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Title: The conservation of energy

Author: Balfour Stewart

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Language: English

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  THE INTERNATIONAL SCIENTIFIC SERIES.

  THE

  CONSERVATION OF ENERGY.

  BY

  BALFOUR STEWART, LL. D., F.R.S.,
  PROFESSOR OF NATURAL PHILOSOPHY AT THE OWENS COLLEGE, MANCHESTER.


  _WITH AN APPENDIX_,

  TREATING OF THE VITAL AND MENTAL APPLICATIONS OF THE
  DOCTRINE


  NEW YORK:
  D. APPLETON AND COMPANY,
  549 & 551 BROADWAY.
  1875.




  ENTERED, according to Act of Congress, in the year 1874, by
  D. APPLETON & COMPANY,
  In the Office of the Librarian of Congress, at Washington.




NOTE TO THE AMERICAN EDITION.


The great prominence which the modern doctrine of the Conservation of
Energy or Correlation of Forces has lately assumed in the world of
thought, has made a simple and popular explanation of the subject very
desirable. The present work of Dr. Balfour Stewart, contributed to the
International Scientific Series, fully meets this requirement, as it
is probably the clearest and most elementary statement of the question
that has yet been attempted. Simple in language, copious and familiar
in illustration, and remarkably lucid in the presentation of facts and
principles, his little treatise forms just the introduction to the
great problem of the interaction of natural forces that is required by
general readers. But Professor Stewart having confined himself mainly
to the physical aspects of the subject, it was desirable that his views
should be supplemented by a statement of the operation of the principle
in the spheres of life and mind. An Appendix has, accordingly, been
added to the American edition of Dr. Stewart’s work, in which these
applications of the law are considered.

Professor Joseph Le Conte published a very able essay fourteen years
ago on the Correlation of the Physical and Vital Forces, which was
extensively reprinted abroad, and placed the name of the author among
the leading interpreters of the subject. His mode of presenting it was
regarded as peculiarly happy, and was widely adopted by other writers.
After further investigations and more mature reflection, he has
recently restated his views, and has kindly furnished the revised essay
for insertion in this volume.

Professor A. Bain, the celebrated Psychologist of Aberdeen, who
has done so much to advance the study of mind in its physiological
relations, prepared an interesting lecture not long ago on the
“Correlation of the Nervous and Mental Forces,” which was read with
much interest at the time of its publication, and is now reprinted as a
suitable exposition of that branch of the subject. These two essays, by
carrying out the principle in the field of vital and mental phenomena,
will serve to give completeness and much greater value to the present
volume.

 NEW YORK, _December, 1873_.




PREFACE.


We may regard the Universe in the light of a vast physical machine, and
our knowledge of it may be conveniently divided into two branches.

The one of these embraces what we know regarding the structure of the
machine itself, and the other what we know regarding its method of
working.

It has appeared to the author that, in a treatise like this, these two
branches of knowledge ought as much as possible to be studied together,
and he has therefore endeavored to adopt this course in the following
pages. He has regarded a universe composed of atoms with some sort of
medium between them as the machine, and the laws of energy as the laws
of working of this machine.

The first chapter embraces what we know regarding atoms, and gives
also a definition of Energy. The various forces and energies of Nature
are thereafter enumerated, and the law of Conservation is stated. Then
follow the various transmutations of Energy, according to a list, for
which the author is indebted to Prof. Tait. The fifth chapter gives
a short historical sketch of the subject, ending with the law of
Dissipation; while the sixth and last chapter gives some account of the
position of living beings in this universe of Energy.

  B. S.

  _The Owens College, Manchester,
  August, 1873._




CONTENTS.


  NOTE TO THE AMERICAN EDITION,                                        v

  PREFACE,                                                           vii


  CHAPTER

  I.--WHAT IS ENERGY?                                                  1

  II.--MECHANICAL ENERGY AND ITS CHANGE INTO HEAT,                    23

  III.--THE FORCES AND ENERGIES OF NATURE: THE LAW OF CONSERVATION,   48

  IV.--TRANSMUTATIONS OF ENERGY,                                      87

  V.--HISTORICAL SKETCH: THE DISSIPATION OF ENERGY,                  131

  VI.--THE POSITION OF LIFE,                                         154


  APPENDIX

  I.--CORRELATION OF VITAL WITH CHEMICAL AND PHYSICAL FORCES.
  By JOSEPH LE CONTE, Professor of Geology and Natural
  History in the University of California,                           171

  II.--CORRELATION OF NERVOUS AND MENTAL FORCES. By ALEXANDER
  BAIN, Professor of Logic and Mental Philosophy in
  the University of Aberdeen,                                        205




THE CONSERVATION OF ENERGY.




CHAPTER I.

_WHAT IS ENERGY?_


_Our Ignorance of Individuals._

1. Very often we know little or nothing of individuals, while we yet
possess a definite knowledge of the laws which regulate communities.

The Registrar-General, for example, will tell us that the death-rate
in London varies with the temperature in such a manner that a very
low temperature is invariably accompanied by a very high death-rate.
But if we ask him to select some one individual, and explain to us in
what manner his death was caused by the low temperature, he will, most
probably, be unable to do so.

Again, we may be quite sure that after a bad harvest there will be a
large importation of wheat into the country, while, at the same time,
we are quite ignorant of the individual journeys of the various
particles of flour that go to make up a loaf of bread.

Or yet again, we know that there is a constant carriage of air from the
poles to the equator, as shown by the trade winds, and yet no man is
able to individualize a particle of this air, and describe its various
motions.

2. Nor is our knowledge of individuals greater in the domains of
physical science. We know nothing, or next to nothing, of the ultimate
structure and properties of matter, whether organic or inorganic.

No doubt there are certain cases where a large number of particles
are linked together, so as to act as one individual, and then we can
predict its action--as, for instance, in the solar system, where the
physical astronomer is able to foretell with great exactness the
positions of the various planets, or of the moon. And so, in human
affairs, we find a large number of individuals acting together as one
nation, and the sagacious statesman taking very much the place of the
sagacious astronomer, with regard to the action and reaction of various
nations upon one another.

But if we ask the astronomer or the statesman to select an individual
particle and an individual human being, and predict the motions of
each, we shall find that both will be completely at fault.

3. Nor have we far to look for the cause of their ignorance. A
continuous and restless, nay, a very complicated, activity is the order
of nature throughout all her individuals, whether these be living
beings or inanimate particles of matter. Existence is, in truth, one
continued fight, and a great battle is always and everywhere raging,
although the field in which it is fought is often completely shrouded
from our view.

4. Nevertheless, although we cannot trace the motions of individuals,
we may sometimes tell the result of the fight, and even predict how the
day will go, as well as specify the causes that contribute to bring
about the issue.

With great freedom of action and much complication of motion in the
individual, there are yet comparatively simple laws regulating the
joint result attainable by the community.

But, before proceeding to these, it may not be out of place to take a
very brief survey of the organic and inorganic worlds, in order that
our readers, as well as ourselves, may realize our common ignorance of
the ultimate structure and properties of matter.

5. Let us begin by referring to the causes which bring about disease.
It is only very recently that we have begun to suspect a large number
of our diseases to be caused by organic germs. Now, assuming that we
are right in this, it must nevertheless be confessed that our ignorance
about these germs is most complete. It is perhaps doubtful whether we
ever saw one of these organisms,[1] while it is certain that we are in
profound ignorance of their properties and habits.

We are told by some writers[2] that the very air we breathe is
absolutely teeming with germs, and that we are surrounded on all sides
by an innumerable array of minute organic beings. It has also been
conjectured that they are at incessant warfare among themselves, and
that we form the spoil of the stronger party. Be this as it may, we
are at any rate intimately bound up with, and, so to speak, at the
mercy of, a world of creatures, of which we know as little as of the
inhabitants of the planet Mars.

6. Yet, even here, with profound ignorance of the individual, we are
not altogether unacquainted with some of the habits of these powerful
predatory communities. Thus we know that cholera is eminently a low
level disease, and that during its ravages we ought to pay particular
attention to the water we drink. This is a general law of cholera,
which is of the more importance to us because we cannot study the
habits of the individual organisms that cause the disease.

Could we but see these, and experiment upon them, we should soon
acquire a much more extensive knowledge of their habits, and perhaps
find out the means of extirpating the disease, and of preventing its
recurrence.

Again, we know (thanks to Jenner) that vaccination will prevent the
ravages of small-pox, but in this instance we are no better off than
a band of captives who have found out in what manner to mutilate
themselves, so as to render them uninteresting to their victorious foe.

7. But if our knowledge of the nature and habits of organized molecules
be so small, our knowledge of the ultimate molecules of inorganic
matter is, if possible, still smaller. It is only very recently that
the leading men of science have come to consider their very existence
as a settled point.

In order to realize what is meant by an inorganic molecule, let us
take some sand and grind it into smaller and smaller particles, and
these again into still smaller. In point of fact we shall never
reach the superlative degree of smallness by this operation--yet in
our imagination we may suppose the sub-division to be carried on
continuously, always making the particles smaller and smaller. In
this case we should, at last, come to an ultimate molecule of sand or
oxide of silicon, or, in other words, we should arrive at the smallest
entity retaining all the properties of sand, so that were it possible
to divide the molecule further the only result would be to separate it
into its chemical constituents, consisting of silicon on the one side
and oxygen on the other.

We have, in truth, much reason to believe that sand, or any other
substance, is incapable of infinite sub-division, and that all we can
do in grinding down a solid lump of anything is to reduce it into lumps
similar to the original, but only less in size, each of these small
lumps containing probably a great number of individual molecules.

8. Now, a drop of water no less than a grain of sand is built up of a
very great number of molecules, attached to one another by the force of
cohesion--a force which is much stronger in the sand than in the water,
but which nevertheless exists in both. And, moreover, Sir William
Thomson, the distinguished physicist, has recently arrived at the
following conclusion with regard to the size of the molecules of water.
He imagines a single drop of water to be magnified until it becomes
as large as the earth, having a diameter of 8000 miles, and all the
molecules to be magnified in the same proportion; and he then concludes
that a single molecule will appear, under these circumstances, as
somewhat larger than a shot, and somewhat smaller than a cricket ball.

9. Whatever be the value of this conclusion, it enables us to realize
the exceedingly small size of the individual molecules of matter,
and renders it quite certain that we shall never, by means of the
most powerful microscope, succeed in making visible these ultimate
molecules. For our knowledge of the sizes, shapes, and properties
of such bodies, we must always, therefore, be indebted to indirect
evidence of a very complicated nature.

It thus appears that we know little or nothing about the shape or size
of molecules, or about the forces which actuate them; and, moreover,
the very largest masses of the universe share with the very smallest
this property of being beyond the direct scrutiny of the human
senses--the one set because they are so far away, and the other because
they are so small.

10. Again, these molecules are not at rest, but, on the contrary, they
display an intense and ceaseless energy in their motions. There is,
indeed, an uninterrupted warfare going on--a constant clashing together
of these minute bodies, which are continually maimed, and yet always
recover themselves, until, perhaps, some blow is struck sufficiently
powerful to dissever the two or more simple atoms that go to form a
compound molecule. A new state of things thenceforward is the result.

But a simple elementary atom is truly an immortal being, and enjoys the
privilege of remaining unaltered and essentially unaffected amid the
most powerful blows that can be dealt against it--it is probably in a
state of ceaseless activity and change of form, but it is nevertheless
always the same.

11. Now, a little reflection will convince us that we have in this
ceaseless activity another barrier to an intimate acquaintance with
molecules and atoms, for even if we could see them they would not
remain at rest sufficiently long to enable us to scrutinize them.

No doubt there are devices by means of which we can render visible, for
instance, the pattern of a quickly revolving coloured disc, for we may
illuminate it by a flash of electricity, and the disc may be supposed
to be stationary during the extremely short time of the flash. But we
cannot say the same about molecules and atoms, for, could we see an
atom, and could we illuminate it by a flash of electricity, the atom
would most probably have vibrated many times during the exceedingly
small time of the flash. In fine, the limits placed upon our senses,
with respect to space and time, equally preclude the possibility of our
ever becoming directly acquainted with these exceedingly minute bodies,
which are nevertheless the raw materials of which the whole universe is
built.


_Action and Reaction, Equal and Opposite._

12. But while an impenetrable veil is drawn over the individual in this
warfare of clashing atoms, yet we are not left in profound ignorance
of the laws which determine the ultimate result of all these motions,
taken together as a whole.


_In a Vessel of Goldfish._

Let us suppose, for instance, that we have a glass globe containing
numerous goldfish standing on the table, and delicately poised on
wheels, so that the slightest push, the one way or the other, would
make it move. These goldfish are in active and irregular motion, and he
would be a very bold man who should venture to predict the movements of
an individual fish. But of one thing we may be quite certain: we may
rest assured that, notwithstanding all the irregular motions of its
living inhabitants, the globe containing the goldfish will remain at
rest upon its wheels.

Even if the table were a lake of ice, and the wheels were extremely
delicate, we should find that the globe would remain at rest. Indeed,
we should be exceedingly surprised if we found the globe going away of
its own accord from the one side of the table to the other, or from
the one side of a sheet of ice to the other, in consequence of the
internal motions of its inhabitants. Whatever be the motions of these
individual units, yet we feel sure that the globe cannot move itself
_as a whole_. In such a system, therefore, and, indeed, in every system
left to itself, there may be strong internal forces acting between
the various parts, but these _actions and reactions are equal and
opposite_, so that while the small parts, whether visible or invisible,
are in violent commotion among themselves, yet the system as a whole
will remain at rest.


_In a Rifle._

13. Now it is quite a legitimate step to pass from this instance of the
goldfish to that of a rifle that has just been fired. In the former
case, we imagined the globe, together with its fishes, to form one
system; and in the latter, we must look upon the rifle, with its powder
and ball, as forming one system also.

Let us suppose that the explosion takes place through the application
of a spark. Although this spark is an external agent, yet if we reflect
a little we shall see that its only office in this case is to summon
up the internal forces already existing in the loaded rifle, and bring
them into vigorous action, and that in virtue of these internal forces
the explosion takes place.

The most prominent result of this explosion is the out-rush of the
rifle ball with a velocity that may, perhaps, carry it for the best
part of a mile before it comes to rest; and here it would seem to us,
at first sight, that the law of equal action and reaction is certainly
broken, for these internal forces present in the rifle have at least
propelled part of the system, namely, the rifle ball, with a most
enormous velocity in one direction.

14. But a little further reflection will bring to light another
phenomenon besides the out-rush of the ball. It is well known to all
sportsmen that when a fowling-piece is discharged, there is a kick or
recoil of the piece itself against the shoulder of the sportsman, which
he would rather get rid of, but which we most gladly welcome as the
solution of our difficulty. In plain terms, while the ball is projected
forwards, the rifle stock (if free to move) is at the same moment
projected backwards. To fix our ideas, let us suppose that the rifle
stock weighs 100 ounces, and the ball one ounce, and that the ball is
projected forwards with the velocity of 1000 feet per second; then it
is asserted, by the law of action and reaction, that the rifle stock is
at the same time projected backwards with the velocity of 10 feet per
second, so that the mass of the stock, multiplied by its velocity of
recoil, shall precisely equal the mass of the ball, multiplied by its
velocity of projection. The one product forms a measure of the action
in the one direction, and the other of the reaction in the opposite
direction, and thus we see that in the case of a rifle, as well as in
that of the globe of fish, action and reaction are equal and opposite.


_In a Falling Stone._

15. We may even extend the law to cases in which we do not perceive
the recoil or reaction at all. Thus, if I drop a stone from the
top of a precipice to the earth, the motion seems all to be in one
direction, while at the same time it is in truth the result of a mutual
attraction between the earth and the stone. Does not the earth move
also? We cannot see it move, but we are entitled to assert that it
does in reality move upwards to meet the stone, although quite to an
imperceptible extent, and that the law of action and reaction holds
here as truly as in a rifle, the only difference being that in the
one case the two objects are rushing together, while in the other
they are rushing apart. Inasmuch, however, as the mass of the earth
is very great compared with that of the stone, it follows that its
velocity must be extremely small, in order that the mass of the earth,
multiplied into its velocity upwards, shall equal the mass of the
stone, multiplied into its velocity downwards.

16. We have thus, in spite of our ignorance of the ultimate atoms and
molecules of matter, arrived at a general law which regulates the
action of internal forces. We see that these forces are always mutually
exerted, and that if A attracts or repels B, B in its turn attracts or
repels A. We have here, in fact, a very good instance of that kind of
generalization, which we may arrive at, even in spite of our ignorance
of individuals.

But having now arrived at this law of action and reaction, do we know
all that it is desirable to know? have we got a complete understanding
of what takes place in all such cases--for instance, in that of the
rifle which is just discharged? Let us consider this point a little
further.


_The Rifle further considered._

17. We define quantity of motion to mean the product of the mass by
the velocity; and since the velocity of recoil of the rifle stock,
multiplied by the mass of the stock, is equal to the velocity of
projection of the rifle ball, multiplied by the mass of the ball, we
conceive ourselves entitled to say that the quantity of motion, or
momentum, generated is equal in both directions, so that the law of
action and reaction holds here also. Nevertheless, it cannot but occur
to us that, _in some sense_, the motion of the rifle ball is a very
different thing from that of the stock, for it is one thing to allow
the stock to recoil against your shoulder and discharge the ball into
the air, and a very different thing to discharge the ball against your
shoulder and allow the stock to fly into the air. And if any man
should assert the absolute equality between the blow of the rifle stock
and that of the rifle ball, you might request him to put his assertion
to this practical test, with the absolute certainty that he would
decline. Equality between the two!--Impossible! Why, if this were the
case, a company of soldiers engaged in war would suffer much more than
the enemy against whom they fired, for the soldiers would certainly
feel each recoil, while the enemy would suffer from only a small
proportion of the bullets.


_The Rifle Ball possesses Energy._

18. Now, what is the meaning of this great difference between the two?
We have a vivid perception of a mighty difference, and it only remains
for us to clothe our naked impressions in a properly fitting scientific
garb.

_The something which the rifle ball possesses in contradistinction to
the rifle stock is clearly the power of overcoming resistance._ It
can penetrate through oak wood or through water, or (alas! that it
should be so often tried) through the human body, and this power of
penetration is the distinguishing characteristic of a substance moving
with very great velocity.

19. Let us define by the term _energy_ this power which the rifle
ball possesses of overcoming obstacles or of doing work. Of course
we use the word work without reference to the moral character of the
thing done, and conceive ourselves entitled to sum up, with perfect
propriety and innocence, the amount of work done in drilling a hole
through a deal board or through a man.

20. A body such as a rifle ball, moving with very great velocity,
has, therefore, energy, and it requires very little consideration
to perceive that this _energy will be proportional to its weight or
mass_, for a ball of two ounces moving with the velocity of 1000 feet
per second will be the same as two balls of one ounce moving with this
velocity, but the energy of two similarly moving ounce balls will
manifestly be double that of one, so that the energy is proportional
to the weight, if we imagine that, meanwhile, the velocity remains the
same.

21. But, on the other hand, the energy is not simply proportional to
the velocity, for, if it were, the energy of the rifle stock and of the
rifle ball would be the same, inasmuch as the rifle stock would gain as
much by its superior mass as it would lose by its inferior velocity.
Therefore, the energy of a moving body increases with the velocity more
quickly than a simple proportion, so that if the velocity be doubled,
the energy is more than doubled. Now, in what manner does the energy
increase with the velocity? That is the question we have now to answer,
and, in doing so, we must appeal to the familiar facts of everyday
observation and experience.

22. In the first place, it is well known to artillerymen, that if
a ball have a double velocity, its penetrating power or energy is
increased nearly fourfold, so that it will pierce through four, or
nearly four, times as many deal boards as the ball with only a single
velocity--in other words, they will tell us in mathematical language,
that the energy varies as the square of the velocity.


_Definition of Work._

23. And now, before proceeding further, it will be necessary to tell
our readers how to measure work in a strictly scientific manner. We
have defined energy to be the power of doing work, and although every
one has a general notion of what is meant by work, that notion may not
be sufficiently precise for the purpose of this volume. How, then, are
we to measure work? Fortunately, we have not far to go for a practical
means of doing this. Indeed, there is a force at hand which enables us
to accomplish this measurement with the greatest precision, and this
force is gravity. Now, the first operation in any kind of numerical
estimate is to fix upon our unit or standard. Thus we say a rod is
so many inches long, or a road so many miles long. Here an inch and
a mile are chosen as our standards. In like manner, we speak of so
many seconds, or minutes, or hours, or days, or years, choosing that
standard of time or duration which is most convenient for our purpose.
So in like manner we must choose our unit of work, but in order to
do so we must first of all choose our units of weight and of length,
and for these we will take the _kilogramme_ and the _metre_, these
being the units of the metrical system. The kilogramme corresponds
to about 15,432·35 English grains, being rather more than two pounds
avoirdupois, and the metre to about 39·371 English inches.

Now, if we raise a kilogramme weight one metre in vertical height,
we are conscious of putting forth an effort to do so, and of being
resisted in the act by the force of gravity. In other words, we spend
energy and do work in the process of raising this weight.

Let us agree to consider the energy spent, or the work done, in this
operation as one unit of work, and let us call it the _kilogrammetre_.

24. In the next place, it is very obvious that if we raise the
kilogramme two metres in height, we do two units of work--if three
metres, three units, and so on.

And again, it is equally obvious that if we raise a weight of two
kilogrammes one metre high, we likewise do two units of work, while if
we raise it two metres high, we do four units, and so on.

From these examples we are entitled to derive the following
rule:--_Multiply the weight raised (in kilogrammes) by the vertical
height (in metres) through which it is raised, and the result will be
the work done (in kilogrammetres)._


_Relation between Velocity and Energy._

25. Having thus laid a numerical foundation for our superstructure,
let us next proceed to investigate the relation between velocity and
energy. But first let us say a few words about velocity. This is one
of the few cases in which everyday experience will aid, rather than
hinder, us in our scientific conception. Indeed, we have constantly
before us the example of bodies moving with variable velocities.

