can estimate at
least approximately how much radiant energy in the
form of heat, light, actinism, and so on, comes to us
per second from the sun ; and therefore we can esti-
160 TRANSFORMA TION OF ENERG Y.
mate what amount of energy leaves the sun's whole
surface every second, that is to say, what number of
foot-pounds of energy the sun is spending per unit of
time.
According to Thomson (calculating from the data of
Pouillet and Herschel), the sun's radiation is equiva-
lent to about 7000 horse-power per square foot of his
surface somewhere about thirty-fold that of the same
area of the furnace of a locomotive and somewhere
about 6x io 30 units of heat (c.) leave his whole surface
per annum.
In addition to the data which I have just given you,
I shall conclude this morning by giving one or two
others. Let us take the case of the earth's motion in
its orbit. The immense mass of the earth moving round
in its circle of over 90,000,000 miles radius in one year
is moving at what we should consider an enormous rate,
far greater than that of a cannon ball (being in fact
about 80 times as great), and yet the whole kinetic
energy it would supply, if it were accidentally to impinge
upon a huge target, as an Armstrong projectile goes
against an iron plate, is a mere trifle to what we have
been considering ; it could only supply by that fright-
ful crash an amount of heat equal to the sun's loss
in about 80 days. But if instead of taking its energy
of motion in its orbit, you were to take its potential
energy, as a heavy body which, if allowed, would
fall into the sun, and there produce an immense
development of heat by impact, the calculation leads
us to this result, that it would acquire, on reaching
the sun's surface, such a speed that the energy of the
impact would be equivalent to the heat at present
given out by the sun in about 91 years. But the
TRANSFORMA TION OF ENERG Y. 161
planet Jupiter is not only enormously more massive
than the earth, but is also very much farther away
from the sun, and therefore on both accounts it would
produce a much greater development of heat if it were
to fall into the sun. The calculations made on the
same data for the planet Jupiter give something like
32,000 years, that is to say, Jupiter alone falling into
the sun would supply its present loss for 32,000 years
to come.
Then, there is one final datum with which I shall con-
clude to-day, and it is this : I shall give more detailed
explanation of it in my next lecture, but I wish to men-
tion it before concluding, that the lowest possible
estimate which we can make of the capacity of the sun
for heat is such that, cooling at the present rate losing
energy at its present rate the sun cannot possibly
cool more than a single degree Centigrade in seven
years. It may be, on the highest estimate we can take,
one degree in 7000 years ; the data are very uncertain ;
but we may say that these are the limits between which
it must lie. Startling as are many of the matter-of-fact
statements I have made to you to-day, I cannot help
once more repeating this, by far the strangest of them
all : the sun has such an enormous capacity for heat
that it takes at least seven years, at its present enormous
rate of radiation, to cool by one degree Centigrade !
LECTURE VII.
SOURCES AND TRANSFERENCE OF ENERGY.
Available Sources of Energy on the Earth. Whence these have been derived
Uniformitarian School of Geologists. Sir W. Thomson's arguments as
to the length of time during which life has been possible on the earth.
Transference of Energy through Solids, Fluids, and through the Ether.
Test of the Receptivity of a body or system for energy in a vibratory form
Physical Analogies introductory to Spectrum Analysis.
IN my last lecture I considered, in as great detail as
our necessarily limited time permitted, the origin of the
energy of the solar system. I must now consider in
part of to-day's lecture a smaller, but much more im-
portant matter, much more directly personal to us,
namely, our available sources of terrestrial energy. In
my little work upon Thermo-Dynamics, I have arranged
these sources in order as follows :
First. Our available sources of potential energy.
1st, Fuel. Under the head of fuel I should include
not merely coal, wood, and so on, but also all that may
properly be called fuel the zinc used in a galvanic
battery, for instance, and various other things of that
kind.
2d, The food of animals.
3d, Ordinary water-power.
4th, Tidal water-power.
All these are forms of potential energy.
SOURCES AND TRANSFERENCE OFENEJfGY. 163
Then, Secondly, in the Kinetic form, we have
(i.) Winds.
(2.) Currents of water, especially ocean currents ; and
finally we have
(3.) Hot springs and volcanoes.
There are other very small sources known to us,
exceedingly small ; but these I have named include
our principal resources.
Now comes the question, what are the sources of these
supplies themselves ? I find I have classified them also
under four heads.
The first is primitive chemical affinity, chemical
affinity which we may suppose to have existed between
particles of matter from the earliest times, and still to
exist between them, because these portions of matter
-have not combined with one another nor with other
matter. If, for instance, when the materials of which
the earth is at present composed were widely separated
from one another, there were particles of meteoric iron
and native sulphur which, when the materials did come
together to form the earth and heated one another by
mutual impact, did not combine together but have still
remained through long periods of time separate from
one another, we should consider that the mutual chemi-
cal potential energy of the iron and sulphur remains to
us as a portion of energy primordially connected with
the universe. But of that, so far as we know, at least
near the surface of the earth there is very little. There
may be towards the interior enormous masses of as yet
uncombined iron and uncombined sulphur, or various
other materials, but towards the surface, where they
could be of any direct use to us, the quantities of these
are excessively small.
1 64 SOURCES AND TRANSFERENCE OF ENERGY.
The second source is that which I have several times
alluded to, solar radiation, and that is by far the most
abundant source we have.
Then we have two very instructive forms, viz., the
energy of the earth's rotation about its axis, and the
internal heat of the earth.
Now, if we take in turn the enumeration which I gave
at first of our available stock, and compare it with the
sources from which we derive that stock, we shall easily
see how the two are connected with one another.
First, we have fuel. Now, our supplies of fuel are
almost entirely due to the sun. That is to say, in times
long gone by, the sun's rays by their energy, as absorbed
in the green leaves of plants, decomposed carbonic acid
and stored up the carbon. That carbon, and various
other things stored up ages ago along with it, we have
still as an immense reserve fund of coal.
Then for the food of animals we are mainly indebted
to the sun again, because the food of animals must ulti-
mately be vegetable food, even of the animals which
live upon animal food. Then for ordinary water-power
we are also indebted to the sun, because it is mainly
the energy of the radiation from the sun in its heat
form which evaporates water from the plains or seas,
and allows it to be precipitated again at such a height
that it has potential energy in virtue of its elevation.
Ordinary currents of water are a mere transformation
of this potential energy, because water on a height may
convert part of its potential energy into kinetic energy
of visible motion as it flows down.
But when we come to tidal water-power we must look
to another source. If we employ tidal power for the
purpose of driving an engine, we take it in the rise of
SOURCES AND TRANSFERENCE OF ENERGY. 165
the water as the tide-wave passes us. We secure a por-
tion of water at a certain elevation, wait till the tide has
gone back, and then take advantage of the descent of
that portion of water. Now, if we were to go on doing
that for any considerable period of time, and doing it
over large tracts of sea-coast, we should find that the
effect of it in time would be to gradually slacken the
rate of rotation of the earth ; so that if all our important
sources of power, such as coal, and direct solar radia-
tion, were to fail us in great part, and if we were driven
finally as a last resource to use tidal water-power, it
might come to be a very serious international question
between those kingdoms which possessed sea-board and
those which had none. For if it were largely employed,
the period of the rotation of the earth might be in a
moderate period of years seriously affected. And there
seems to be no known compensating advantage for
those nations who are not possessed of an extensive
sea-board within the Temperate or Torrid Zones, where
alone this source of power would be of much avail.
Then we have, next to these, winds and ocean cur-
rents. These are almost entirely due to solar radiant
heat. And, finally, hot springs and volcanoes, which
have never been employed for any direct production of
work, but which might possibly be so used. Their
energy depends, mainly at least, upon the internal heat
of the earth ; partly perhaps on potential energy of
chemical affinity.
So you see that mainly to solar radiation, but partly
to the other three sources of supply, are due the various
stores of energy which we have at our disposal. This,
however, is a mere bare enumeration. I might spend
many lectures developing small parts of this grand
1 66 SOURCES AND TRANSFERENCE OF ENERGY.
subject ; but I have given you in these few words the
large heads, and it is scarcely compatible with the time
at our disposal to devote another couple of lectures to
pursuing the subject into its minute details.
The next question I take up is this, intimately con-
nected with what we have just considered : the question
of how long something like the present state of things
has been going on on the earth's surface. This is an
extremely important question, and can be approached
from various sides, from the geological side, for in-
stance, by consideration of the thickness of strata, of
amounts of erosion, and such like ; but it can also be
approached directly from the point of view of energy,
and from that point of view alone I shall now attempt
briefly to treat it.
The old notion of what was called the Uniformitarian
school of Geology, was simply that things had been
going on and were to go on, both in the past for many
millions of years, and in the future for many other mil-
lions of years, at as nearly as possible the same uniform
rate, that we were getting a steady supply of heat
from the sun, that even if energy (it was not called
energy in those days), even if some source of supply, call
it what you like, was disappearing in some portion of
the interior of the earth, at its disappearance it was
producing say electric currents, and decomposing some
compound substance ; so that, if ever lost by chemical
combination at one place, electric currents would be
produced, and something equivalent thereby given out
in some other place, so that the stock should be main-
tained as nearly as possible at a uniform state.
Now, this is totally inconsistent with modern physical
knowledge as to the dissipation of energy. Transfer-
SOURCES AND TRANSFERENCE OF ENERGY. 167
mations must be going on now (at least on the average)
at a much slower rate than they were going ages ago.
Just as when you take a red-hot ball from a furnace ;
it cools at a certain rate, but as it becomes colder it
cools more and more slowly. And this is not a mere
analogy, but an almost absolute identity, with the case
of the earth and the sun. There is no doubt that at
some period long ago the earth was so hot as to be at
all events plastic, if not absolutely liquid throughout
its mass ; and there is no doubt that at the present
moment, even after ages of expenditure of energy at a
very great rate, the sun must be still liquid in great
part, and even gaseous in very large part.
Now, we can apply the theory of energy, especially
from Carnot's point of view, to the state of things in
the earth and in the sun, and can at all events roughly
approximate to the period during which the earth has
been habitable for animals and plants such as we find
upon it now. We do not say, of course, that it was in-
habited for such periods by animals and plants such as
we see now, or find fossil remains of ; but we can trace
approximately backwards for how long the earth was
habitable by such, and that is the problem we propose
to solve.
This subject was taken up very carefully within the
last few years by Sir William Thomson, and the brief
resume I shall give of his results contains nearly all that
is accurately and definitely acquired to science upon
the subject. He divides his arguments upon it into
three heads. The first is an argument from the internal
heat of the earth ; the second is from the tidal retarda-
tion of the earth's rotation ; and the third is from the
sun's temperature.
1 68 SOURCES AND TRANSFERENCE OF ENERGY.
Now, as regards the internal heat of the earth, we
know by actual observation that as we go down a deep
mine we find the temperature almost invariably increas-
ing. We know also that whenever a body is hotter at
one part than another, the tendency of heat is always
to flow from the hotter part of the body to the colder.
Therefore, as the earth's crust is warmer and warmer as
we go farther and farther down, there must be a steady
flow of heat outwards from the interior to the surface.
The earth is therefore even now losing heat at a certain
perfectly measurable and calculable rate. But if it
is losing heat now we can calculate by known physical
laws and known mathematical processes, from the pre-
sent state of distribution of temperature, we can cal-
culate backwards how its heat was arranged a hundred
thousand or a thousand thousand years ago, just as
certainly if physical laws as we know them now were
in existence in the past as we can predict from our
mathematical calculations what will be its distribution
at any time future, if these physical laws continue to
hold. In working out such a question as this, it is
found that the rise of temperature, taken (over the
whole earth's surface) at an average of about one
degree for 100 feet of descent, leads to this conclusion,
that about ten millions of years ago the surface of the
earth had just consolidated, or was just about to con-
solidate; and in the course of a comparatively few
thousands of years after that, the surface which had
been consolidated had become so moderately warm
as to be fitted, at all events in some parts, for the exist-
ence of life such as we know it. That is to say, the
surface temperature, in certain regions at least, was not
greater than that which is perfectly easily borne by
SOURCES AND TRANSFERENCE OF ENERGY. 169
animals and vegetables in the tropics at the present
day ; and the rate of increase of temperature in going
down below the surface was one degree in perhaps
every six inches, or every ten inches, or something of
that sort. That would not interfere very greatly with
the growth of vegetables ; so from this point of view
we are led to a limit of something like ten million
years as the utmost we can give to geologists for their
speculations as to the history even of the lowest
orders of fossils.
If we were to trace the state of affairs back, instead
of to ten millions, to a hundred millions of years, we
should find that (if the earth then existed at all, if that
collocation of matter which we call the earth was then
actually formed), and if the physical laws which at
present hold have been in operation during that
hundred million years, then the surface of the earth
would undoubtedly have been liquid and at a high
white heat, so that it would have been utterly incom-
patible with the existence of life of any kind such as
we can conceive from what we are acquainted with.
Thus we can say at once to geologists, that granting
this premiss, that physical laws have remained as they
are now, and that we know of all the physical laws
which have been operating during that time, we can-
not give more scope for their speculations than about
ten or (say at most) fifteen millions of years.
But I daresay many of you are acquainted with the
speculations of Lyell and others, especially of Darwin, 1
who tell us that even for a comparatively brief portion
of recent geological history three hundred millions of
years will not suffice !
1 Origin of Species (1859), p. 287.
i;o SOURCES AND TRANSFERENCE OF ENERGY.
We say So much the worse for geology as at present
understood by its chief authorities, for, as you will
presently see, physical considerations from various inde-
pendent points of view render it utterly impossible that
more than ten or fifteen millions of years can be granted.
You see, then, that the argument from the internal
heat of the earth depends upon working the problem
backwards, and finding what is the utmost limit of time
back at which the surface of the earth could possibly
have been fitted for the life of either animals or plants.
And this leads me to say a word or two about one
of the most remarkable results of investigations of this
kind, investigations conducted as purely mathematical
problems, and based entirely upon physical experimental
data, viz., upon the observed laws of conduction of
heat. In the great majority of problems where the
data are of the nature of those we have as to the under-
ground temperature of the earth, the question of the
future is a perfectly definite one. If we knew the pre-
sent thermal condition of every part of the earth's mass,
we could calculate what would be the temperature at
any depth below the earth's surface at any time future,
provided things went on under the same conditions as
they are going at present, and our results would be
always perfectly and directly intelligible. But when
we try to work the problem the other way, when we
ask what must have been the thermal state of such a
body as the earth at such and such a time past, then
we invariably, or almost invariably, find a limit of time
beyond which our equations become uninterpretable. So
far as our equations represent what would be the course
of nature provided the existing physical laws remained
true, there must have been at this definite epoch of
SOURCES AND TRANSFERENCE OF ENERGY. 171
past time the introduction of a new state of affairs,
something which arose from a previous state by
means of a process not contemplated in our investiga-
tion.
In the case of the earth there is no particular diffi-
culty in understanding what might have been that an-
terior state of affairs. We can trace matters back to
the time when the earth was molten throughout. Going
farther and farther back, we come to a distribution
(which might be pretty nearly uniform) of heat through-
out the whole mass. Now, a uniform distribution of
heat throughout the whole mass could have had no
existence for more than an instant, so far as we know ;
and we cannot conceive it to have arisen from any pre-
vious distribution of heat in the mass. But we can
understand how a high temperature throughout the
whole mass might have been produced by the materials
of which the earth is composed falling together. If
they fell together in such a way that the whole mass of
the earth was agglomerated together almost at once ;
and if the different parts impinged together with pro-
perly arranged velocities, it is possible the earth may
have been agglomerated together, so as to have for a
moment the same temperature throughout, thus giving
us something like what we have deduced from our for-
mulae. But you will notice the state of things before
and after that moment. Before that moment it was
cold masses of matter, separated perhaps by millions of
miles, or far more than that, but having potential energy
of gravitation gradually being transformed into kinetic
energy of approach. Then, at the instant of impact,
came the critical change. Instead of the cold scattered
masses of matter, there was suddenly an agglomerated
172 SOURCES AND TRANSFERENCE OF ENERGY.
mass of almost uniform temperature throughout, and it
has been cooling and shrinking ever since.
The second of these arguments of Sir William Thom-
son depends upon the tidal retardation. In my first
lecture I mentioned to you that there was such an
effect, and that it had been actually observed by astro-
nomers in a very peculiar way ; because, on calculating
back from the known present motion of the moon, it
was found that there must be some unrecognised pecu-
liarity in that motion, which had not been deduced by
calculations founded upon gravitation, either as attrac-
tion or as disturbance. The moon, in fact, seems to
have been moving quicker as time has gone on, since the
eclipses of the fifth and eighth centuries before our era.
The only way, as Laplace put it, in which it could be
accounted for in his time, was by what he called ' secular
acceleration of the moon's mean motion.' In other
words, the average angular velocity with. which the
moon moves round the earth appears to have been in-
creasing for the last 2000 years or more. He showed
that there was a mode of accounting for this by planet-
ary disturbance of the earth's orbit, and as calculated
by him, this explanation seemed to account for exactly
the amount of acceleration which was observed in the
moon's motion. Using his formulae and the numbers
calculated from them, and working back to those old
days, we find we arrive at almost the circumstances of
those eclipses as described by historians.
Fortunately, Adams, a few years ago, revised La-
place's investigation, and found that he had neglected
a portion of the necessary terms, and that the expla-
nation given by Laplace, when properly corrected, ac-
counted for only one-half of the phenomenon observed ;
SOURCES AND TRANSFERENCE OF ENERGY. 173
so that there still remained one-half of the quantity to be
accounted for. This could not be accounted for by the
disturbance of other bodies attracting the moon. Why
then does the moon appear every revolution to be moving
faster and faster round the earth ? Well, the only way
in which we can explain it, after we have made every
possible allowance for effects of disturbance by other
planets, is simply to inquire, Does our measure of time
continue the same ?
We measure the time of the moon's revolution in
terms of hours, minutes, and seconds ; but these hours,
minutes, and seconds are measured for us not by our
clocks, as you may at first think. We set our clocks
by the earth's rotation, and therefore it is in terms
of the earth's rotation that we measure the time of the
moon's revolution round the earth. So that the moon
will appear to be moving quicker round the earth,
even supposing her orbit be altogether undisturbed, if
the earth itself, which is furnishing the unit of time in
which her revolution is to be measured, is rotating
slower and slower from age to age.
Then comes the question, Is there a cause which
tends to slacken the earth's rotation ? Newton laid it
down, in his First Law of Motion, that motion unresisted
remains uniform for ever, and referred to the earth as a
particular instance where there is nothing in the attrac-
tion of the sun or moon, or the disturbance caused by
any of the other planets, affecting the rate of its rota-
tion about its axis. But it was left to Kant, first of all,
to point out, and even to approximate in amount to,
a resistance to the earth's rotation due to the tide-wave ;
and to show that the earth, because the tide-wave is
lifted up towards the moon, and on the opposite side
174 SOURCES AND TRANSFERENCE OF ENERGY.
from the moon, has constantly to rotate inside what is
practically a friction-brake. The water is held back by
the attraction of the sun and moon, and the earth has
to move inside this shell of water. There is therefore
a source of constant friction, and friction of course
constantly produces development of heat. The heat
must be accounted for by some energy transformed,
and what is here transformed is part of the energy of
the earth's rotation about its axis. So long as tides go
on, there will therefore be constantly a retardation of
the rate of the earth's rotation.
Now let us see when this relaxation of the earth's
rotation would cease. Obviously this would be at the
instant when the earth at last ceased to rotate within
the tide-wave ; in other words, when the tide-wave
rotates along with the earth, when it is always full tide
at one and the same portion of the earth's surface, the
tide-wave being fixed (as it were) upon the earth's sur-
face. But the ^tide-wave is always, approximately at
least, directed towards the moon, so this part of the sur-
face where the tide-wave is fixed for ever must be con-
stantly turned towards the moon. In other words, if
there were no sun producing tides, but the moon only,
the final effect of the tides in stopping or quenching the
earth's rotation would be to bring the earth constantly
to turn the same portion of its surface towards the
moon, and therefore to rotate about its axis in the same
period as that in which the moon revolves about it.