Thus a railway train is approaching a station and is just beginning to
slacken its pace. When we begin to observe, it is moving at the rate of
forty miles an hour. A minute afterwards it is moving at the rate of
twenty miles only, and a minute after that it is at rest. For no two
consecutive moments has this train continued to move at the same rate,
and yet we may say, with perfect propriety, that at such a moment the
train was moving, say, at the rate of thirty miles an hour. We mean, of
course, that had it continued to move for an hour with the speed which
it had when we made the observation, it would have gone over thirty
miles. We know that, as a matter of fact, it did not move for two
seconds at that rate, but this is of no consequence, and hardly at all
interferes with our mental grasp of the problem, so accustomed are we
all to cases of variable velocity.

26. Let us now imagine a kilogramme weight to be shot vertically
upwards, with a certain initial velocity--let us say, with the velocity
of 9·8 metres in one second. Gravity will, of course, act against the
weight, and continually diminish its upward speed, just as in the
railway train the break was constantly reducing the velocity. But yet
it is very easy to see what is meant by an initial velocity of 9·8
metres per second; it means that if gravity did not interfere, and if
the air did not resist, and, in fine, if no external influence of any
kind were allowed to act upon the ascending mass, it would be found to
move over 9·8 metres in one second.

Now, it is well known to those who have studied the laws of motion,
that a body, shot upwards with the velocity of 9·8 metres in one
second, will be brought to rest when it has risen 4·9 metres in height.
If, therefore, it be a kilogramme, its upward velocity will have
enabled it to raise itself 4·9 metres in height against the force of
gravity, or, in other words, it will have done 4·9 units of work; and
we may imagine it, when at the top of its ascent, and just about to
turn, caught in the hand and lodged on the top of a house, instead of
being allowed to fall again to the ground. We are, therefore, entitled
to say that a kilogramme, shot upwards with the velocity of 9·8 metres
per second, has energy equal to 4·9, inasmuch as it can raise itself
4·9 metres in height.

27. Let us next suppose that the velocity with which the kilogramme
is shot upwards is that of 19·6 metres per second. It is known to all
who have studied dynamics that the kilogramme will now mount not only
twice, but four times as high as it did in the last instance--in other
words, it will now mount 19·6 metres in height.

Evidently, then, in accordance with our principles of measurement,
the kilogramme has now four times as much energy as it had in the
last instance, because it can raise itself four times as high, and
therefore do four times as much work, and thus we see that the energy
is increased four times by doubling the velocity.

Had the initial velocity been three times that of the first instance,
or 29·4 metres per second, it might in like manner be shown that the
height attained would have been 44·1 metres, so that by tripling the
velocity the energy is increased nine times.

28. We thus see that whether we measure the energy of a moving body by
the thickness of the planks through which it can pierce its way, or by
the height to which it can raise itself against gravity, the result
arrived at is the same. _We find the energy to be proportional to the
square of the velocity_, and we may formularize our conclusion as
follows:--

Let _v_ = the initial velocity expressed in metres per second, then
the energy in kilogrammetres = _v_²/19·6. Of course, if the body shot
upwards weighs two kilogrammes, then everything is doubled, if three
kilogrammes, tripled, and so on; so that finally, if we denote by
_m_ the mass of the body in kilogrammes, we shall have the energy in
kilogrammetres = _mv_²/19·6. To test the truth of this formula, we have
only to apply it to the cases described in Arts. 26 and 27.

29. We may further illustrate it by one or two examples. For instance,
let it be required to find the energy contained in a mass of five
kilogrammes, shot upwards with the velocity of 20 metres per second.

Here we have _m_ = 5 and _v_ = 20, hence--

  Energy = 5(20)²/(19·6) = 2000/(19·6) = 102·04 nearly.

Again, let it be required to find the height to which the mass of the
last question will ascend before it stops. We know that its energy is
102·04, and that its mass is 5. Dividing 102·04 by 5, we obtain 20·408
as the height to which this mass of five kilogrammes must ascend in
order to do work equal to 102·04 kilogrammetres.

30. In what we have said we have taken no account either of the
resistance or of the buoyancy of the atmosphere; in fact, we have
supposed the experiments to be made in vacuo, or, if not in vacuo,
made by means of a heavy mass, like lead, which will be very little
influenced either by the resistance or buoyancy of the air.

We must not, however, forget that if a sheet of paper, or a feather,
be shot upwards with the velocities mentioned in our text, they will
certainly not rise in the air to nearly the height recorded, but
will be much sooner brought to a stop by the very great resistance
which they encounter from the air, on account of their great surface,
combined with their small mass.

On the other hand, if the substance we make use of be a large light bag
filled with hydrogen, it will find its way upwards without any effort
on our part, and we shall certainly be doing no work by carrying it
one or more metres in height--it will, in reality, help to pull us up,
instead of requiring help from us to cause it to ascend. In fine, what
we have said is meant to refer to the force of gravity alone, without
taking into account a resisting medium such as the atmosphere, the
existence of which need not be considered in our present calculations.

31. It should likewise be remembered, that while the energy of a moving
body depends upon its velocity, it is independent of the direction in
which the body is moving. We have supposed the body to be shot upwards
with a given velocity, but it might be shot horizontally with the same
velocity, when it would have precisely the same energy as before. A
cannon ball, if fired vertically upwards, may either be made to spend
its energy in raising itself, or in piercing through a series of deal
boards. Now, if the same ball be fired horizontally with the same
velocity it will pierce through the same number of deal boards.

In fine, direction of motion is of no consequence, and the only reason
why we have chosen vertical motion is that, in this case, there is
always the force of gravity steadily and constantly opposing the motion
of the body, and enabling us to obtain an accurate measure of the work
which it does by piercing its way upwards against this force.

32. But gravity is not the only force, and we might measure the energy
of a moving body by the extent to which it would bend a powerful
spring or resist the attraction of a powerful magnet, or, in fine,
we might make use of the force which best suits our purpose. If this
force be a constant one, we must measure the energy of the moving body
by the space which it is able to traverse against the action of the
force--just as, in the case of gravity, we measured the energy of the
body by the space through which it was able to raise itself against its
own weight.

33. We must, of course, bear in mind that if this force be more
powerful than gravity, a body moved a short distance against it will
represent the expenditure of as much energy as if it were moved a
greater distance against gravity. In fine, we must take account both of
the strength of the force and of the distance moved over by the body
against it before we can estimate in an accurate matter the work which
has been done.


FOOTNOTES:

[1] It is said that there are one or two instances where the microscope
has enlarged them into visibility.

[2] _See_ Dr. Angus Smith on Air and Rain.




CHAPTER II.

_MECHANICAL ENERGY AND ITS CHANGE INTO HEAT._


_Energy of Position. A Stone high up._

34. In the last chapter it was shown what is meant by energy, and how
it depends upon the velocity of a moving body; and now let us state
that this same energy or power of doing work may nevertheless be
possessed by a body absolutely at rest. It will be remembered (Art.
26) that in one case where a kilogramme was shot vertically upwards,
we supposed it to be caught at the summit of its flight and lodged on
the top of a house. Here, then, it rests without motion, but yet not
without the power of doing work, and hence not without energy. For we
know very well that if we let it fall it will strike the ground with
as much velocity, and, therefore, with as much energy, as it had when
it was originally projected upwards. Or we may, if we choose, make use
of its energy to assist us in driving in a pile, or utilize it in a
multitude of ways.

In its lofty position it is, therefore, not without energy, but this is
of a quiet nature, and not due in the least to motion. To what, then,
is it due? We reply--to the position which the kilogramme occupies at
the top of the house. For just as a body in motion is a very different
thing (as regards energy) from a body at rest, so is a body at the top
of a house a very different thing from a body at the bottom.

To illustrate this, we may suppose that two men of equal activity and
strength are fighting together, each having his pile of stones with
which he is about to belabour his adversary. One man, however, has
secured for himself and his pile an elevated position on the top of a
house, while his enemy has to remain content with a position at the
bottom. Now, under these circumstances, you can at once tell which of
the two will gain the day--evidently the man on the top of the house,
and yet not on account of his own superior energy, but rather on
account of the energy which he derives from the elevated position of
his pile of stones. We thus see that there is a kind of energy derived
from position, as well as a kind derived from velocity, and we shall,
in future, call the former _energy of position_, and the latter _energy
of motion_.


_A Head of Water._

35. In order to vary our illustration, let us suppose there are two
mills, one with a large pond of water near it and at a high level,
while the other has also a pond, but at a lower level than itself. We
need hardly ask which of the two is likely to work--clearly the one
with the pond at a low level can derive from it no advantage whatever,
while the other may use the high level pond, or head of water, as
this is sometimes called, to drive its wheel, and do its work. There
is, thus, a great deal of work to be got out of water high up--real
substantial work, such as grinding corn or thrashing it, or turning
wood or sawing it. On the other hand, there is no work at all to be got
from a pond of water that is low down.


_A Cross-bow bent. A Watch wound up._

36. In both of the illustrations now given, we have used the force of
gravity as that force against which we are to do work, and in virtue
of which a stone high up, or a head of water, is in a position of
advantage, and has the power of doing work as it falls to a lower
level. But there are other forces besides gravity, and, with respect to
these, bodies may be in a position of advantage and be able to do work
just as truly as the stone, or the head of water, in the case before
mentioned.

Let us take, for instance, the force of elasticity, and consider what
happens in a cross-bow. When this is bent, the bolt is evidently in a
position of advantage with regard to the elastic force of the bow; and
when it is discharged, this energy of position of the bolt is converted
into energy of motion, just as, when a stone on the top of a house
is allowed to fall, its energy of position is converted into that of
actual motion.

In like manner a watch wound up is in a position of advantage with
respect to the elastic force of the mainspring, and as the wheels of
the watch move this is gradually converted into energy of motion.


_Advantage of Position._

37. It is, in fact, the fate of all kinds of energy of position to be
ultimately converted into energy of motion.

The former may be compared to money in a bank, or capital, the latter
to money which we are in the act of spending; and just as, when we have
money in a bank, we can draw it out whenever we want it, so, in the
case of energy of position, we can make use of it whenever we please.
To see this more clearly, let us compare together a watermill driven by
a head of water, and a windmill driven by the wind. In the one case we
may turn on the water whenever it is most convenient for us, but in the
other we must wait until the wind happens to blow. The former has all
the independence of a rich man; the latter, all the obsequiousness of
a poor one. If we pursue the analogy a step further, we shall see that
the great capitalist, or the man who has acquired a lofty position, is
respected because he has the disposal of a great quantity of energy;
and that whether he be a nobleman or a sovereign, or a general in
command, he is powerful only from having something which enables him
to make use of the services of others. When the man of wealth pays a
labouring man to work for him, he is in truth converting so much of
his energy of position into actual energy, just as a miller lets out a
portion of his head of water in order to do some work by its means.


_Transmutations of Visible Energy.--A Kilogramme shot upwards._

38. We have thus endeavoured to show that there is an energy of repose
as well as a living energy, an energy of position as well as of motion;
and now let us trace the changes which take place in the energy of a
weight, shot vertically upwards, as it continues to rise. It starts
with a certain amount of energy of motion, but as it ascends, this is
by degrees changed into that of position, until, when it gets to the
top of its flight, its energy is entirely due to position.

To take an example, let us suppose that a kilogramme is projected
vertically upwards with the velocity of 19·6 metres in one second.
According to the formula of Art. 28, it contains 19·6 units of energy
due to its actual velocity.

If we examine it at the end of one second, we shall find that it has
risen 14·7 metres in height, and has now the velocity of 9·8. This
velocity we know (Art. 26) denotes an amount of actual energy equal
to 4·9, while the height reached corresponds to an energy of position
equal to 14·7. The kilogramme has, therefore, at this moment a total
energy of 19·6, of which 14·7 units are due to position, and 4·9 to
actual motion.

If we next examine it at the end of another second, we shall find that
it has just been brought to rest, so that its energy of motion is
_nil_; nevertheless, it has succeeded in raising itself 19·6 metres in
height, so that its energy of position is 19·6.

There is, therefore, no disappearance of energy during the rise of
the kilogramme, but merely a gradual change from one kind to another.
It starts with actual energy, and this is gradually changed into that
of position; but if, at any stage of its ascent, we add together the
actual energy of the kilogramme, and that due to its position, we shall
find that their sum always remains the same.

39. Precisely the reverse takes place when the kilogramme begins its
descent. It starts on its downward journey with no energy of motion
whatever, but with a certain amount of energy of position; as it falls,
its energy of position becomes less, and its actual energy greater, the
sum of the two remaining constant throughout, until, when it is about
to strike the ground, its energy of position has been entirely changed
into that of actual motion, and it now approaches the ground with the
velocity, and, therefore, with the energy, which it had when it was
originally projected upwards.


_The Inclined Plane._

40. We have thus traced the transmutations, as regards energy, of a
kilogramme shot vertically upwards, and allowed to fall again to the
earth, and we may now vary our hypothesis by making the kilogramme
rise vertically, but descend by means of a smooth inclined plane
without friction--imagine in fact, the kilogramme to be shaped like a
ball or roller, and the plane to be perfectly smooth. Now, it is well
known to all students of dynamics, that in such a case the velocity
which the kilogramme has when it has reached the bottom of the plane
will be equal to that which it would have had if it had been dropped
down vertically through the same height, and thus, by introducing a
smooth inclined plane of this kind, you neither gain nor lose anything
as regards energy.

In the first place, you do not gain, for think what would happen if the
kilogramme, when it reached the bottom of the inclined plane, should
have a greater velocity than you gave it originally, when you shot it
up. It would evidently be a profitable thing to shoot up the kilogramme
vertically, and bring it down by means of the plane, for you would get
back more energy than you originally spent upon it, and in every sense
you would be a gainer. You might, in fact, by means of appropriate
apparatus, convert the arrangement into a perpetual motion machine, and
go on accumulating energy without limit--but this is not possible.

On the other hand, the inclined plane, unless it be rough and angular,
will not rob you of any of the energy of the kilogramme, but will
restore to you the full amount, when once the bottom has been reached.
Nor does it matter what be the length or shape of the plane, or
whether it be straight, or curved, or spiral, for in all cases, if it
only be smooth and of the same vertical height, you will get the same
amount of energy by causing the kilogramme to fall from the top to the
bottom.

41. But while the energy remains the same, the time of descent will
vary according to the length and shape of the plane, for evidently the
kilogramme will take a longer time to descend a very sloping plane
than a very steep one. In fact, the sloping plane will take longer to
generate the requisite velocity than the steep one, but both will have
produced the same result as regards energy, when once the kilogramme
has arrived at the bottom.


_Functions of a Machine._

42. Our readers are now beginning to perceive that energy cannot be
created, and that by no means can we coax or cozen Dame Nature into
giving us back more than we are entitled to get. To impress this
fundamental principle still more strongly upon our minds, let us
consider in detail one or two mechanical contrivances, and see what
they amount to as regards energy.

[Illustration: Fig. 1.]

Let us begin with the second system of pulleys. Here we have a power
P attached to the one end of a thread, which passes over all the
pulleys, and is ultimately attached, by its other extremity, to a
hook in the upper or fixed block. The weight W is, on the other hand,
attached to the lower or moveable block, and rises with it. Let us
suppose that the pulleys are without weight and the cords without
friction, and that W is supported by six cords, as in the figure.
Now, when there is equilibrium in this machine, it is well known
that W will be equal to six times P; that is to say, a power of one
kilogramme will, in such a machine, balance or support a weight of six
kilogrammes. If P be increased a single grain more, it will overbalance
W, and P will descend, while W will begin to rise. In such a case,
after P has descended, say six metres, its weight being, say, one
kilogramme, it has lost a quantity of energy of position equal to six
units, since it is at a lower level by six metres than it was before.
We have, in fact, expended upon our machine six units of energy. Now,
what return have we received for this expenditure? Our return is
clearly the rise of W, and mechanicians will tell us that in this case
W will have risen one metre.

But the weight of W is six kilogrammes, and this having been raised
one metre represents an energy of position equal to six. We have thus
spent upon our machine, in the fall of P, an amount of energy equal to
six units, and obtained in the rise of W an equivalent amount equal to
six units also. We have, in truth, neither gained nor lost energy, but
simply changed it into a form more convenient for our use.

[Illustration: Fig. 2.]

43. To impress this truth still more strongly, let us take quite a
different machine, such as the hydrostatic press. Its mode of action
will be perceived from Fig. 2. Here we have two cylinders, a wide and
a narrow one, which are connected together at the bottom by means of
a strong tube. Each of these cylinders is provided with a water-tight
piston, the space beneath being filled with water. It is therefore
manifest, since the two cylinders are connected together, and since
water is incompressible, that when we push down the one piston the
other will be pushed up. Let us suppose that the area of the small
piston is one square centimetre,[3] and that of the large piston
one hundred square centimetres, and let us apply a weight of ten
kilogrammes to the smaller piston. Now, it is known, from the laws of
hydrostatics, that every square centimetre of the larger piston will be
pressed upwards with the force of ten kilogrammes, so that the piston
will altogether mount with the force of 1000 kilogrammes--that is to
say, it will raise a weight of this amount as it ascends.

Here, then, we have a machine in virtue of which a pressure of ten
kilogrammes on the small piston enables the large piston to rise with
the force of 1000 kilogrammes. But it is very easy to see that, while
the small piston falls one metre, the large one will only rise one
centimetre. For the quantity of water under the pistons being always
the same, if this be pushed down one metre in the narrow cylinder, it
will only rise one centimetre in the wide one.

Let us now consider what we gain by this machine. The power of ten
kilogrammes applied to the smaller piston is made to fall through one
metre, and this represents the amount of energy which we have expended
upon our machine, while, as a return, we obtain 1000 kilogrammes raised
through one single centimetre. Here, then, as in the case of the
pulleys, the return of energy is precisely the same as the expenditure,
and, provided we ignore friction, we neither gain nor lose anything
by the machine. All that we do is to transmute the energy into a
more convenient form--what we gain in power we lose in space; but we
are willing to sacrifice space or quickness of motion in order to
obtain the tremendous pressure or force which we get by means of the
hydrostatic press.


_Principle of Virtual Velocities._

44. These illustrations will have prepared our readers to perceive the
true function of a machine. This was first clearly defined by Galileo,
who saw that in any machine, no matter of what kind, if we raise a
large weight by means of a small one, it will be found that the small
weight, multiplied into the space through which it is lowered, will
exactly equal the large weight, multiplied into that through which it
is raised.

This principle, known as that of virtual velocities, enables us to
perceive at once our true position. We see that the world of mechanism
is not a manufactory, in which energy is created, but rather a mart,
into which we may bring energy of one kind and change or barter it
for an equivalent of another kind, that suits us better--but if we
come with nothing in our hand, with nothing we shall most assuredly
return. A machine, in truth, does not create, but only transmutes, and
this principle will enable us to tell, without further knowledge of
mechanics, what are the conditions of equilibrium of any arrangement.

For instance, let it be required to find those of a lever, of which the
one arm is three times as long as the other. Here it is evident that if
we overbalance the lever by a single grain, so as to cause the long arm
with its power to fall down while the short one with its weight rises
up, then the long arm will fall three inches for every inch through
which the short arm rises; and hence, to make up for this, a single
kilogramme on the long arm will balance three kilogrammes on the short
one, or the power will be to the weight as one is to three.

[Illustration: Fig. 3.]

45. Or, again, let us take the inclined plane as represented in Fig.
3. Here we have a smooth plane and a weight held upon it by means of a
power P, as in the figure. Now, if we overbalance P by a single grain,
we shall bring the weight W from the bottom to the top of the plane.
But when this has taken place, it is evident that P has fallen through
a vertical distance equal to the length of the plane, while on the
other hand W has only risen through a vertical distance equal to the
height. Hence, in order that the principle of virtual velocities shall
hold, we must have P multiplied into its fall equal to W multiplied
into its rise, that is to say,

  P × Length of plane = W × Height of plane,

  or P/W = (Height.)/(Length.)


_What Friction does._

46. The two examples now given are quite sufficient to enable our
readers to see the true function of a machine, and they are now
doubtless disposed to acknowledge that no machine will give back more
energy than is spent upon it. It is not, however, equally clear that
it will not give back less; indeed, it is a well-known fact that it
constantly does so. For we have supposed our machine to be without
friction--but no machine is without friction--and the consequence is
that the available out-come of the machine is more or less diminished
by this drawback. Now, unless we are able to see clearly what part
friction really plays, we cannot prove the conservation of energy.
We see clearly enough that energy cannot be created, but we are
not equally sure that it cannot be destroyed; indeed, we may say
we have apparent grounds for believing that it is destroyed--that
is our present position. Now, if the theory of the conservation
of energy be true--that is to say, if energy is in any sense
indestructible--friction will prove itself to be, not the destroyer
of energy, but merely the converter of it into some less apparent and
perhaps less useful form.

47. We must, therefore, prepare ourselves to study what friction really
does, and also to recognize energy in a form remote from that possessed
by a body in visible motion, or by a head of water. To friction we may
add percussion, as a process by which energy is apparently destroyed;
and as we have (Art. 39) considered the case of a kilogramme shot
vertically upwards, demonstrating that it will ultimately reach the
ground with an energy equal to that with which it was shot upwards,
we may pursue the experiment one step further, and ask what becomes
of its energy after it has struck the ground and come to rest? We
may vary the question by asking what becomes of the energy of the
smith’s blow after his hammer has struck the anvil, or what of the
energy of the cannon ball after it has struck the target, or what of
that of the railway train after it has been stopped by friction at
the break-wheel? All these are cases in which percussion or friction
appears at first sight to have destroyed visible energy; but before
pronouncing upon this seeming destruction, it clearly behoves us to ask
if anything else makes its appearance at the moment when the visible
energy is apparently destroyed. For, after all, energy may be like the
Eastern magicians, of whom we read that they had the power of changing
themselves into a variety of forms, but were nevertheless very careful
not to disappear altogether.


_When Motion is destroyed, Heat appears._

48. Now, in reply to the question we have put, it may be confidently
asserted that whenever visible energy is apparently destroyed by
percussion or friction, something else makes its appearance, and that
something is _heat_. Thus, a piece of lead placed upon an anvil may
be greatly heated by successive blows of a blacksmith’s hammer. The
collision of flint and steel will produce heat, and a rapidly-moving
cannon ball, when striking against an iron target, may even be heated
to redness. Again, with regard to friction, we know that on a dark
night sparks are seen to issue from the break-wheel which is stopping a
railway train, and we know, also, that the axles of railway carriages
get alarmingly hot, if they are not well supplied with grease.

Finally, the schoolboy will tell us that he is in the habit of rubbing
a brass button upon the desk, and applying it to the back of his
neighbour’s hand, and that when his own hand has been treated in this
way, he has found the button unmistakeably hot.


_Heat a species of Motion._

49. For a long time this appearance of heat by friction or percussion
was regarded as inexplicable, because it was believed that heat was
a kind of matter, and it was difficult to understand where all this
heat came from. The partisans of the material hypothesis, no doubt,
ventured to suggest that in such processes heat might be drawn from the
neighbouring bodies, so that the Caloric (which was the name given to
the imaginary substance of heat) was squeezed or rubbed out of them,
according as the process was percussion or friction. But this was
regarded by many as no explanation, even before Sir Humphry Davy, about
the end of last century, clearly showed it to be untenable.

50. Davy’s experiments consisted in rubbing together two pieces of ice
until it was found that both were nearly melted, and he varied the
conditions of his experiments in such a manner as to show that the heat
produced in this case could not be abstracted from the neighbouring
bodies.

51. Let us pause to consider the alternatives to which we are driven
by this experiment. If we still choose to regard heat as a substance,
since this has not been taken from the surrounding bodies, it must
necessarily have been created in the process of friction. But if we
choose to regard heat as a species of motion, we have a simpler
alternative, for, inasmuch as the energy of visible motion has
disappeared in the process of friction, we may suppose that it has been
transformed into a species of molecular motion, which we call heat; and
this was the conclusion to which Davy came.

52. About the same time another philosopher was occupied with a similar
experiment. Count Rumford was superintending the boring of cannon at
the arsenal at Munich, and was forcibly struck with the very great
amount of heat caused by this process. The source of this heat appeared
to him to be absolutely inexhaustible, and, being unwilling to regard
it as the creation of a species of matter, he was led like Davy to
attribute it to motion.

53. Assuming, therefore, that heat is a species of motion, the next
point is to endeavour to comprehend what kind of motion it is, and in
what respects it is different from ordinary visible motion. To do this,
let us imagine a railway carriage, full of passengers, to be whirling
along at a great speed, its occupants quietly at ease, because,
although they are in rapid motion, they are all moving at the same rate
and in the same direction. Now, suppose that the train meets with a
sudden check;--a disaster is the consequence, and the quiet placidity
of the occupants of the carriage is instantly at an end.

Even if we suppose that the carriage is not broken up and its occupants
killed, yet they are all in a violent state of excitement; those
fronting the engine are driven with force against their opposite
neighbours, and are, no doubt, as forcibly repelled, each one taking
care of himself in the general scramble. Now, we have only to
substitute particles for persons, in order to obtain an idea of what
takes place when percussion is converted into heat. We have, or suppose
we have, in this act the same violent collision of atoms, the same
thrusting forward of A upon B, and the same violence in pushing back on
the part of B--the same struggle, confusion, and excitement--the only
difference being that particles are heated instead of human beings, or
their tempers.

54. We are bound to acknowledge that the proof which we have now given
is not a direct one; indeed, we have, in our first chapter, explained
the impossibility of our ever seeing these individual particles, or
watching their movements; and hence our proof of the assertion that
heat consists in such movements cannot possibly be direct. We cannot
see that it does so consist, but yet we may feel sure, as reasonable
beings, that we are right in our conjecture.

In the argument now given, we have only two alternatives to start
with--either heat must consist of a motion of particles, or, when
percussion or friction is converted into heat, a peculiar substance
called caloric must be created, for if heat be not a species of motion
it must necessarily be a species of matter. Now, we have preferred to
consider heat as a species of motion to the alternative of supposing
the creation of a peculiar kind of matter.

55. Nevertheless, it is desirable to have something to say to an
opponent who, rather than acknowledge heat to be a species of motion,
will allow the creation of matter. To such an one we would say that
innumerable experiments render it certain that a hot body is not
sensibly heavier than a cold one, so that if heat be a species of
matter it is one that is not subject to the law of gravity. If we burn
iron wire in oxygen gas, we are entitled to say that the iron combines
with the oxygen, because we know that the product is heavier than the
original iron by the very amount which the gas has lost in weight. But
there is no such proof that during combustion the iron has combined
with a substance called caloric, and the absence of any such proof is
enough to entitle us to consider heat to be a species of motion, rather
than a species of matter.


_Heat a Backward and Forward Motion._

56. We shall now suppose that our readers have assented to our
proposition that heat is a species of motion. It is almost unnecessary
to add that it must be a species of backward and forward motion; for
nothing is more clear than that _a heated substance is not in motion as
a whole_, and will not, if put upon a table, push its way from the one
end to the other.

Mathematicians express this peculiarity by saying that, although there
is violent internal motion among the particles, yet the centre of
gravity of the substance remains at rest; and since, for most purposes,
we may suppose a body to act as if concentrated at its centre of
gravity, we may say that the body is at rest.

57. Let us here, before proceeding further, borrow an illustration from
that branch of physics which treats of sound. Suppose, for instance,
that a man is accurately balanced in a scale-pan, and that some water
enters his ear; of course he will become heavier in consequence, and if
the balance be sufficiently delicate, it will exhibit the difference.
But suppose a sound or a noise enters his ear, he may say with truth
that something has entered, but yet that something is not matter, nor
will he become one whit heavier in consequence of its entrance, and he
will remain balanced as before. Now, a man into whose ear sound has
entered may be compared to a substance into which heat has entered;
we may therefore suppose a heated body to be similar in many respects
to a sounding body, and just as the particles of a sounding body move
backwards and forwards, so we may suppose that the particles of a
heated body do the same.

We shall take another opportunity (Art. 162) to enlarge upon this
likeness; but, meanwhile, we shall suppose that our readers perceive
the analogy.


_Mechanical Equivalent of Heat._

58. We have thus come to the conclusion that when any heavy body, say
a kilogramme weight, strikes the ground, the visible energy of the
kilogramme is changed into heat; and now, having established the fact
of a relationship between these two forms of energy, our next point
is to ascertain according to what law the heating effect depends upon
the height of fall. Let us, for instance, suppose that a kilogramme of
water is allowed to drop from the height of 848 metres, and that we
have the means of confining to its own particles and retaining there
the heating effect produced. Now, we may suppose that its descent
is accomplished in two stages; that, first of all, it falls upon a
platform from the height of 424 metres, and gets heated in consequence,
and that then the heated mass is allowed to fall other 424 metres. It
is clear that the water will now be doubly heated; or, in other words,
the heating effect in such a case will be proportional to the height
through which the body falls--that is to say, it will be proportional
to the actual energy which the body possesses before the blow has
changed this into heat. In fact, just as the actual energy represented
by a fall from a height is proportional to the height, so is the
heating effect, or molecular energy, into which the actual energy is
changed proportional to the height also. Having established this point,
we now wish to know through how many metres a kilogramme of water must
fall in order to be heated one degree centigrade.

59. For a precise determination of this important point, we are
indebted to Dr. Joule, of Manchester, who has, perhaps, done more than
any one else to put the science of energy upon a sure foundation. Dr.
Joule made numerous experiments, with the view of arriving at the
exact relation between mechanical energy and heat; that is to say, of
determining the mechanical equivalent of heat. In some of the most
important of these he took advantage of the friction of fluids.

[Illustration: Fig. 4.]

60. These experiments were conducted in the following manner. A certain
fixed weight was attached to a pulley, as in the figure. The weight
had, of course, a tendency to descend, and hence to turn the pulley
round. The pulley had its axle supported upon friction wheels, at _f_
and _f_, by means of which the friction caused by the movement of the
pulley was very much reduced. A string, passing over the circumference
of the pulley, was wrapped round _r_, so that, as the weight descended,
the pulley moved round, and the string of the pulley caused _r_ to
rotate very rapidly. Now, the motion of the axis _r_ was conducted
within the covered box B, where there was attached to _r_ a system of
paddles, of which a sketch is given in figure; and therefore, as _r_
moved, these paddles moved also. There were, altogether, eight sets of
these paddles revolving between four stationary vanes. If, therefore,
the box were full of liquid, the paddles and the vanes together would
churn it about, for these stationary vanes would prevent the liquid
being carried along by the paddles in the direction of rotation.

Now, in this experiment, the weight was made to descend through a
certain fixed distance, which was accurately measured. As it descended,
the paddles were set in motion, and the energy of the descending weight
was thus made to churn, and hence to heat some water contained in the
box B. When the weight had descended a certain distance, by undoing a
small peg _p_, it could be wound up again without moving the paddles
in B, and thus the heating effect of several falls of the weight could
be accumulated until this became so great as to be capable of being
accurately measured by a thermometer. It ought to be mentioned that
great care was taken in these experiments, not only to reduce the
friction of the axles of the pulley as much as possible, but also to
estimate and correct for this friction as accurately as possible; in
fact, every precaution was taken to make the experiment successful.

61. Other experiments were made by Joule, in some of which a disc was
made to rotate against another disc of cast-iron pressed against it,
the whole arrangement being immersed in a cast-iron vessel filled
with mercury. From all these experiments, Dr. Joule concluded that
the quantity of heat produced by friction, if we can preserve and
accurately measure it, will always be found proportional to the
quantity of work expended. He expressed this proportion by stating the
number of units of work in kilogrammetres necessary to raise by 1° C.
the temperature of one kilogramme of water. This was 424, as determined
by his last and most complete experiments; and hence we may conclude
that if a kilogramme of water be allowed to fall through 424 metres,
and if its motion be then suddenly stopped, sufficient heat will be
generated to raise the temperature of the water through 1° C., and so
on, in the same proportion.

62. Now, if we take the kilogrammetre as our unit of work, and the heat
necessary to raise a kilogramme of water 1° C. as our unit of heat,
this proportion may be expressed by saying that _one heat unit is equal
to 424 units of work_.

This number is frequently spoken of as the mechanical equivalent of
heat; and in scientific treatises it is denoted by J., the initial of
Dr. Joule’s name.

63. We have now stated the exact relationship that subsists between
mechanical energy and heat, and before proceeding further with proofs
of the great law of conservation, we shall endeavour to make our
readers acquainted with other varieties of energy, on the ground that
it is necessary to penetrate the various disguises that our magician
assumes before we can pretend to explain the principles that actuate
him in his transformations.


FOOTNOTES:

[3] That is to say, a square the side of which is one centimetre, or
the hundredth part of a metre.




CHAPTER III.

_THE FORCES AND ENERGIES OF NATURE: THE LAW OF CONSERVATION._


64. In the last chapter we introduced our readers to two varieties of
energy, one of them visible, and the other invisible or molecular; and
it will now be our duty to search through the whole field of physical
science for other varieties. Here it is well to bear in mind that all
energy consists of two kinds, that of _position_ and that of _actual
motion_, and also that this distinction holds for invisible molecular
energy just as truly as it does for that which is visible. Now, energy
of position implies a body in a position of advantage with respect
to some force, and hence we may with propriety begin our search by
investigating the various forces of nature.


_Gravitation._

65. The most general, and perhaps the most important, of these
forces is _gravitation_, and the law of action of this force may be
enunciated as follows:--_Every particle of the universe attracts every
other particle with a force depending jointly upon the mass of the
attracting and of the attracted particle, and varying inversely as the
square of distance between the two._ A little explanation will make
this plain.

Suppose a particle or system of particles of which the mass is unity to
be placed at a distance equal to unity from another particle or system
of particles of which the mass is also unity--the two will attract each
other. Let us agree to consider the mutual attraction between them
equal to unity also.

Suppose, now, that we have on the one side two such systems with a mass
represented by 2, and on the other side the same system as before,
with a mass represented by unity, the distance, meanwhile, remaining
unaltered. It is clear the double system will now attract the single
system with a twofold force. Let us next suppose the mass of both
systems to be doubled, the distance always remaining the same. It is
clear that we shall now have a fourfold force, each unit of the one
system attracting each unit of the other. In like manner, if the mass
of the one system is 2, and that of the other 3, the force will be 6.
We may, for instance, call the components of the one system A_{1},
A₂, and those of the other A_{3}, A_{4}, A_{5}, and we shall have
A_{1} pulled towards A_{3}, A_{4}, and A_{5}, with a threefold force,
and A₂ pulled towards A_{3}, A_{4}, and A_{5}, with a threefold
force, making altogether a force equal to 6.

In the next place, let the masses remain unaltered, but let the
distance between them be doubled, then the force will be reduced
fourfold. Let the distance be tripled, then the force will be reduced
ninefold, and so on.

66. Gravitation may be described as a very weak force, capable of
acting at a distance, or at least of appearing to do so. It takes the
mass of the whole earth to produce the force with which we are so
familiar at its surface, and the presence of a large mass of rock or
mountain does not produce any appreciable difference in the weight of
any substance. It is the gravitation of the earth, lessened of course
by distance, which acts upon the moon 240,000 miles away, and the
gravitation of the sun influences in like manner the earth and the
various other planets of our system.


_Elastic Forces._

67. Elastic forces, although in their mode of action very different
from gravity, are yet due to visible arrangements of matter; thus,
when a cross-bow is bent, there is a visible change produced in the
bow, which, as a whole, resists this bending, and tends to resume its
previous position. It therefore requires energy to bend a bow, just as
truly and visibly as it does to raise a weight above the earth, and
elasticity is, therefore, as truly a species of force as gravity is.
We shall not here attempt to discuss the various ways in which this
force may act, or in which a solid elastic substance will resist all
attempts to deform it; but in all cases it is clearly manifest that
work must be spent upon the body, and the force of elasticity must be
encountered and overcome throughout a certain space before any sensible
deformation can take place.


_Force of Cohesion._

68. Let us now leave the forces which animate large masses of matter,
and proceed to discuss those which subsist between the smaller
particles of which these large masses are composed. And here we must
say one word more about molecules and atoms, and the distinction we
feel ourselves entitled to draw between these very small bodies, even
although we shall never be able to see either the one or the other.

In our first chapter (Art. 7) we supposed the continual sub-division of
a grain of sand until we had arrived at the smallest entity retaining
all the properties of sand--this we called a _molecule_, and nothing
smaller than this is entitled to be called sand. If we continue this
sub-division further, the molecule of sand separates itself into its
chemical constituents, consisting of silicon on the one side, and
oxygen on the other. Thus we arrive at last at the smallest body which
can call itself silicon, and the smallest which can call itself oxygen,
and we have no reason to suppose that either of these is capable of
sub-division into something else, since we regard oxygen and silicon as
elementary or simple bodies. Now, these constituents of the silicon
molecule are called _atoms_, so that we say the sand molecule is
divisible into atoms of silicon and of oxygen. Furthermore, we have
strong reason for supposing that such molecules and atoms really exist,
but into the arguments for their existence we cannot now enter--it is
one of those things that we must ask our readers to take for granted.

69. Let us now take two molecules of sand. These, when near together,
have a very strong attraction for each other. It is, in truth, this
attraction which renders it difficult to break up a crystalline
particle of sand or rock crystal. But it is only exerted when the
molecules are near enough together to form a homogeneous crystalline
structure, for let the distance between them be somewhat increased, and
we find that all attraction entirely vanishes. Thus there is little
or no attraction between different particles of sand, even although
they are very closely packed together. In like manner, the integrity
of a piece of glass is due to the attraction between its molecules;
but let these be separated by a flaw, and it will soon be found that
this very small increase of distance greatly diminishes the attraction
between the particles, and that the structure will now fall to pieces
from the slightest cause. Now, these examples are sufficient to show
that molecular attraction or _cohesion_, as this is called, is a force
which acts very powerfully through a certain small distance, but which
vanishes altogether when this distance becomes perceptible. Cohesion
is strongest in solids, while in liquids it is much diminished, and in
gases it may be said to vanish altogether. The molecules of gases are,
in truth, so far away from one another, as to have little or no mutual
attraction, a fact proved by Dr. Joule, whose name was mentioned in the
last chapter.


_Force of Chemical Affinity._

70. Let us now consider the mutual forces between atoms. These may be
characterized as even stronger than the forces between molecules, but
as disappearing still more rapidly when the distance is increased. Let
us, for instance, take carbon and oxygen--two substances which are
ready to combine together to form carbonic acid, whenever they have a
suitable opportunity. In this case, each atom of carbon will unite with
two of oxygen, and the result will be something quite different from
either. Yet under ordinary circumstances carbon, or its representative,
coal, will remain unchanged in the presence of oxygen, or of
atmospheric air containing oxygen. There will be no tendency to combine
together, because although the particles of the oxygen would appear to
be in immediate contact with those of the carbon, yet the nearness is
not sufficient to permit of chemical affinity acting with advantage.
When, however, the nearness becomes sufficient, then chemical affinity
begins to operate. We have, in fact, the familiar act of combustion,
and, as its consequence, the chemical union of the carbon or coal with
the oxygen of the air, carbonic acid being the result. Here, then, we
have a very powerful force acting only at a very small distance, which
we name _chemical affinity_, inasmuch as it represents the attraction
exerted between atoms of different bodies in contradistinction to
cohesion, which denotes the attraction between molecules of the same
body.

71. If we regard gravitation as the representative of forces that act
or appear to act, at a distance, we may regard cohesion and chemical
affinity as the representatives of those forces which, although very
powerful, only act or appear to act through a very small interval of
distance.

A little reflection will show us how inconvenient it would be if
gravitation diminished very rapidly with the distance; for then
even supposing that the bond which retains us to the earth were to
hold good, that which retains the moon to the earth might vanish
entirely, as well as that which retains the earth to the sun, and the
consequences would be far from pleasant. Reflection will also show
us how inconvenient it would be if chemical affinity existed at all
distances; if coal, for instance, were to combine with oxygen without
the application of heat, it would greatly alter the value of this fuel
to mankind, and would materially check the progress of human industry.


_Remarks on Molecular and Atomic Forces._

72. Now, it is important to remember that we must treat cohesion and
chemical affinity exactly in the same way as gravity has been treated;
and just as we have energy of position with respect to gravity, so
may we have as truly a species of energy of position with respect to
cohesion and chemical affinity. Let us begin with cohesion.

73. We have hitherto regarded heat as a peculiar motion of the
molecules of matter, without any reference to the force which actuates
these molecules. But it is a well-known fact that bodies in general
expand when heated, so that, in virtue of this expansion, the molecules
of a body are driven violently apart against the force of cohesion.
Work has in truth been done against this force, just as truly as, when
a kilogramme is raised from the earth, work is done against the force
of gravity. When a substance is heated, we may, therefore, suppose that
the heat has a twofold office to perform, part of it going to increase
the actual motions of the molecules, and part of it to separate these
molecules from one another against the force of cohesion. Thus, if I
swing round horizontally a weight (attached to my hand by an elastic
thread of india-rubber), my energy will be spent in two ways--first
of all, it will be spent in communicating a velocity to the weight;
and, secondly, in stretching the india-rubber string, by means of the
centrifugal tendency of the weight. Work will be done against the
elastic force of the string, as well as spent in increasing the motion
of the weight.

Now, something of this kind may be taking place when a body is heated,
for we may very well suppose heat to consist of a vertical or circular
motion, the tendency of which would be to drive the particles asunder
against the force of cohesion. Part, therefore, of the energy of heat
will be spent in augmenting the motion, and part in driving asunder the
particles. We may, however, suppose that, in ordinary cases, the great
proportion of the energy of heat goes towards increasing the molecular
motion, rather than in doing work against the force of cohesion.

74 In certain cases, however, it is probable that the greater part
of the heat applied is spent in doing work against molecular forces,
instead of increasing the motions of molecules.

Thus, when a solid melts, or when a liquid is rendered gaseous, a
considerable amount of heat is spent in the process, which does not
become sensible, that is to say, does not affect the thermometer. Thus,
in order to melt a kilogramme of ice, heat is required sufficient to
raise a kilogramme of water through 80° C., and yet, when melted, the
water is no warmer than the ice. We express this fact by saying that
the latent heat of water is 80. Again, if a kilogramme of water at
100° be converted entirely into steam, as much heat is required as
would raise the water through 537° C., or 537 kilogrammes of water
through one degree; but yet the steam is no hotter than the water, and
we express this fact by saying that the latent heat of steam is 537.
Now, in both of these instances it is at least extremely probable that
a large portion of the heat is spent in doing work against the force
of cohesion; and, more especially, when a fluid is converted into a
gas, we know that the molecules are in that process separated so far
from one another as to lose entirely any trace of mutual force. We may,
therefore, conclude that although in most cases the greater portion of
the heat applied to a body is spent in increasing its molecular motion,
and only a small part in doing work against cohesion, yet when a solid
melts, or a liquid vaporizes, a large portion of the heat required
is not improbably spent in doing work against molecular forces. But
the energy, though spent, is not lost, for when the liquid again
freezes, or when the vapour again condenses, this energy is once more
transformed into the shape of sensible heat, just as when a stone is
dropped from the top of a house, its energy of position is transformed
once more into actual energy.

75. A single instance will suffice to give our readers a notion of
the strength of molecular forces. If a bar of wrought iron, whose
temperature is 10° C. above that of the surrounding medium, be tightly
secured at its extremities, it will draw these together with a force of
at least one ton for each square inch of section. In some cases where
a building has shown signs of bulging outwards, iron bars have been
placed across it, and secured while in a heated state to the walls.
On cooling, the iron contracted with great force, and the walls were
thereby pulled together.

76. We are next brought to consider atomic forces, or those which lead
to chemical union, and now let us see how these are influenced by heat.
We have seen that heat causes a separation between the molecules of a
body, that is to say, it increases the distance between two contiguous
molecules, but we must not suppose that, meanwhile, the molecules
themselves are left unaltered.

The tendency of heat to cause separation is not confined to increasing
the distance between molecules, but acts also, no doubt, in increasing
the distance between parts of the same molecule: in fact, the energy
of heat is spent in pulling the constituent atoms asunder against the
force of chemical affinity, as well as in pulling the molecules asunder
against the force of cohesion, so that, at a very high temperature, it
is probable that most chemical compounds would be decomposed, and many
are so, even at a very moderate heat.