This most remarkable ultimate effect we see already
produced in the moon, it is precisely the same thing,
we see the moon turning almost exactly the same
portion of its surface to the earth at all times. The
little deviation we see occasionally is precisely ac-
SOURCES AND TRANSFERENCE OF ENERGY. 175
counted for by the fact that the moon's orbit is not
exactly a circle, and therefore the moon does not
move in it with the same rapidity when it is nearest the
earth as it does when it is farthest away from the earth.
We are thus, as it were, enabled occasionally to see a
little round the corner. The moon is now rotating pre-
cisely in the way in which the earth will in time rotate
when as much as possible of its energy of rotation is
used up in producing heat by tidal friction. And that
the moon should already have come into this state so
long before the earth has arrived at it, need not sur-
prise us. The moon's seas (when she had them) were of
molten lava, far more viscous than water ; the tide-
raising force on her surface depended on the mass of the
earth, some eighty times greater than that of the moon,
which is the main agent in our comparatively puny tides :
and, in addition, the moon's moment of inertia is very
small compared with that of the earth.
It being thus established that the rate of rotation of
the earth is constantly becoming slower, the question
comes : How long ago must it have solidified in order
that it might then have the particular amount of polar
flattening which it shows at present ? Suppose for
instance it had not consolidated less than a thousand
million years ago. Calculation shows us that at that
time, on the most moderate computation, it must have
been rotating at least twice as fast as it is now rotating.
That is to say, the day must have been 12 hours long
instead of 24. Now, if that had been the case, and the
earth still fluid throughout, or even pasty, that double
rate of rotation would have produced four times as great
centrifugal force at the equator as at present, and the
flattening of the earth at the poles and the bulging at
i ;6 SOURCES AND TRANSFERENCE OF ENERGY.
the equator -itfould both have been much greater than
we find them to be.
We say then, that because the earth is so little
flattened it must have been rotating at very nearly the
same rate as it is now rotating, when it became solid.
Therefore, as its rate of rotation is undoubtedly be-
coming slower and slower, it cannot have been many
millions of years back when it became solid, else it
would have solidified into something very much flatter
than we find it. That argument, taken along with the
first one, probably reduces the possible period which can
be allowed to geologists to something less than ten
millions of years.
Then comes the third argument, it is not quite so
emphatic in its demands for restricted periods as either
of the other two, the argument from the length of
time that the sun can be imagined by its radiation to
have kept the earth in a state fit for the habitation of
animals and vegetables. The argument from this point
of view, I say, is not so trenchant as the others, because
we can imagine that when the sun was immensely hot,
as it must have been at some previous time, enor-
mously hotter than at present, we can imagine that
one effect of its heat was to throw off from its surface
such enormous clouds of absorbing vapour, which cooled
as they left the surface, that the effective amount of
radiation reaching the earth might not have been greater
than at present. So it is possible to conceive a sort of
uniformitarian state of radiation from the sun: account-
ing for it by saying that when the sun was hottest and
was radiating the most, it was simultaneously raising the
greatest amount of obstructions to the propagation of
radiations from its surface. A similar argument might,
SOURCES AND TRANSFERENCE OF ENERGY. 177
of course, be devised with reference to the greater
amount of vapour which increased solar radiation would
raise to be condensed in the earth's atmosphere. How-
ever, if we make the supposition that the sun has been
cooling even at a uniform rate, we find that this mode
of calculation leads us, in spite of the enormous amount
of heat which must have been produced in the sun by
the impact of its materials when they fell together, to
the conclusion that on the very highest computation
which can be permitted, it cannot have supplied the
earth, even at the present rate, for more than about
fifteen or twenty million years. 1
This, I again say, is not so trenchant an argument as
either of the other two ; but the conclusion from these
three arguments is not, as some of Thomson's opponents
seem to imagine, only as strong as the weakest of the
three. In order to upset the conclusions drawn from
them, it would be necessary to disprove two of these
arguments, and greatly to damage the third. But each
of these arguments is quite independent of the other
two, and is for all tend to something about the same
to the effect that ten millions of years is about the
utmost that can be allowed, from the physical point of
view, for all the changes that have taken place on the
earth's surface since vegetable life of the lowest known
form was capable of existing there.
I leave this part of the subject for a time. This has
been a developed application of the theory of energy
f 1 Note to Third Edition. Several critics, as well as some writers of a
higher order, think they have detected inconsistency between this passage
and another in p. 156. There is no such inconsistency. At p. 156 the
whole supply was spoken of; while here we are dealing with what has
been already expended.]
M
178 SOURCES AND TRANSFERENCE OF ENERGY.
to the solar system first, and then in particular to our
own earth.
Now, I pass to one or two other applications of the
second law of thermodynamics, especially in the beau-
tiful part of it furnished by Carnot's reasoning. We
have now to take up the consideration of the transfer-
ence of energy from one body to another, not the
passage of energy from one part of a body to another
portion of the same body. That is in the main the
question of the conduction of heat, to which I shall
devote another lecture. But now we are to speak
of the radiation of heat and light from one body to
another.
But before I take up that I shall direct your atten-
tion to one or two experiments, some of them long
known but at their epoch hardly explained, others only
recently made.
First of all, let us take as the medium of communica-
tion between two bodies : the medium through which
the energy is to be transferred from one body to an-
other: a strong wooden framework such as this. I
have two pendulums with very massive bobs suspended
from it, and have carefully made these two pendulums as
nearly as possible of the same length, so that their
times of vibration are as nearly as possible the same.
Both pendulums are now at rest, but suppose I set
one to vibrate, leaving the other at rest, you will notice,
if you watch the second for a short time, that it begins
to vibrate in its turn, and as time goes on it swings
through larger and larger arcs of vibration, till at last
the first pendulum is reduced to rest. Now, this is
quite obviously a case of transference of energy from
one pendulum to the other, effected, you will see,
SOURCES AND TRANSFERENCE OF ENERGY. 179
through the wooden structure ; but it has been effected
thus completely on account of the simple fact that the
two pendulums had been (as it were) previously tuned
together and made to vibrate in precisely equal times.
We shall presently try the experiment with the two
pendulums not tuned together, and then you will see
that there may be transference of energy for a few
minutes, but it will be far less complete, and in the
course of a very short time the whole will be given
back again to the first pendulum, and so on. In the
case before us, a short time will suffice for the whole of
the energy to be transferred from the one pendulum to
the other, and it will then be just as if we had turned
i8o SOURCES AND TRANSFERENCE OF ENERGY.
the whole apparatus round through two right angles.
You will have the second pendulum vibrating with the
whole original energy in place of the first, then the
transference will go on again in the opposite direction,
and the first will get back what it lost, except what has
been unavoidably dissipated in producing air vibrations,
and in producing heat in the materials of the frame-
work, which is not a perfectly elastic body, and all
throughout which friction and various other disturb-
ing causes operate. Notice particularly that the mode
of transference in this case is through a solid body, and
that it is simply by vibration of the solid body that it
has been effected.
I pass from the consideration of transference through
a solid body to transference by a gaseous body ; and
we shall easily realise precisely the same effect by
means of a couple of tuning-forks. These forks are
tuned precisely to the same note. They are furnished
with resonating cavities, to enable them to communi-
cate to the air as much of their energy as possible. If
I set one in vibration, the effect of the resonating cavity
is to enable it to set in lively motion, at its own period
SOURCES AND TRANSFERENCE OF ENERGY. 181
of vibration, the air surrounding it. But here is another
cavity which is tuned to that particular time of vibra-
tion. The tuning-fork attached to it is also tuned to
precisely the same note, and now we find that when I
first of all start the first tuning-fork, then turn it so as
to place its resonating cavity with the mouth towards
the mouth of the resonating cavity of the other, through
the gas-filled space between the two, there is a trans-
ference of energy which is such that if, after a second
or two, I suddenly stop with my finger and thumb the
vibrations of the first fork once for all, you will hear
the other resounding with considerable loudness. The
transference of energy has here been made through the
air instead of through a solid body, as in the case of
the wooden framework connecting the pendulums.
[I now call your attention once more to the massive
pendulums, because the first has again handed over the
greater portion of the energy to the second. My
assistant will now put them out of tune, and we will
try the experiment again.]
Connected with these, and to be explained on precisely
the same physical principles, we have another strikingly
182 SOURCES AND TRANSFERENCE OF ENERGY.
illustrative experiment. Consider this third arrange-
ment, where we are to have the transference of energy
effected, not as in the case of the pendulums through a
solid bar, nor as in the case of the tuning-forks, through
the gaseous medium between the two, but simply by
magnetic action : force acting between a couple of steel
bars ; an action which, as you all know, is not affected
by the interposition of any non-magnetisable body
whatever, and which is as energetic through what we
call a vacuum as through air. These bar magnets are as
nearly as possible of equal mass, and are supported by
strings or wires of equal length. If I take one of them
away, the time of oscillation of the other will be the
same, whichever I take. In their position of equili-
brium they hang in the same horizontal line. Now
they are both at rest at this moment. Suppose I com-
municate vibration to one of them in the direction of
its length. You notice how very rapidly the energy is
transferred from the one to the other. The magnet
which was at first at rest has now gained the greater part
of the energy, and in the course of a very few seconds
more you will see the other has lost it all. There it is :
absolutely at rest for a moment ; and now the process
recommences the other way. After exactly the same
interval of time as that which elapsed from the com-
mencement of the experiment to the instant of the
first magnet's being brought to rest, the second will
be brought to rest in its turn. There it is at rest now
for an instant only ; and the same transference will go
on again indefinitely. Now, what is it that conveys the
energy in this case ? The transference of energy is due
entirely to the magnetic attraction of one of those bars
for the other ; because, though the apparatus is con-
SOURCES AND TRANSFERENCE OF ENERGY. 183
structed suspiciously like that which I employed a few
minutes ago for the massive pendulums, the masses of
these bars are not sufficient to produce any appretiable
effect upon the supporting beam, so that it would be
impossible, if we were to demagnetise these bars, to
obtain any appretiable transference of energy from the
one to the other. This then is transference of energy
from one body to another, not through a solid, nor
through a gas, as in our recent experiments, but through
the magnetic medium, whatever that may be, what
Clerk-Maxwell has given us strong reason to believe is
the same medium as that which conveys light and
radiant heat. So we have here, as it were, a third
mode of transference of energy from one body to
another ; and this resembles much more nearly than
either of the other two the cases to which I am about
to proceed.
[But before I so proceed, you will notice that I have got
the original pair of massive pendulums on the wooden
frame put out of tune, and you can now study how the
oscillations are handed on from the one to the other.
You see that the transference, if any at all, is very much
more slight than before, and not only is it slight, but
after a short time it ceases, and then sets in the other way.
The energy of the second pendulum is sometimes falling
and sometimes increasing, but it never rises to any great
percentage of what remains in the first. In fact, because
of the dissimilarity of their periods of oscillation, the
one comes sometimes into a position in which it can
gain energy from the other, and a second or two later
it puts itself into such a position as to lose energy, and
so on backwards and forwards ; whereas, when the two
were tuned almost exactly to one another, if they were
1 84 SOURCES AND TRANSFERENCE OF ENERGY.
at any instant in such a position that the one was giving
energy to the other, they would remain for a very long
period in such a relative position. The one would
always be throughout that period in the most favour-
able position for communicating energy to the other,
and this solely because their periods of oscillation were
alike ; whereas when their periods of oscillation differ,
the one is sometimes getting away from the other, and
sometimes getting pulled back.]
All of you must have noticed this in the ringing of a
massive bell. Even a child can ring an immensely mas-
sive bell with very slight application of force, provided
he perseveres in pulling exactly at the proper moments.
Just as the bell is about to descend, let him pull, so as
to quicken the motion, but let him slacken when the
motion is such that a pull would tend to stop it. By
waiting till the exact moment, and properly timing the
impulse, he is capable of giving large oscillations to a
mass which otherwise he is almost incapable of setting
in motion.
In the same way it is possible to check it by apply-
ing retardations exactly at the proper moment. This
would be at exactly equal intervals of time, represent-
ing the vibration of the bell if it were left to itself.
Thus all these experiments depend upon the trans-
ference of energy in a kinetic form between two bodies,
and the test of the capability of the one for receiving the
energy which is sent out by the other is this, that the
natural undisturbed times of vibration of the two bodies
shall be as nearly as possible precisely the same. I
have not time to enter more deeply into the subject
to-day, but I shall endeavour, in the few minutes which
remain to me, to sketch briefly what is to be our appli-
SOURCES AND TRANSFERENCE OF ENERGY. 185
cation, to modern science, of these purely mechanical
experiments.
Suppose we have a substance which, instead of giving
off sound, in consequence of its vibrations, is vibrating
so rapidly as to be giving off some particular colour of
light or of radiant heat. Then the substance which
will be best qualified to absorb that particular colour of
light or of radiant heat, will be another body of pre-
cisely the same kind as the first, because the two speci-
mens of the same matter will, under the same circum-
stances, vibrate according to precisely the same laws ;
and therefore if you define a particular beam of light
by having it sent out from a particular substance which
is rendered incandescent, another specimen of the same
substance will find in the beam precisely those particular
times of vibration which most aptly suit it, and there-
fore will be best fitted to absorb them.
This is, briefly, the dynamical principle at which
Professor Stokes arrived more than twenty years ago,
and which, if its applications had been properly pursued
at the time, would have given us ten years' start in our
knowledge of celestial chemistry. Stokes' illustration
was this : He imagined a space, such as this room for
instance, to be filled with tuning-forks (with resonat-
ing cavities let us say) or with pianoforte wires stretched
about in all directions so as not to interfere with one
another, but as nearly as possible to fill the whole space.
If all the tuning-forks, or all the pianoforte wires, are
tuned to the same note, that arrangement will form a
medium which is capable, when agitated in the simplest
manner, of giving out only that particular note. Set
all the tuning-forks to vibrate, they all conspire to
strengthen one another and give out their one particular
1 86 SOURCES AND TRANSFERENCE OF ENERGY.
note, and that note only. On the other hand, when you
use that arrangement not as a source of sound, but as
a medium through which you endeavour to make sound
pass, then from what I have just shown you, you will
obviously find it to be particularly opaque to that par-
ticular note, and to that note only. Suppose a per-
former with a powerful instrument (such as a cornopean)
placed at one side of the room, and a listener at the other.
Then let the player play any note he pleases except the
note belonging to the forks or strings, that note will
be heard in full intensity, except in so far as the strings
(merely as obstacles) intercept the passage of the sound.
Such a note will be heard almost as powerfully on the
other side of the room as if there had been no tuning-
forks or wires present. But as soon as he plays the
particular note which belongs to all the forks or all the
strings, it comes to be just the question of the pendulums
or magnets, or the two tuning-forks which I have just
shown you. The contents of the room gradually absorb
each a portion of the sound which reaches it, and are
set into vibration by it. If there be enough of them
they take all the energy of the sound, and of course
completely prevent the sound from passing through
the medium, except in so far as they give it out them-
selves.
Here, then, is a medium which of itself can give out
one definite note, and one note alone, when it is a
source of sound ; but which, when it is employed as
a sort of sifter of sound, can sift out from a mixed or
confused sound only that particular note. That then
is mechanically or physically the analogy to which
we shall have to reduce the fundamental principles of
spectrum analysis.
LECTURE VIII.
RADIATION AND ABSORPTION.
History of the discovery of the Physical Basis of Spectrum Analysis. First
result of Spectrum Analysis applied to* non-terrestrial bodies ; There is
Sodium gas in the Sun's Atmosphere. Elaborate experiments of Stewart
and Kirchhoff. Identity of Light and Radiant Heat. Distinctive char-
acters of a particular ray. Application of Carnot's principle to establish
the equality of radiating and absorbing powers. Black, transparent, and
perfectly reflecting bodies.
I ENDED my last lecture by considering various modes
of transference of energy of vibration from one body to
another. I took in particular three cases, in the first
of which the transference took place through a solid
body, in the second the vehicle was ordinary air, and
in the third case it was the medium which propagates
magnetic and electric actions. But in every one of
these cases we found that the condition which is abso-
lutely necessary for a complete handing over of the
energy of one vibrating body to another, whatever be
the intervening medium of communication, was that
the time of vibration of the second body should be
adjusted to be exactly equal to the time of vibration of
the body which had the energy at first.
I then went on to suppose a finite space to be filled
with a number of such vibrating bodies, all tuned (as
it were) to vibrate in precisely the same time ; and I
showed you that if we considered a space so filled to
act as a medium, it would be such as when set in
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190 RADIA TION AND ABSORPTION.
continuously) along a straight line on the screen ; so
that there must be a constant overlapping of a great
many of these successive spots at any one point of the
spectrum, and therefore it must be practically impos-
sible by this method to detect the absence of any one
particular shade of colour.
Now, though the optical method which Newton 1
devised for the purpose of avoiding this difficulty is
a very simple one, it deserves a word or two, as it will
help you to understand the experimental illustrations
I mean to give in my next lecture. Instead of using a
round hole we now use a narrow slit whose sides are
perfectly parallel to each other, and which can be made
(by proper mechanical adjustment) as wide or as narrow
as we choose. The light from the sun or electric lamp,
or whatever source we employ, comes through this slit
as a thin sheet, and falls upon an achromatic lens ; that
is, a lens which behaves in almost precisely the same
way to all the differently coloured rays falling upon It.
It is usually convenient to place the lens at such a
distance from the slit that at exactly the same dis-
tance beyond the lens an image of the slit, equal to
it in size, will be formed on the screen. If, then,
sunlight pass through the slit, and fall upon the lens,
we shall have, on a screen placed at the proper dis-
tance, simply an intensely bright white line, con-
sisting of all the different rays belonging to sunlight.
But if you interpose in the course of those rays, just
after they come through the lens, a prism, with its edge
parallel to the slit, the effect will be a change of direc-
tion of those cones of rays which are converging to-
wards the image. The prism will most refract the
1 Optics, Book I. Parti. Exp. u, Illustration.
RA DIA TION AND ABSORP TION. 1 9 1
violet rays, and all the others will be less and less
refracted as their wave-lengths grow longer and longer
till we reach the lowest red in the spectrum ; and there-
fore instead of having a set of coloured discs, as by
the first method, succeeding one another with their
centres along a line, and overlapping, you will have a set
of parallel coloured images, each no broader than the
slit itself, and you can make the slit as narrow as you
please. In every part the consecutive images lie side by
side, contiguous to one another ; but if there be light of
any wave-length or any particular refrangibility which
is wanting, then the space corresponding to that will
be left as a dark line (an unilluminated image of the
slit) across the otherwise continuous coloured band.
You see hanging on the wall a coloured plate repre-
senting the solar spectrum, formed in the way I have
just pointed out, and you can see those dark lines
across it. Only a few of the chief ones are figured.
The number of those whose position is already care-
fully measured, or photographically registered, amounts
to many thousands. [See diagram, p. 192.] They were
first noticed by Dr. Wollaston, about the beginning of
this century, but he paid very little attention to them ;
and they were re-discovered a considerable time after-
wards by the great optician Fraunhofer, whence they
have been called Fraunhofer's lines.
Of those lines one of the most remarkable is that to
which Fraunhofer gave the name of D, which you will
see upon the picture near the boundary between orange
and yellow. When, however, a very perfect prism is
used, and a telescope is employed instead of the screen
to receive the spectrum, then we are enabled to see that
this line is double. This gives it a very remarkable
192 RADIATION AND ABSORPTION.
characteristic, two almost
equally strong dark lines
across the spectrum, so close
together as to be quite in-
capable of being separated
from each other without the
use of a telescope, or of a
great number of prisms in-
stead of one.
Now,Fraunhofer observed
that in the flame of an or-
dinary tallow candle, when
he tested it just as he had
tested sunlight, there ap-
peared a pair of bright lines,
brighter than the rest of the
otherwise continuous spec-
trum, that there were no
other lines in the spectrum
but those two bright ones,
and that they occupied, so
far as his instrumental mea-
surements enabled him to
discover, precisely the same
place in the spectrum as the
two dark lines D of the solar
spectrum. That is to say,
the candlelight possessed in
excess precisely one of those
definite components in which
sunlight had been found to
be either wholly, or at least
to a great extent, deficient.
RADIA TION AND ABSORPTION. 193
No further actiori seems to have been taken with
regard to this very remarkable coincidence, until Pro-
fessor Miller of Cambridge, in 1849 or ^S * made a
more exact experiment, with the view of comparing
these yellow lines in the flame of a spirit-lamp with the
dark lines of the solar spectrum, so as to test whether
they are exactly coincident with one another or not.
The result of his measurements was that the close-
ness of coincidence was so great that it was impossible,
with his finest instruments, to find any divergence
between them. The two bright lines exactly corre-
sponded with the two dark ones as to refrangibility, and
therefore also wave-length. It had been conclusively
shown by Swan, that the two bright lines in the light
of a candle are due to common salt, which pervades
the air everywhere, and of which the very minutest
trace is capable of producing this yellow light. It
was then that Stokes at once took the additional step
required, and explained that the glowing vapour, which
is capable, when it is the source of light, of giving these
definite bright lines, is itself, when used as an absorbing
medium, capable of absorbing these and these only ;
and therefore that Miller's test of the exact coincidence
of the bright and dark lines was a complete proof that
there exists in the sun's atmosphere this vapour of sodium.
That occurred about 1850, and ever since that time the
fact that sodium exists in an incandescent state in the
sun's atmosphere, has been taught (as an experimentally
ascertained truth) by Sir William Thomson and others.
This was the birth of Spectrum Analysis, as applied to
celestial objects.
It is curious to find that the deservedly celebrated
Foucault had in 1849 made the same experiment in an
N
194 RADIA TION AND ABSORPTION.
even more convincing form than that which Miller had
adopted. He found that the light, of what is called the
electric arc, has in its spectrum these two bright lines ;
but that when he looked at sunlight through the electric
arc and allowed the sunlight to come in so strongly as
to overpower the electric light, then the electric light
actually cut out the D lines from the solar spectrum more
powerfully than if it had not been present. Although
it was there giving out these lines strongly, it was not
competent to fill up the wants in the solar spectrum, but
actually made the deficiency more glaring than before.
Then, to test whether it was really the case that this
electric arc was absorbing these particular kinds of light,
Foucault very ingeniously took advantage of the fact that
the carbon points between which the electric arc is
usually formed become incandescent and, reaching a
higher temperature, are very much more brilliant than
the arc itself. By means of a small mirror he reflected
the white light from these carbon points through the
electric arc, and found that whenever it passed through
the arc, instead of getting brighter at those places,
it had those very lines cut out of it ; but whenever it
passed beside the electric arc it had no deficiencies.
Curiously enough, he seems to have derived no defini-
tive conclusion from this.
Then, again, exactly the same statement was made in
Sweden by Angstrom in 1853. He says, as the result
of experiment, that an incandescent gas gives out
luminous rays of the same refrangibility as those which
it absorbs.
Each one of these three thus completely made and
recorded the discovery of the physical basis of spectrum
analysis before 1854; but, of the three, Stokes alone
RADIATION AND ABSORPTION. 195
made the application which really constitutes celestial
chemistry. Fox Talbot had, long before, distinctly
pointed out the use of the prismatic method for dis-
tinguishing terrestrial substances in a flame.
As I have already told you, Sir W. Thomson has,
certainly ever since 1852 (probably a year or two sooner),
regularly given in his public lectures in Glasgow Uni-
versity the statement that there is sodium vapour in the
sun's atmosphere ; and that, to find other constituents
of solar and stellar atmospheres, all that is wanted is a
comparison of the dark lines in their spectra with the
bright lines in the incandescent vapours of various
terrestrial substances. 1 But it was not till 1859 or 1860
that this was known generally, or was applied to any
purpose further than to the mere recording of the
existence of sodium in the vapours around the sun. I
should like to read a quotation from some remarks I
made a year or two ago to the Royal Society of
Edinburgh upon this curious subject : 2
It is difficult now-a-days, when so many philosophers are en-
gaged almost simultaneously at the same problem, to decide which
of their successive steps in advance is that to which should really
be attached the title of discovery (in its highest sense) as distin-
guished from mere improvement or generalisation. You have only
to look at the recent voluminous discussions as to the discoverer
of the Conservation of Energy, to see that critics may substantially
agree as to facts and dates, while differing in the most extraor-
1 President's Address, Brit. Ass. 1871. See Stokes, Nature, January 6,
1876. Thomson writes to me with reference to this (January 23, 1876) :
' I never imagined that Stokes thought I was generalising too fast, or that
/was generalising at all. I felt that I had learned the whole thing from
him on a foundation of absolute certainty. . . . All I said in my
Edinburgh Address on this matter is, I believe, irrefragable.'
* Proceedings R.S.E., May 15, 1871.
196 RADIA T1ON AND ABSORPTION.
dinary manner as to their deductions from them. 1 Some of these
writers, no doubt, put themselves out of court at once by habitually
attributing the gaseous laws of Boyle and Charles to Mariotte and
Gay-Lussac. Men who persist in error on a point so absolutely
clear as this, show themselves unfit to judge in any case of even a
little more difficulty. Others, who strongly support the so-called
claims of Mayer in the matter of Conservation of Energy, and who
should (to be consistent) therefore far more strongly advocate the
real claims of Talbot, Stokes, Angstrom, Stewart, etc., to the dis-
covery or spectrum analysis, are found to uphold Kirchhoff as
alone entitled to any merit in the matter.
The question of priority just alluded to illustrates in a very
curious way a singular and lamentable, though in one sense
honourable, characteristic of many of the highest class of British
scientific men ; i.e. their proneness to consider that what appears
evident to them cannot but be known to others. I do not think
that this can be called modesty ; it is rather a species of diffidence
due to their consciousness that in general their accurate knowledge
of the published developments of science is confined mainly to
those branches to which they have specially devoted themselves.
Their foreign competitors, on the other hand (especially the Ger-
mans), are often profoundly aware of all that has been done, or, at
least, have some one at hand who is, and can thus, when a new
idea occurs to them, at once recognise, or have determined for
them, its novelty, and so instantly put it in type and secure it.
Neither Stokes nor Thomson, in 1850, seems to have had the least
idea that he had hit on anything new . . . the matter
appeared so simple and obvious to them and, but for the fact
that Thomson has given it in his public lectures ever since (at
first giving it as something well known), they might have thus
forfeited all claim to mention in connection with the discovery.
I went on to show how this lamentable state of things
could easily be rendered impossible for the future, by
the regular publication, at very short intervals, of a
digest of all new advances in science. 2
1 Some frantic partisans of Papin, etc., deny almost all credit to Watt
in the matter of the steam-engine ! No further examples need be cited.
2 [Note to Third Edition. To a great extent this desideratum is now t
RADIATION AND ABSORPTION. . 197
I come now to the question of what was done on
this subject in 1858 and 1859. The first of these dates
belongs to Balfour Stewart, and the second to Kirch-
hoff. Balfour Stewart treated the subject almost
entirely from the point of view of what is called the
Theory of Exchanges, and he demonstrated a very
remarkable generalisation or extension of the law long
before laid down by Prevost. Kirchhoff treated the
subject from an, at first sight, somewhat higher theo-
retical point of view, and used reasoning considerably
more complex and a good deal more mathematical ;
but in reality the fundamental point upon which the
reasoning is based was precisely the same in both their
investigations. What they established by their different
processes was this, the absolute equality of the radiat-
ing and absorbing powers of a substance for every
definite ray. It was not merely what had been known
to Leslie and others, that a body which is a good
absorber of heat is also a good radiator of heat, with
many other indefinite statements of that sort ; but it
was the precise limitation to each and every particular
wave-length, and not only that, but something higher
than that, not merely to rays of a particular shade of
colour, but also to rays polarised in particular planes.
Stewart and Kirchhoff thus came to the conclusion
that if you consider any one definite colour of light,
and have it polarised in one definite direction, then a
body which has a power of absorbing that, measured in
any way whatever, will have an exactly equal power of
radiating it, if measured according to the same units.
So if we adopt the same units for radiating and for
supplied by the Beibldtter zu den Annalen der Physik ; for which the whole
scientific world is indebted to the disinterested labour of the Wiedemanns.]
198 RADIA TION AND ABSORPTION.
absorbing power, in all bodies the measure of the
absorbing power for any particular ray (strictly defined
as I have just stated) is the measure of the radiating
power for that same ray.
Stewart shows first, by very simple reasoning, that the
absorption of a body at a given temperature must be
equal to its radiation, for every given description of heat;
and then he shows experimentally that a plate of rock-
salt, which is an exceedingly bad absorber of heat, is
also an exceedingly bad radiator of heat. Then he
shows that a body is in general more opaque to radia-
tions from another portion of the same body than it is
to radiations from other bodies at the same tempera-
ture ; in other words, if you measure how much of the
heat radiated by a piece of hot glass is absorbed by
rock-salt, and if you measure also how much of the
radiation from an equally hot piece of rock-salt, instead
of the glass, is absorbed by rock-salt, you find that rock-
salt absorbs of the heat wh.ich is radiated by rock-salt
a very much larger percentage than it absorbs of the
heat which is radiated from glass at the same tempera-
ture ; and this he showed to be true, with the change of
a word or two, for mica, glass, and other substances.
Then he showed also and this is a very important
addition that a thick plate of rock-salt radiates more
than a thin plate, being at the same temperature ; and
therefore it follows of course that the radiation from a
hot body is radiation not merely from its surface, but
also from layers under the surface, and in some sub-
stances it may be radiation from layers at a very great
distance under the surface ; so that radiatttffi, like
absorption, is not a mere surface phenomenon, but
depends (when the substance is at all transparent) upon
RADIATION AND ABSORPTION. 199
the depth or thickness of the absorbing or radiating
stratum.
In order experimentally to show some of these results,
though only in a qualitative not a quantitative manner,
Stewart first tried a substance such as pottery ware,
where you have a surface in some places white and in
others black. If you look at such a piece of pottery
ware by daylight, the reason why some markings on its
surface are darker than others is simply that they
absorb more of the incident light. These are portions
of the body which absorb more than other portions, and
therefore we should expect, if this law be true, and if it
be capable of extension from heat rays to luminous
rays, that on making the piece of pottery ware itself in
turn the source of light, making it hot enough to give
off light, then, as those portions which, when it was
cold, appeared darkest, did so because they absorbed
most, they should, when it is itself a source of light,
appear brightest, because they ought to radiate most.
That is an experiment which any of you can try very
easily for himself with a piece of pottery which has a
well-marked pattern on it. You will see, as soon as
you have heated it to whiteness in the fire, taken it out
and looked at it in the dark, a white pattern on a dark
ground, instead of a dark pattern on a white ground.
And it is very striking if, while thus looking at it, you
suddenly flash daylight on it, when you see at once the
inversion.
I can show to a few at a time, but not in a marked
way at a distance, the same phenomenon, by taking a
piece of platinum foil and writing letters on it with ink.
When it is once heated there is a deposit, on the surface
of the otherwise polished platinum foil, of oxide of iron
200 RA DIA TION AND A BSORP TION.
which tarnishes the surface and makes it absorb con-
siderably more light than a polished reflecting surface
will do. We should expect, then, when this is heated
(as I now heat it in a powerful but very slightly luminous
flame), and becomes in turn the source of light, to see
bright letters on a dark ground. The difference of
brightness is not so marked in this case as in the last,
but still those who are nearest to me will see the pheno-
menon distinctly enough.
But you will see another phenomenon still more start-
ling on looking at the back of the heated foil instead of
the front of it. You saw faint traces of bright letters on
the dark ground when I turned the inked side to you,
but when I turn the other side you see dark letters on a
bright ground. Now, the reason why on the one side
we have bright letters on a dark ground, while the other
side of the same piece of metal shows dark letters on
a white ground, is still more confirmatory of the result
of Balfour Stewart's, which I have just stated, since
these letters appear dark while at present cold, because
they are absorbing more than the rest of the polished
surface. They appear brighter than the polished sur-
face when heated, because they radiate more ; but just
because they radiate more they must become colder,
must be kept permanently colder than the rest of the
foil, and therefore the parts at the back of the foil,
behind those which are radiating most, remain perman-
ently colder. This is made evident when we look at the
side which is without any difference of surface, as we
then see, by the relative amounts of brightness, a marked
distinction between the parts which are hotter and those
which are colder. This is a still more complete proof
of Stewart's proposition.
RADIA TION AND ABSORPTION. 201
Stewart extended his reasoning still further when he
explained the behaviour of coloured glass when heated.
If you look at a bright fire through a red glass (for in-
stance); so long as the red glass is cold, that is to say,
is absorbing light but not radiating any, it absorbs the
green and lets the red through. That is why we call it a
red glass, because it absorbs green and almost every ray
but the red. When you put it into the fire and it has
acquired exactly the same temperature as the coals, it
shows no colour, and you cannot distinguish it from
the coals. In fact, it is transmitting red light but is
radiating green and other rays : namely, those which
it is capable of absorbing, and it is just making up by
radiation for the amount which it is absorbing ; and
therefore the light which is coming through it from the
coals behind is just as much strengthened both in
quantity and quality by its radiation, as it is weakened
by its absorption, and thus on the whole it comes to our
eyes uncoloured. If you put in behind it, leaving it in
the fire at a bright heat, a less hot coal, you will see it
appears green, because then the glass is hotter than the
background, and takes from the background less green
than it gives out, and therefore the light which actually
reaches the eye, partly through it and partly from it,
is more green than that from the coal behind. Thus
the coloured glass loses its colour when exactly at
the temperature of the objects behind it, and takes the
complementary colour when it is hotter than the ob-
jects behind it.
KirchhofT gave a good many experimental illustra-
tions of the relation between emission and absorption,
of which I can allude to only two or three. The
first was the very simple one of taking a bead of a trans-
202 RADIA TION AND ABSORPTION.
parent salt and heating it in a blow-pipe when supported
in a loop of platinum wire. When the platinum wire
and the bead were at the same high temperature, the
platinum wire glowed bright, as we all know an incan-
descent wire does, but the bead of melted salt remained
scarcely glowing at all. That is to say, this body, which
is exceedingly transparent, and therefore a bad absorber,
is also a bad radiator. On the other hand, the platinum
wire is perfectly opaque ; it is a good absorber, and
therefore a good radiator.
But Kirchhoff carried his experiments after this at
once to sunlight. Knowing that there is one particular
definite red ray which is given out by the metal lithium
when in a state of incandescent vapour, he noticed that
there was no corresponding dark line in the solar spec-
trum. So he attempted with full success to make a new
dark line in the solar spectrum by letting sunlight pass
through a slit, and placing near the slit an otherwise
slightly luminous flame (that of a Bunsen lamp) in which
there was a large supply of lithium vapour, which caused
it to give out light of one homogeneous red. When the
sunlight came through it, the lithium vapour cut out that
very red, and a new line was formed in the solar spec-
trum. As the sunlight was gradually weakened, the
line gradually disappeared, though there was still a very
visible supply of sunlight ; and after a further weaken-
ing, the lithium line came brightly out on the darker
background. Thus by regulating properly the intensity
of the sunlight you may have at pleasure a dark line or
a bright line, or no line at all, at this particular place in
the spectrum. That was conclusive as to the possibility
of producing these dark lines in new positions by the
help of some incandescent gas.
RADIA TION AND ABSORPTION. 203
But Kirchhoff also showed that if you take the direct
radiation from a terrestrial body instead of as in the last
experiment I described gradually checking or weaken-
ing the sunlight, if you had taken the light directly from
a terrestrial source, then you could get the dark line
only when the absorbing flame is colder than the source
of light. In order to produce new dark lines in the sun's
spectrum, we must use absorbing bodies which are colder
than the sun. That of course presents no difficulty,
because we cannot produce any terrestrial temperature
which at all equals that of the sun ; but it comes to be a
point of very great importance when we wish to produce
these absorption bands in an otherwise continuous
spectrum of artificial light, as, for instance, the light
from an incandescent lime-ball. The temperature of
the incandescent lime-ball is very low, compared with
even the electric arc, and extremely low compared with
the sun, but the light from it gives a perfectly continu-
ous spectrum. If we try to produce in that spectrum
the dark lines of lithium or sodium by the process just
described, we find the process fail. Bright lines appear
in place of dark ones. A Bunsen-lamp flame is not cold
enough. In other words, if sodium be in the Bunsen
flame, though it absorbs no doubt that particular orange
light which comes from the lime-ball, yet in place of it
it gives out a great deal more of the same kind, and
therefore you have bright lines instead of dark ones. But
if, instead of a Bunsen-lamp, you take an ordinary spirit-
lamp, and put sodium vapour into its flame, you find you
get your dark line in the spectrum of the lime-ball.
Kirchhoff thus experimentally showed that for the pro-
duction of an absorption-line (at least when the source
and absorber are both behind the slit) it is necessary
204 RADIATION AND ABSORPTION.
that the incandescent source should be at a higher tem-
perature than the absorbing vapour.
We shall see that this is not only in itself a very
important result, but that it is of the utmost importance
when we come to interpret the spectrum we obtain from
various portions of the sun's disc, and from various stars.
It shows whether the radiating or absorbing matter in
any of these cases is the hotter or the colder.
Finally, I may mention a discovery which was made
almost simultaneously by Kirchhoff and by Stewart ; the
beautiful application, to absorbing bodies, of the polarisa-
tion of light. There are various transparent substances,
which, although colourless, or but slightly coloured,
nevertheless absorb all vibrations of light which take
place in a particular direction. The simplest is a plate
of tourmaline, cut parallel to the axis of the crystal. It
is not yet absolutely certain whether the rays which it
absorbs are those which vibrate parallel to the axis of
the crystal or those whose vibrations are perpendicular
to it, but that does not matter to our present purpose.
Light which has passed through such a slice of crystal
is vibrating in one definite direction only, and therefore
is said to be polarised. As we have experimental proof
that common light is subject to no such restriction, the
portion of the incident light which has been absorbed
must have been that whose vibrations were in the direc-
tion perpendicular to that of those which passed through,
and therefore what was absorbed was also polarised
light. Here, then, is a body which absorbs polarised
light : make it in its turn (by heating) a source of light,
and it should then, if the proposition we are dealing
with be universally true, radiate polarised light. Now
the experiment has been made, and made with complete
RADIA TION AND ABSORPTION. 205
success. The light radiated by the red-hot crystal, if
you view it against a dark background, is polarised ; but
if the background be itself as hot as the crystal (and be
of non-polarising material), no polarisation is observed.
The crystal transmits one part of the light unaltered,
and though it stops the other half, it makes up for it by
the light which it radiates.
Before I go further with the reasoning on this part of
the subject, I must make a slight digression as to our
knowledge, or rather our reasons for conviction, of the
identity of radiant heat and light. I must, in fact, show
how we satisfy ourselves that there is no more difference
between radiant heat and light, or even the so-called
actinic sun rays, etc., than between waves of sound or
waves of water of different lengths. The precise nature
of the vibration which constitutes a wave of light, does
not matter to this question at all.
We all know that sound-waves differ practically from
water-waves. In the case of sound-waves the particles
of air are vibrating back and forward in the direction in
which the sound travels ; but in the case of waves on
water, the particles are moving partly up and down
and partly back and forwards, so that near the surface
of the water each particle is describing almost a
circle.
In the case of luminous waves, all we know is, that
whatever be the precise nature of the vibration, its direc-
tion is transverse to the direction in which the light is
moving. Now, the proof that radiant heat and light are
the same, or only variations of the same thing, is to be
arrived at by comparing their properties in a great
number of different ways. I cannot enter very deeply
into this, but I can at all events mention several of
206 RADIA TION AND ABSORPTION.
these properties, and show how conclusive the evidence
is for the identity in question.
First of all, it is to be considered they both move
in straight lines. The radiant heat from the sun goes
along with the light from the sun, and when you shut
one off, put an opaque screen so as to intercept the
one, the other is intercepted at the same time. In the
case of a solar eclipse, you have part of the sun's heat as
long as you can see the smallest portion of the sun's
disc. The instant the last portion of the disc is obscured,
the heat disappears with the light. That shows that the
heat and light take not only the same course, but also
the same time to come to us. If the one lagged ever so
little behind the other, if the heat disappeared sooner
than the light, or the light sooner than the heat, it would
show that though they both moved in straight lines, the
one moved faster than the other ; but the result of
observation is that we find, so far as our most delicate
measurements show, that heat and light pass from the
moon to the earth, i.e. over a space of a quarter of a
million miles, in sensibly the same time. Therefore we
have the proposition that radiant heat moves at the rate
of about 1 86,000 miles per second, because that is the velo-
city of light. Thus, even our very first analogy between
them seems to be almost convincing as to their identity.