Thus the attraction between oxygen and silver is so slight that at
a comparatively low temperature the oxide of silver is decomposed.
In like manner, limestone, or carbonate of lime, is decomposed when
subjected to the heat of a lime-kiln, carbonic acid being given off,
while quick-lime remains behind. Now, in separating heterogeneous
atoms against the powerful force of chemical affinity, work is done as
truly as it is in separating molecules from one another against the
force of cohesion, or in separating a stone from the earth against the
force of gravity.

77. Heat, as we have seen, is very frequently influential in performing
this separation, and its energy is spent in so doing; but other
energetic agents produce chemical decomposition as well as heat. For
instance, certain rays of the sun decompose carbonic acid into carbon
and oxygen in the leaves of plants, and their energy is spent in the
process; that is to say, it is spent in pulling asunder two such
powerfully attracting substances against the affinity they have for one
another. And, again, the electric current is able to decompose certain
substances, and of course its energy is spent in the process.

Therefore, whenever two powerfully attracting atoms are separated,
energy is spent in causing this separation as truly as in separating
a stone from the earth, and when once the separation has been
accomplished we have a species of energy of position just as truly as
we have in a head of water, or in a stone at the top of a house.

78. It is this chemical separation that is meant when we speak of coal
as a source of energy. Coal, or carbon, has a great attraction for
oxygen, and whenever heat is applied the two bodies unite together.
Now oxygen, as it exists in the atmosphere, is the common inheritance
of all, and if, in addition to this, some of us possess coal in our
cellars, or in pits, we have thus secured a store of energy of
position which we can draw upon with more facility than if it were a
head of water, for, although we can draw upon the energy of a head of
water whenever we choose, yet we cannot carry it about with us from
place to place as we can with coal. We thus perceive that it is not
the coal, by itself, that forms the source of energy, but this is due
to the fact that we have coal, or carbon, in one place, and oxygen in
another, while we have also the means of causing them to unite with
each other whenever we wish. If there were no oxygen in the air, coal
by itself would be of no value.


_Electricity: its Properties._

79. Our readers have now been told about the force of cohesion that
exists between molecules of the same body, and also about that of
chemical affinity existing between atoms of different bodies. Now,
heterogeneity is an essential element of this latter force--there must
be a difference of some kind before it can exhibit itself--and under
these circumstances its exhibitions are frequently characterized by
very extraordinary and interesting phenomena.

We allude to that peculiar exhibition arising out of the forces
of heterogeneous bodies which we call _electricity_, and, before
proceeding further, it may not be out of place to give a short sketch
of the mode of action of this very mysterious, but most interesting,
agent.

80. The science of electricity is of very ancient origin; but its
beginning was very small. For a couple of thousand years it made little
or no progress, and then, during the course of little more than a
century, developed into the giant which it now is. The ancient Greeks
were aware that amber, when rubbed with silk, had the property of
attracting light bodies; and Dr. Gilbert, about three hundred years
ago, showed that many other things, such as sulphur, sealing-wax, and
glass, have the same property as amber.

In the progress of the science it came to be known that certain
substances are able to carry away the peculiar influence produced,
while others are unable to do so; the former are called _conductors_,
and the latter _non-conductors, or insulators_, of electricity. To make
the distinction apparent, let us take a metal rod, having a glass stem
attached to it, and rub the glass stem with a piece of silk, care being
taken that both silk and glass are warm and dry. We shall find that the
glass has now acquired the property of attracting little bits of paper,
or elder pith; but only where it has been rubbed, for the peculiar
influence acquired by the glass has not been able to spread itself over
the surface.

If, however, we take hold of the glass stem, and rub the metal rod,
we may, perhaps, produce the same property in the metal, but it will
spread over the whole, not confining itself to the part rubbed. Thus
we perceive that metal is a conductor, while glass is an insulator, or
non-conductor, of electricity.

[Illustration: Fig. 5.]

81. We would next observe that _this influence is of two kinds_. To
prove this, let us perform the following experiment. Let us suspend a
small pith ball by a very slender silk thread, as in Fig. 5. Next, let
us rub a stick of warm, dry glass with a piece of warm silk, and with
this excited stick touch the pith ball. The pith ball, after being
touched, will be repelled by the excited glass. Let us next excite, in
a similar manner, a stick of dry sealing-wax with a piece of warm, dry
flannel, and on approaching this stick to the pith ball it will attract
it, although the ball, in its present state, is repelled by the excited
glass.

Thus a pith ball, touched by excited glass, is repelled by excited
glass, but attracted by excited sealing-wax.

In like manner, it might be shown that a pith ball, touched by excited
sealing-wax, will be afterwards repelled by excited sealing-wax, but
attracted by excited glass.

Now, what the excited glass did to the pith ball, was to communicate to
it part of its own influence, after which the ball was repelled by the
glass; or, in other words, _bodies charged with similar electricities
repel one another_.

Again, since the pith ball, when charged with the electricity from
glass, was attracted to the electrified sealing-wax, we conclude that
_bodies charged with unlike electricities attract one another_. The
electricity from glass is sometimes called _vitreous_, and that from
sealing-wax _resinous_, electricity, but more frequently the former
is known as _positive_, and the latter as _negative_, electricity--it
being understood that these words do not imply the possession of a
positive nature by the one influence, or of a negative nature by the
other, but are merely terms employed to express the apparent antagonism
which exists between the two kinds of electricity.

82. The next point worthy of notice is that _whenever one electricity
is produced, just as much is produced of an opposite description_.
Thus, in the case of glass excited by silk, we have positive
electricity developed upon the glass, while we have also negative
electricity developed upon the silk to precisely the same extent.
And, again, when sealing-wax is rubbed with flannel, we have negative
electricity developed upon the sealing-wax, and just as much positive
upon the flannel.

83. These facts have given rise to a theory of electricity, or at
least to a method of regarding it, which, if not absolutely correct,
seems yet to unite together the various phenomena. According to this
hypothesis, a neutral, unexcited body is supposed to contain a store of
the two electricities combined together, so that whenever such a body
is excited, a separation is produced between the two. The phenomena
which we have described are, therefore, due to this electrical
separation, and inasmuch as the two electricities have a great affinity
for one another, it requires the expenditure of energy to produce this
separation, just as truly as it does to separate a stone from the earth.

84. Now, it is worthy of note that _electrical separation is only
produced when heterogeneous bodies are rubbed together_. Thus, if
flannel be rubbed upon glass, we have electricity; but if flannel be
rubbed upon glass covered with flannel, we have none. In like manner,
if silk be rubbed upon sealing-wax covered with silk, or, in fine,
if two portions of the same substance be rubbed together, we have no
electricity.

On the other hand, a very slight difference of texture is sometimes
sufficient to produce electrical separation. Thus, if two pieces of the
same silk ribbon be rubbed together lengthwise, we have no electricity;
but if they be rubbed across each other, the one is positively, and the
other negatively, electrified.

In fact, this element of heterogeneity is an all important one
in electrical development, and this leads us to conjecture that
_electrical attraction may probably be regarded as peculiarly allied to
that force which we call chemical affinity_. At any rate, electricity
and chemical affinity are only manifested between bodies that are, in
some respects, dissimilar.

85. The following is a list of bodies arranged according to the
electricity which they develop when rubbed together, each substance
being positively electrified when rubbed with any substance beneath it
in the list.

  1. Cat’s skin.
  2. Flannel.
  3. Ivory.
  4. Glass.
  5. Silk.
  6. Wood.
  7. Shellac.
  8. Resin.
  9. Metals.
  10. Sulphur.
  11. Caoutchouc.
  12. Gutta-percha.
  13. Gun-cotton.

Thus, if resin be rubbed with cat’s skin, or with flannel, the
cat’s skin or flannel will be positively, and the resin negatively,
electrified; while if glass be rubbed with silk, the glass will be
positively, and the silk negatively, electrified, and so on.

86. It is not our purpose here to describe at length the _electrical
machine_, but we may state that it consists of two parts, one for
generating electricity by means of the friction of a rubber against
glass, and another consisting of a system of brass tubes, of
considerable surface, supported on glass stems, for collecting and
retaining the electricity so produced. This latter part of the machine
is called its _prime conductor_.


_Electric Induction._

[Illustration: Fig. 6.]

87. Let us now suppose that we have set in action a machine of this
kind, and accumulated a considerable quantity of positive electricity
in its prime conductor at A. Let us next take two vessels, B and C,
made of brass, supported on glass stems. These two vessels are supposed
to be in contact, but at the same time to be capable of being separated
from one another at their middle point, where the line is drawn in Fig.
6. Now let us cause B and C to approach A together. At first, B and C
are not electrified, that is to say, their two electricities are not
separated from each other, but are mixed together; but mark what will
happen as they are pushed towards A. The positive electricity of A will
decompose the two electricities of B and C, attracting the negative
towards itself, and repelling the positive as far away as possible.
The disposition of electricities will, therefore, be as in the figure.
If we now pull C away from B, we have obtained a quantity of positive
electricity on C, by help of the original electricity which was in A;
in fact, we have made use of the original stock or electrical capital
in A, in order to obtain positive electricity in C, without, however,
diminishing the amount of our original stock. Now, this distant action
or help, rendered by the original electricity in separating that of B
and C, is called electric induction.

88. The experiment may, however, be performed in a somewhat different
manner--we may allow B and C to remain together, and gradually push
them nearer to A. As B and C approach A, the separation of their
electricities will become greater and greater, until, when A and
B are only divided by a small thickness of air, the two opposite
electricities then accumulated will have sufficient strength to rush
together through the air, and unite with each other by means of a spark.

89. The principle of induction may be used with advantage, when it is
wished to accumulate a large quantity of electricity.

[Illustration: Fig. 7.]

In this case, an instrument called a _Leyden jar_ is very frequently
employed. It consists of a glass jar, coated inside and outside with
tin foil, as in Fig. 7. A brass rod, having a knob at the end of it,
is connected metallically with the inside coating, and is kept in its
place by being passed through a cork, which covers the mouth of the
jar. We have thus two metallic coatings which are not electrically
connected with one another. Now, in order to charge a jar of this kind,
let the outside coating be connected by a chain with the earth, while
at the same time positive electricity from the prime conductor of an
electrical machine is communicated to the inside knob.

The positive electricity will accumulate on the inside coating
with which the knob is connected. It will then decompose the two
electricities of the outside coating, driving the positive electricity
to the earth, and there dissipating it, but attracting the negative
to itself. There will thus be positive electricity on the inside,
and negative on the outside coating. These two electricities may be
compared to two hostile armies watching each other, and very anxious
to get together, while, however, they are separated from one another
by means of an insurmountable obstacle. They will thus remain facing
each other, and at their posts, while each side is, meanwhile, being
recruited by the same operation as before. We may by this means
accumulate a vast quantity of opposite electricities on the two
coatings of such a jar, and they will remain there for a long time,
especially if the surrounding atmosphere and the glass surface of the
jar be quite dry. When, however, electric connection of any kind is
made between the two coatings, the electricities rush together and
unite with one another in the shape of a spark, while if the human body
be the instrument of connecting them a severe shock will be felt.

90. It would thus appear that, when two bodies charged with opposite
electricities are brought near each other, the two electricities rush
together, forming a current, and the ultimate result is a spark.
Now, this spark implies heat, and is, in truth, nothing else than
small particles of intensely heated matter of some kind. We have here,
therefore, first of all, the conversion of electrical separation into a
current of electricity, and, secondly, the conversion of this current
into heat. In this case, however, the current lasts only a very small
time; the discharge, as it is called, of a Leyden jar being probably
accomplished in ¹⁄₂₄₀₀₀th of a second.


_The Electric Current._

91. In other cases we have electrical currents which, although not so
powerful as that produced by discharging a Leyden jar, yet last longer,
and are, in fact, continuous instead of momentary.

We may see a similar difference in the case of visible energy. Thus we
might, by means of gunpowder, send up in a moment an enormous mass of
water; or we might, by means of a fountain, send up the same mass in
the course of time, and in a very much quieter manner. We have the same
sort of difference in electrical discharges, and having spoken of the
rushing together of two opposite electricities by means of an explosion
and a spark, let us now speak of the eminently quiet and effective
_voltaic current_, in which we have a continuous coming together of the
same two agents.

[Illustration: Fig. 8.]

92. It is not our object here to give a complete description, either
historical or scientific, of the voltaic battery, but rather to give
such an account as will enable our readers to understand what the
arrangement is, and what sort of effect it produces; and with this
object we shall at once proceed to describe the battery of Grove, which
is perhaps the most efficacious of all the various arrangements for the
purpose of producing an electric current. In this battery we have a
number of cells connected together, as in Fig. 8, which shows a battery
of three cells. Each cell consists of two vessels, an outer and an
inner one; the outer vessel being made of glass or ordinary stone ware,
while the inner one is made of unglazed porcelain, and is therefore
porous. The outer vessel is filled with dilute sulphuric acid, and a
plate of amalgamated zinc--that is to say, of metallic zinc having
its outer surface brightened with mercury,--is immersed in this acid.
Again, in the inner or porous vessel we have strong nitric acid, in
which a plate of platinum foil is immersed, this being at the same time
electrically connected with the zinc plate of the next outer vessel,
by means of a clamp, as in the figure. Both metals must be clean where
they are pressed together, that is to say, the true metallic surfaces
of both must be in contact. Finally, a wire is metallically connected
with the platinum of the left-hand cell, and a similar wire with the
zinc of the right-hand cell, and these connecting wires ought, except
at their extremities, to be covered over with gutta-percha or thread.
The loose extremities of these wires are called the _poles_ of the
battery.

93. Let us now suppose that we have a battery containing a good many
cells of this description, and let the whole arrangement be insulated,
by being set upon glass supports, or otherwise separated from the
earth. If now we test, by appropriate methods, the extremity of the
wire connected with the left-hand platinum plate, it will be found to
be charged with positive electricity, while the extremity of the other
wire will be found charged with negative electricity.

94. In the next place, if we connect these poles of the battery with
one another, the two electricities will rush together and unite, or,
in other words, there will be an electric current; but it will not be
a momentary but a continuous one, and for some time, provided these
poles are kept together, a current of electricity will pass through the
wires, and indeed through the whole arrangement, including the cells.

The direction of the current will be such that _positive electricity
may be supposed to pass from the zinc to the platinum, through the
liquid; and back again through the wire, from the platinum at the
left hand, to the zinc at the right_; in fact, to go in the direction
indicated by the arrow-head.

95. Thus we have two things. In the first place, before the two
terminals, or poles, have been brought together, we have them charged
with opposite electricities; and, secondly, when once they have been
brought together, we have the production of a continuous current of
electricity. Now, this current is an energetic agent, in proof of which
we shall proceed to consider the various properties which it has,--the
various things which it can do.


_Its Magnetic Effects._

96. In the first place, _it can deflect the magnetic needle_. For
instance, let a compass needle be swung freely, and let a current of
electricity circulate along a wire placed near this needle, and in the
direction of its length, then the direction in which the needle points
will be immediately altered. This direction will now depend upon that
of the current, conveyed by the wire, and the needle will endeavour to
place itself at right angles to this wire.

In order to remember the connection between the direction of the
current and that of the magnet, imagine your body to form part of the
positive current, which may be supposed to enter in at your head, and
go out at your feet; also imagine that your face is turned towards
the magnet. In this case, the pole of the magnet, which points to the
north, will always be deflected by the current towards your right
hand. The strength of a current may be measured by the amount of the
deflection it produces upon a magnetic needle, and the instrument by
which this measurement is made is called a _galvanometer_.

97. In the next place, _the current is able_, not merely to deflect
a magnet, but also _to render soft iron magnetic_. Let us take, for
instance, the wire connected with the one pole of the battery, and
cover it with thread, in order to insulate it, and let us wrap this
wire round a cylinder of soft iron, as in Fig. 9. If we now make a
communication between the other extremity of the wire, and the other
pole of the battery, so as to make the current pass, it will be found
that our cylinder of soft iron has become a powerful magnet, and that
if an iron keeper be attached to it as in the figure, the keeper will
be able to sustain a very great weight.

[Illustration: Fig. 9.]


_Its Heating Effect._

98. _The electric current has likewise the property of heating a wire
through which it passes._ To prove this, let us connect the two poles
of a battery by means of a fine platinum wire, when it will be found
that the wire will, in a few seconds, become heated to redness. In
point of fact, the current will heat a thick wire, but not so much as a
thin one, for we may suppose it to rush with great violence through the
limited section of the thin wire, producing in its passage great heat.


_Its Chemical Effect._

99. Besides its magnetic and heating effects, _the current has also the
power of decomposing compound substances_, under certain conditions.
Suppose, for instance, that the poles of a battery, instead of being
brought together, are plunged into a vessel of water, decomposition
will at once begin, and small bubbles of oxygen will rise from the
positive pole, while small bubbles of hydrogen will make their
appearance at the negative. If the two gases are collected together in
a vessel, they may be exploded, and if collected separately, it may
be proved by the ordinary tests, that the one is oxygen and the other
hydrogen.


_Attraction and Repulsion of Currents._

100. We have now described very shortly the magnetic, the heating, and
the chemical effects of currents; it remains for us to describe the
effects of currents upon one another.

In the first place, suppose that we have two wires which are parallel
to one another, and carry currents going in the same direction; and
let us further suppose that these wires are capable of moving, then it
is found that they will attract one another. If, however, the wires,
although parallel, convey currents going in opposite directions, they
will then repel one another. A good way of showing this experimentally
is to cause two circular currents to float on water. If these currents
both go either in the same direction as the hands of a watch, or in
the opposite direction, then the two will attract one another; but if
the one goes in the one direction, and the other in the other, they
will then repel one another.


_Attraction and Repulsion of Magnets._

101. Ampère, who discovered this property of currents, has likewise
shown us that in very many respects a magnet may be likened to a
collection of circular currents all parallel to one another, their
direction being such that, if you look towards the north pole of a
freely suspended cylindrical magnet facing it, the positive current
will descend on the east or left-hand side, and ascend on the west or
right-hand side. If we adopt this method of viewing magnets, we can
easily account for the attraction between the unlike and the repulsion
between the like poles of a magnet, for when unlike poles are placed
near each other, the circular currents which face each other are then
all going in the same direction, and the two will, therefore, attract
one another, but if like poles are placed in this position, the
currents that face each other are going in opposite directions, and the
poles will, therefore, repel one another.

[Illustration: Fig. 10.]

_Induction of Currents._

102. Before closing this short sketch of electrical phenomena, we must
allude to the inductive effect of currents upon each other. Let us
suppose (Fig. 10) that we have two circular coils of wire, covered with
thread, and placed near each other. Let both the extremities of the
right-hand coil be connected with the poles of a battery, so as to make
a current of electricity circulate round the coil. On the other hand,
let the left-hand coil be connected with a galvanometer, thus enabling
us to detect the smallest current of electricity which may pass through
this coil. Now, it is found that when we first connect the right-hand
coil, so as to pass the battery current through it, a momentary current
will pass through the left-hand coil, and will deflect the needle of
the galvanometer, but this current will go in an opposite direction to
that which circulates round the right-hand coil.

103. Again, as long as the current continues to flow through the
right-hand coil there will be no current through the other, but at
the moment of breaking the contact between the right-hand coil and
the battery there will again be a momentary current in the left-hand
coil, but this time in the same direction as that of the right-hand
coil, instead of being, as before, in the opposite direction. In other
words, when contact is _made_ in the right-hand coil, there is a
momentary current in the left-hand coil, but in an opposite direction
to that in the right, while, when contact is _broken_ in the right-hand
coil, there is a momentary current in the left-hand coil in the same
direction as that in the right.

104. In order to exemplify this induction of currents, it is not even
necessary to make and break the current in the right-hand coil, for we
may keep it constantly going and arrange so as to make the right-hand
coil (always retaining its connection with the battery) alternately
approach and recede from the other; when it approaches the other, the
effect produced will be the same as when the contact was made in the
above experiment--that is to say, we shall have an induced current in
an opposite direction to that of the primary, while, when it recedes
from the other, we shall have a current in the same direction as that
of the primary.

105. Thus we see that whether we keep both coils stationary, and
suddenly produce a current in the right-hand coil, or whether, keeping
this current constantly going, we suddenly bring it near the other
coil, the inductive effect will be precisely the same, for in both
cases the left-hand coil is suddenly brought into the presence of a
current. And again, it is the same, whether we suddenly break the
right-hand current, or suddenly remove it from the left-hand coil, for
in both cases this coil is virtually removed from the presence of a
current.


_List of Energies._

106. We are now in a position to enumerate the various kinds of
energy which occur in nature; but, before doing so, we must warn our
readers that this enumeration has nothing absolute or complete about
it, representing, as it does, not so much the present state of our
knowledge as of our want of knowledge, or rather profound ignorance, of
the ultimate constitution of matter. It is, in truth, only a convenient
classification, and nothing more.

107. To begin, then, with visible energy. We have first of all--


_Energy of Visible Motion._

 (A.) Visible energy of actual motion--in the planets, in meteors, in
 the cannon ball, in the storm, in the running stream, and in other
 instances of bodies in actual visible motion, too numerous to be
 mentioned.


_Visible Energy of Position._

 (B.) We have also visible energy of position--in a stone on the top of
 a cliff, in a head of water, in a rain cloud, in a cross-bow bent, in
 a clock or watch wound up, and in various other instances.

108. Then we have, besides, several cases in which there is an
alternation between (A) and (B).

A pendulum, for instance, when at its lowest point, has only the
energy (A), or that of actual motion, in virtue of which it ascends a
certain distance against the force of gravity. When, however, it has
completed its ascent, its energy is then of the variety (B), being
due to position, and not to actual motion; and so on it continues to
oscillate, alternately changing the nature of its energy from (A) to
(B), and from (B) back again to (A).