Then we have, as you all know, when you use either
a burning mirror or a burning lens for the purpose of
condensing the sun's heat into a focus, to adjust this
by taking advantage of the sun's light. You form an
image by means of the light, and then you find the
heat rays concentrated at the same point. That is to
say, the laws of reflection and refraction are precisely
the same for light and radiant heat.
RADIATION AND ABSORPTION. 207
Then again, I dare say you all know for it was
shown early in this century as the true explanation of
phenomena known to Newton, and before him that
two sets of rays of light can be made so to interfere
with one another as to produce darkness. This ex-
periment is conclusive 1 as to the non-materiality of
light, and shows that light must be something of
the nature of a vibration of some kind, so that two
opposite motions meeting in one place, or rather simul-
taneously affecting one part of a medium, may produce
simple rest or non-existence of motion. If we test this
with sunlight, as was done by Fizeau and Foucault, we
find that precisely at the places where the sunlight has
disappeared, at these same places the sun's heat has
disappeared. Radiant heat, therefore, has, as light
has, the property of interference ; that is to say, two
portions of either are, in certain circumstances, capable
of mutually destroying one another.
Another very striking analogy between them is fur-
nished by absorption. Let us take the case of light
first. If I take a number of pieces of the same blue glass,
light which has passed through one of these is capable
of passing in greater part or percentage through the next,
and what has been sifted through two of them will in
still greater percentage pass through the third, and so
on. Precisely the same thing holds with reference to
radiant heat. What we call colourless glass happens to
be extremely opaque to radiant heat, especially to the
lower forms ; but if you force, by using a powerful
source, a considerable beam of radiant heat through a
single plate of window glass, you will find that though
1 Compare foot-note to p. 66. The applicability of the word ' con-
clusive ' is matter of opinion.
208 RADIA TION AND ABSORPTION.
the window glass is exceedingly opaque to such heat in
general, what you can force through it will pass in very
much increased percentage through the second plate,
and in still greater percentage through the third, and
so on. And, just as Melloni used the word Thermo-
chrose, we may say that a pane of window glass, which
is colourless or almost so as regards light, would be
regarded as coloured by larger beings than ourselves :
beings with such very coarse-grained optical apparatus
as to have the sense of light produced in them by such
waves only as to our senses produce radiant heat. Such
creatures would speak of our most transparent glass as
being exceedingly opaque, while they would speak of
rock-salt as being transparent, for it is found to transmit
heat almost as freely as it does light.
There are various other analogies, such as, for instance,
that the intensity of light from any source varies in-
versely as the square of the distance. The same thing
is true of radiant heat. That, however, is necessarily
true of all emanations in straight lines from a centre
when there is no absorption, so that it does not
strengthen the argument. It is, in fact, merely a
consequence of the geometrical truth that the surface
of a sphere is as the square of its radius.
Then again and this is perhaps the grand proof
we have the discovery by Principal Forbes of the polar-
isation of heat. You can polarise radiant heat as you
can light, and this is the most conclusive argument ; one
which, taken with what I have just told you, leaves no
possibility of escape from the conclusion that the differ-
ence between radiant heat and light is simply the
difference between a low note and a high one. There-
fore, in reasoning upon radiation, it is quite indifferent
RAD I A TION AND ABSORPTION. 209
whether we speak of radiant heat or radiant light, or
even higher waves which are invisible to the eye except
through fluorescence. So we need speak of nothing
but radiation, under which we suppose them all in-
cluded.
Now comes this question By what marks can you
distinguish one particular radiation from every other ?
Well, you can do that just as you can perfectly define
any particular sound. You can define a sound if you
are told three things about it, its intensity, its pitch,
and its quality. Well, the quality has of late been
shown by the beautiful analytic and synthetic methods
of Helmholtz to depend upon the admixture of other
sounds (harmonics) with the primitive sound ; so sup-
pose you take the simplest quality of all, that which
has no admixture, then a musical sound or note is
completely defined if we know its intensity, if we know
its pitch, and if we know its quality to be the simplest.
Conversely, if you have any disturbance of the air which
has that intensity, and that pitch, and the simplest
quality, it will be that same sound. That, then, is our
mark by which we detect a particular kind of motion of
the air.
Now we have precisely the same sort of marks by
which we can distinguish a particular kind of radiation.
Take the simplest form, that is, the simplest quality,
there are other three things to be attended to. The
first is the intensity ; the second is the wave-length or
colour, what corresponds to the pitch ; and the third,
how it is polarised, or whether it is polarised or not. If
these be attended to, and if you were to specify them
for any one radiation, and if any other radiation what-
ever satisfied the same conditions, then it must neces-
O
210 RADIA TION AND ABSORPTION.
sarily be the same radiation. That is the stamp of
equivalence between the two.
And now we come to the question how we prove that
the radiation from a body must be equal to the absorp-
tion by the same body under similar circumstances.
We have seen how we can test the equality or identity
of two radiations, and now it remains, having that pre-
liminary settled, to apply reasoning to see why the
absorbing and radiating powers are necessarily equal.
The best way we can do it is by applying reasoning
very similar to Carnot's, but in this case it happens to be
capable of being applied even more simply. Suppose
we have a space, the walls of which are either perfect
reflectors or are always kept at a definite temperature.
It is an experimental fact that bodies (whatever they
be) which have been long enough kept in either kind
of enclosure will at last acquire precisely the tempera-
ture of the enclosure. That is a fact which has been
ascertained over and over again. We say, in fact, that
bodies are at the same temperature when neither parts
with heat to the other, when there is on the whole no
transference of heat from the one to the other when
they are placed in contact. Suppose one of these
bodies more capable of absorbing than it is capable of
radiating. That body would be constantly taking in
more heat than it was giving out, and therefore though
the other bodies would of course absorb the heat which
was given out by it, they would necessarily cool, because
they would get back from it less than they gave to it.
It would be getting hotter at the expense of all the
other bodies inside the enclosure.
So far then the reasoning appears, at least at first
sight, to be nearly complete ; but it is not, because we
RADIA TION AND ABSORPTION. 211
have been taking the radiations as a whole. Suppose
we have then inside this enclosure, between two of the
bodies, some body which we may call a screen, and
which shall allow to pass a perfectly definite kind of
radiation and that alone, completely reflecting every-
thing else. Then whatever radiation passes from the
first towards the second body must pass through the
screen, and will be, therefore, of this definite kind only.
It will be partly absorbed and partly rejected by the
second ; but if there is to be a constant equality of
temperature maintained and that is our fundamental
proposition the fraction of the amount of this definite
kind of radiation given out by the first and absorbed
by the second must be exactly equal to the fraction of
that given out by the second, and absorbed by the first,
else one of the bodies would rise in temperature at the
expense of the other, and that, you know, is impossible.
Such a screen, in fact, while (with regard to the par-
ticular radiation in question) it forms one of three
bodies in the enclosure, virtually (for all other radia-
tions) makes it into two separate enclosures.
You will notice that our reasoning is in reality based
upon Carnot's : the same which led to the second
law of thermo-dynamics, because it is founded on this
principle, that without expenditure of work we cannot
cool down a body below the temperature of all the
surrounding bodies. If a body is at the same tempera-
ture as the surrounding bodies, we cannot use its heat
to do work. In fact, we require to spend work to
make this body colder. Now, if it could make itself
colder by radiating away more than it absorbs, then we
should have an enclosure containing two kinds of
bodies, one of which heated itself at the expense of the
212 RADIA TION AND ABSORPTION.
other, so that work could be got from bodies all
originally at the same temperature, and kept in an
enclosure which is throughout constantly at that
temperature. [But, just as we have seen that Carnot's
principle is only true in the statistical sense, and
would not hold if we could deal with individual
particles of matter, so this assertion of the equality of
radiating and absorbing powers is true in a similar
statistical sense only.]
A word or two about the differences between different
bodies. There are some bodies which absorb every
radiation which falls upon them. These are such
bodies as lamp-black, and we may call them black
bodies in general. Now, as a black body is capable,
by definition, of absorbing every kind of radiation
which falls upon it, so it must, by applying to it the
proof we have given, be a body which when heated must
give off every kind of radiation. There can be nothing
wanting, no dark lines in its spectrum when incan-
descent, because as it is capable of absorbing everything,
it is capable of radiating and will radiate everything.
The next class of bodies we may call transparent
bodies. A transparent body is a body which absorbs
nothing at all. If we had a perfectly transparent body
it would absorb nothing, and therefore would radiate
nothing if you made it hot, so that the body could not
be seen either by itself stopping a certain amount of the
light which falls upon it, nor could it be seen by making
itself a source of light, because, in consequence of its
not being able to absorb, it would not be able to radiate.
It might, of course, be seen in virtue of its displacing, or
distorting, the images of other bodies as seen through it.
Then we have, finally, a class of bodies which may be
RADIATION AND ABSORPTION. 213
distinguished from the other two as those into which heat
cannot be absorbed at all, because it never penetrates the
surface, those which are perfectly reflecting bodies.
We have, then, black bodies, transparent bodies, and
reflecting bodies. We have none of them in perfection,
but we may take lamp-black as an example of the first ;
rock-salt for the second ; and a polished metal, such as
silver, for the third. None of these is perfect ; but they
are all approximations, and are as good approximations
as we find in Nature to the mathematical ideas of rigid
bodies and perfect fluids, and sufficiently near approxi-
mations to enable us to deduce from our reasoning on
them valuable explanations of physical phenomena.
Let us suppose for a moment that we have two
of these bodies inside a perfectly reflecting enclosure.
Suppose one to be a black body and the other a transpa-
rent body, only let it be imperfectly transparent. Then
the black body takes up absolutely any radiation which
may come to it, and sends out absolutely all kinds of
radiation ; but the transparent body is incapable of
absorbing any but one kind of radiation, let us say. It
will go on absorbing that one kind of radiation from
the black body, but the black body gets back by re-
flection and transmission, all except that one kind of
radiation, and therefore that must be the one kind of
radiation which the transparent body can give out : and
it must give it out, being at the same temperature as
the other body in the enclosure, it must give it out pre-
cisely at the same rate at which it absorbs it ; and thus
we have from a somewhat varied point of view another
demonstration of the same principle. I shall endeavour
in my next lecture to illustrate these theoretical conclu-
sions by experiments.
LECTURE IX,
SPECTRUM ANALYSIS.
Spectrum of incandescent black body ; of incandescent gas or vapour. Ab-
sorption by vapour of parts of spectrum of incandescent black body.
Application to sunlight, and starlight. Solar spots and protuberances.
Period of life of various stars. Fluorescence.
THE point at which I had arrived in my last lecture
was the practical results of the independent discoveries
because we can call them no less of Foucault, Stokes,
Angstrom, Balfour Stewart, KirchhofT, and others, with
regard to the equality of the radiating and absorbing
powers of any one body for any definite ray of heat or
light. I explained very fully in that lecture how we
can test, by separating them from one another, all the
different forms of radiation that proceed from any par-
ticular incandescent body, and so discover whether any
are wanting. It only now remains that I try these
experiments with the help of a galvanic battery, of
which I have a pretty powerful specimen down-stairs,
connected by wires with the electric lamp here.
In an ordinary galvanic battery, if you have only a
moderately great number of cells, say 100, no elec-
tricity will pass between the terminals until you bring
them into contact ; but if after bringing them into con-
tact you then separate them, a spark will follow, and
heat the air between them so much that, if the battery
SPECTRUM ANAL YSr$^^ 215
be powerful enough, we may have a steady current of
electricity passing between the two, and keeping the
intervening air in a state of incandescence.
Now everything in the path of this portion of the
current is so intensely hot that any ordinary metals
such as copper, would be melted at once, or at least in
a very short time, if placed in it ; and therefore the sub-
stance we employ for the poles of the battery is gas coke,
the hard deposit of carbon found in gas retorts. Bars
of this are cut and connected with the poles of the bat-
tery. When the voltaic arc is passing in hot air between
the two poles, the ends of these bars become vividly in-
candescent, and you have therefore two very hot black
bodies, and between them a hot semi-transparent body.
Now, you will remember from my last lecture that a
black body is black because it absorbs all kinds of light
which fall upon it. A transparent body is transparent
because it absorbs little of the light which falls upon it.
Therefore, if our proposition be true, and we know
it must be, in the same sense at least as is the second
law of the dynamical theory of heat, it will follow that
if you make the black body incandescent it will give
out all kinds of radiations, just as it is capable of absorb-
ing all kinds ; and the gaseous or semi-transparent body,
which is capable of absorbing only few kinds of light
or radiations, will be capable, when self-luminous, of
giving out only the same few. The contrast between
the two will be well seen by adopting the optical method
I described in my last lecture. We separate from each
other the various kinds of radiation given by the two
bodies simultaneously.
The radiation which you see just now [throwing the
spectrum of light from one of the carbon points on the
216 SPECTRUM ANAL YSIS.
screen] is mainly, almost wholly, from one of the hot
carbon points, and you see that in its spectrum there is
no discontinuity. You have every colour, or rather
wave-length, of visible light, from the lowest red which
the eye can see, up to the highest violet which the eye
can see. There are irregularities of brightness in the
spectrum, but these are due to the fact that we have
the glowing gas as well as the luminous black body.
But if I pass to the spectrum of the glowing gas by
altering (as I now do) the position of the carbon points
inside the electric lamp, you now see in the dark in-
terval between the two continuous spectra on the screen,
each belonging to one of the carbon points, bright lines
showing definite kinds of radiation and those only,
while the black bodies give you every possible variety of
tint, as it were, from the lowest up to the highest visible.
This glowing gas, which is the arc between the two
poles, gives you only certain definite kinds of light.
At present it is very difficult to tell, without careful
measurement, to what particular vapour each of these
rays belongs, because the composition of the glowing
gas between the poles depends for the moment entirely,
or almost entirely, upon the impurities in the carbon
points, which have been vaporised by the intense heat ;
and, therefore, though I can at once see, partly from its
position and colour, but much more definitely from its
brightness, that the orange-coloured ray belongs to the
metal sodium, I could not, without careful measure-
ment, tell what other substances are incandescent in the
spark there to produce the other bright lines. But if I
were to introduce some substance into the arc (placing
it upon the comparatively large upper surface of the lower
pole), I should be able to see what lines it produces,
SPECTRUM ANALYSIS. 217
whether by new lines appearing or by the strengthening
of those already present. To illustrate this, I shall take
a small piece of metallic sodium, and render it incan-
descent upon one of the carbon points ; then, as it is
highly volatile, the space between the two carbon
points will immediately be filled principally with vapour
of sodium. You see at once that the orange line, to
which I have already called your attention, is very
greatly intensified the others being but little affected,
though, if anything, rather weaker than before. That
depends upon the fact that the sodium vapour offers
much less resistance to the voltaic arc than does air.
The arc is both longer and at a lower temperature than
it was before I introduced the sodium.
To show the testing nature of this mode of discrimi-
nating between different substances, I take a small por-
tion of a metal which was discovered by the help of the
spectroscope almost immediately after this method of
observation was brought into practical use. You see
that, in addition to the feeble bands which cross the com-
paratively dark space between the continuous spectra of
the carbon poles, we have a new one of great intensity
and of an exquisite green colour. This is characteristic
of the vapour of the metal Thallium (closely allied to
lead in many of its physical and chemical properties),
a small portion of which I had placed upon the lower
carbon.
The final experiment I have to show in this connec-
tion is the converse of this. We are now going to take
as the source of light one of the carbon points, an incan-
descent black body which gives us all kinds of radia-
tions, from the lowest to the highest, and we are going
to make the sodium vapour, whose particular kind of
2 1 8 SPECTR UM ANAL YSIS.
radiation we have already studied, the absorbing body,
and see what part of the continuous spectrum of the
incandescent black body it cuts out or refuses to allow
to pass. And in this experiment of course rests the
definite proof, so far as one single case of experiment
can give a definite proof, that the absorption and radia-
tion are exactly equivalent to one another in every
particular glowing gas.
I place near the slit of the electric lamp a powerful
Bunsen burner, into which my assistant will introduce
a pellet of metallic sodium in a little iron spoon. You
see first the combustion of the naphtha in which the
sodium was kept (to prevent its oxidation), then in a
few moments you have an excessively bright mono-
chromatic flame, whose light is due almost entirely to
the incandescent sodium vapour. You see the weird
expression of one another's countenances as this
snap-dragon flame becomes more and more intense.
I interpose a sheet of pasteboard to prevent its direct
light from falling on the screen where the spectrum of
the carbon point is for the moment seen continuous.
I now, move the Bunsen lamp slightly, so that the
carbon point must shine through the sodium flame, and
you see at once a dark, almost perfectly black, band
cut out of the otherwise continuous spectrum, just as if
a pencil or other opaque body had been interposed.
You see it is exactly a prolongation of the orange band
of sodium still furnished by the voltaic arc, and you
see that it appears and disappears exactly as I put the
lamp in front of the slit or withdraw it.
It would be easy to extend a series of experiments
of this kind, but there would be a very great deal of
sameness about them, because all we could do would
SPECTRUM ANAL YSIS. 219
be to show over and over again that certain bodies
when incandescent give perfectly definite kinds of light ;
and that the same bodies when incandescent, but suffi-
ciently colder than the carbon pole of the electric lamp,
cut out from the otherwise continuous spectrum of the
carbon pole precisely the kind of light they give out
when they are themselves made the source of light.
But in order to convert this rude experiment into a
perfectly definite physical method of measurement and
proof, it is necessary to take more refined means of com-
parison than the methods I have just used. First of all,
it is important to make the slit an extremely narrow one.
I was obliged to make the slit moderately wide that you
might see the various coloured images of it ; but in
order that we may have a thoroughly trustworthy mea-
surement, I must make the slit extremely narrow, and
then we shall have perfectly sharp definite lines, only of
the breadth of the slit itself, showing these colours. You
see them now perhaps half-an-inch or one-third of an
inch broad ; but it is perfectly possible and necessary
for exact physical measurement, to make them exces-
sively narrow, and to measure with the most extreme
care their relative positions with regard to one another.
Another necessary detail is to place the prism, or prisms,
exactly in the position of minimum deviation as it is
called in which case the rays make equal angles with
the surfaces of the prism at which they enter and escape.
Then and only then are we entitled to conclude that
there is absolute coincidence between the dark absorp-
tion lines and the bright lines due to the same incan-
descent vapour, according as it is employed to absorb
or to radiate. When this is to be carried out with the
utmost perfection attainable in modern optics, we employ,
220 SPECTRUM ANAL YSIS.
not the method of projection upon a screen, which
I have used just now, but a far more delicate method,
invented by Fraunhofer, in which the rays are received
by the object-glass of a telescope, so that in the air,
at its focus, an image of the spectrum may be formed.
This may be examined by means of an eye-piece, as
powerful as we choose, so that we may separate the
different kinds of light radiated by a glowing gas, by
telescopic power as well as by increasing the number
of prisms. By using telescopes more and more powerful,
and greater numbers of prisms, as you can easily con-
ceive, this method will enable us to measure with the
utmost nicety, to any degree of approximation that may
be desired, the relative distances between the various lines
of the spectrum. So we have the means, if we apply
these refined methods to light from celestial sources, and
also to that from known terrestrial sources, of determining
whether the different radiations and absorptions observed
belong to precisely the same wave-lengths, that is, have
precisely the same positions in the spectrum ; and there-
fore we have as complete physical proof as it is possible
to desire of the presence (somewhere or other in the
path of the light which comes to us from a celestial
body) of the incandescent vapour of a particular known
terrestrial substance.
This, then, is the basis of spectrum analysis as applied
to problems connected with the physical universe. I
shall now say a few words about the results of the
application of this method of investigation to the sun,
stars, nebulae, and comets. The literature of this sub-
ject has become very extensive considering how new it
is. Seeing that the subject is barely fourteen years
old in its definite applications, it is astonishing to find
SPECTR UM ANAL YSIS. 22 1
that it already fills many volumes of special treatises
and a host of scattered papers, and still more to find
that a great deal of what is there contained is thoroughly
popular and yet thoroughly trustworthy.
On a point of this kind, therefore, most of you by a
little reading can acquire at least as much information
as I have to give you. Therefore, while I must take
some notice of it, I need not at all dilate upon it,
though it is a very important and interesting part of
our subject.
First of all, let us consider what we do see when we
treat sunlight as it comes to us from the sun, as a whole,
that is without specifying any particular portion of the
surface. Take a beam of sunlight and subject it to the
same scrutiny which we have employed to-day upon the
light of the electric arc and the carbon points. It is
impossible in any coloured diagram to represent accu-
rately the solar spectrum, and therefore no graphical
delineation will at all supply the place of an actual
examination of the phenomena. Nor will a verbal
description ; so I shall be very brief. We find at once
that the solar spectrum is crossed over by an enormous
number of black lines, perpendicular to its length ;
precisely as the black line lay which you saw a little
ago across the otherwise complete spectrum from which
it had cut out a portion. We arrive therefore at the
conclusion that the sunlight must have come originally
from some black body, or opaque body, which is in-
tensely self-luminous, and which may be either in a
solid or in a liquid state, possibly even in the state of
extremely compressed gas. However this may be, the
source of light in the sun, whatever it is, must, in so
far as we can see, give off all kinds of radiations, so it
SPECTRUM ANALYSIS.
is practically a black body. These black lines, or gaps,
in what would otherwise be a continuous spectrum, must
therefore be due to absorption by vapours (self-luminous
or not) which are somewhere in the path by which
these sun rays arrive at our earth.
Now, the source of a part of these lines has been
known for a very long time, since Sir David Brew-
ster's early days, in fact, for he discovered that they
were due to absorption by the earth's atmosphere. We
know the earth's atmosphere does absorb a great deal
of sunlight. The rising sun, when we see it obscured
by vapours, is by no means comparable with the sun
in the zenith ; but that is mainly a kind of absorption
which would be given by neutral tinted coloured glass,
which would tone down the various rays in only slightly
different proportions, very much, in fact, as they are
toned down by reflection, as when you see an image
of the sun in a pool. The reflected sun is very much
less bright than the direct, and after two or three reflec-
tions from a glass surface may be looked at without
injury to the eye. But here the effect is a mere general
weakening of the light, there is no special or selective
absorption. The atmosphere might merely have
weakened the various kinds of sunlight in some such
nearly constant proportion, but Sir David Brewster
found it did more than that. He found that when you
compare the solar spectrum when the sun is high with
that of the same sun when it is rising or setting, there
are a great many more lines crossing it in the latter
than in the former case ; and he concluded that, as the
only difference of circumstances between the two cases
is that the same rays had to pass through a much
longer extent of the earth's atmosphere (and especially
SPECTRUM ANAL YSIS. 223
through the dense part of it), at sunrise or sunset, than
when the sun is high, therefore these new lines at least
are due to absorption by the air, or by aqueous or
other vapour in the air.
It is possible, by that very simple comparison of the
spectrum of the sun at rising with the spectrum of the
sun at mid-day, to classify the missing rays, and say
there are some whose absence is obviously due to the
earth's atmosphere ; the remaining ones we cannot
account for by anything terrestrial, we must go either
to the space between us and the sun, or to the sun's
atmosphere for the explanation of their cause.
Now, it is obvious that if the absorption were due
not to the sun's atmosphere or to the earth's atmosphere,
but to some other medium between us and the sun, that
medium would treat the light of all the other stars just
as it treats the light of the sun ; and therefore if these
lines in the solar spectrum which are not accounted for
by the earth's atmosphere can be accounted for by
anything in space, all stars should have spectra con-
taining the same dark lines as are found in that of
the sun.
Now that has been found to be by no means the case.
Many stars have spectra totally different from that of
the sun, as well as from one another. Therefore the
spectrum given by any particular sun or star is due
mainly to its own atmosphere of incandescent vapour,
and we can thus study the chemical composition of the
atmosphere of that sun by simply finding what terres-
trial substances, put into a Bunsen flame, or rendered
incandescent by electricity, will produce bright lines in
its spectrum corresponding to the dark lines we find
in the spectrum of the star. Here is a small portion
224
SPECTRUM ANALYSIS.
of the grand drawing made by Angstrom, a mere frag-
ment of his map of the solar spectrum, not above one-
thirtieth of the whole he has depicted. The numbers
above indicate the wave-length, in fractions of a milli-
metre. Thus the three conspicuous green lines of mag-
nesium, forming the group called b by Fraunhofer (see
diagram, p. 192), are seen here to have wave-lengths
of o mm 'O005i67, o mm '0005i72, and O mm> ooo5i83 respec-
tively. This portion, as you see, contains a number
52
t&KC&KJfa Cr Ti Cu/ n Cojfob
of dark lines. Well, when you pass sunlight through
one-half of the slit of the spectroscope, and light from
incandescent materials (in the electric arc or in an
induction spark, or even a Bunsen lamp) through the
remaining half, and examine them through the same
train of prisms, you get two spectra as here represented,
the one of sunlight and the other of the terrestrial sub-
stance, spread out side by side. Any two rays which,
SPECTRUM ANAL YSIS. 225
in passing through a very long series of prisms, undergo
exactly the same treatment, must be of the same refran-
gibility ; and therefore, by what I have just explained
to you, due to the same definite substance.
In the band just below the portion denoting the solar
spectrum, all the full lines represent lines which are
actually observed in the spectrum of metallic iron.
Looking up, you see the exact coincidence of each
with a corresponding line in the solar spectrum. You
see there are about thirty coincidences even in this
small part of the solar spectrum ; and so throughout
the spectrum the number of coincidences between
actual bright lines given by incandescent iron, and
absorption lines in the solar spectrum, may amount
to several hundreds. By recording both spectra pho-
tographically, it appears probable, from some recent
experiments, that these hundreds of observed coinci-
dences may in a short time become thousands. Now,
as Kirchhoff has shown, even if there were not an
absolutely ascertained coincidence in any one of these
cases, if it were only so near a coincidence that we could
not be perfectly certain, by means of our instruments,
that it was an exact coincidence, still, looking at the
question from the point of view of the theory of pro-
babilities, the chances of iron's not existing as an
absorbing medium in the sun's atmosphere, as estimated
by a person who has seen even a moderate series of at
least approximate coincidences, would be represented
by one against a number which I cannot pretend to
understand, but which contains some thirty-five places
of figures. You can see then what extraordinary sort
of probability there is that iron is there ; and when I
say that that probability was derived from only a com-
p
226 SPECTRUM ANAL YSIS.
paratively few coincidences in the solar spectrum, how
enormously greater would it not be were we to take
account of all now known. And not only this. Lines
which, in the iron spectrum, are strong, are correspond-
ingly strong in the solar spectrum to every grade of
nicety. So far, then, iron must be in large quantities in
the sun's atmosphere. We find also that nickel must
exist there. Every bright line shown by incandescent
vapour of specimens of nickel in our laboratories (whether
these specimens be terrestrial or cosmical, i.e. meteoric)
corresponds to a dark line in the solar spectrum. Not
only so, but the character of each bright line and the
corresponding absorption line is the same. Very bright
lines correspond with very dark ones, broad lines with
broad, narrow with narrow, double with double. Some
lines appear to be given by two different substances,
as iron and nickel, for instance. This is probably, in
the great majority of cases, due to slight impurities
of the specimens tried. Various other substances
are shown in this small portion of the spectrum,
magnesium, manganese, cobalt, chromium, sodium,
titanium, and calcium. The number of titanium lines
has been shown by Thalen to be very much in excess
of even the enormous number of iron lines I have
mentioned.
So far then this has been a question of the spectrum
of light taken from the whole surface of the sun ; but
it becomes an exceedingly curious question, Are there
local differences in the light from that surface, and if
so, what are they ? when we reflect that there are such
things as sun-spots, and also when we think of those
peculiar red flames, as they used to be called, which
are seen round the dark body of the moon during a
SPECTRUM ANALYSIS.
227
total eclipse. It becomes an exceedingly curious
question what we shall get if we take sunlight from a
limited portion of the sun's surface, as we can do by
using a telescope lens of long focus. We form by means
of it an image of the sun of an inch or so in diameter,
and place the slit of our spectroscope successively on
various parts of that image.
It was to be expected that some very important addi-
tional information would thus be obtained. Now, such
information you can quite easily procure for yourselves
by reading works like that of Lockyer, but I may just
very briefly indicate its nature. In the first place, we
_ Di Da T)3
find that from sun-spots in general we have those
absorption lines a little thicker and darker than from
sunlight as a whole, so that it appears that there is
associated with the sun-spot something which produces
an excess of absorption. There is a more powerfully
absorbing medium at the place where the sun-spot
appears than at the places where faculae or bright spots
appear. In the particular spot, a portion of whose
spectrum is here figured, the lines (D l and Z> 3 ) of sodium
appear not only broadened over the spot, but reversed :
i.e. bright instead of dark : just over the middle of
the spot.
Then, when we come to examine the red flames or
228 SPECTRUM ANAL YSIS.
prominences, we find that in general their spectra con-
sist simply of bright lines. Such then is the spectrum
of part at least of the gaseous matter which surrounds
the sun, and it is the upper portion of the absorbing
medium which cuts out these black lines from what
would otherwise be a continuous spectrum, and you
easily trace what lines it does cut out. For instance,
here is a dark line (C) in the red [see diagram, p. 192,
which shows, as through the same slit, the spectra of
the sun and of a prominence], which is due to hydrogen
gas. Well, we find these red flames owe their redness
to the particular colour of this line of hydrogen. So
this bright red line is one of the main features of the
prominences. Then we find a yellow line very nearly
coincident, as you see, with the lines of sodium. No-
body as yet knows what is the chemical substance
which produces this particular line. It corresponds to
no absorption line usually found in the sun's spectrum
SPECTR UM ANAL YSIS. 229
(though you observe a trace of it in the spot spectrum
which I last showed you), and therefore it must be due
to a substance in a peculiar condition capable of radiat-
ing, but of having its absorption made up for, some
substance which possibly we may not yet know. Pos-
sibly it may not be a terrestrial substance at all. But
it occurs here, very nearly giving a coincidence with
sodium ; but its light is not only more refrangible, but
it wants the distinctive property which sodium has of
giving a double line. Then we find several other lines,
including two or I may say three more, due to hydro-
gen ; so that the spectrum of these flames consists
mainly of the spectrum of incandescent hydrogen gas.
Here is another drawing of a small portion of the
spectra of the sun and a prominence, which shows the
exact coincidence of the bright and dark lines.
Suppose now we had a telescope to which the spec-
troscope could be adjusted : on looking at a red promi-
nence without the spectroscope we should see one
image, but it would be an image which consisted partly
of the red, partly of the green, partly of the blue, partly
of the violet rays of hydrogen ; but if we combine tele-
scope and spectroscope, the combination would enable
us to separate from each other, along the line of disper-
sion, the various colours ; and the edge of the sun
would be treated in the same way. All its colours
would be spread out from one another, but they would
be spread out at a disadvantage compared with the
colour of a monochromatic line. Because however far
you separate one such line from another, you do not
weaken either. They remain, except in so far as re-
flection from the surfaces of the prisms, and ab-
sorption within the prisms, weaken them, as strong
230 SPECTR UM ANAL YSIS.
as ever. But if you take a corresponding portion of
sunlight, then, since it gives practically a continuous
spectrum, you spread it uniformly over as long a space
as you choose. So by the aid of this property, as the
solar spectrum is practically continuous, except where
there are interceptions of light, you can spread it out,
and thus weaken it throughout as much as you please ;
whereas the other spectrum consists of perfectly definite
bright lines, which you may spread as far apart from
one another as you please, but which you cannot
individually weaken. Hence, however strong be the
glare of sunlight, sufficient dispersive power will enable
us in fine weather to examine the spectrum of the red
flames.
This is perfectly analogous to the observing stars by
daylight, which, you are aware, is done in every fixed
observatory by means of a good telescope. It is simply
because the diffused light of the sky allows itself to be
weakened farther and farther as we spread it over a
larger and larger image, while the light of the star
always comes from the same definite point ; because
no one has yet made a telescope showing a star's disc
(except as a delusive appearance due to diffraction), so
that, magnify it as you please, its light comes from the
same definite point. So it remains of the same bright-
ness, while the background may be made as dark as
you please by spreading it out. In that way, by com-
bining the spectroscope with the telescope, and widen-
ing, or altogether dispensing with the slit, it is possible
to study the phenomena of these red flames, and, in
fact, the whole behaviour of gaseous matters round the
edge of the sun's disc, without waiting for a total
eclipse. This is an extremely beautiful adaptation of
SPECTR UM ANAL YSIS. 23 1
means first made theoretically by Lockyer, and after-
wards by Janssen, but brought into practice nearly
simultaneously by the two astronomers.
Here is the result as applied to a particular portion
of the sun's circumference. The body of the sun we
will suppose to be under that picture. These are simply
eruptions of glowing gas from the sun's apparent sur-
face. On the same scale there would be another image,
a green image, situated almost at the end of the room ;
then a long way beyond, an indigo, and finally a violet
one. But we have by means of the prisms separated
that particular image from the others, and thus we
have here a monochromatic representation of what is
above the surface of the sun, in so far at least as incan-
descent hydrogen gas is involved. When I point out
232 SPECTR UM ANAL YSIS.
that the change from the first figure to the second took
place in the course of a few minutes, you will see what
exceedingly rapid changes are going on in these self-
luminous clouds ; and when I further tell you that the
height of this prominence, which is a stream of hydro-
gen rushing violently up from a rent in the surface of
the sun, is something like 70,000 miles, you will see on
what a stupendous scale, and with what tremendous
velocities, these phenomena are constantly taking place.
So far then for the sun. When we compare the
spectra of different stars with that of the sun, we come
to some very curious conclusions. We find four classes
of spectra, as a rule, among the different fixed stars
which have seemed of importance enough to be separ-
ately examined. The first class of spectra are those of
ivhite or blue stars. You see an admirable example in
Vega, and another in Sirius, or the dog-star. All these
white stars have this characteristic, that they have an
almost continuous spectrum with few and broad dark
lines crossing it, and these few for the most part lines
of hydrogen. These stars are in all probability at a
considerably higher temperature than the sun ; and
their atmospheres are in even more violent agitation
than is that of the sun. Then you come to the class
of yellow stars, of which our sun is an example. In
their spectra you have many more dark lines than in
those of the white stars, but you have nothing of the
nature of nebulous bands crossing the spectrum, such
as you find in the third class ; still less have you certain
curious zones of shaded lines which you have in the
fourth class of stars. This classification seems to point
out the period of life, or phase of life, of each particular
star or sun. When it is first formed, by the impact of
SPECTRUM ANAL YSIS. 233
enormous quantities of matter coming together by gravi-
tation, you have the very nearly continuous spectrum
of a glowing white hot liquid or solid body (or, it may
be, dense gas), the sole, or nearly sole, absorbent being
gaseous hydrogen in comparatively small quantity, and
the spectrum having therefore few absorption lines.
As it gradually cools, more and more of those gases
surrounding its glowing surface become absorbent,
and so you have a greater number and variety of lines.
Then, as it still further cools, you have those nebulous
bands which seem to indicate the presence of com-
pound substances ; which could not exist in the first
two classes, because there the temperature is so high
as to produce dissociation. Still further complexity
of compounds will be found in the atmospheres of the
fourth class. But sometimes, as in the case of tem-
porary stars, a spectrum of the fourth class is suddenly
crossed by the bright lines of hydrogen showing either
a last effort at the discharging of red flames, or a flicker
due to some last chance impact of meteoric matter.
So that we can study, as it were, not the succession of
phases of life in any one particular star, but different
simultaneous phases in many : we can study some stars,
as it were starting into life, others getting older, others
older and older ; and we occasionally find a most re-
markable circumstance happening with a star that has
practically died out, a star which is scarcely notice-
able by the astronomer. Such a star occasionally has
an outburst, rendering it for a little time sometimes
for several years as bright as Jupiter itself. One
such case very luckily occurred within the spectro-
scope period. It was carefully examined by Huggins,
and the result of the examination was to show that it was
234 SPECTRUM ANAL YSIS.
a star which had gone on cooling, or at all events had
reached the lowest of its cooling stages, but suddenly
became bright, because of an outburst of hydrogen.
Bright lines broke out across its spectrum, showing
that the incandescent gas which was in its atmosphere
was at a higher temperature than at least the surface of
the star itself. Now, this leads me to another and a
curious remark about the lines of hydrogen which we
see in the sun. Here is a portion of the solar spectrum
as seen under particular conditions. It belongs to a
solar spot, where of course the whole amount of radiation
is less than that from the general body of the sun
around it. Over that spot there must have floated an
incandescent hydrogen cloud at a much higher tempera-
ture than the radiating portion of the sun at the spot,
and therefore it was capable of radiating more of the
hydrogen light than there was to absorb, so it behaved
as a radiating medium instead of an absorbing one ; and
therefore the green line in the solar spectrum which is
due to hydrogen came out as a bright line. After
watching this phenomenon for a short time in this par-
ticular form, the observer saw it change into a line with
a bright portion at one side and a relatively black portion
SPECTRUM ANAL YS1S. 235
at the other, one part evidently due to radiation, the
other to absorption, but both closely connected. Why
did one half become bright and the other half black ?
The answer to that leads us to a study of a very curious
kind, but I must defer this to another lecture. Mean-
while, as I have the electric apparatus at hand, there is
another experiment I wish to show, though it is not
directly connected with the subject I have been discuss-
ing.
I have here a cube of the well-known Canary glass,
whose colour is due to oxide of Uranium. When I place
it in the path of the rays from the electric arc it shows
brilliantly its characteristic yellowish green light. But
observe that this dark violet glass, when interposed
between you and the cube, renders it practically in-
visible in spite of its brilliant illumination. The violet
glass is practically opaque to this yellowish green light.
So far the experiment presents nothing very remark-
able. But I now close the aperture of the electric lamp
with the violet glass; and there, in the middle of the
almost invisible beam which it allows to pass, is the
cube of canary glass showing its characteristic colour
almost as brightly as before.
Obviously the canary glass has changed the light
which falls upon it : for light can pass through the
violet glass and afterwards develop the greenish colour
to which the violet glass is almost opaque. This is one
of the very beautiful experiments by which Stokes
physically explained Fluorescence as a change produced
by certain bodies on the refrangibility or, more directly,
on the period of vibration of light.
Here is another exquisite experiment of the same
kind. I illuminate (very feebly) a sheet of white paper
236 SPECTR UM ANAL YSIS.
by the radiation through the violet glass. With a brush
dipped in a solution of sulphate of quinine, slightly
acidulated by sulphuric acid, I write letters on the
paper, and these at once shine out brilliantly with a
light blue colour. This also is nearly invisible through
the violet glass.
In both experiments the altered light is of lower
refrangibility, i.e. of longer vibration-period, than the
incident light another instance of degradation of
energy.
The point I shall first take up in next lecture is the
point left unexplained to-day, how it is possible for a
line which was originally dark in the solar spectrum to
broaden out and become bright, and then for one por-
tion to become dark while the other portions remain
bright.
LECTURE X.
SPECTRUM ANALYSIS.
Change of colour of Light by relative velocity of source and observer. Analogy
from Sound. Causes of broadening of spectral lines. Spectrum of Solar
Corona ; of Double Stars ; of Comets. Probable nature of Comets ; of
Saturn's rings ; of the Zodiacal Light.
YOU remember I closed my last lecture by pointing
out to you, for the second time, a diagram of a portion
of the solar spectrum, in which we had side by side a
bright line and a dark one, due to the same substance,
namely, hydrogen. I told you that there is a very
beautiful point of theory involved in the explanation of
this phenomenon, and I proceed to give it. It generally
goes by the name of Doppler's principle, but it depends
upon precisely the same idea as that which led Romer
to the discovery of the finite speed of light.
Let us take the simplest possible analogy. Suppose,
for instance, that we had Mr. Perkins' steam-gun, and
caused it to project bullets in the same direction, suc-
ceeding one another once every half-second. Then, if
a target were held in the path of these bullets, it would
of course be struck 120 times per minute. But suppose
that the target were to move up towards the gun, while
the gun still kept on discharging the bullets at the
same rate, it is obvious that it would meet more bullets
in the course of a minute than it would meet if it were
238 SPECTR UM ANAL YSIS.
standing still. If you were to withdraw the target
gradually, keeping it always however in the line of fire,
you would get fewer bullets per minute ; and if you
were to make it move away from the gun at exactly
the rate at which the bullets are coming, then no bullets
would reach it at all. One bullet would be in its neigh-
bourhood, and would remain constantly at the same
distance from it ; for, in fact, the target and the bullet
would be moving with the same rapidity.