109. A vibrating body is another instance of this alternation. Each
particle of such a body may be compared to an exceedingly small
pendulum oscillating backwards and forwards, only very much quicker
than an ordinary pendulum; and just as the ordinary pendulum in passing
its point of rest has its energy all of one kind, while in passing its
upper point it has it all of another, so when a vibrating particle is
passing its point of rest, its energy is all of the variety (A), and
when it has reached its extreme displacement, it is all of the variety
(B).


_Heat Motion._

 110. (C.) Coming now to molecular or invisible energy, we have, in
 the first place, that motion of the molecules of bodies which we term
 heat. A better term would be _absorbed heat_, to distinguish it from
 _radiant heat_, which is a very different thing. That peculiar motion
 which is imparted by heat when absorbed into a body is, therefore, one
 variety of molecular energy.


_Molecular Separation._

 (D.) Analogous to this is that effect of heat which represents
 position rather than actual motion. For part of the energy of absorbed
 heat is spent in pulling asunder the molecules of the body under the
 attractive force which binds them together (Art. 73), and thus a store
 of energy of position is laid up, which disappears again after the
 body is cooled.


_Atomic or Chemical Separation._

 111. (E.) The two previous varieties of energy may be viewed as
 associated with molecules rather than with atoms, and with the force
 of cohesion rather than with that of chemical affinity. Proceeding now
 to atomic force, we have a species of energy of position due to the
 separation of different atoms under the strong chemical attraction
 they have for one another. Thus, when we possess coal or carbon and
 also oxygen in a state of separation from one another, we are in
 possession of a source of energy which may be called that of chemical
 separation.


_Electrical Separation._

 112 (F.) The attraction which heterogeneous atoms possess for one
 another, sometimes, however, gives rise to a species of energy which
 manifests itself in a very peculiar form, and appears as electrical
 separation, which is thus another form of energy of position.


_Electricity in Motion._

 113 (G.) But we have another species of energy connected with
 electricity, for we have that due to electricity in motion, or in
 other words, an electric current which probably represents some form
 of actual motion.


_Radiant Energy._

 114 (H.) It is well known that there is no ordinary matter, or at
 least hardly any, between the sun and the earth, and yet we have a
 kind of energy which we may call radiant energy, which proceeds
 to us from the sun, and proceeds also with a definite, though very
 great velocity, taking about eight minutes to perform its journey.
 Now, this radiant energy is known to consist of the vibrations of an
 elastic medium pervading all space, which is called ether, or the
 _ethereal medium_. Inasmuch, therefore, as it consists of vibrations,
 it partakes of the character of pendulum motion, that is to say, the
 energy of any ethereal particle is alternately that of position and
 that of actual motion.


_Law of Conservation._

115. Having thus endeavoured, provisionally at least, to catalogue our
various energies, we are in a position to state more definitely what
is meant by the conservation of energy. For this purpose, let us take
the universe as a whole, or, if this be too large, let us conceive, if
possible, a small portion of it to be isolated from the rest, as far as
force or energy is concerned, forming a sort of microcosm, to which we
may conveniently direct our attention.

This portion, then, neither parts with any of its energy to the
universe beyond, nor receives any from it. Such an isolation is, of
course, unnatural and impossible, but it is conceivable, and will,
at least, tend to concentrate our thoughts. Now, whether we regard
the great universe, or this small microcosm, the principle of the
conservation of energy asserts that the sum of all the various energies
is a constant quantity, that is to say, adopting the language of
Algebra--

 (A) + (B) + (C) + (D) + (E) + (F) + (G) + (H) = a constant quantity.

116. This does not mean, of course, that (A) is constant in itself, or
any other of the left-hand members of this equation, for, in truth,
they are always changing about into each other--now, some visible
energy being changed into heat or electricity; and, anon, some heat or
electricity being changed back again into visible energy--but it only
means that the sum of all the energies taken together is constant. We
have, in fact, in the left hand, eight variable quantities, and we
only assert that their sum is constant, not by any means that they are
constant themselves.

117. Now, what evidence have we for this assertion? It may be replied
that we have the strongest possible evidence which the nature of the
case admits of. The assertion is, in truth, a peculiar one--peculiar
in its magnitude, in its universality, in the subtle nature of the
agents with which it deals. If true, its truth certainly cannot be
proved after the manner in which we prove a proposition in Euclid.
Nor does it even admit of a proof so rigid as that of the somewhat
analogous principle of the conservation of matter, for in chemistry we
may confine the products of our chemical combination so completely
as to prove, beyond a doubt, that no heavy matter passes out of
existence that--when coal, for instance, burns in oxygen gas--what we
have is merely a change of condition. But we cannot so easily prove
that no energy is destroyed in this combination, and that the only
result is a change from the energy of chemical separation into that of
absorbed heat, for during the process it is impossible to isolate the
energy--do what we may, some of it will escape into the room in which
we perform the experiment; some of it will, no doubt, escape through
the window, while a little will leave the earth altogether, and go
out into space. All that we can do in such a case is to estimate, as
completely as possible, how much energy has gone away, since we cannot
possibly prevent its going. But this is an operation involving great
acquaintance with the laws of energy, and very great exactness of
observation: in fine, our readers will at once perceive that it is much
more difficult to prove the truth of the conservation of energy than
that of the conservation of matter.

118. But if it be difficult to prove our principle in the most rigorous
manner, we are yet able to give the strongest possible indirect
evidence of its truth.

Our readers are no doubt familiar with a method which Euclid frequently
adopts in proving his propositions. Starting with the supposition
that they are not true, and reasoning upon this hypothesis, he comes
to an absurd conclusion--hence he concludes that they are true. Now,
we may adopt a method somewhat similar with regard to our principle,
only instead of supposing it untrue, let us suppose it true. It may
then be shown that, if it be true, under certain test conditions we
ought to obtain certain results--for instance, if we increase the
pressure, we ought to lower the freezing point of water. Well, we make
the experiment, and find that, in point of fact, the freezing point of
water is lowered by increasing the pressure, and we have thus derived
an argument in favour of the conservation of energy.

119. Or again, if the laws of energy are true, it may be shown that,
whenever a substance contracts when heated, it will become colder
instead of hotter by compression. Now, we know that ice-cold water,
or water just a little above its freezing point, contracts instead
of expanding up to 4° C.; and Sir William Thomson has found, by
experiment, that water at this temperature is cooled instead of heated
by sudden compression. India-rubber is another instance of this
relation between these two properties, for if we stretch a string of
india-rubber it gets hotter instead of colder, that is to say, its
temperature rises by extension, and gets lower by contraction; and
again, if we heat the string, we find that it contracts in length
instead of expanding like other substances as its temperature increases.

120. Numberless instances occur in which we are enabled to predict
what will happen by assuming the truth of the laws of energy; in other
words, these laws are proved to be true in all cases where we can put
them to the test of rigorous experiment, and probably we can have no
better proof than this of the truth of such a principle. We shall
therefore proceed upon the assumption that the conservation of energy
holds true in all cases, and give our readers a list of the various
transmutations of this subtle agent as it goes backwards and forwards
from one abode to another, making, meanwhile, sundry remarks that may
tend, we trust, to convince our readers of the truth of our assumption.






CHAPTER IV.

_TRANSMUTATIONS OF ENERGY._


_Energy of Visible Motion._

121. Let us begin our list of transmutations with the energy of
visible motion. This is changed into _energy of position_ when a stone
is projected upwards above the earth, or, to take a case precisely
similar, when a planet or a comet goes from perihelion, or its position
nearest the sun, to aphelion, or its position furthest from the sun.
We thus see why a heavenly body should move fastest at perihelion, and
slowest at aphelion. If, however, a planet were to move round the sun
in an orbit exactly circular, its velocity would be the same at all the
various points of this orbit, because there would be no change in its
distance from the centre of attraction, and therefore no transmutation
of energy.

122. We have already (Arts. 108, 109) said that the energy in an
oscillating or vibrating body is alternately that of actual motion, and
that of position. In this respect, therefore, a pendulum is similar to
a comet or heavenly body with an elliptical orbit. Nevertheless the
change of energy is generally more complete in a pendulum or vibrating
body than it is in a heavenly body; for in a pendulum, when at its
lowest point, the energy is entirely that of actual motion, while at
its upper point it is entirely that of position. Now, in a heavenly
body we have only a lessening, but not an entire destruction, of the
velocity, as the body passes from perihelion to aphelion--that is to
say, we have only a partial conversion of the one kind of energy into
the other.

123. Let us next consider the change of actual visible energy into
_absorbed heat_. This takes place in all cases of friction, percussion,
and resistance. In friction, for instance, we have the conversion of
work or energy into heat, which is here produced through the rubbing
of surfaces against each other; and Davy has shown that two pieces of
ice, both colder than the freezing point, may be melted by friction.
In percussion, again, we have the energy of the blow converted into
heat; while, in the case of a meteor or cannon ball passing through the
air with great velocity, we have the loss of energy of the meteor or
cannon ball through its contact with the air, and at the same time the
production of heat on account of this resistance.

The resistance need not be atmospheric, for we may set the cannon ball
to pierce through wooden planks or through sand, and there will equally
be a production of heat on account of the resistance offered by the
wooden planks or by the sand to the motion of the ball. We may even
generalize still further, and assert that whenever the visible momentum
of a body is transferred to a larger mass, there is at the same time
the conversion of visible energy into heat.

124. A little explanation will be required to make this point clear.

The third law of motion tells us that action and reaction are equal and
opposite, so that when two bodies come into collision the forces at
work generate equal and opposite quantities of momentum. We shall best
see the meaning of this law by a numerical example, bearing in mind
that momentum means the product of mass into velocity.

For instance, let us suppose that an inelastic body of mass 10 and
velocity 20 strikes directly another inelastic body of mass 15 and
velocity 15, the direction of both motions being the same.

Now, it is well known that the united mass will, after impact, be
moving with the velocity 17. What, then, has been the influence of the
forces developed by collision? The body of greater velocity had before
impact a momentum 10 × 20 = 200, while its momentum after impact is
only 10 × 17 = 170; it has therefore suffered a loss of 30 units as
regards momentum, or we may consider that a momentum of 30 units has
been impressed upon it in an opposite direction to its previous motion.

On the other hand, the body of smaller velocity had before impact a
momentum 15 × 15 = 225, while after impact it has 15 × 17 = 255 units,
so that its momentum has been increased by 30 units in its previous
direction.

The force of impact has therefore generated 30 units of momentum in two
opposite directions, so that, taking account of direction, the momentum
of the system is the same before and after impact; for before impact we
had a momentum of 10 × 20 + 15 × 15 = 425, while after it we have the
united mass 25 moving with the velocity 17, giving the momentum 425 as
before.

125. But while the momentum is the same before and after impact, the
visible energy of the moving mass is undoubtedly less after impact
than before it. To see this we have only to turn to the expression
of Art. 28, from which we find that the energy before impact was as
follows:--Energy in kilogrammetres = (_m v_²)/(19 · 6) = (10 × 20² + 15
× 15²)/19·6 = 376 nearly; while that after impact = (25 × 17²)/19·6 =
368 nearly.

126. The loss of energy will be still more manifest if we suppose an
inelastic body in motion to strike against a similar body at rest. Thus
if we have a body of mass 20 and velocity 20 striking against one of
equal mass, but at rest, the velocity of the double mass after impact
will obviously be only 10; but, as regards energy, that before impact
will be (20 × 20²)/19·6 = ⁸⁰⁰⁰⁄₁₉·6 while that after impact will be
(40 × 10²)/19·6 = ⁴⁰⁰⁰⁄₁₉·6 or only half the former.

127. Thus there is in all such cases an apparent loss of visible
energy, while at the same time there is the production of heat on
account of the blow which takes place. If, however, the substances that
come together be perfectly elastic (which no substance is), the visible
energy after impact will be the same as that before, and in this case
there will be no conversion into heat. This, however, is an extreme
supposition, and inasmuch as no substance is perfectly elastic, we
have in all cases of collision a greater or less conversion of visible
motion into heat.

128. We have spoken (Art. 122) about the change of energy in an
oscillating or vibrating body, as if it were entirely one of actual
energy into energy of position, and the reverse.

But even here, in each oscillation or vibration, there is a greater
or less conversion of visible energy into heat. Let us, for instance,
take a pendulum, and, in order to make the circumstances as favourable
as possible, let it swing on a knife edge, and in vacuo; in this case
there will be a slight but constant friction of the knife edge against
the plane on which it rests, and though the pendulum may continue to
swing for hours, yet it will ultimately come to rest.

And, again, it is impossible to make a vacuum so perfect that there is
absolutely no air surrounding the pendulum, so that part of the motion
of the pendulum will always be carried off by the residual air of the
vacuum in which it swings.

129. Now, something similar happens in that vibratory motion which
constitutes sound. Thus, when a bell is in vibration, part of the
energy of the vibration is carried off by the surrounding air, and it
is in virtue of this that we hear the sound of the bell; but, even if
there were no air, the bell would not go on vibrating for ever. For
there is in all bodies a greater or less amount of internal viscosity,
a property which prevents perfect freedom of vibration, and which
ultimately converts vibrations into heat.

A vibrating bell is thus very much in the same position as an
oscillating pendulum, for in both part of the energy is given off to
the air, and in both there is unavoidable friction--in the one taking
the shape of internal viscosity, and in the other that of friction of
the knife edge against the plane on which it rests.

130. In both these cases, too, that portion of the energy which goes
into the air takes ultimately the shape of heat. The oscillating
pendulum communicates a motion to the air, and this motion ultimately
heats the air. The vibrating bell, or musical instrument, in like
manner communicates part of its energy to the air. This communicated
energy first of all moves through the air with the well-known velocity
of sound, but during its progress it, too, no doubt becomes partly
converted into heat. Ultimately, it is transmitted by the air to other
bodies, and by means of their internal viscosity is sooner or later
converted into heat. Thus we see that heat is the form of energy, into
which all visible terrestrial motion, whether it be rectilinear, or
oscillatory, or vibratory, is ultimately changed.

131. In the case of a body in visible rectilinear motion on the earth’s
surface, this change takes place very soon--if the motion be rotatory,
such as that of a heavy revolving top, it may, perhaps, continue longer
before it is ultimately stopped, by means of the surrounding air, and
by friction of the pivot; if it be oscillatory, as in the pendulum, or
vibratory, as in a musical instrument, we have seen that the air and
internal friction are at work, in one shape or another, to carry it
off, and will ultimately succeed in converting it into heat.

132. But, it may be said, why consider a body moving on the earth’s
surface? why not consider the motion of the earth itself? Will this
also ultimately take the shape of heat?

No doubt it is more difficult to trace the conversion in such a case,
inasmuch as it is not proceeding at a sensible rate before our eyes. In
other words, the very conditions that make the earth habitable, and a
fit abode for intelligent beings like ourselves, are those which unfit
us to perceive this conversion of energy in the case of the earth. Yet
we are not without indications that it is actually taking place. For
the purpose of exhibiting these, we may divide the earth’s motion into
two--a motion of rotation, and one of revolution.

133. Now, with regard to the earth’s rotation, the conversion of the
visible energy of this motion into heat is already well recognized. To
understand this we have only to study the nature of the moon’s action
upon the fluid portions of our globe. In the following diagram (Fig.
11) we have an exaggerated representation of this, by which we see that
the spherical earth is converted into an elongated oval, of which one
extremity always points to the moon. The solid body of the earth itself
revolves as usual, but, nevertheless, this fluid protuberance remains
always pointing towards the moon, as we see in the figure, and hence
the earth rubs against the protuberance as it revolves. The friction
produced by this action tends evidently to lessen the rotatory energy
of the earth--in other words, it acts like a break--and we have, just
as by a break-wheel, the conversion of visible energy into heat. This
was first recognized by Mayer and J. Thomson.

[Illustration: Fig. 11.]

134. But while there can be no doubt about the fact of such a
conversion going on, the only question is regarding its rate of
progress, and the time required before it can cause a perceptible
impression upon the rotative energy of the earth.

Now, it is believed by astronomers that they have detected evidence of
such a change, for our knowledge of the motions of the sun and moon has
become so exact, that not only can we carry forward our calculations so
as to predict an eclipse, but also carry them backwards, and thus fix
the dates and even the very details of the ancient historical eclipses.

If, however, between those times and the present, the earth has lost a
little rotative energy on account of this peculiar action of the moon,
then it is evident that the calculated circumstances of the ancient
total eclipse will not quite agree with those actually recorded; and by
a comparison of this nature it is believed that we have detected a very
slight falling off in the rotative energy of our earth. If we carry out
the argument, we shall be driven to the conclusion that the rotative
energy of our globe will, on account of the moon’s action, always get
less and less, until things are brought into such a state that the
rotation comes to be performed in the same time as the revolution of
the moon, so that then the same portion of the terrestrial surface
being always presented to the moon, it is evident that there will be no
effort made by the solid substance of the earth, to glide from under
the fluid protuberance, and there will in consequence be no friction,
and no further loss of energy.

135. If the fate of the earth be ultimately to turn the same face
always to the moon, we have abundant evidence that this very fate has
long since overtaken the moon herself. Indeed, the much stronger effect
of our earth upon the moon has produced this result, probably, even in
those remote periods when the moon was chiefly fluid; and it is a fact
well known, not merely to astronomers, but to all of us, that the moon
nowadays turns always the same face to the earth.[4] No doubt this fate
has long since overtaken the satellites of Jupiter, Saturn, and the
other large planets; and there are independent indications that, at
least in the case of Jupiter, the satellites turn always the same face
to their primary.

136. To come now to the energy of revolution of the earth, in her
orbit round the sun, we cannot help believing that there is a material
medium of some kind between the sun and the earth; indeed, the
undulatory theory of light requires this belief. But if we believe in
such a medium, it is difficult to imagine that its presence will not
ultimately diminish the motion of revolution of the earth in her orbit;
indeed, there is a strong scientific probability, if not an absolute
certainty, that such will be the case. There is even some reason to
think that the energy of a comet of small period, called Encke’s
comet, is gradually being stopped from this cause; in fine, there can
be hardly any doubt that the cause is really in operation, and will
ultimately affect the motions of the planets and other heavenly bodies,
even although its rate of action may be so slow that we are not able to
detect it.

We may perhaps generalize by saying, that wherever in the universe
there is a differential motion, that is to say, a motion of one part
of it towards or from another, then, in virtue of the subtle medium,
or cement, that binds the various parts of the universe together, this
motion is not unattended by something like friction, in virtue of which
the differential motion will ultimately disappear, while the loss of
energy caused by its disappearance will assume the form of heat.

137. There are, indeed, obscure intimations that a conversion of this
kind is not improbably taking place in the solar system; for, in the
sun himself, we have the matter near the equator, by virtue of the
rotation of our luminary, carried alternately towards and from the
various planets. Now, it would seem that the sun-spots, or atmospheric
disturbances of the sun, affect particularly his equatorial regions,
and have likewise a tendency to attain their maximum size in that
position, which is as far away as possible from the influential
planets, such as Mercury or Venus;[5] so that if Venus, for instance,
were between the earth and the sun, there would be few sun-spots in the
middle of the sun’s disc, because that would be the part of the sun
nearest Venus.

But if the planets influence sun-spots, the action is no doubt
reciprocal, and we have much reason to believe that sun-spots
influence, not only the magnetism, but also the meteorology of our
earth, so that there are most displays of the Aurora Borealis, as well
as most cyclones, in those years when there are most sun-spots.[6] Is
it not then possible that, in these strange, mysterious phenomena, we
see traces of the machinery by means of which the differential motion
of the solar system is gradually being changed into heat?

138. We have thus seen that visible energy of actual motion is not
unfrequently changed into visible energy of position, and that it is
also very often transformed into absorbed heat. We have now to state
that it may likewise be transformed into _electrical separation_.
Thus, when an ordinary electrical machine is in action, considerable
labour is spent in turning the handle; it is, in truth, harder to turn
than if no electricity were being produced--in other words, part of
the energy which is spent upon the machine goes to the production of
electrical separation. There are other ways of generating electricity
besides the frictional method. If, for instance, we bring an insulated
conducting plate near the prime conductor of the electrical machine,
yet not near enough to cause a spark to pass, and if we then touch the
insulated plate, we shall find it, after contact, to be charged with an
electricity the opposite of that in the machine; we may then remove it
and make use of this electricity.

It requires a little thought to see what labour we have spent in this
process. We must bear in mind that, by touching the plate, we have
carried off the electricity of the same name as that of the machine,
so that, after touching the insulated plate it is more strongly
attracted to the conductor than it was before. When we begin to remove
it, therefore, it will cost us an effort to do so, and the mechanical
energy which we spend in removing it will account for the energy of
electrical separation which we then obtain.

139. We may thus make use of a small nucleus of electricity, to assist
us in procuring an unlimited supply, for in the above process the
electricity of the prime conductor remains unaltered, and we may repeat
the operation as often as we like, and gather together a very large
quantity of electricity, without finally altering the electricity of
the prime conductor, but not, however, without the expenditure of an
equivalent amount of energy, in the shape of actual work.

140. While, as we have seen, there is a tendency in all motion to be
changed into heat, there is one instance where it is, in the first
place at least, changed into _a current of electricity_. We allude
to the case where a conducting substance moves in the presence of an
electric current, or of a magnet.

In Art. 104 we found that if one coil connected with a battery were
quickly moved into the presence of another coil connected with a
galvanometer, an induced current would be generated in the latter coil,
and would affect the galvanometer, its direction being the reverse of
that passing in the other. Now, an electric current implies energy, and
we may therefore conclude that some other form of energy must be spent,
or disappear, in order to produce the current which is generated in the
coil attached to the galvanometer.

Again, we learn from Art. 100 that two currents going in opposite
directions repel one another. The current generated in the coil
attached to the galvanometer or secondary current will, therefore,
repel the primary current, which is moving towards it; this repulsion
will either cause a stoppage of motion, or render necessary the
expenditure of energy, in order to keep up the motion of this moving
coil. We thus find that two phenomena occur simultaneously. In the
first place, there is the production of energy in the secondary coil,
in the shape of a current opposite in direction to that of the primary
coil; in the next case, owing to the repulsion between this induced
current and the primary current, there is a stoppage or disappearance
of the energy of actual motion of the moving coil. We have, in fact,
the creation of one species of energy, and at the same time the
disappearance of another, and thus we see that the law of conservation
is by no means broken.