Precisely the same thing may be observed in passing
over a set of waves. If you were steaming through a
set of waves in the direction in which the waves are
going, it is quite conceivable that you may be steaming
so fast as to be riding on the crest of a definite wave
all the way ; but steam a little more slowly, and you
will see waves gradually passing you ; steam still more
slowly, and a greater number of them will pass you per
minute. If, on the other hand, you are steaming so as
to meet the waves, then you meet more than if you
were not moving. The faster you go you meet the
more waves per minute ; and there is absolutely no
limit to the number you may meet per minute, if you
could only move fast enough to meet them. Now the
impression, be it of pitch or of colour, that is produced
upon the ear by sound, or upon the eye by a luminous
radiation, depends entirely, so far as our present pur-
pose is concerned, upon the number of these waves
which meet them per second. Therefore, if we are
moving towards a sounding body which is giving out
a particular note, the number of waves which reach our
ear per second will be greater than it would be if we
were standing still, or (generally) if we were at rest rela-
tively to the body. And as a higher note corresponds
SPECTR UM ANAL YSIS. 239
to a greater number of waves reaching our ear per
second, it is obvious that in the former case, whether
we are moving to the sounding body or the sounding
body is moving to us, there will be a greater number of
waves reaching our ears than if we were at relative
rest ; so that we should perceive a higher pitched
sound than what is actually given off by the sounding
body. The experiment has been made by the help of
a railway engine first in Holland, and since in other
countries by stationing upon the engine a trumpeter,
who had beside him a musician to control exactly the
note that he should play. The musician, of course,
was moving along with the trumpeter, and therefore
heard precisely the note that the trumpet was sound-
ing. The sound, however, was also heard by other
musicians who were placed at the side of the line, and
they noted that the faster the engine came up to them,
the higher did they hear the note which was played by
the trumpet ; and the faster the engine went away after
passing them, the faster it retreated from them, the
lower did this note appear to be. I have no doubt
that you at all events those of you who have paid any
special attention to musical sounds will be able at once
to perceive this effect by means of such a simple instru-
ment as this tuning-fork, even with such comparatively
slight velocity as I can give it by swinging it in my
hand. For the success of an experiment of this kind,
it is better that you should close your eyes, in order
that you may not associate the result with any move-
ment which you may observe on my part ; and I shall
endeavour to perform the experiment without making
any noise which might indicate to you how I am
moving, or whether I am moving, the apparatus at the
240 SPECTR UM ANAL YSfS.
instant. [Experiment shown.] You notice, then, that
during the interval that I allowed the fork to sound,
there was a period at which its pitch appeared to you
to rise ; then immediately afterwards it appeared to fall ;
then it rose again, and so on. We had a musical sound
which was alternately higher and lower in pitch as I
sharply moved the vibrating fork to or from you, and
then, when the fork was held steady, we had the original
sound. Now, precisely the same thing happens with
regard to waves of light. If you move so as to meet more
waves of light in a second, that will correspond to an im-
pression upon your retina of a higher order of colour than
if you were not moving to meet those waves, or if the body
which was sending those waves to you were not moving
towards you. Thus you see that the light which comes
to us from a star is capable, not only, as I pointed out
in my last lecture, of showing what chemical substances
are incandescent in the atmosphere of the star, whether
as giving out light on their own account or as absorb-
ing portions from an otherwise continuous spectrum,
but is also capable of pointing out to us whether the
star is moving to us or from us ; or still more minutely,
whether a portion of its atmosphere is moving on the
whole from us, and another portion on the whole to us.
The first application of this by the spectroscope to the
study of the relative motion of a star with reference to
the solar system, was made by Mr. Huggins with refer-
ence to the dog-star. Of course, in order to find out
from such experiments (which tell us only the relative
velocity of the earth and the star in the direction of
the line of sight) what the corresponding velocity
of Sirius is with regard to the sun, it is necessary to
consider in what part of its orbit the earth is during the
SPECTRUM ANAL YS1S. 241
observation, because when the earth lies in a line from
the sun, making a right angle with the line drawn to
Sirius, the earth is moving much faster or much slower
towards Sirius than the sun is moving. On the other
hand, when the earth is 180 from that position, it is
moving slower or faster towards Sirius than the sun is
moving. When the earth is so placed that Sirius and
the sun are nearly on the same or on opposite sides of
it, it is moving transversely to the line joining the sun
and Sirius, and its motion relatively to the sun pro-
duces no modification of the observed phenomenon.
We should have in such a case the full effect due to the
relative motion of Sirius and the sun. Correcting, then,
for the velocity of the earth relatively to the sun, Mr.
Huggins found that the velocity of Sirius relatively to
the sun is about twenty miles per second in a direction
tending to increase their distance ; so that ever since
the time when Sirius was first observed, it has been
steadily moving away from the solar system at the rate
of something like twenty miles per second, and yet we
have not the least documentary or other proof that
the brightness or apparent magnitude of Sirius has
become at all diminished in consequence. It has been
leaving us at that tremendous rate, and yet so far is it,
or has it been, from us all this time, that even this in-
crement of distance, growing at such a tremendous
rate, has made during historical periods no perceptible
change in the amount of light that we receive from it.
The next application that was made of this principle
was to verify the fact of the sun's rotation about its
axis. It is obvious that, as the sun rotates about its
axis in the same direction as the earth rotates, one por-
tion of the solar equator, the portion to the left as we
Q
242 SPEC TR UM ANAL YSIS.
look at the sun in our northern hemisphere the left-
hand side of the sun is coming towards us, and the
right-hand side of the sun is going away from us. The
sun's rotation about its axis takes place in what is called
the positive direction ; that is, the opposite direction to
that of the hands of a watch, as looked at from the north
pole side of the plane of the ecliptic. Now, although
the sun's rotation is very slow, that is to say, though
the sun takes about twenty-six days to execute a whole
revolution, still, because of its enormous diameter, the
linear velocity of all parts of its equator is very consid-
erable : more than a mile per second. Therefore if we
examine, by means of a spectroscope, the light which
comes from, let us say, incandescent hydrogen at different
parts of the solar equator, it should correspond to rather
higher light (more refrangible rays more waves per
second) from the left-hand side of the sun's equator
which is approaching us, than from the right-hand side,
which is retiring from us ; and, therefore, if we could by
a proper optical combination place side by side, as com-
ing through the same spectroscope slit, the light given
out by incandescent hydrogen at these two extreme ends
of the sun's equator as seen by us, then we should find
of the two hydrogen lines, the one from the left-hand
side shifted a little up in the scale, and the one from the
right-hand shifted a little downwards. Therefore we
should find, of course, the hydrogen line in different
places of the two spectra ; and by measuring the
amount of displacement between the two, we could
calculate what is the rate of the motion of these points
in the sun's equator to us or from us, compared with
the whole velocity of light in space.
Now, carry this just a step further, especially thinking
SPECTRUM ANALYSIS.
243
of the enormous velocities (which I discoursed upon in
last lecture) with which these masses of flaming hydro-
gen are thrown out in explosions or eruptions from
below the visible surface of the sun. Think of a rate of
several hundred miles per second, or something like it,
with which these masses of glowing gas are thrown out,
and you can easily see that if something of the nature
of, but incomparably superior in dimensions to, a cyclone,
such as we have in our tropical regions, were taking
place, accompanied by down-rushes of colder gas, and
up-rushes of warmer gas, both of these being incandes-
cent hydrogen, the general down-rush of the cold will
correspond to absorption, and the up-rush of the hot to
radiation. There will be cold gas absorbing, but going
from us, and an up-rush of (on the whole) radiating gas
which is coming towards us ; and therefore we should
find the absorption correspond to a lower position in
the spectrum than the natural hydrogen line, while the
bright line corresponding to the gas coming towards us
will belong to a higher position in the spectrum ; and
so we account for the double line referred to in my last
lecture, the lower half of it nearest the red being dark
or due to absorption, and the other side being bright or
due to radiation. Thus, even with a slit, the motion of
these hydrogen clouds is easily seen by the blurred and
broken form presented, whether by their absorption
244
SPECTRUM ANALYSIS.
lines as seen on the spectrum of the solar surface ; or
their radiation lines as seen in the spectrum of the
regions round the edge of the disc. Curious examples
of these two phenomena are shown in the diagrams
before you. Both represent appearances presented by
the green line of hydrogen in the first partly absorbent,
partly radiating, the line is on the disc in the second
it is seen in a prominence, parts of which are moving
with very great velocity. [Hence these pictures arc not
pictures of the prominence, as it would be seen by a
telescope during a total eclipse, but pictures distorted by
the Doppler principle.]
If we think for a moment of the whole light sent us by
the sun, in which absorption by hydrogen far exceeds
radiation by hydrogen, and think of the different rela-
tive rates of motion of different parts of the surface,
we see a physical reason for broadening of the hydrogen
lines altogether independent of pressure and cyclone
currents. Hence a star in which the absorption bands
are very broad may not necessarily have a dense
atmosphere, but may be merely rotating rapidly about
its axis. Thus caution is requisite in interpreting such
appearances. And all the more so because Lord Rayleigh
SPECTRUM ANAL YSIS. 245
has called attention to the fact that even when a mass
of incandescent gas is at rest as regards the spectator,
its individual particles are in motion with sufficient
relative rapidity to render a very narrow bright or
dark line an impossibility. Even very rare hydrogen,
if very hot, will therefore give broad absorption bands
or bright lines. Other two causes, which may in
certain cases lead to similar results, I must presently
point out to you.
I may mention, before leaving this part of the sub-
ject, that Fox Talbot has proposed to apply the same
principle to double stars, in order to find what is the
distance of a physical system of two stars from us ; at
least when they have one common absorbing con-
stituent in their atmospheres. If we can observe a
double star, the plane of whose relative orbit passes
(let us say, for example) nearly through the earth,
then we may perform upon these two stars precisely
the same operation as I have described with reference
to the light coming from the two ends of the solar
equator ; and therefore of course we shall be able to
tell what is the actual velocity of the one star in its
orbit relatively to the other. We shall be able to cal-
culate the relative velocity of the two, which is in fact
the actual velocity of the one star in its orbit round the
other ; and knowing that actual velocity, we shall be able
to calculate, from the observed periodic time, from the
actual velocity thus determined, and from the apparent
size of the orbit, not only what the actual size of the orbit
is, but also how far that orbit is removed from us in
order to appear so small as it does. So that by the help
of this method, when properly applied, we shall be able
to get perhaps a much closer approximation to the dis-
246 SPECTR UM ANAL YSIS.
tance of various fixed stars from us than we can get by
the only method hitherto employed, namely, by the
determination of what is called their annual parallax.
In fact, we may conceivably thus obtain a measure of
the distance of stars so far off as to show no measur-
able, or even observable, annual parallax at all.
You see, then, that the light from a heavenly body
can give us new information of very varied kinds, infor-
mation which was not sought nor even thought of as
attainable until the introduction of spectrum analysis.
We can find out, first of all, whether the light which
it sends to us is light from a body of the nature of a
solid or liquid, or at all events, a body of high general
absorbing power, or whether it is light from a body of
comparatively small and specific absorbing power, such
as a glowing gas. Then, we can also tell and this is
perhaps one of the most curious of all the applications
if it be a glowing gas, at what pressure and at what
temperature it exists in order to give off the spectrum
that we find, because we can operate upon terrestrial
hydrogen, etc., at various temperatures, and combine
these with various pressures, and examine the spectrum
under all such possible combinations, and then compare
these variations in the spectrum with the varieties of
hydrogen spectrum, which we get from the sun as a
whole, from different parts of .the sun^s surface, and
from various fixed stars. Therefore we are able to
assign, not merely that it is this particular chemical
substance, but also in what particular physical condi-
tions it is found in order that it may give that parti-
cular kind of spectrum. Then we can tell, as we have
just seen, the rate at which that particular radiating
body is coming to us or going from us. The rate at
SPECTR UM ANAL YSIS. 247
which it is moving in a direction transverse to the line
of sight is of course to be measured by ordinary astro-
nomical processes, and therefore this fills up a lacuna
something that was wanting to ordinary astronomical
processes, because we could tell perfectly well how a
body moves transversely to the line of sight, but it
is quite a novelty, at all events when the body
is one whose dimensions are invisible in the tele-
scope, to find the rate at which it is moving to or
from us.
With reference to other possible causes (which are
often at work at least we may reasonably suppose so),
besides variations of temperature and pressure, for the
broadening of lines in the solar spectrum, let us think
first of a particular effect that may take place in conse-
quence of the currents of hydrogen gas in the sun's
atmosphere. If part of the gas were going down slowly,
part of it in a locality immediately contiguous going
down faster, and then another stream going down still
faster, then that part which was going down slowest
would give the higher absorption line, and the part
which is going down fastest from us will give the lowest
absorption line ; and you would have, therefore, instead
of the single definite narrow line which would be given
by hydrogen remaining at rest, a broad band of absorp-
tion, parts of it corresponding to the different velocities
of portions of the gas. All these absorption bands
may fine off, as it were, continuously into one another ;
so that although it is the same definite substance which
is producing them all, it is producing them in different
places in the spectrum, and filling with comparative
darkness a definite breadth of the spectrum, because
its different parts are moving from us with different
248 SPECTR UM ANAL YSIS.
velocities. That is another way in which the broadening
of a band may occur in the solar spectrum.
But, as I said before, it may depend upon the
fact that differences of temperature and pressure in
general produce changes in the spectrum which a body
gives. I shall come in another lecture to the considera-
tion of the molecular theory of gases, when I shall speak
of the particles flying about with very great velocity and
impinging upon one another, and upon the sides of the
containing vessel, and so producing what we call the
pressure of the gas. Meanwhile, I shall anticipate so
far as to say that when a gas is at the ordinary pres-
sure of the atmosphere, each particle has to move a
distance, let us say, of something like a(7oVoTr tn or
sWowth of an i ncn n the average before it comes
into collision with another particle, and is sent into a
new path ; but if you were partially to exhaust the
gas in the receiver of an air-pump, there would be so
much fewer particles in a given space that the length
of the average path of any one particle, between one
collision and the next, would be notably increased. On
the other hand, if you were to compress the gas, then
you might bring the particles so much closer together
that no one would, on the average, be able to move
more than, let us say, ToWoTTou-th part of an inch, even
at its very greatest excursion, before it would come
into collision with another, and be sent into a new path
altogether. And the more you compress the gas, the
greater will of course be the number of such impacts for
every particle in a given time, and therefore the shorter
will be its average path between one collision and
the next. Now the effect of heat also is to increase this
number of impacts, because it makes the average velo-
SPECTR UM ANAL YSIS. 24C
49
city of the particles greater than before. The average
square of the velocity of the particles corresponds in fact
with what we call the energy of heat in the gas ; and there-
fore corresponds nearly to what we call the temperature ;
so that as you compress the gas, you give its particles
less way to go before they impinge upon one another,
and as you still heat it under compression, you make
them go faster and faster through the little range which
they can compass before collision. Therefore, by these
processes you make the collisions more numerous and
more violent, and you also make the length of time dur-
ing which a particle is in collision a larger percentage of
the whole time of its motion. If it has only a collision
now and then, it has a very small percentage of its
time occupied by the collision, because the actual time
of a collision is exceedingly short, and during the rest
of the time it is moving free ; but if collisions occur
with very great frequency, then the time occupied in
collisions becomes a serious fraction of the whole ; and
when a gas can be so far condensed as to approach
the liquid state, its particles are scarcely ever free
from collisions. Finally, when you get a body in the
solid state, its particles are practically in a permanent
state of collision with one another, or, at all events,
the time occupied in collisions is by far the greater
part of the whole time. Now, during a collision, a
particle of gas is not free ; it is jammed against an-
other or others ; and therefore we may expect some
modification to take place in the periods in which
it is capable of vibrating. It is vibrating not by
itself, but, as it were, only so far as the other or
others will permit it, and thus the particles inter-
fere with and modify one another's vibrations. Thus
250 SPECTRUM ANAL YSIS.
we see that if we have a very rare gas, we may ex-
pect that the spectrum which it gives off when heated
will be in the main the spectrum due to the vibrations
of the individual particles of the gas as they are flying
about free from the others ; but as we gradually com-
press it, the part of the whole time which is occupied
in collisions increases, and then you do not get the pure
spectrum of the gas, what each particle would give
on its own account, but in addition to that, you get the
modification which is introduced by the action of one
particle upon the next ; and as you more and more
compress it, and also as it is more and more heated,
you get more and more of this interference of particles
with one another. From free particles we get in general
a few definite forms of vibration, corresponding each to
a fine line in the spectrum, except in so far as this is
modified by the relative velocities of the particles with
regard to one another. When there are collisions, but
not very numerous, we get slight modifications, gener-
ally as much in the way of increase of refrangibility as
the opposite, so these lines broaden out on both' sides.
But as the amount of collision becomes more and more
serious, and occupies more and more of the whole time,
these effects spread themselves over larger and larger
spaces in the spectrum ; and so the effect of increased
pressure and temperature is to make all the bands
broader and broader, and finally, when we compress
sufficiently, to reduce the gas to what is practically a
solid, or at all events an incandescent liquid, the bands
have so spread out that they have met one another, and
you have in fact got a practically continuous spectrum.
Thus the source of sunlight may not be a solid or even
liquid globe it may be merely a great thickness of
SPECTRUM ANAL YSIS. 25 1
very hot and highly compressed gas ; in fact it seems
quite possible that no portion of the body of the sun
may be as yet even liquid.
Attending then to this, in addition to the other pos-
sible causes of modification which I have just men-
tioned, let us consider some of the data which are
obtained by actual observation. I spoke to you in my
last lecture about the spectrum of the incandescent
part of the sun itself, and also of the protuberances
which are seen during a total eclipse. But now let us
consider the spectrum of what is called the corona,
the pearly white light which is seen round the body of
the moon during a solar eclipse. There are parts of it,
according to many drawings by accurate observers,
which are obviously due to motes and ice crystals and
various other things floating in the earth's atmosphere,
because, of course, when you consider the enormous
dimensions of the sun itself, it is quite certain that there
can be no solar atmosphere (in the ordinary accepta-
tion of the word), extending to a height of something
like two or three diameters above his surface. Con-
sider the enormous mass of the sun and its consequent
attraction, and you will see at once that the idea of a
solar atmosphere extending to anything like that dis-
tance is altogether preposterous. For in spite of the
very high temperature at the sun's apparent surface, the
density of the atmosphere there, due to the immense
pressure, would in such a case be so great that a layer
of moderate thickness from its lower part might easily
have a density exceeding that of the sun as a whole ; so
that the sun would thus be in unstable equilibrium in a
fluid denser than itself. Besides, there is a well-ascer-
tained fact of quite a different character which goes
252 SPECTRUM ANAL YSIS.
against the notion altogether ; that is, that no two ob-
servers drawing such a corona, even at very short inter-
vals of time from one another, or at very short intervals
of distance from one another at the same time, ever
draw at all nearly the same thing. That is a complete
proof that at least the outer part of what has often been
called the corona is a phenomenon due to the state of
the terrestrial atmosphere in the observer's line of sight.
But, even when the atmosphere is in its very clearest
state, as it happily was in the south of India during the
great eclipse of 1871, when most perfect observations
were made, it is still found that there is a silvery
light surrounding the sun, but extending to a height
of, at the utmost, only fifteen or twenty minutes of arc
above the dark circumference of the moon. That light
has been analysed by the spectroscope, and its spectrum
has been found to consist of two things, one of them
light from a glowing gas, the other reflected sunlight,
so that the true corona owes its light to two sources.
One is self-luminous gas, of whose composition I shall
speak immediately ; the other, scattered particles which
are capable of sending back sunlight. In fact, the
spectrum of the corona as observed by Janssen, with an
instrument specially contrived for the purpose, a tele-
scope with very large aperture as compared with its
length, constructed for the special purpose of enormously
increasingthe brightness of the image of the phenomenon,
was simply a weak solar spectrum, not continuous, but
having the dark lines, just like the spectrum of moon-
light (which is merely reflected sunlight). But crossing
it there were bright lines of hydrogen, the C line, the
Ftine, and the G line, which I described to you formerly
[diagram, p. 192] : and, in addition to these, there was
SPECTRUM ANAL YSIS. 253
a green line, which cannot as yet be assigned to any
known substance. That line appeared, in a detailed ex-
amination, to be given out even in the uppermost regions
of the corona, regions farther from the sun than the
highest in which hydrogen lines were seen. This would
appear to indicate a gaseous element, one not only giving
a simpler spectrum than hydrogen, but also a lighter
element, capable of rising to higher elevations against
the action of the sun's attraction. There must, then, be
in the corona a solar atmosphere extending to a height
of rather more than one-half the radius of the sun from
his surface. It is possible it may extend still farther ;
but in addition to that, there must be matter which is
capable of reflecting sunlight, and giving the continuous
spectrum which Janssen observed.
Some very curious observations made in America
upon the corona led to the detection of three bright
lines which were found to coincide with lines which
occur in the spectrum of the aurora. Now, it is a
very singular fact that the terrestrial substance which
gives these lines has not yet been discovered ; and
it is a problem of the most curious, interest to us at
present what substance it can be which, incandescent
by electricity no doubt, during a terrestrial aurora,
gives us the peculiar homogeneous green light which
every aurora shows, and which is almost the only light
given by the great majority of auroras. But the pre-
cise similarity and coincidence between the three auro-
ral lines observed by one American observer, and the
three lines observed by another American in the corona
of the sun, seem to promise us wonderful information
as to the similarity of the upper regions of the earth's
atmosphere to those of the sun's atmosphere.
254 SPECTRUM ANALYSIS.
I shall now add a word or two to what I said in my
last lecture with reference to double stars. I spoke
to you about the spectra of fixed stars as indicating
what may be called periods of life ; but there are, be-
sides, some very curious observations made specially
upon double stars. All of you who have looked through
even a moderately good telescope at double stars, must
have noticed that many of such stars have extremely
fine colours, very often directly complementary colours.
Now, it was of course an interesting application of the
spectroscope to find out to what these complementary
colours are due. You can see at a glance when the
spectra of the components of a double star are placed
side by side, in what they differ. Now one of the first
pairs examined showed for the first component the
spectrum of a white star nearly ; but the other com-
ponent showed in its spectrum an enormous group of
bands, cutting out almost the whole of the blue and
green regions. Hence the group consists of a white
star, with a practically red star revolving round it. But
for an optical, or rather a physiological reason, of which
it is not my business now to inquire the nature, a white
body in the neighbourhood of a red body has a tendency
to appear green. It is, then, merely an effect of contrast,
as it were, that this double star appears in the telescope
as an extremely fine green star, associated with an ex-
tremely fine red one. For when the spectroscope is
appealed to, it tells us that there is a direct reason
obviously due to absorption in its atmosphere for the
one star's appearing red ; but that there is absolutely
no reason, except the physiological reason just alluded
to, for the principal star's appearing green, for we see the
spectrum it gives is almost devoid of absorption bands.
SPECTRUM ANALYSIS.
255
A few additional remarks remain to be made, chiefly
with reference to comets. Unfortunately, the last very
fine comet that was observed came before any one was
prepared to apply the spectroscope to it ; and, since
spectroscopes have been in every observatory, no comets
have appeared, except small and usually mere tele-
scopic ones. There is no doubt, however, that the next
fine comet 1 that appears will, especially by the help of
spectroscopes, give us an amount of information as to
the nature of comets immensely exceeding all that we
have already gathered during thousands of years.
But such small comets as have been observed have
given spectra which are extremely well worth noticing.
Observations of these seem to show, first of all, that the
tail of a comet gives a spectrum like that of the moon
or other body illuminated by sunlight ; in other words,
that the tail of the comet is not self-luminous, that it
shines by scattered sunlight. But the head of the comet
shows in general a spectrum which indicates the presence
of glowing gas ; that is to say, its spectrum is not con-
tinuous, nor is it visibly intersected by dark lines : it
consists in general of a small number of bright lines
1 These lectures were given in the spring of 1874, before the appearance
of Coggia's comet. This was a magnificent object, but unfortunately ill
situated for spectroscopic observation, having to be examined either very
low in the horizon or in very strong twilight.
SPECTRUM ANALYSIS.
standing markedly out in relief from a feeble continuous
spectrum. There (in the lower figure) is one of these
the spectrum of what is called Winnecke's comet, from
the discoverer. It consists of three bright bands of
light, each sharply terminated towards the red end of
the spectrum, and shading away upwards to the violet
end. Now Mr. Huggins, who first observed this, was
struck by the resemblance of this spectrum (as he saw
it in the telescope) to a terrestrial spectrum which he
had noted before ; and going over his note-book, he
found it closely resembled the delineation of the spec-
trum of a hydro-carbon such as olefiant gas, rendered
incandescent by passing an electric discharge through it.
He then adopted the method to which I have already
several times referred, of sending light from the two
sources simultaneously through the upper and lower
parts of the same slit, so that the spectra of light from
the two sources should be placed side by side, and sub-
jected to precisely the same series of refractions. When
that was done the result was as shown in the diagram.
The upper figure is the spectrum of some hydro-carbon,
as given by an electric spark through the olefiant gas ;
the lower is the spectrum of the comet. Now, just as
we had concluded that there is hydrogen in the sun's
spectrum from the coincidence of the bright lines of
terrestrial hydrogen with dark lines in the solar spec-
trum, here is a similar telling coincidence. Here is the
coincidence of the three bands : a coincidence perfectly
exact so far as the enlargement by the spectroscope
enabled Huggins to measure it, not only of the bright
terminations of these bands, but also in the gradual
shading-ofif of each of them.
Now, this is a most remarkable phenomenon. It at
SPECTRUM ANAL YSIS. 257
once suggests the question How does the hydro-carbon
get into this incandescent state in the head of a comet ?
A word or two on that subject may be of considerable
interest, but we must lead up to it gradually. A great
astronomical discovery of modern times is, that meteor-
ites, the so-called falling stars, especially those of
August and November, as they are called, follow a
perfectly definite track in space, and that this track is
in each case the path of a known comet ; so that :
whether, as Schiaparelli and others imagine, the meteor-
ites are only a sort of attendants on the comet ; or
whether, as there is, I think, more reason to believe, the
mass of meteorites forms the comet itself : there is no
doubt whatever that there is at least an intimate con-
nection between the two. The path of the meteorites is
the path of the comet. Well, let us consider a swarm of
such meteorites (regarded each as a fragment of stone),
like a shower, in fact, of Macadamised stones, or
bricks, or even boulders : what would be the appear-
ances presented by such a cloud ? It must in all cases
be of enormous dimensions, because the earth takes
two or three days and nights to pass through even the
breadth of the stratum of the November meteors.
Consider the rate at which the earth moves in its orbit,
and you can see through what an enormous extent of
space these masses are scattered. Now, if you think
for a moment what would be the aspect of such a
shower of stones when illuminated by sunlight, you
will see at once that, seen from a distance, it would be
like a cloud of ordinary dust : and an easy mathematical
investigation shows that it should give when sufficiently
thick, except in extreme cases, a brightness equal to
about half that of a solid slab of the same material
R
258 SPECTRUM ANAL YSIS.
similarly illuminated. The spectrum of its reflected or
scattered light should be the spectrum of sunlight, only
a great deal weaker. It is easy without calculation, but
by simply looking at a cloud of dust on a chalky road
in sunshine, to assure one's-self of the property just
mentioned of such a cloud of dust or small particles.
Remember that in cosmical questions we can speak
of masses like bricks, or even paving-stones, as being
mere dust of the solar system, and we may suppose
them as far separated from one another, in propor-
tion to their size, as the particles of ordinary dust are.
Whether, then, it be common terrestrial dust, or
cosmical dust, with particles of the size of brickbats
or boulders, does not matter to the result of this
calculation. Spread them about in a swarm or cloud,
as sparsely as you please : only make that cloud deep
enough, and illuminate it by the sun, then it can send
back one-half as much light as if it had been one con-
tinuous slab of the material. Now, look at the moon.
You see there a continuous slab of material, and you
know what a great amount of brightness that gives. And
a shower of stones in space at the same distance from the
sun as the moon, and of the same material as the moon,
could, if it were only deep enough, however scattered
its materials, shine with half the moon's brightness.
Now, no comet's tail has ever been seen with brightness
at all comparable to that of the moon ; and therefore it
is perfectly possible, and, so far as our present means
enable us to judge, it is extremely probable, that the
tail of the comet is merely a shower of such stones, large
or small.
But now we come to the question How does the light
from the head of the comet happen to contain portions
SPECTR UM ANAL YSIS. 259
obviously due to glowing gas, in addition to other por-
tions giving apparently a faint continuous spectrum of
sunlight, and perhaps also light from an incandescent
solid ? The answer is to be found at least so it
appears to me in the impacts of those various masses
upon one another. Consider what would be the effect
if a couple of masses of stone, or of lumps of native
iron such as occasionally fall on the earth's surface
from cosmical space, impinged upon each other even
with ordinary terrestrial, not with planetary, velocities.
In comparison with these latter, of course, the velocity
of the shot of any of the big guns at Shoeburyness
would be a mere trifle ; yet we know that when a
shot from one of them impinges upon an iron plate
there is an enormous flash of light and heat, and
splinters fly off in all directions. Now, mere dif-
ferences among the cosmical velocities of the particles
of a comet, due to different paths round the sun, or to
mutual gravitation among the constituents of a cloud,
may easily amount to 1400 feet per second, which is
about the rate of a cannon-ball. Masses so impinging
upon one another will produce several effects, incan-
descence, melting, the development of glowing gas,
the crushing of both bodies, and smashing them up into
fragments or dust with a great variety of velocities of the
several parts. Some parts of them may be set on mov-
ing very much faster than before ; others may be thrown
Out of the race altogether by having their motions sud-
denly checked, or may even be driven backwards ; so
that this mode of looking at the subject will enable us
to account for the jets of light which suddenly rush out
from the head of a comet (on the whole, forwards), and
appear gradually to be blown backwards, whereas in
2<5o SPECTRUM ANAL YSIS.
fact they are checked partly by impacts upon other
particles, partly by the comet's attraction. Other very
singular phenomena often presented by comets have
recently been explained by a general rotation of the
whole. And it is, of course, excessively improbable
that a cosmical cluster of stones should not, whatever its
origin, have a certain amount of moment of momentum
in itself. Therefore, so far as can be said until we get
a good comet to which to apply the spectroscope, this
excessively simple hypothesis appears easily able to
account for many even of the most perplexing of the ob-
served phenomena. I must warn you, however, that this
is not the hypothesis generally received by astronomers. 1
There are various other phenomena in the solar
system to which I might call your attention as capable of
similar simple explanation, but I shall mention only two
of them. The first is the wonderful appendage of Saturn,
what is known as Saturn's rings. There can be no
doubt now that these rings are clouds of separate
masses. This follows first from telescopic observation,
which has shown us stars through one of the rings of
Saturn, proving that there are numberless gaps in it, just
as there are such gaps not only in the tail but in the head
of a comet, through which we can see a star, even a small
star, with almost absolutely undiminished brightness, and
without refraction-change of apparent position. Again,
1 [See Proc. R.S.E. 1868-9, and Cosmical Astronomy, V., Good Words,
1875. Recent researches, mainly due to Bredichin, have thrown very
great additional light on this subject : but have not added any new argu-
ments in favour of the intrinsically improbable electrical hypothesis alluded
to in the text. They have, however, made it possible that an action, some-
what akin to that which is shown by the Radiometer, may play a consider-
able part in causing the outrushes of tail-dust from the comet. Added to
Third Edition^
SPECTRUM ANAL YSIS. 261
mathematical calculation, founded on the laws of mo-
tion, has proved that rings like those of Saturn, if solid
or liquid, would be broken up in a very short time by the
enormous forces which are exerted upon them. The
solid would either be broken up into pieces, or else it
would as a whole go against Saturn on one side or
another. The liquid would be broken up by enormous
forced waves travelling round it, like the waves pro-
duced by a canal boat, which would go on increasing
and increasing until they ruptured it. Clerk-Maxwell
has shown, in his Adams' Prize Essay, that no hypo-
thesis whatever will account for the form and perma-
nence of these rings, except the supposition that they
consist of clouds of stones, or fragments of matter
of some kind or another, flying round, each almost
like an independent member of a family of satel-
lites, but still, of course, acting upon one another by
their mutual gravitation. That mutual gravitation is,
no doubt, sufficient to produce among them impacts
with considerable relative velocity ; so that it is possible
that we may some day find bright lines in the spec-
trum of the light from the rings. Thus these rings of
Saturn, like everything cosmical, must be gradually
decaying, because in the course of their motion round
the planet there must be continual impacts amongst
the separate portions of the mass ; and of two which
impinge, one may be accelerated, butjit will be acceler-
ated at the expense of the other. The other falls
out of the race, as it were, and is gradually drawn in
towards the planet. The consequence is that, possibly
not so much on account of the improvement of tele-
scopes of late years, but perhaps simply in consequence
of this gradual closing in of the whole system, a new
262 SPECTRUM ANAL YSIS.
ring of Saturn has been observed inside the two old
ones, what is called from its appearance the crape
ring, which was narrow when first observed, but is
gradually becoming broader. That is formed of the
laggards, as it were, which have been thrown out of the
race, and which are gradually falling in towards the
planet's surface.
The second instance I refer to is the zodiacal light,
which obviously cannot possibly be part of the gaseous
atmosphere of the sun, nor can it be any solid or liquid
body. It must be of the nature of detached portions of
solid or liquid, floating as separate satellites, revolving
about the sun, though by no means necessarily in orbits
nearly circular. The spectrum of the zodiacal light has
been examined. It is an extremely difficult thing to
examine it ; however, the task has been at least partially
accomplished. The light is far too faint to enable even
the most skilled observer, with the most perfect of our
present instruments, to say whether there are dark lines
across its spectrum or not The spectrum has been
found to be at least practically continuous ; that is to
say, it has been found to be probably that of reflected
sunlight simply. Thus the zodiacal light reveals to us
the existence of enormous amounts of small cosmical
masses which have been somehow or other detached
from comets or swarms of meteorites, and forced,
whether by planetary attraction or by resistance, to
revolve in orbits of moderate size about the sun. As
they have been seized at different times and from
different sources of supply, they probably move in all
sorts of orbits with all sorts of eccentricities and in-
clinations somewhere about half of them probably
going round in the opposite direction to that in which
SPECTRUM ANALYSIS. 263
the planets move. Meteorites or aerolites, which every
now and then reach the earth, may often be portions
of this source of the zodiacal light. These scattered
fragments, gradually resisted, or impinging upon one
another, fall in age after age towards the sun's surface.
They must thus form a supply, although an extremely
small and inadequate supply, of potential energy, which
has the effect of, to a certain extent, maintaining the
sun's heat
I must now take leave of this part of the subject, and
I do so by recurring to what I said at the commence-
ment of it. I began by saying that, after studying the
laws of heat and thermo-dynamics, we should consider
some very important cases of the transference of heat
or energy from one body to another. We have already
treated of the radiation of heat and the absorption of
heat. Now we come to another case of the transference
of energy: the case in which energy is transferred
continuously from one part of a body to another part of
the same body ; and here we must deal, first of all, with
what is called conduction of heat. This subject was
very fully worked out as a mathematical problem long
before the period to which these lectures are professedly
confined, but great additional information has been
obtained about it within that period, and therefore I
propose in my next lecture to give a brief sketch of
the early development of it ; and then to go more fully
into the recent extensions and additions which it has
obtained. Along with the conduction of heat I shall,
virtually at least, treat of other things which, although
having apparently no connection whatever with conduc-
tion of heat, really have precisely the same laws. These
are the conduction of electricity, as, for instance, in a
264 SPECTR UM ANAL YSIS.
submarine cable, and the diffusion of a salt or an acid
in a solution in water. Perfectly different as these
phenomena appear to be, they are all, when treated
mathematically, dependent upon the same differential
equation (merely, of course, because their elementary
laws, which are summed up with all their possible con-
sequences in that equation, are of precisely similar
form) ; and therefore by the change of a word or two,
any statement made with regard to the one can be
transformed into an equally true statement with regard
to either of the others.
LECTURE XL
CONDUCTION OF HEAT.
Fourier's Mathematical Theory. His Definition of Conducting Power. Ana-
logy between Thermal and Electric Conductivities. Forbes's method and
results. Angstrom's method. Penetration of Surface temperature into
the earth's crust. Analogy between conduction of heat and conduction
of electricity. Diffusion also analogous to these. Diffusion of matter, of
kinetic energy, and of momentum.
As I promised in my last lecture, I now proceed to a
consideration of the subject of the conduction of heat.
A great deal was known about the conduction of heat
before the period to which my lectures specially refer,
but during that period a very great deal of quite un-
expected information has been obtained on the subject.
Perhaps it will conduce to the intelligibility of what I
have to say about the new matter, if I briefly run over
what was known about the time when Principal Forbes
commenced his experimental inquiries into the question
before us.
It was Fourier who first put the laws of conduction of
heat into a perfectly definite mathematical form, and
who invented, for the purpose of investigating detailed
problems on the subject, a mathematical method of ex-
quisite power. Fourier defined conductivity the con-
ducting power of a substance in a manner which has
not been improved since. He defines it, in fact, in this
266 CONDUCTION OF HE A T.
-way. Suppose that you have a slab of unit thickness,
but in surface practically infinite, composed of some
material whose conductivity you wish to measure. Sup-
pose one of its sides to be kept permanently at a tem-
perature one degree hotter than the other side. Then,
as we know that there is a constant flow of heat from a
hot body to a colder one, there will be in this case (after
things have settled down to a permanent condition) a
definite rate of flow of heat through every unit of sur-
face of the slab in a direction perpendicular to the slab.
In fact, because we have supposed that the slab is of
practically infinite extent, and that its surfaces are kept
each throughout at a perfectly definite temperature,
the flow of heat will necessarily be in the common perpen-
dicular to the surfaces of the slab ; and the measure of
conductivity then, according to Fourier, is the number of
units of heat which pass per square unit of surface of the
slab from one side to the other in unit of time. You see,
then, how all the different units come in. You have
unit of length for the thickness of the slab: you consider
the square of this unit that is, unit of surface as the
portion of the slab through which the heat is passing.
You have the unit of heat defined as the quantity of heat
which can raise the temperature of a pound of water one
degree. You have unit, that is one degree, difference of
temperatures on the two sides of the slab, and you have
unit of time during which the process of conduction is
supposed to go on. Now, in an arrangement of the kind
described, after a time, practically very short though
theoretically infinite, the temperature will distribute itself
permanently in this way : The temperature will fall off
steadily by a uniform gradient from the value on the one
side to that on the other of the slab. It follows from this
COND UCTION OF HE A T. 267
that the rate at which heat passes through the slab
depends only upon two things, the gradient or rate at
which the temperature falls off per unit of length in the
direction of its thickness, and the specific conductivity
or conducting power of the material. Now, taking this
datum, Fourier gave completely the mathematical
formulae which are necessary for applying it to any
case however complex of the conduction of heat, in
a solid of which the conductivity is not altered by
temperature.