141. We see also the necessary connection between the two electrical
laws described in Arts. 100 and 104. Indeed, had these laws been other
than what they are, the principle of conservation of energy would have
been broken.

For instance, had the induced current in the case now mentioned been
in the same direction as that of the primary, the two currents would
have attracted each other, and thus there would have been the creation
of a secondary current, implying energy, in the coil attached to the
galvanometer, along with an increase of the visible energy of motion
of the primary current--that is to say, instead of the creation of
one kind of energy, accompanied with the disappearance of another, we
should have had the simultaneous creation of both; and thus the law of
conservation of energy would have been broken.

We thus see that the principle of conservation enables us to deduce
the one electrical law from the other, and this is one of the many
instances which strengthen our belief in the truth of the great
principle for which we are contending.

142. Let us next consider what will take place if we cause the primary
current to move from the secondary coil instead of towards it.

In this case we know, from Art. 104, that the induced current will be
in the same direction as the primary, while we are told by Art. 100
that the two currents will now attract each other. The tendency of this
attraction will be to stop the motion of the primary current from
the secondary one, or, in other words, there will be a disappearance
of the energy of visible motion, while at the same time there is the
production of a current. In both cases, therefore, one form of energy
disappears while another takes its place, and in both there will be a
very perceptible resistance experienced in moving the primary coil,
whether towards the secondary or from it. Work will, in fact, have to
be spent in both operations, and the outcome of this work or energy
will be the production of a current in the first place, and of heat in
the second; for we learn from Art. 98 that when a current passes along
a wire its energy is generally spent in heating the wire.

We have thus two phenomena occurring together. In the first place, in
moving a current of electricity to and from a coil of wire, or any
other conductor, or (which is the same thing, since action and reaction
are equal and opposite) in moving a coil of wire or any other conductor
to and from a current of electricity, a sense of resistance will be
experienced, and energy will have to be spent upon the process; in the
second place, an electrical current will be generated in the conductor,
and the conductor will be heated in consequence.

143. The result will be rendered very prominent if we cause a metallic
top, in rapid rotation, to spin near two iron poles, which, by means
of the battery, we can suddenly convert into the poles of a powerful
electro-magnet. When this change is made, and the poles become
magnetic, the motion of the top is very speedily brought to rest,
just as if it had to encounter a species of invisible friction. This
curious result can easily be explained. We have seen from Art. 101
that a magnet resembles an assemblage of electric currents, and in the
metallic top we have a conductor alternately approaching these currents
and receding from them; and hence, according to what has been said, we
shall have a series of secondary currents produced in the conducting
top which will stop its motion, and which will ultimately take the
shape of heat. In other words, the visible energy of the top will be
changed into heat just as truly as if it were stopped by ordinary
friction.

144. The electricity induced in a metallic conductor, moved in
the presence of a powerful magnet, has received the name of
Magneto-Electricity; and Dr. Joule has made use of it as a convenient
means of enabling him to determine the mechanical equivalent of heat,
for it is into heat that the energy of motion of the conductor is
ultimately transformed. But, besides all this, these currents form,
perhaps, the very best means of obtaining electricity; and recently
very powerful machines have been constructed by Wild and others with
this view.

145. These machines, when large, are worked by a steam-engine, and
their mode of operation is as follows:--The nucleus of the machine
is a system of powerful permanent steel magnets, and a conducting
coil is made to revolve rapidly in presence of these magnets. The
current produced by this moving coil is then used in order to produce
an extremely powerful electro-magnet, and finally a coil is made to
move with great rapidity in presence of this powerful electro-magnet,
thus causing induced currents of vast strength. So powerful are these
currents, that when used to produce the electric light, small print may
be read on a dark night at the distance of two miles from the scene of
operation!

It thus appears that in this machine a double use is made of
magneto-electricity. Starting with a nucleus of permanent magnetism,
the magneto-electric currents are used, in the first instance, to
form a powerful electro-magnet much stronger than the first, and this
powerful electro-magnet is again made use of in the same way as the
first, in order to give, by means of magneto-electricity, an induced
current of very great strength.

146. There is, moreover, a very great likeness between a
magneto-electric machine like that of Wild’s for generating electric
currents, and the one which generates statical electricity by means of
the method already described Art. 139. In both cases advantage is taken
of a nucleus, for in the magneto-electric machine we have the molecular
currents of a set of permanent magnets, which are made the means of
generating enormous electric currents without any permanent alteration
to themselves, yet not without the expenditure of work.

Again, in an induction machine for generating statical electricity,
we have an electric nucleus, such as we have supposed to reside in the
prime conductor of a machine; and advantage may be taken, as we have
seen, of this nucleus in order to generate a vast quantity of statical
electricity, without any permanent alteration of the nucleus, but not
without the expenditure of work.

147. We have now seen under what conditions the visible energy of
actual motion may be changed--1stly, into energy of position; 2ndly,
into the two energies which embrace absorbed heat; 3rdly, into
electrical separation; and finally into electricity in motion. As far
as we know, visible energy cannot directly be transformed into chemical
separation, or into radiant energy.


_Visible Energy of Position._

148. Having thus exhausted the transmutations of the energy of
visible motion, we next turn to that of position, and find that it
is transmuted into motion, but not immediately into any other form
of energy; we may, therefore, dismiss this variety at once from our
consideration.


_Absorbed Heat._

140. Coming now to these two forms of energy which embrace _absorbed
heat_, we find that this may be converted into (A) or _actual visible
energy_ in the case of the steam-engine, the air-engine, and all
varieties of heat engines. In the steam-engine, for instance, part
of the heat which passes through it disappears as heat, utterly and
absolutely, to reappear as mechanical effect. There is, however, one
condition which must be rigidly fulfilled, whenever heat is changed
into mechanical effect--there must be a difference of temperature, and
_heat will only be changed into work, while it passes from a body of
high temperature to one of low_.

Carnot, the celebrated French physicist, has ingeniously likened the
mechanical power of heat to that of water; for just as you can get
no work out of heat unless there be a flow of heat from a higher
temperature level to a lower, so neither can you get work out of water
unless it be falling from a higher level to a lower.

150. If we reflect that heat is essentially distributive in its nature,
we shall soon perceive the reason for this peculiar law; for, in virtue
of its nature, heat is always rushing from a body of high temperature
to one of low, and if left to itself it would distribute itself equally
amongst all bodies, so that they would ultimately become of the same
temperature. Now, if we are to coax work out of heat, we must humour
its nature, for it may be compared to a pack of schoolboys, who are
always ready to run with sufficient violence out of the schoolroom into
the open fields, but who have frequently to be dragged back with a very
considerable expenditure of energy. So heat will not allow itself to be
confined, but will resist any attempt to accumulate it into a limited
space. Work cannot, therefore, be gained by such an operation, but
must, on the contrary, be spent upon the process.

151. Let us now for a moment consider the case of an enclosure in which
everything is of the same temperature. Here we have a dull dead level
of heat, out of which it will be impossible to obtain the faintest
semblance of work. The temperature may even be high, and there may be
immense stores of heat energy in the enclosure, but not a trace of this
is available in the shape of work. Taking up Carnot’s comparison, the
water has already fallen to the same level, and lies there without any
power of doing useful work--dead, in a sense, as far as visible energy
is concerned.

152. We thus perceive that, firstly, we can get work out of heat when
it passes from a higher to a lower temperature, but that, secondly,
we must spend work upon it in order to make it pass from a lower
temperature to a higher one; and that, thirdly and finally, nothing
in the shape of work can be got out of heat which is all at the same
temperature level.

What we have now said enables us to realize the conditions under which
all heat engines work. The essential point about such engines is, not
the possession of a cylinder, or piston, or fly wheels, or valves,
but the possession of two chambers, one of high and the other of low
temperature, while it performs work in the process of carrying heat
from the chamber of high to that of low temperature.

Let us take, for example, the low-pressure engine. Here we have the
boiler or chamber of high, and the condenser or chamber of low,
temperature, and the engine works while heat is being carried from
the boiler to the condenser--never while it is being carried from the
condenser to the boiler.

In like manner in the locomotive we have the steam generated at a high
temperature and pressure, and cooled by injection into the atmosphere.

153. But, leaving formal engines, let us take an ordinary fire, which
plays in truth the part of an engine, as far as energy is concerned.
We have here the cold air streaming in over the floor of the room,
and rushing into the fire, to be there united with carbon, while
the rarefied product is carried up the chimney. Dismissing from our
thoughts at present the process of combustion, except as a means of
supplying heat, we see that there is a continual in-draught of cold
air, which is heated by the fire, and then sent to mingle with the
air above. Heat is, in fact, distributed by this means, or carried
from a body of high temperature, _i.e._ the fire, to a body of low
temperature, _i.e._ the outer air, and in this process of distribution
mechanical effect is obtained in the up-rush of air through the chimney
with considerable velocity.

154. Our own earth is another instance of such an engine, having
the equatorial regions as its boiler, and the polar regions as its
condensers; for, at the equator, the air is heated by the direct
rays of the sun, and we have there an ascending current of air, up a
chimney as it were, the place of which is supplied by an in-draught of
colder air along the ground or floor of the world, from the poles on
both sides. Thus the heated air makes its way from the equator to the
poles in the upper regions of the atmosphere, while the cold air makes
its way from the poles to the equator along the lower regions. Very
often, too, aqueous vapour as well as air is carried up by means of
the sun’s heat to the upper and colder atmospheric regions, and there
deposited in the shape of rain, or hail, or snow, which ultimately
finds its way back again to the earth, often displaying in its passage
immense mechanical energy. Indeed, the mariner who hoists his sail,
and the miller who grinds his corn (whether he use the force of the
wind or that of running water), are both dependent upon this great
earth-engine, which is constantly at work producing mechanical effect,
but always in the act of carrying heat from its hotter to its colder
regions.

155. Now, if it be essential to an engine to have two chambers, one
hot and one cold, it is equally important that there should be a
considerable temperature difference between the two.

If Nature insists upon a difference before she will give us work, we
shall not be able to pacify her, or to meet her requirements by making
this difference as small as possible. And hence, _cæteris paribus_, we
shall obtain a greater proportion of work out of a certain amount of
heat passing through our engine when the temperature difference between
its boiler and condenser is as great as possible. In a steam-engine
this difference cannot be very great, because if the water of the
boiler were at a very high temperature the pressure of its steam would
become dangerous; but in an air-engine, or engine that heats and
cools air, the temperature difference may be much larger. There are,
however, practical inconveniences in engines for which the temperature
of the boiler is very high, and it is possible that these may prove
so formidable as to turn the scale against such engines, although in
theory they ought to be very economical.

156. The principles now stated have been employed by Professor J.
Thomson, in his suggestion that the application of pressure would be
found to lower the freezing point of water; and the truth of this
suggestion was afterwards proved by Professor Sir W. Thomson. The
following was the reasoning employed by the former:--

Suppose that we have a chamber kept constantly at the temperature 0°
C., or the melting point of ice, and that we have a cylinder, of which
the sectional area is one square metre, filled one metre in height with
water, that is to say, containing one cubic metre of water. Suppose,
next, that a well-fitting piston is placed above the surface of the
water in this cylinder, and that a considerable weight is placed upon
the piston. Let us now take the cylinder, water and all, and carry it
into another room, of which the temperature is just a trifle lower. In
course of time the water will freeze, and, as it expands in freezing,
it will push up the piston and weight about ⁹⁄₁₀₀ths of a metre; and we
may suppose that the piston is kept fastened in this position by means
of a peg. Now carry back the machine into the first room, and in the
course of time the ice will be melted, and we shall have water once
more in the cylinder, but there will now be a void space of ⁹⁄₁₀₀ths
of a metre between the piston and the surface. We have thus acquired
a certain amount of energy of position, and we have only to pull out
the peg, and allow the piston with its weight to fall down through
the vacant space, in order to utilize this energy, after which the
arrangement is ready to start afresh. Again, if the weight be very
great, the energy thus gained will be very great; in fact, the energy
will vary with the weight. In fine, the arrangement now described is
a veritable heat engine, of which the chamber at 0° C. corresponds to
the boiler, and the other chamber a trifle lower in temperature to
the condenser, while the amount of work we get out of the engine--or,
in other words, its efficiency--will depend upon the weight which is
raised through the space of ⁹⁄₁₀₀ths of a metre, so that, by increasing
this weight without limit, we may increase the efficiency of our engine
without limit. It would thus at first sight appear that by this device
of having two chambers, one at 0° C., and the other a trifle lower,
we can get any amount of work out of our water engine; and that,
consequently, we have managed to overcome Nature. But here Thomson’s
law come into operation, showing that we cannot overcome Nature by any
such device, but that if we have a large weight upon our piston, we
must have a proportionally large difference of temperature between our
two chambers--that is to say, the freezing point of water, under great
pressure, will be lower in temperature than its freezing point, if the
pressure upon it be only small.

Before leaving this subject we must call upon our readers to realize
what takes place in all heat engines. It is not merely that heat
produces mechanical effect, but that _a given quantity of heat
absolutely passes out of existence as heat in producing its equivalent
of work_. If, therefore, we could measure the mere heat produced in an
engine by the burning of a ton of coals, we should find it to be less
when the engine was doing work than when it was at rest.

In like manner, when a gas expands suddenly its temperature falls,
because a certain amount of its heat passes out of existence in the act
of producing mechanical effect.

157. We have thus endeavoured to show under what conditions absorbed
heat may be converted into mechanical effect. This absorbed heat
embraces (Art. 110) two varieties of energy, one of these being
molecular motion, and the other molecular energy of position.

Let us now, therefore, endeavour to ascertain under what circumstances
the one of these varieties may be changed into the other. It is well
known that it takes a good deal of heat to convert a kilogramme of ice
into water, and that when the ice is melted the temperature of the
water is not perceptibly higher than that of the ice. It is equally
well known that it takes a great deal of heat to convert a kilogramme
of boiling water into steam, and that when the transformation is
accomplished, the steam produced is not perceptibly hotter than the
boiling water. In such cases the heat is said to become latent.

Now, in both these cases, but more obviously in the last, we may
suppose that the heat has not had its usual office to perform, but
that, instead of increasing the motion of the molecules of water, it
has spent its energy in tearing them asunder from each other, against
the force of cohesion which binds them together.

Indeed, we know as a matter of fact that the force of cohesion which is
perceptible in boiling water is apparently absent from steam, or the
vapour of water, because its molecules are too remote from one another
to allow of this force being appreciable. We may, therefore, suppose
that a large part, at least, of the heat necessary to convert boiling
water into steam is spent in doing work against molecular forces.

When the steam is once more condensed into hot water, the heat thus
spent reassumes the form of molecular motion, and the consequence
is that we require to take away somehow all the latent heat of a
kilogramme of steam before we can convert it into boiling water. In
fact, if it is difficult and tedious to convert water into steam, it is
difficult and tedious to convert steam into water.

158. Besides the case now mentioned, there are other instances in
which, no doubt, molecular separation becomes gradually changed into
heat motion. Thus, when a piece of glass has been suddenly cooled,
its particles have not had time to acquire their proper position, and
the consequence is that the whole structure is thrown into a state of
constraint. In the course of time such bodies tend to assume a more
stable state, and their particles gradually come closer together.

It is owing to this cause that the bulb of a thermometer recently blown
gradually contracts, and it is no doubt owing to the same cause that a
Prince Rupert’s drop, formed by dropping melted glass into water, when
broken, falls into powder with a kind of explosion. It seems probable
that in all such cases these changes are attended with heat, and that
they denote the conversion of the energy of molecular separation into
that of molecular motion.

159. Having thus examined the transmutations of (C) into (D), and
of (D) back again into (C), let us now proceed with our list, and
see under what circumstances absorbed heat is changed into _chemical
separation_.

It is well known that when certain bodies are heated, they are
decomposed; for instance, if limestone or carbonate of lime be heated,
it is decomposed, the carbonic acid being given out in the shape of
gas, while quick-lime remains behind. Now, heat is consumed in this
process, that is to say, a certain amount of heat energy absolutely
passes out of existence _as heat_ and is changed into the energy of
chemical separation. Again, if the lime so obtained be exposed, under
certain circumstances, to an atmosphere of carbonic acid, it will
gradually become changed into carbonate of lime; and in this change
(which is a gradual one) we may feel assured that the energy of
chemical separation is once more converted into the energy of heat,
although we may not perceive any increment of temperature, on account
of the slow nature of the process.

At very high temperatures it is possible that most compounds are
decomposed, and the temperature at which this takes place, for any
compound, has been termed its _temperature of disassociation_.

160. Heat energy is changed into _electrical separation_ when
tourmalines and certain other crystals are heated.

Let us take, for instance, a crystal of tourmaline and raise its
temperature, and we shall find one end positively, and the other
negatively, electrified. Again, let us take the same crystal, and
suddenly cool it, and we shall find an electrification of the
opposite kind to the former, so that the end of the axis, which
was then positive, will now be negative. Now, this separation of
the electricities denotes energy; and we have, therefore, in such
crystals a case where the energy of heat has been changed into that
of electrical separation. In other words, a certain amount of heat has
passed out of existence _as heat_, while in its place a certain amount
of electrical separation has been obtained.

161. Let us next see under what circumstances heat is changed
into _electricity in motion_. This transmutation takes place in
thermo-electricity.

Suppose, for instance, that we have a bar of copper or antimony, say
copper, soldered to a bar of bismuth, as in Fig. 12. Let us now heat
one of the junctions, while the other remains cool. It will be found
that a current of positive electricity circulates round the bar, in
the direction of the arrow-head, going from the bismuth to the copper
across the heated junction, the existence of which may be detected by
means of a compass needle, as we see in the figure.

[Illustration: Fig. 12.]

Here, then, we have a case in which heat energy goes out of existence,
and is converted into that of an electric current, and we may even
arrange matters so as to make, on this principle, an instrument which
shall be an extremely delicate test of the existence of heat.

By having a number of junctions of bismuth and antimony, as in Fig.
13, and heating the upper set, while the lower remain cool, we get a
strong current going from the bismuth to the antimony across the heated
junctions, and we may pass the current so produced round the wire of
a galvanometer, and thus, by increasing the number of our junctions,
and also by using a very delicate galvanometer, we may get a very
perceptible effect for the smallest heating of the upper junctions.
This arrangement is called the _thermopile_, and, in conjunction with
the reflecting galvanometer, it affords the most delicate means known
for detecting small quantities of heat.

[Illustration: Fig. 13.]

162. The last transmutation on our list with respect to absorbed heat
is that in which this species of energy is transformed into _radiant
light and heat_. This takes place whenever a hot body cools in an open
space--the sun, for instance, parts with a large quantity of his heat
in this way; and it is due, in part at least, to this process that
a hot body cools in air, and wholly to it that such a body cools in
vacuo. It is, moreover, due to the penetration of our eye by radiant
energy that we are able to see hot bodies, and thus the very fact that
we see them implies that they are parting with their heat.

Radiant energy moves through space with the enormous velocity of
188,000 miles in one second. It takes about eight minutes to come
from the sun to our earth, so that if our luminary were to be suddenly
extinguished, we should have eight minutes respite before the
catastrophe overtook us. Besides the rays that affect the eye, there
are others which we cannot see, and which may therefore be termed dark
rays. A body, for instance, may not be hot enough to be self-luminous,
and yet it may be rapidly cooling and changing its heat into radiant
energy, which is given off by the body, even although neither the eye
nor the touch may be competent to detect it. It may nevertheless be
detected by the thermopile, which was described in Art. 161. We thus
see how strong is the likeness between a heated body and a sounding
one. For just as a sounding body gives out part of its sound energy
to the atmosphere around it, so does a heated body give out part of
its heat energy to the ethereal medium around it. When, however, we
consider the rates of motion of these energies through their respective
media, there is a mighty difference between the two, sound travelling
through the air with the velocity of 1100 feet a second, while radiant
energy moves over no less a space than 188,000 miles in the same
portion of time.


_Chemical Separation._

163. We now come to the energy denoted by chemical separation, such
as we possess when we have coal or carbon in one place, and oxygen in
another. Very evidently this form of energy of position is transmuted
into _heat_ when we burn the coal, or cause it to combine with the
oxygen of the air; and generally, whenever chemical combination
takes place, we have the production of heat, even although other
circumstances may interfere to prevent its recognition.

Now, in accordance with the principle of conservation, it may be
expected that, if a definite quantity of carbon or of hydrogen be
burned under given circumstances, there will be a definite production
of heat; that is to say, a ton of coals or of coke, when burned, will
give us so many heat units, and neither more or less. We may, no doubt,
burn our ton in such a way as to economize more or less of the heat
produced; but, as far as the mere production of heat is concerned, if
the quantity and quality of the material burned and the circumstances
of combustion be the same, we expect the same amount of heat.

164. The following table, derived from the researches of Andrews, and
those of Favre and Silbermann, shows us how many units of heat we may
get by burning a kilogramme of various substances.


UNITS _of_ HEAT _developed by_ COMBUSTION _in_ OXYGEN.

                  Kilogrammes of Water raised 1° C.
  Substance         by the combustion of one kilogramme
   Burned.          of each substance.

  Hydrogen                     34,135
  Carbon                        7,990
  Sulphur                       2,263
  Phosphorus                    5,747
  Zinc                          1,301
  Iron                          1,576
  Tin                           1,233
  Olefiant Gas                 11,900
  Alcohol                       7,016

165. There are other methods, besides combustion, by which chemical
combination takes place.

When, for instance, we plunge a piece of metallic iron into a solution
of copper, we find that when we take it out, its surface is covered
with copper. Part of the iron has been dissolved, taking the place of
the copper, which has therefore been thrown, in its metallic state,
upon the surface of the iron. Now, in this operation heat is given
out--we have in fact burned, or oxidized, the iron, and we are thus
furnished with a means of arranging the metals, beginning with that
which gives out most heat, when used to displace the metal at the other
extremity of the series.

166. The following list has been formed, on this principle, by Dr.
Andrews:--

  1. Zinc
  2. Iron
  3. Lead
  4. Copper
  5. Mercury
  6. Silver
  7. Platinum

--that is to say, the metal platinum can be displaced by any other
metal of the series, but we shall get most heat if we use zinc to
displace it.