But this question very naturally arose Is the con-
ducting power of a substance the same at all tempera-
tures ? It had been assumed in Fourier's calculations
that it was so ; but Forbes seriously shook this assump-
tion by pointing out a curiously complete analogy
between the conducting powers of metals for electricity
and their conducting powers for heat. It was found by
experiment that those metals which conduct electricity
well, also conduct heat well, and not only so : Forbes
pointed out that the order of conducting power for elec-
tricity is also, in the main, the order of conducting power
for heat. [This observation of Forbes, which had been
founded on the published experiments of other physi-
cists, was confirmed by the experiments of Wiedemann
and Franz, which were specially devised for the purpose
of testing it] Now, a point which has become of very
serious importance of late years, especially in conse-
quence of the development of submarine cables, is the
very great change of electric conducting power of sub-
stances by change of temperature. Metals, in general,
conduct electricity very much worse when hot than
when cold ; so that it occurred to Forbes that as there
was an analogy a prima facie analogy, at all events
268 COND UCTION OF HE A T.
between the conducting powers of different metals
for heat and electricity, and as the conducting power
for electricity is rendered very much worse by increase
of temperature, so there might be an effect of this kind
upon the conducting power of metals for heat. He
therefore established a series of experiments, which,
unfortunately, he lived to develop only as regarded the
one metal, iron ; but the results of these experiments
were perfectly decisive in proving that the conducting
power of iron for heat becomes worse and worse as it
is hotter, and almost in the same proportion as it
becomes by heat a worse conductor of electricity. 1
I may say a word or two as to the process by which
we investigate the conducting power, before I describe
Forbes's experimental apparatus. Take an analogy
first : suppose we consider the stock-in-trade of a cer-
tain business. There are two ways of investigating
how that stock-in-trade may alter. One way consists
simply in periodically taking stock, or going through
the whole collection and seeing what it consists of.
But there is another and equally good way, provided
it could be carried out as well, and that is to keep
an account of purchases and sales ; so much has come
in on the whole during the period ; so much has gone
out during the period ; and the difference between the
quantity which has come in and the quantity which
1 [This, however, is true only of what is called the Thermometric Con-
ductivity ; in which the amount of heat conducted is measured in terms of
the rise of temperature which it would produce in unit volume of the
conducting substance at the temperature of conduction. But the specific
heat in all substances alters with temperature. Thus Forbes's results are
subject to serious modification when they are reduced to the usual thermal
unit implied in Fourier's definition of conductivity. Note to Third
Edition.']
COND UCTION OF HEA T. 269
has gone out is the quantity by which the whole stock
has changed during the period ; so that there are these
two ways of getting at it. Now, precisely the same
idea is applied in ascertaining the conditions of the
conduction of heat in a solid. We picture to our-
selves a small portion in the interior of the solid,
and for reasons of simplicity in calculation, we con-
sider that small portion brick-shaped. We consider
how much heat comes in through any one side,
then how much during the same period of time goes
out by the opposite side; and extend the process to
the other two pairs of parallel sides. A mathemati-
cal expression can easily be formed for these various
quantities, as I have already explained. They will be
expressed in terms of the gradients of temperature,
and the conducting powers (which may not be the
same in all directions), parallel to the three sets of
edges of the brick. But then there is the other way
of looking at it. Instead of thinking what comes in
and what goes out, think of how the temperature of
the whole is altered during the period. You will see
that in terms of the rise of temperature, the specific
heat of the body, and the mass of the brick-shaped
portion, we can make an independent calculation of
how much heat has come in (of course on the assump-
tion that no heat has been generated or destroyed
within the brick). The latter of these expressions de-
pends upon the rate of rise of temperature with time
at any one point ; the former depends upon the rates
of increase of temperature per unit of length (or what
may be called thermometric gradients) in three selected
directions at right angles to one another. The gradients
and the conductivity tell us how much comes in : the
270
CONDUCTION OF HE A T.
rate of change of gradient, per unit of length, and the
conductivity, therefore, tell us how much more comes
in than goes out ; while the rate of rise of temperature,
per unit of time, gives us another expression for the same
quantity. It is the determination of relations between
these two which is the object of every experimental
inquiry on the subject.
Forbes's apparatus may be briefly described as
follows : These bars (showing), which were made for
my own experiments, are made exactly of the dimen-
sions of Forbes's original bar. You will notice they
are bars of ij inch square section, and somewhere
about 8 feet long, but that is not usually a matter of
any great consequence. Along the length of each bar
there are at intervals, first of three inches, and then of
six inches, and finally of a foot, little holes cut verti-
cally into the bar. In Forbes's iron bar these holes
were simply filled with mercury, and the bulbs of
thermometers were placed in them. In copper bars,
and in German silver bars, si^ch as those before you, it
>i^n
COND UCTION OF HE A T. 27 1
was necessary that these little holes should be lined
with iron cups like arrow-heads, in order to prevent the
mercury from attacking the substance of the bar. Now,
matters being arranged in this way, a crucible was slid
on, as you see, upon one end of the bar, and filled with
melted metal, and a powerful lamp being applied to it,
the temperature of the molten metal was kept as nearly
as possible uniform for eight, or nine, or sometimes even
ten hours. There was, therefore, a constant source of
heat applied at one end of the bar, and all the rest of
the bar was exposed simply to the air of the room. In
the case of iron bars, Forbes found that even with the
highest temperature to which he raised the crucible of
molten metal, there was scarcely any perceptible rise
of temperature in eight hours at the far end of the
bar ; but in my own experiments, I have found that
because copper is so very .much better a conductor
than iron, it is absolutely necessary, if we keep the
pot of metal at any moderately high temperature, to
have a constant stream of cold water flowing over
the farther end of the bar, in order to keep it from
gradually increasing in temperature, even after eight
hours' experimenting. However, the action of the
cold water at the farther end introduces only a slight
and simple modification of the formula, and in the mode
of deducing the final results from it, but does not inter-
fere with the mode of reasoning from the experiment.
The first effect of applying heat is to produce a
gradual rise of temperature, which is of course observed
first in the holes nearest the crucible. The thermo-
meters farthest off are the last to give any indication
of increase of temperature, and (after a steady state
has been arrived at) are found to have risen the least,
it
272 CONDUCTION OF HE A T.
What we wish to study now is the rate at which
heat is being conveyed along ; what our thermometers
tell us is the temperature at different points of the
bar. We must take care in making the deductions to
remember that while our information is about tempera-
tures, our conclusions require to be about heat.
Heat, then, gradually flows from the hot end of the
bar to the cold one ; and as the bar rises in tempera-
ture above the surrounding air, there is a loss of heat
by radiation from its surface, and also by convection,
by currents of heated air rising from the bar. This
state of matters, strictly speaking, would go on inde-
finitely, approximating to a steady state. The steady
state of temperature should (theoretically) never be
actually arrived at ; but practically in all our experi-
mental work, a sufficient approximation to the steady
state is arrived at in bars like these in at most eight
or nine hours. After that time, provided we keep
the temperature of the molten metal as nearly as
possible steady, and provided the temperature of the
air in the room remain unchanged, it is found that
the thermometers have assumed definite readings
from which they do not practically alter more than
by very small fractions of a degree. There is then
a steady state of temperature at every point of the
bar, and that is the essence of the method. In such a
steady state of temperature, of course, there is a steady
thermometric gradient maintained at each point along
the length of the bar ; and it is found that practically we
may assume, without risk of sensible error, the tempera-
ture to have the same value at all points of the same
transverse section. The process I have just described
to you may be applied to any thin transverse slice of the
COND UCT1ON OF HEA T. 273
bar, so far as its supply, etc., of heat is concerned. First,
in consequence of the greater steepness of the gradient
of temperature at the warmer side of it, there is a greater
quantity of heat passing into the slice by conduction
than passes out of it by the same process. But be-
cause the temperature remains unchanged, that excess
of heat must be lost by radiation and convection into
the air. If, then, we could only measure how much
heat is given off by radiation and convection from any
given part of the bar, we should be able to measure
how much more heat comes in than goes out in conse-
quence of the difference of gradient at its ends. The
temperatures are observed ; from these the gradients and
the difference of gradients can be calculated; multiply
the difference of gradients by the conducting power, and
by the area of the cross section, and you get the excess
of the quantity of heat which goes in over the quantity
which goes out per unit of time. Now that excess is pre-
cisely the loss from the external surface, also during unit
of time. Forbes therefore made an addition to the usual
experiment. He took a separate bar of the same
material, of the same section, and in every respect similar
to the first, only much shorter : and having heated this
up, to a high uniform temperature, he allowed it to cool,
simply noting its temperature after the lapse of successive
equal intervals of time. Thence he calculated the rate
at which it lost heat per unit of surface by radiation
and convection together at each temperature. We have
now by these two experiments an equation between two
expressions, one involving, besides known quantities,
the conductivity which is unknown, the other consisting
entirely of known quantities and from this equation
the conductivity is found. By that very ingenious
S
274 COND UCTION OF HE A T.
method, then, carried out by extremely careful experi-
ments, the difficulty of which you may very well judge
when I tell you that this pot of metal was usually
heated to a temperature of somewhere about 300 or
350 C, and had to be kept sometimes for more than
eight hours together without varying more than a single
degree from that temperature, Forbes arrived at the
conclusion which I have already stated, that the [ther-
mometric] conducting power of iron falls off very
rapidly with increase of temperature. He found that
the conducting power at various temperatures is ex-
pressed by the following numbers, the units being the
foot, minute, and degree Centigrade :
o C, 0-0133
100 C M . ... 0-0107
200 C, . . . . . 0-0082
showing a remarkably steady diminution with increase
of temperature. On looking at these numbers, we find
that they almost exactly agree with the empirical law
that the conducting power of iron for heat is inversely
as the absolute temperature ; that is to say, if you add
274 to each of these temperatures, you will find that the
product of temperature so altered into the correspond-
ing conductivity of iron is very nearly the same for each.
Thus the conducting power is, as far as this determina-
tion allows us to judge, nearly inversely as the absolute
temperature. This, if a general law, would appear to
show that could we get an iron bar cooled down to a
temperature of 274 under zero, its conducting power
would become practically infinite ; at least that, when
the bar is almost deprived of heat, it has the power of
conducting heat at an enormously great rate. That, of
course, is arguing from results at a certain limited range
CONDUCTION OF HEA T. 275
of easily obtained temperatures to a range of tempera-
tures on which we have not the least prospect of ever
being able to make experiments at all.
I may mention, in passing, a curious form in which
this semi-empirical statement as to thermal conductivity
may be put. If we assume the principle of dissipation
of energy to hold not merely for cases in which heat is
altogether left to itself in a conducting body, but also
in cases of artificially-sustained distribution of tempera-
ture, such as in this long bar of Forbes's, we have no
difficulty in accounting for the fact that the conductivity
may be inversely as the absolute temperature.
For (to take our earliest illustration of conduction) we
conclude that any three consecutive slices of the infinite
slab, of equal thickness, will have the least available
energy when the absolute temperature of the middle
one is the geometric mean of the temperatures of the
others. Then the gradient will be as the absolute
temperature, and (to make the flow of heat uniform)
the conductivity must be inversely as the absolute tem-
perature. This is on the assumption that the specific
heat is unaltered by change of temperature, and must
be modified accordingly.
I shall now say a word or two about a repetition of
Forbes's experiments, and an extension of them to other
bodies than iron, which has been carried on for some
time in my own laboratory. You see there two copper
bars, between which it would be exceedingly difficult for
any of you, even with the aid of careful chemical ana-
lysis, to find much difference. The two bars are as alike
as possible in their ordinary properties in colour,
specific gravity, elasticity, hardness, etc., and yet this
mysterious energy, which we call heat, has far greater
276 COND UCTION OF HE A T.
facility in passing along one of these bars than the
other. , One of them has somewhere about 40 per cent,
greater conductivity than the other. Now, the only
difference which we can detect between them is this,
that in the manufacture of one there seems to have
been a, very small quantity of oxide of copper mixed
up with the molten mass, and this small trace (which it
is difficult to measure by chemical processes) makes
the metal a very much worse conductor of heat. These
bars were obtained for the purpose of trying whether
Forbes's analogy between different metals in their con-
ducting powers for heat and electricity would extend
to different specimens of the same metal. The bars
were procured for me by Mr. Willoughby Smith, one
being made of copper of very high, the other of copper
of very low, electric conductivity. In fact that which
conducts heat 40 per cent, better than the other con-
ducts electricity about 73 per cent better. 1
But then there comes in another and a very curious
thing. You have seen that in all pure metals, as iron,
copper, and so on, the electric conductivity falls off as
the temperature rises. This is not the case with such
an alloy as German silver. It is, in fact, used for electric
resistance-coils because of the slight change produced
in its electric conductivity even by serious changes of
temperature. Here is a German silver bar of the same
dimensions as the iron and copper bars. We find, on
making the same experiments with it, that its conduc-
1 [The experiments on the bars of copper and German silver, here de-
scribed, had been made before these Lectures were delivered, but the
extremely laborious process of deducing the conductivity from them had
not been fully carried out. A full account of the results was given in
Trans. R.S.E., ifyZ.Note to Third Edition.'}
COND UCTION OF HE A T. 277
tivity for heat is much less affected by temperature
than that of iron.
I have described one modern method by which con-
ducting powers have been found. I have discoursed
upon it so long that I must dismiss more briefly the
other also modern method which has been applied to
the purpose of experiment by Angstrom, but which had
been virtually employed in observations on a gigantic
scale long previously to his time.
He, like Forbes, employs a bar, only instead of heating
it steadily at one end, and waiting till a steady state of
temperature has been set up in it, he produces a peri-
odical change of temperature at one end. He heats it
for a certain time, then cools it for an equal period, and
repeats this operation until a steady state of oscillation of
temperature has been practically attained at all points
of the bar where observations are to be made. He
observes at selected stations the range and the epoch
of each wave of heat which thus travels along the bar,
becoming less and less marked as it proceeds. This is
in fact quite analogous to the process of telegraphing
through a submarine cable. You apply one pole of a
battery to the end of the submarine cable for a certain
time : then remove it and so on : and certain waves
of electric potential run along the wire, by which intelli-
gible signals are transmitted to the other end. Pre-
cisely the same thing, then, has Angstrom done with
reference to the conduction of heat by bars ; and his
method has given nearly the same conductivity as
Forbes's for iron, which was the only metal experi-
mented on by both. You will get some idea of Ang-
strom's method and of the results deduced from it, if,
instead of speaking of the more complex circumstances
278 COND UCTION OF HE A T.
of the wave running along a bar, I speak of the simpler
case in which we have a large slab of metal, heated
periodically at one side, and kept cold at the other.
Further, instead of metal, let us take the crust of the
earth. Here is a diagram 1 prepared by Principal Forbes
from continued observations of thermometers, whose
bulbs were sunk, some in the porphyritic rock of the
Calton Hill, within the Observatory grounds, some in
the sandstone of Craigleith quarry, and some in the
sandy soil of the Experimental Gardens. The curves
on the diagram show the temperatures as indicated by
these thermometers throughout the course of a whole
year. The first thermometer at each locality has its
bulb three feet below the surface of the ground ; the
second six feet below, the third twelve, and the fourth
twenty-four feet under the surface. The observations
are here figured in four groups, each containing three
curves corresponding to the simultaneous indications at
the different localities given by thermometers buried
to equal depths under the surface. These thermometers
(with the exception of one which was broken by the
intense cold of the winter 1860-1) have been regularly
read since they were buried. [This very valuable series
of observations was interrupted by the wilful destruction
of the instruments (September, 1876); but new ones
have since been sunk, and the observations resumed.]
You will notice here that for the upper thermometer
in the trap rock of the Calton Hill, you have the periodic
wave of temperature lowest, not about the middle of
winter, but about the middle of February. That is at
1 It has not been judged necessary to reproduce this very elaborate
diagram from Trans. R.S.E. t 1846, to which the reader is referred for
fuller information on the question of terrestrial surface-temperature.
COND UCTION OF HE A T. 279
a depth of about three feet below the surface. We
get the highest temperature at that depth about the
middle of August ; and so on down again to the lowest
temperature in the middle of February next year.
Now, another great point to be observed is that there
is a considerable range of temperature at this depth ;
for the lowest is somewhere about 39 R, and the
highest somewhere about 54 F. ; so that there you
have a range of somewhere about 15 F. And remem-
bering that the three lines which you see running along-
side one another are for three such excessively different
materials as porphyry, sandstone, and common light
sandy soil, you see their general coincidence is very
marked. They of course agree with one another in
showing slight irregularities of temperature, due to
periods of what we call ' change of weather ' at the sur-
face ; but the ranges and epochs are not very widely
different in spite of the variety of materials.
But see what a different state of things has been arrived
at when you go only three feet farther down under the
surface. There you find a far less range of temperature,
though the mean temperature is nearly the same ; the
lowest temperature is now somewhere about 41, and
the highest somewhere about 51, so that you have a
range of only 10 altogether. When you go still farther
down, to a depth of twelve feet, you will find a similar
modification. [The,irregularities here and there in some
one of the three curves of each group, but not in the
others, are evidently due to the percolation of water
from the upper surface, or to some other purely local
disturbance.] On the average, the twelve-foot observa-
tions show a range of from 44 to 49, being a range of
only 5. And when you come down to the 24 feet
280 CONDUCTION OF HE A T.
thermometers you find barely a range of i'5 through-
out the whole year.
Then remark, besides, that the minimum temperature
arrives at the 6 feet thermometer somewhere about
the beginning of March instead of the middle of Feb-
ruary ; it arrives at the 12 feet about the 2Oth of April ;
and at the lowest or 24 feet thermometer just about
the middle of July, that is to say, the winter's cold
takes somewhere about half a year to penetrate twenty-
four feet downwards into this kind of surface material.
Now this is almost precisely the same thing as only
on a much larger scale than Angstrom's experiment.
The only difference is that Angstrom had to allow
for the loss of heat by radiation from the surface of his
bar, while in the case I have been speaking of, there
is no conduction except in a vertically downward or
upward direction. Still you notice that the character-
istics of the results are, on the whole, the same as
those for the earth temperatures, that the ranges of
the various thermometers diminish with great rapidity
as you go farther and farther from the source of heat,
and the periods at which the maximum and minimum
arrive at any point are later and later as it is farther
from the source.
Supposing the earth's crust to be of uniform material,
and to have conducting power the same at all tempera-
tures, the law made out by Fourier long ago was that
as you go down successive depths in arithmetical pro-
gression, the range of the thermometers for a simple
harmonic wave of any period, such as for instance the
annual one should fall off in geometrical progression.
If, for instance, at three feet down you had a range of
20, and if at six feet down you had a range of only 10,
COND UCTION OF HE A T. 28 1
then on going down three feet farther, you should have
a range of only 5, and so on. Also the time at which
you have what is called a particular phase of the wave
of temperature (say its maximum or its minimum) should
be later and later in proportion simply as you go farther
down, so that if it be a month later at three feet, it
should be two months later at six feet, four months
later at twelve feet, and so on, a month later for every
three feet you go down. But notice that it would be
so only on the supposition that the conducting power
is the same at all temperatures.
In performing the bar experiment according to
Angstrom's method, the wave of temperature which
passes the thermometers does not in general give, for its
simple harmonic components, ranges diminishing in
geometrical progression as we advance along the bar in
arithmetical progression, nor are the periods of maximum
constantly later and later by equal amounts for equal
successive intervals along the bar ; but it would be so if
the surface-loss were very small, and the conductivity
the same at all temperatures. Any such deviations
then are due to these causes, and by them the amounts
of the causes can be separately calculated.
Precisely the same statements that I made with re-
ference to the distribution of temperature and the con-
sequent flux of heat will apply, if instead of the word
*heat,' we use the word 'electricity,' and if instead of
the word ' temperature,' we use the word ' potential,'
which corresponds, in the theory of electricity, precisely
to temperature in the theory of heat ; so that when we
write a mathematical formula to express the conduction
of electricity in any body whatever, that formula will
apply equally well to a corresponding case of the con-
282 CONDUCTION OF HE A T.
duction of heat. There is no difference whatever be-
tween them till we come to the interpretations. We
interpret a certain symbol in them to mean in the one
case potential, in the other case temperature.
One of the most curious instances of imitation, on an
exceedingly small scale, of what takes place on a very-
large scale, is suggested by this analogy. If I take a
small piece of copper, an inch or so long, and, keeping
one end of it in connection with a thermo-electric junction
and a galvanometer, so as to measure very accurately any
little changes of temperature that may arrive at that end,
apply a lamp to the other end, just as you would apply
to the near end of the Atlantic cable the pole of a gal-
vanic battery ; if I signal with this lamp just as the
telegraph operator does with the galvanic battery
through the Atlantic cable, exactly the same results
may be produced on the galvanometers in the two
cases, the tiny dimensions of the heat-conductor being
necessitated by the time required to sensibly alter the
temperature at the far end of the bar. You require to
take a very short bar, indeed, in order to represent the
phenomena on the same time scale, but you can have
precisely the same effects in the two cases. And it is
not at the ends merely, but at all similarly situated
points in the two conductor 