We may therefore assume that if we displace a definite quantity of
platinum by a definite quantity of zinc, we shall get a definite amount
of heat. Suppose, however, that instead of performing the operation
in one step, we make two of it. Let us, for instance, first of all
displace copper by means of zinc, and then platinum by means of copper.
Is it not possible that the one of these processes may be more fruitful
in heat giving than the other? Now, Andrews has shown us that we cannot
gain an advantage over Nature in this way, and that if we use our zinc
first of all to displace iron, or copper, or lead, and then use this
metal to displace platinum, we shall obtain just the very same amount
of heat as if we had used the zinc to displace the platinum at once.

167. It ought here to be mentioned that, very generally, chemical
action is accompanied with a change of molecular condition.

A solid, for instance, may be changed into a liquid, or a gas into
a liquid. Sometimes the one change counteracts the other as far as
apparent heat is concerned; but sometimes, too, they co-operate
together to increase the result. Thus, when a gas is absorbed by water,
much heat is evolved, and we may suppose the result to be due in part
to chemical combination, and in part to the condensation of the gas
into a liquid, by which means its latent heat is rendered sensible. On
the other hand, when a liquid unites with a solid, or when two solids
unite with one another, and the product is a liquid, we have very often
the absorption of heat, the heat rendered latent by the dissolution
of the solid being more than that generated by combination. Freezing
mixtures owe their cooling properties to this cause; thus, if snow and
salt be mixed together, they liquefy each other, and the result is
brine of a temperature much lower than that of either the ingredients.

168. When heterogeneous metals, such as zinc and copper, are soldered
together, we have apparently a conversion of the energy of chemical
separation into that of _electrical separation_. This was first
suggested by Volta as the origin of the electrical separation which
we see in the voltaic current, and recently its existence has been
distinctly proved by Sir W. Thomson.

To render manifest this conversion of energy, let us solder a piece of
zinc and copper together--if we now test the bar by means of a delicate
electrometer we shall find that the zinc is positively, while the
copper is negatively, electrified. We have here, therefore, an instance
of the transmutation of one form of energy of position into another; so
much energy of chemical separation disappearing in order to produce so
much electrical separation. This explains the fact recorded in Art. 93,
where we saw that if a battery be insulated and its poles kept apart,
the one will be charged with positive, and the other with negative,
electricity.

169. But further, when such a voltaic battery is in action, we have a
transmutation of chemical separation into _electricity in motion_. To
see this, let us consider what takes place in such a battery.

Here no doubt the sources of electrical excitement are the points of
contact of the zinc and platinum, where, as we see by our last article,
we have electrical separation produced. But this of itself would not
produce a current, for an electrical current implies very considerable
energy, and must be fed by something. Now, in the voltaic battery we
have two things which accompany each other, and which are manifestly
connected together. In the first place we have the combustion, or
at least the oxidation and dissolution, of the zinc; and we have,
secondly, the production of a powerful current. Now, evidently, the
first of these is that which feeds the second, or, in other words, the
energy of chemical separation of the metallic zinc is transmuted into
that of an electrical current, the zinc being virtually burned in the
process of transmutation.

170. Finally, as far as we are aware, the energy of chemical separation
is not directly transmuted into radiant light and heat.


_Electrical Separation._

171. In the first place the energy of electrical separation is
obviously transmuted into that of _visible motion_, when two oppositely
electrified bodies approach each other.

172. Again, it is transmuted into a _current of electricity_, and
ultimately into heat, when a spark passes between two oppositely
electrified bodies.

It ought, therefore, to be borne in mind that when the flash is seen
there is no longer electricity, what we see being merely air, or some
other material, intensely heated by the discharge. Thus a man might
be rendered insensible by a flash of lightning without his seeing the
flash--for the effect of the discharge upon the man, and its effect in
heating the air, might be phenomena so nearly simultaneous that the man
might become insensible before he could perceive the flash.


_Electricity in Motion._

173. This energy is transmuted into that of _visible motion_ when two
wires conveying electrical currents in the same direction attract each
other. When, for instance, two circular currents float on water, both
going in the direction of the hands of a watch, we have seen from Art.
100 that they will move towards each other. Now, here there is, in
truth, a lessening of the intensity of each current when the motion is
taking place, for we know (Art. 104) that when a circuit is moved into
the presence of another circuit conveying a current, there is produced
by induction a current in the opposite direction; and hence we perceive
that, when two similar currents approach each other, each is diminished
by means of this inductive influence--in fact, a certain amount of
current energy disappears from existence in order that an equivalent
amount of the energy of visible motion may be produced.

174. Electricity in motion is transmuted into _heat_ during the passage
of a current along a thin wire, or any badly conducting substance--the
wire is heated in consequence, and may even become white hot. Most
frequently the energy of an electric current is spent in heating the
wires and other materials that form the circuit. Now, the energy
of such a current is fed by the burning or oxidation of the metal
(generally zinc) which is used in the circuit, so that the ultimate
effect of this combustion is the heating of the various wires and other
materials through which the current passes.

175. We may, in truth, burn or oxidize zinc in two ways--we may oxidize
it, as we have just seen, in the voltaic battery, and we shall find
that by the combustion of a kilogramme of zinc a definite amount of
heat is produced. Or we may oxidize our zinc by dissolving it in acid
in a single vessel, when, without going through the intermediate
process of a current, we shall get just as much heat out of a
kilogramme of zinc as we did in the former case. In fact, whether we
oxidize our zinc by the battery, or in the ordinary way, the quantity
of heat produced will always bear the same relation to the quantity of
zinc consumed; the only difference being that, in the ordinary way of
oxidizing zinc, the heat is generated in the vessel containing the zinc
and acid, while in the battery it may make its appearance a thousand
miles away, if we have a sufficiently long wire to convey our current.

176. This is, perhaps, the right place for alluding to a discovery
of Peltier, that a current of positive electricity passing across a
junction of bismuth and antimony in the direction from the bismuth to
the antimony appears to produce cold.

[Illustration: Fig. 14.]

To understand the significance of this fact we must consider it in
connection with the thermo-electric current, which we have seen, from
Art. 161, is established in a circuit of bismuth and antimony, of
which one junction is hotter than the other. Suppose we have a circuit
of this kind with both its junctions at the temperature of 100° C.
to begin with. Suppose, next, that while we protect one junction, we
expose the other to the open air--it will, of course, lose heat, so
that the protected junction will now be hotter than the other. The
consequence will be (Art. 161) that a current of positive electricity
will pass along the protected junction from the bismuth to the
antimony.

Now, here we have an apparent anomaly, for the circuit is cooling--that
is to say, it is losing energy--but at the very same time it is
manifesting energy in another shape, namely, in that of an electric
current, which is circulating round it. Clearly, then, some of the heat
of this circuit must be spent in generating this current; in fact,
we should expect the circuit to act as a heat engine, only producing
current energy instead of mechanical energy, and hence (Art. 152)
we should expect to see a conveyance of heat from the hotter to the
colder parts of the circuit. Now, this is precisely what the current
does, for, passing along the hotter junction, in the direction of the
arrow-head, it cools that junction, and heats the colder one at C,--in
other words, it carries heat from the hotter to the colder parts of the
circuit. We should have been very much surprised had such a current
cooled C and heated H, for then we should have had a manifestation of
current energy, accompanied with the conveyance of heat from a colder
to a hotter substance, which is against the principle of Art. 152.

177. Finally, the energy of electricity in motion is converted into
that of _chemical separation_, when a current of electricity is made to
decompose a body. Part of the energy of the current is spent in this
process, and we shall get so much less heat from it in consequence.
Suppose, for instance, that by oxidizing so much zinc in the battery we
get, under ordinary circumstances, 100 units of heat. Let us, however,
set the battery to decompose water, and we shall probably find that by
oxidizing the same amount of zinc we get now only 80 units of heat.
Clearly, then, the deficiency or 20 units have gone to decompose the
water. Now, if we explode the mixed gases which are the result of the
decomposition, we shall get back these 20 units of heat precisely, and
neither more nor less; and thus we see that amid all such changes the
quantity of energy remains the same.


_Radiant Energy._

178. This form of energy is converted into _absorbed heat_ whenever
it falls upon an opaque substance--some of it, however, is generally
conveyed away by reflexion, but the remainder is absorbed by the body,
and consequently heats it.

It is a curious question to ask what becomes of the radiant light from
the sun that is not absorbed either by the planets of our system, or by
any of the stars. We can only reply to such a question, that _as far as
we can judge from our present knowledge_, the radiant energy that is
not absorbed must be conceived to be traversing space at the rate of
188,000 miles a second.

179. There is only one more transmutation of radiant energy that we
know of, and that is when it promotes _chemical separation_. Thus,
certain rays of the sun are known to have the power of decomposing
chloride of silver, and other chemical compounds. Now, in all such
cases there is a transmutation of radiant energy into that of chemical
separation. The sun’s rays, too, decompose carbonic acid in the leaves
of plants, the carbon going to form the woody fibre of the plant, while
the oxygen is set free into the air; and of course a certain proportion
of the energy of the solar rays is consumed in promoting this change,
and we have so much less heating effect in consequence.

But all the solar rays have not this power--for the property of
promoting chemical change is confined to the blue and violet rays,
and some others which are not visible to the eye. Now, these rays are
entirely absent from the radiation of bodies at a comparatively low
temperature, such as an ordinary red heat, so that a photographer would
find it impossible to obtain the picture of a red-hot body, whose only
light was in itself.

180. The actinic, or chemically active, rays of the sun decompose
carbonic acid in the leaves of plants, and they disappear in
consequence, or are absorbed; this may, therefore, be the reason why
very few such rays are either reflected or transmitted from a sun-lit
leaf, in consequence of which the photographer finds it difficult to
obtain an image of such a leaf; in other words, the rays which would
have produced a chemical change on his photographic plate have all been
used up by the leaf for peculiar purposes of its own.

181. And here it is important to bear in mind that while animals in
the act of breathing consume the oxygen of the air, turning it into
carbonic acid, plants, on the other hand, restore the oxygen to the
air; thus the two kingdoms, the animal and the vegetable, work into
each other’s hands, and the purity of the atmosphere is kept up.


FOOTNOTES:

[4] This explanation was first given by Professors Thomson and Tait
in their Natural Philosophy, and by Dr. Frankland in a lecture at the
Royal Institution of London.

[5] _See_ De La Rue, Stewart, and Loewy’s researches on Solar Physics.

[6] _See_ the Magnetic Researches of Sir E. Sabine, also C. Meldrum on
the Periodicity of Cyclones.




CHAPTER V.

_HISTORICAL SKETCH: THE DISSIPATION OF ENERGY._


182. In the last chapter we have endeavoured to exhibit the various
transmutations of energy, and, while doing so, to bring forward
evidence in favour of the theory of conservation, showing that it
enables us to couple together known laws, and also to discover new
ones--showing, in fine, that it bears about with it all the marks of a
true hypothesis.

It may now, perhaps, be instructive, to look back and endeavour to
trace the progress of this great conception, from its first beginning
among the ancients, up to its triumphant establishment by the labours
of Joule and his fellow-workers.

183. Mathematicians inform us that if matter consists of atoms or
small parts, which are actuated by forces depending only upon the
distances between these parts, and not upon the velocity, then it may
be demonstrated that the law of conservation of energy will hold good.
Thus we see that conceptions regarding atoms and their forces are
allied to conceptions regarding energy. A medium of some sort pervading
space seems also necessary to our theory. In fine, a universe composed
of atoms, with some sort of medium between them, is to be regarded as
the machine, and the laws of energy as the laws of working of this
machine. It may be that a theory of atoms of this sort, with a medium
between them, is not after all the simplest, but we are probably not
yet prepared for any more general hypothesis. Now, we have only to
look to our own solar system, in order to see on a large scale an
illustration of this conception, for there we have the various heavenly
bodies attracting one another, with forces depending only on the
distances between them, and independent of the velocities; and we have
likewise a medium of some sort, in virtue of which radiant energy is
conveyed from the sun to the earth. Perhaps we shall not greatly err
if we regard a molecule as representing on a small scale something
analogous to the solar system, while the various atoms which constitute
the molecule may be likened to the various bodies of the solar system.
The short historical sketch which we are about to give will embrace,
therefore, along with energy, the progress of thought and speculation
with respect to atoms and also with respect to a medium, inasmuch as
these subjects are intimately connected with the doctrines of energy.


_Heraclitus on Energy._

184. Heraclitus, who flourished at Ephesus, B.C. 500, declared that
fire was the great cause, and that all things were in a perpetual
flux. Such an expression will no doubt be regarded as very vague in
these days of precise physical statements; and yet it seems clear that
Heraclitus must have had a vivid conception of the innate restlessness
and energy of the universe, a conception allied in character to, and
only less precise than that of modern philosophers, who regard matter
as essentially dynamical.


_Democritus on Atoms._

185. Democritus, who was born 470 B.C., was the originator of the
doctrine of atoms, a doctrine which in the hands of John Dalton
has enabled the human mind to lay hold of the laws which regulate
chemical changes, as well as to picture to itself what is there taking
place. Perhaps there is no doctrine that has nowadays a more intimate
connection with the industries of life than this of atoms, and it
is probable that no intelligent director of chemical industry among
civilized nations fails to picture to his own mind, by means of this
doctrine, the inner nature of the changes which he sees with his eyes.
Now, it is a curious circumstance that Bacon should have lighted upon
this very doctrine of atoms, in order to point one of his philosophical
morals.

 “Nor is it less an evil” (says he), “that in their philosophies and
 contemplations men spend their labour in investigating and treating of
 the first principles of things, and the extreme limits of nature, when
 all that is useful and of avail in operation is to be found in what is
 intermediate. Hence it happens that men continue to abstract Nature
 till they arrive at potential and unformed matter; and again they
 continue to divide Nature, until they have arrived at the atom; things
 which, even if true, can be of little use in helping on the fortunes
 of men.”

Surely we ought to learn a lesson from these remarks of the great
Father of experimental science, and be very cautious before we dismiss
any branch of knowledge or train of thought as essentially unprofitable.


_Aristotle on a Medium._

186. As regards the existence of a medium, it is remarked by Whewell
that the ancients also caught a glimpse of the idea of a medium, by
which the qualities of bodies, as colours and sounds are perceived, and
he quotes the following from Aristotle:--

 “In a void there could be no difference of up and down; for, as in
 nothing there are no differences, so there are none in a privation or
 negation.”

Upon this the historian of science remarks, “It is easily seen that
such a mode of reasoning elevates the familiar forms of language, and
the intellectual connexions of terms, to a supremacy over facts.”

Nevertheless, may it not be replied that our conceptions of matter are
deduced from the familiar experience, that certain portions of space
affect us in a certain manner; and, consequently, are we not entitled
to say there must be something where we experience the difference of
up or down? Is there, after all, a very great difference between this
argument and that of modern physicists in favour of a plenum, who tell
us that matter cannot act where it is not?

Aristotle seems also to have entertained the idea that light is not any
body, or the emanation of any body (for that, he says, would be a kind
of body), and that therefore light is an energy or act.


_The Ideas of the Ancients were not Prolific._

187. These quotations render it evident that the ancients had, in some
way, grasped the idea of the essential unrest and energy of things.
They had also the idea of small particles or atoms, and, finally, of a
medium of some sort. And yet these ideas were not prolific--they gave
rise to nothing new.

Now, while the historian of science is unquestionably right in his
criticism of the ancients, that their ideas were not distinct and
appropriate to the facts, yet we have seen that they were not wholly
ignorant of the most profound and deeply-seated principles of the
material universe. In the great hymn chanted by Nature, the fundamental
notes were early heard, but yet it required long centuries of patient
waiting for the practised ear of the skilled musician to appreciate
the mighty harmony aright. Or, perhaps, the attempts of the ancients
were as the sketches of a child who just contrives to exhibit, in a
rude way, the leading outlines of a building; while the conceptions
of the practised physicist are more allied to those of the architect,
or, at least, of one who has realized, to some extent, the architect’s
views.

188. The ancients possessed great genius and intellectual power, but
they were deficient in physical conceptions, and, in consequence,
their ideas were not prolific. It cannot indeed be said that we of the
present age are deficient in such conceptions; nevertheless, it may be
questioned whether there is not a tendency to rush into the opposite
extreme, and to work physical conceptions to an excess. Let us be
cautious that in avoiding Scylla, we do not rush into Charybdis. For
the universe has more than one point of view, and there are possibly
regions which will not yield their treasures to the most determined
physicists, armed only with kilogrammes and metres and standard clocks.


_Descartes, Newton, and Huyghens on a Medium._

189. In modern times Descartes, author of the vertical hypothesis,
necessarily presupposed the existence of a medium in inter-planetary
spaces, but on the other hand he was one of the originators of that
idea which regards light as a series of particles shot out from a
luminous body. Newton likewise conceived the existence of a medium,
although he became an advocate of the theory of emission. It is
to Huyghens that the credit belongs of having first conceived the
undulatory theory of light with sufficient distinctness to account for
double refraction. After him, Young, Fresnel, and their followers,
have greatly developed the theory, enabling it to account for the most
complicated and wonderful phenomena.


_Bacon on Heat._

190. With regard to the nature of heat, Bacon, whatever may be thought
of his arguments, seems clearly to have recognized it as a species
of motion. He says, “From these instances, viewed together and
individually, the nature of which heat is the limitation seems to be
motion;” and again he says, “But when we say of motion that it stands
in the place of a genus to heat, we mean to convey, not that _heat_
generates _motion_ or _motion heat_ (although even both may be true in
some cases), but that essential heat is motion and nothing else.”

Nevertheless it required nearly three centuries before the true theory
of heat was sufficiently rooted to develop into a productive hypothesis.


_Principle of Virtual Velocities._

191. In a previous chapter we have already detailed the labours in
respect of heat of Davy, Rumford, and Joule. Galileo and Newton, if
they, did not grasp the dynamical nature of heat, had yet a clear
conception of the functions of a machine. The former saw that what we
gain in power we lose in space; while the latter went further, and saw
that a machine, if left to itself, is strictly limited in the amount of
work which it can accomplish, although its energy may vary from that of
motion to that of position, and back again, according to the geometric
laws of the machine.


_Rise of true Conceptions regarding Work._

192. There can, we think, be no question that the great development
of industrial operations in the present age has indirectly furthered
our conceptions regarding work. Humanity invariably strives to escape
as much as possible from hard work. In the days of old those who had
the power got slaves to work for them; but even then the master had
to give some kind of equivalent for the work done. For at the very
lowest a slave is a machine, and must be fed, and is moreover apt to
prove a very troublesome machine if not properly dealt with. The great
improvements in the steam engine, introduced by Watt, have done as
much, perhaps, as the abolition of slavery to benefit the working man.
The hard work of the world has been put upon iron shoulders, that do
not smart; and, in consequence, we have had an immense extension of
industry, and a great amelioration in the position of the lower classes
of mankind. But if we have transferred our hard work to machines, it is
necessary to know how to question a machine--how to say to it, At what
rate can you labour? how much work can you turn out in a day? It is
necessary, in fact, to have the clearest possible idea of what work is.

Our readers will see from all this that men are not likely to err in
their method of measuring work. The principles of measurement have
been stamped as it were with a brand into the very heart and brain of
humanity. To the employer of machinery or of human labour, a false
method of measuring work simply means ruin; he is likely, therefore,
to take the greatest possible pains to arrive at accuracy in his
determination.


_Perpetual Motion._

193. Now, amid the crowd of workers smarting from the curse of labour,
there rises up every now and then an enthusiast, who seeks to escape
by means of an artifice from this insupportable tyranny of work.
Why not construct a machine that will go on giving you work without
limit without the necessity of being fed in any way. Nature must
have some weak point in her armour; there must surely be some way
of getting round her; she is only tyrannous on the surface, and in
order to stimulate our ingenuity, but will yield with pleasure to the
persistence of genius.

Now, what can the man of science say to such an enthusiast? He cannot
tell him that he is intimately acquainted with all the forces of
Nature, and can prove that perpetual motion is impossible; for, in
truth, he knows very little of these forces. But he does think that
he has entered into the spirit and design of Nature, and therefore he
denies at once the possibility of such a machine. But he denies it
intelligently, and works out this denial of his into a theory which
enables him to discover numerous and valuable relations between the
properties of matter--produces, in fact, the laws of energy and the
great principle of conservation.


_Theory of Conservation._

194. We have thus endeavoured to give a short sketch of the history of
energy, including its allied problems, up to the dawn of the strictly
scientific period. We have seen that the unfruitfulness of the earlier
views was due to a want of scientific clearness in the conceptions
entertained, and we have now to say a few words regarding the theory of
conservation.

Here also the way was pointed out by two philosophers, namely, Grove
in this country, and Mayer on the continent, who showed certain
relations between the various forms of energy; the name of Séguin
ought likewise to be mentioned. Nevertheless, to Joule belongs the
honour of establishing the theory on an incontrovertible basis: for,
indeed, this is preeminently a case where speculation has to be tested
by unimpeachable experimental evidence. Here the magnitude of the
principle is so vast, and its importance is so great, that it requires
the strong fire of genius, joined to the patient labours of the
scientific experimentalist, to forge the rough ore into a good weapon
that will cleave its way through all obstacles into the very citadel of
Nature, and into her most secret recesses.

Following closely upon the labours of Joule, we have those of William
and James Thomson, Helmholtz, Rankine, Clausius, Tait, Andrews,
Maxwell, who, along with many others, have advanced the subject; and
while Joule gave his chief attention to the laws which regulate the
transmutation of mechanical energy into heat, Thomson, Rankine, and
Clausius gave theirs to the converse problem, or that which relates to
the transmutation of heat into mechanical energy. Thomson, especially,
has pushed forward so resolutely from this point of view that he has
succeeded in grasping a principle scarcely inferior in importance to
that of the conservation of energy itself, and of this principle it
behoves us now to speak.


_Dissipation of Energy._

195. Joule, we have said, proved the law according to which work may
be changed into heat; and Thomson and others, that according to which
heat may be changed into work. Now, it occurred to Thomson that there
was a very important and significant difference between these two laws,
consisting in the fact that, while you can with the greatest ease
transform work into heat, you can by no method in your power transform
all the heat back again into work. In fact, the process is not a
reversible one; and the consequence is that the mechanical energy of
the universe is becoming every day more and more changed into heat.

It is easily seen that if the process were reversible, one form of a
perpetual motion would not be impossible. For, without attempting to
create energy by a machine, all that would be needed for a perpetual
motion would be the means of utilizing the vast stores of heat that
lie in all the substances around us, and converting them into work.
The work would no doubt, by means of friction and otherwise, be
ultimately reconverted into heat; but if the process be reversible, the
heat could again be converted into work, and so on for ever. But the
irreversibility of the process puts a stop to all this. In fact, I may
convince myself by rubbing a metal button on a piece of wood how easily
work can be converted into heat, while the mind completely fails to
suggest any method by which this heat can be reconverted into work.

Now, if this process goes on, and always in one direction, there can be
no doubt about the issue. The mechanical energy of the universe will
be more and more transformed into universally diffused heat, until the
universe will no longer be a fit abode for living beings.

The conclusion is a startling one, and, in order to bring it more
vividly before our readers, let us now proceed to acquaint ourselves
with the various forms of useful energy that are at present at our
disposal, and at the same time endeavour to trace the ultimate sources
of these supplies.


_Natural Energies and their Sources._

196. Of energy in repose we have the following varieties:--(1.) The
energy of fuel. (2.) That of food. (3.) That of a head of water. (4.)
That which may be derived from the tides. (5.) The energy of chemical
separation implied in native sulphur, native iron, &c.

Then, with regard to energy in action, we have mainly the following
varieties:--

(1.) The energy of air in motion. (2.) That of water in motion.


_Fuel._

197. Let us begin first with the energy implied in fuel. We can, of
course, burn fuel, or cause it to combine with the oxygen of the air;
and we are thereby provided with large quantities of heat of high
temperature, by means of which we may not only warm ourselves and cook
our food, but also drive our heat-engines, using it, in fact, as a
source of mechanical power.

Fuel is of two varieties--wood and coal. Now, if we consider the origin
of these we shall see that they are produced by the sun’s rays. Certain
of these rays, as we have already remarked (Art. 180), decompose
carbonic acid in the leaves of plants, setting free the oxygen, while
the carbon is used for the structure or wood of the plant. Now, the
energy of these rays is spent in this process, and, indeed, there
is not enough of such energy left to produce a good photographic
impression of the leaf of a plant, because it is all spent in making
wood.

We thus see that the energy implied in wood is derived from the sun’s
rays, and the same remark applies to coal. Indeed, the only difference
between wood and coal is one of age: wood being recently turned out
from Nature’s laboratory, while thousands of years have elapsed since
coal formed the leaves of living plants.

198. We are, therefore, perfectly justified in saying that the energy
of fuel is derived from the sun’s rays;[7] coal being the store which
Nature has laid up as a species of capital for us, while wood is our
precarious yearly income.

We are thus at present very much in the position of a young heir, who
has only recently come into his estate, and who, not content with the
income, is rapidly squandering his realized property. This subject has
been forcibly brought before us by Professor Jevons, who has remarked
that not only are we spending our capital, but we are spending the most
available and valuable part of it. For we are now using the surface
coal; but a time will come when this will be exhausted, and we shall be
compelled to go deep down for our supplies. Now, regarded as a source
of energy, such supplies, if far down, will be less effective, for we
have to deduct the amount of energy requisite in order to bring them to
the surface. The result is that we must contemplate a time, however far
distant, when our supplies of coal will be exhausted, and we shall be
compelled to resort to other sources of energy.


_Food._

199. The energy of food is analogous to that of fuel, and serves
similar purposes. For just as fuel may be used either for producing
heat or for doing work, so food has a twofold office to perform. In
the first place, by its gradual oxidation, it keeps up the temperature
of the body; and in the next place it is used as a source of energy,
on which to draw for the performance of work. Thus a man or a horse
that works a great deal requires to eat more food than if he does not
work at all. Thus, also, a prisoner condemned to hard labour requires
a better diet than one who does not work, and a soldier during the
fatigues of war finds it necessary to eat more than during a time of
peace.

Our food may be either of animal or vegetable origin--if it be the
latter, it is immediately derived, like fuel, from the energy of the
sun’s rays; but if it be the former, the only difference is that it has
passed through the body of an animal before coming to us: the animal
has eaten grass, and we have eaten the animal.

In fact, we make use of the animal not only as a variety of nutritious
food, but also to enable us indirectly to utilize those vegetable
products, such as grasses, which we could not make use of directly with
our present digestive organs.


_Head of Water._

200. The energy of a head of water, like that of fuel and food, is
brought about by the sun’s rays. For the sun vaporizes the water,
which, condensed again in upland districts, becomes available as a head
of water.

There is, however, the difference that fuel and food are due to the
actinic power of the sun’s rays, while the evaporation and condensation
of water are caused rather by their heating effect.


_Tidal Energy._

201. The energy derived from the tides has, however, a different
origin. In Art. 133 we have endeavoured to show how the moon acts upon
the fluid portions of our globe, the result of this action being a very
gradual stoppage of the energy of rotation of the earth.

It is, therefore, to this motion of rotation that we must look as the
origin of any available energy derived from tidal mills.


_Native Sulphur, &c._

202. The last variety of available energy of position in our list is
that implied in native sulphur, native iron, &c. It has been remarked
by Professor Tait, to whom this method of reviewing our forces is due,
that this may be the primeval form of energy, and that the interior of
the earth may, as far as we know, be wholly composed of matter in its
uncombined form. As a source of available energy it is, however, of no
practical importance.


_Air and Water in Motion._

203. We proceed next to those varieties of available energy which
represent motion, the chief of which are air in motion and water in
motion. It is owing to the former that the mariner spreads his sail,
and carries his vessel from one part of the earth’s surface to another,
and it is likewise owing to the same influence that the windmill grinds
our corn. Again, water in motion is used perhaps even more frequently
than air in motion as a source of motive power.

Both these varieties of energy are due without doubt to the heating
effect of the sun’s rays. We may, therefore, affirm that with the
exception of the totally insignificant supply of native sulphur, &c.,
and the small number of tidal mills which may be in operation, all our
available energy is due to the sun.


_The Sun--a Source of High Temperature Heat._

204. Let us, therefore, now for a moment direct our attention to that
most wonderful source of energy, the Sun.

We have here a vast reservoir of high temperature heat; now, this
is a kind of superior energy which has always been in much request.
Numberless attempts have been made to construct a perpetual light,
just as similar attempts have been made to construct a perpetual
motion, with this difference, that a perpetual light was supposed to
result from magical powers, while a perpetual motion was attributed to
mechanical skill.

Sir Walter Scott alludes to this belief in his description of the grave
of Michael Scott, which is made to contain a perpetual light. Thus the
Monk who buried the wizard tells William of Deloraine--

  “Lo, Warrior! now the Cross of Red
  Points to the Grave of the mighty dead;
  Within it burns a wondrous light,
  To chase the spirits that love the night.
  That lamp shall burn unquenchably
  Until the eternal doom shall be.”

And again, when the tomb was opened, we read--

  “I would you had been there to see
  How the light broke forth so gloriously,
  Stream’d upward to the chancel roof,
  And through the galleries far aloof!
  No earthly flame blazed e’er so bright.”

No earthly flame--there the poet was right--certainly not of this
earth, where light and all other forms of superior energy are
essentially evanescent.


_A Perpetual Light Impossible._

205. In truth, our readers will at once perceive that a perpetual light
is only another name for a perpetual motion, because we can always
derive visible energy out of high temperature heat--indeed, we do so
every day in our steam engines.

When, therefore, we burn coal, and cause it to combine with the
oxygen of the air, we derive from the process a large amount of high
temperature heat. But is it not possible, our readers may ask, to
take the carbonic acid which results from the combustion, and by
means of low temperature heat, of which we have always abundance
at our disposal, change it back again into carbon and oxygen? All
this would be possible if what may be termed the temperature of
disassociation--that is to say, the temperature at which carbonic acid
separates into its constituents--were a low temperature, and it would
also be possible if rays from a source of low temperature possessed
sufficient actinic power to decompose carbonic acid.

But neither of these is the case. Nature will not be caught in a
trap of this kind. As if for the very purpose of stopping all such
speculations, the temperatures of disassociation for such substances as
carbonic acid are very high, and the actinic rays capable of causing
their decomposition belong only to sources of exceedingly high
temperature, such as the sun.[8]


_Is the Sun an Exception?_

206. We may, therefore, take it for granted that a perpetual light,
like a perpetual motion, is an impossibility; and we have then to
inquire if the same argument applies to our sun, or if an exception
is to be made in his favour. Does the sun stand upon a footing of his
own, or is it merely a question of time with him, as with all other
instances of high temperature heat? Before attempting to answer this
question let us inquire into the probable origin of the sun’s heat.


_Origin of the Sun’s Heat._

207. Now, some might be disposed to cut the Gordian knot of such an
inquiry by asserting that our luminary was at first created hot; yet
the scientific mind finds itself disinclined to repose upon such an
assertion. We pick up a round pebble from the beach, and at once
acknowledge there has been some physical cause for the shape into which
it has been worn. And so with regard to the heat of the sun, we must
ask ourselves if there be not some cause not wholly imaginary, but one
which we know, or at least suspect, to be perhaps still in operation,
which can account for the heat of the sun.

Now, here it is more easy to show what cannot account for the sun’s
heat than what can do so. We may, for instance, be perfectly certain
that it cannot have been caused by chemical action. The most probable
theory is that which was first worked out by Helmholtz and Thomson;[9]
and which attributes the heat of the sun to the primeval energy of
position possessed by its particles. In other words, it is supposed
that these particles originally existed at a great distance from each
other, and that, being endowed with the force of gravitation, they have
since gradually come together, while in this process heat has been
generated just as it would be if a stone were dropped from the top of a
cliff towards the earth.

208. Nor is this case wholly imaginary, but we have some reason
for thinking that it may still be in operation in the case of
certain nebulæ which, both in their constitution as revealed by the
spectroscope, and in their general appearance, impress the beholder
with the idea that they are not yet fully condensed into their ultimate
shape and size.

If we allow that by this means our luminary has obtained his wonderful
store of high-class energy, we have yet to inquire to what extent this
operation is going on at the present moment. Is it only a thing of the
past, or is it a thing also of the present? I think we may reply that
the sun cannot be condensing very fast, at least, within historical
times. For if the sun were sensibly larger than at present his total
eclipse by the moon would be impossible. Now, such eclipses have
taken place, at any rate, for several thousands of years. Doubtless a
small army of meteors may be falling into our luminary, which would
by this fall tend to augment his heat; yet the supply derived from
this source must surely be insignificant. But if the sun be not at
present condensing so fast as to derive any sufficient heat from this
process, and if his energy be very sparingly recruited from without,
it necessarily follows that he is in the position of a man whose
expenditure exceeds his income. He is living upon his capital, and is
destined to share the fate of all who act in a similar manner. We must,
therefore, contemplate a future period when he will be poorer in energy
than he is at present, and a period still further in the future when he
will altogether cease to shine.


_Probable Fate of the Universe._

209. If this be the fate of the high temperature energy of the
universe, let us think for a moment what will happen to its visible
energy. We have spoken already about a medium pervading space, the
office of which appears to be to degrade and ultimately extinguish
all differential motion, just as it tends to reduce and ultimately
equalize all difference of temperature. Thus the universe would
ultimately become an equally heated mass, utterly worthless as far as
the production of work is concerned, since such production depends upon
difference of temperature.

Although, therefore, in a strictly mechanical sense, there is a
conservation of energy, yet, as regards usefulness or fitness
for living beings, the energy of the universe is in process of
deterioration. Universally diffused heat forms what we may call the
great waste-heap of the universe, and this is growing larger year by
year. At present it does not sensibly obtrude itself, but who knows
that the time may not arrive when we shall be practically conscious of
its growing bigness?

210. It will be seen that in this chapter we have regarded the
universe, not as a collection of matter, but rather as an energetic
agent--in fact, as a lamp. Now, it has been well pointed out by
Thomson, that looked at in this light, the universe is a system that
had a beginning and must have an end; for a process of degradation
cannot be eternal. If we could view the universe as a candle not lit,
then it is perhaps conceivable to regard it as having been always in
existence; but if we regard it rather as a candle that has been lit,
we become absolutely certain that it cannot have been burning from
eternity, and that a time will come when it will cease to burn. We are
led to look to a beginning in which the particles of matter were in
a diffuse chaotic state, but endowed with the power of gravitation,
and we are led to look to an end in which the whole universe will be
one equally heated inert mass, and from which everything like life or
motion or beauty will have utterly gone away.


FOOTNOTES:

[7] This fact seems to have been known at a comparatively early period
to Herschel and the elder Stephenson.

[8] This remark is due to Sir William Thomson.

[9] Mayer and Waterston seem first to have caught the rudiments of this
idea.




CHAPTER VI.

_THE POSITION OF LIFE._


211. We have hitherto confined ourselves almost entirely to a
discussion of the laws of energy, as these affect inanimate matter,
and have taken little or no account of the position of life. We have
been content very much to remain spectators of the contest, apparently
forgetful that we are at all concerned in the issue. But the conflict
is not one which admits of on-lookers,--it is a universal conflict in
which we must all take our share. It may not, therefore, be amiss if we
endeavour to ascertain, as well as we can, our true position.


_Twofold nature of Equilibrium._

212. One of our earliest mechanical lessons is on the twofold nature
of equilibrium. We are told that this may be of two kinds, _stable_
and _unstable_, and a very good illustration of these two kinds is
furnished by an egg. Let us take a smooth level table, and place an egg
upon it; we all know in what manner the egg will lie on the table.
It will remain at rest, that is to say, it will be in equilibrium;
and not only so, but it will be in stable equilibrium. To prove
this, let us try to displace it with our finger, and we shall find
that when we remove the pressure the egg will speedily return to its
previous position, and will come to rest after one or two oscillations.
Furthermore, it has required a sensible expenditure of energy to
displace the egg. All this we express by saying that the egg is in
stable equilibrium.


_Mechanical Instability._

213. And now let us try to balance the egg upon its longer axis.
Probably, a sufficient amount of care will enable us to achieve this
also. But the operation is a difficult one, and requires great delicacy
of touch, and even after we have succeeded we do not know how long
our success may last. The slightest impulse from without, the merest
breath of air, may be sufficient to overturn the egg, which is now most
evidently in unstable equilibrium. If the egg be thus balanced at the
very edge of the table, it is quite probable that in a few minutes it
may topple over upon the floor; it is what we may call _an even chance_
whether it will do so, or merely fall upon the table. Not that mere
chance has anything to do with it, or that its movements are without
a cause, but we mean that its movements are decided by some external
impulse so exceedingly small as to be utterly beyond our powers of
observation. In fact, before making the trial we have carefully
removed everything like a current of air, or want of level, or external
impulse of any kind, so that when the egg falls we are completely
unable to assign the origin of the impulse that has caused it to do so.

214. Now, if the egg happens to fall over the table upon the floor,
there is a somewhat considerable transmutation of energy; for the
energy of position of the egg, due to the height which it occupied
on the table, has all at once been changed into energy of motion, in
the first place, and into heat in the second, when the egg comes into
contact with the floor.

If, however, the egg happens to fall upon the table, the transmutation
of energy is comparatively small.

It thus appears that it depends upon some external impulse, so
infinitesimally small as to elude our observation, whether the egg
shall fall upon the floor and give rise to a comparatively large
transmutation of energy, or whether it shall fall upon the table and
give rise to a transmutation comparatively small.


_Chemical Instability._

215. We thus see that a body, or system, in unstable equilibrium may
become subject to a very considerable transmutation of energy, arising
out of a very small cause, or antecedent. In the case now mentioned,
the force is that of gravitation, the arrangement being one of visible
mechanical instability. But we may have a substance, or system, in
which the force at work is not gravity, but chemical affinity, and the
substance, or system, may, under certain peculiar conditions, become
_chemically unstable_.

When a substance is chemically unstable, it means that the slightest
impulse of any kind may determine a chemical change, just as in the
case of the egg the slightest impulse from without occasioned a
mechanical displacement.

In fine, a substance, or system, chemically unstable bears a relation
to chemical affinity somewhat similar to that which a mechanically
unstable system bears to gravity. Gunpowder is a familiar instance
of a chemically unstable substance. Here the slightest spark may
prove the precursor of a sudden chemical change, accompanied by the
instantaneous and violent generation of a vast volume of heated gas.
The various explosive compounds, such as gun-cotton, nitro-glycerine,
the fulminates, and many more, are all instances of structures which
are chemically unstable.


_Machines are of two kinds._

216. When we speak of a structure, or a machine, or a system, we simply
mean a number of individual particles associated together in producing
some definite result. Thus, the solar system, a timepiece, a rifle,
are examples of inanimate machines; while an animal, a human being,
an army, are examples of animated structures or machines. Now, such
machines or structures are of two kinds, which differ from one another
not only in the object sought, but also in the means of attaining that
object.

217. In the first place, we have structures or machines in which
systematic action is the object aimed at, and in which all the
arrangements are of a conservative nature, the element of instability
being avoided as much as possible. The solar system, a timepiece,
a steam-engine at work, are examples of such machines, and the
characteristic of all such is their _calculability_. Thus the skilled
astronomer can tell, with the utmost precision, in what place the
moon or the planet Venus will be found this time next year. Or again,
the excellence of a timepiece consists in its various hands pointing
accurately in a certain direction after a certain interval of time. In
like manner we may safely count upon a steamship making so many knots
an hour, at least while the outward conditions remain the same. In all
these cases we make our calculations, and we are not deceived--the end
sought is regularity of action, and the means employed is a stable
arrangement of the forces of nature.

218. Now, the characteristics of the other class of machines are
precisely the reverse.

Here the object aimed at is not a regular, but a sudden and violent
transmutation of energy, while the means employed are unstable
arrangements of natural forces. A rifle at full cock, with a
delicate hair-trigger, is a very good instance of such a machine,
where the slightest touch from without may bring about the explosion
of the gunpowder, and the propulsion of the ball with a very great
velocity. Now, such machines are eminently characterized by their
_incalculability_.

219. To make our meaning clear, let us suppose that two sportsmen
go out hunting together, each with a good rifle and a good pocket
chronometer. After a hard day’s work, the one turns to his companion
and says:--“It is now six o’clock by my watch; we had better rest
ourselves,” upon which the other looks at his watch, and he would be
very much surprised and exceedingly indignant with the maker, if he did
not find it six o’clock also. Their chronometers are evidently in the
same state, and have been doing the same thing; but what about their
rifles? Given the condition of the one rifle, is it possible by any
refinement of calculation to deduce that of the other? We feel at once
that the bare supposition is ridiculous.

220. It is thus apparent that, as regards energy, structures are
of two kinds. In one of these, the object sought is regularity of
action, and the means employed, a stable arrangement of natural
forces: while in the other, the end sought is freedom of action, and a
sudden transmutation of energy, the means employed being an unstable
arrangement of natural forces.

The one set of machines are characterized by their calculability--the
other by their incalculability. The one set, when at work, are not
easily put wrong, while the other set are characterized by great
delicacy of construction.


_An Animal is a delicately-constructed Machine._

221. But perhaps the reader may object to our use of the rifle as an
illustration.

For although it is undoubtedly a delicately-constructed machine, yet
a rifle does not represent the same surpassing delicacy as that, for
instance, which characterizes an egg balanced on its longer axis. Even
if at full cock, and with a hair trigger, we may be perfectly certain
it will not go off of its own accord. Although its object is to produce
a sudden and violent transmutation of energy, yet this requires to be
preceded by the application of an amount of energy, however small, to
the trigger, and if this be not spent upon the rifle, it will not go
off. There is, no doubt, delicacy of construction, but this has not
risen to the height of incalculability, and it is only when in the
hands of the sportsman that it becomes a machine upon the condition of
which we cannot calculate.

Now, in making this remark, we define the position of the sportsman
himself in the Universe of Energy.

The rifle is delicately constructed, but not surpassingly so; but
sportsman and rifle, together, form a machine of surpassing delicacy,
_ergo_ the sportsman himself is such a machine. We thus begin to
perceive that a human being, or indeed an animal of any kind, is
in truth a machine of a delicacy that is practically infinite, the
condition or motions of which we are utterly unable to predict.

In truth, is there not a transparent absurdity in the very thought that
a man may become able to calculate his own movements, or even those of
his fellow?


_Life is like the Commander of an Army._

222. Let us now introduce another analogy--let us suppose that a war
is being carried on by a vast army, at the head of which there is a
very great commander. Now, this commander knows too well to expose
his person; in truth, he is never seen by any of his subordinates. He
remains at work in a well-guarded room, from which telegraphic wires
lead to the headquarters of the various divisions. He can thus, by
means of these wires, transmit his orders to the generals of these
divisions, and by the same means receive back information as to the
condition of each.

Thus his headquarters become a centre, into which all information is
poured, and out of which all commands are issued.

Now, that mysterious thing called life, about the nature of which we
know so little, is probably not unlike such a commander. Life is not
a bully, who swaggers out into the open universe, upsetting the laws
of energy in all directions, but rather a consummate strategist, who,
sitting in his secret chamber, before his wires, directs the movements
of a great army.[10]

223. Let us next suppose that our imaginary army is in rapid march, and
let us try to find out the cause of this movement. We find that, in the
first place, orders to march have been issued to the troops under them
by the commanders of each regiment. In the next place, we learn that
staff officers, attached to the generals of the various divisions, have
conveyed these orders to the regimental commanders; and, finally, we
learn that the order to march has been telegraphed from headquarters to
these various generals.

Descending now to ourselves, it is probably somewhere in the mysterious
and well-guarded brain-chamber that the delicate directive touch is
given which determines our movements. This chamber forms, as it were,
the headquarters of the general in command, who is so well withdrawn as
to be absolutely invisible to all his subordinates.

224. Joule, Carpenter, and Mayer were at an early period aware of the
restrictions under which animals are placed by the laws of energy,
and in virtue of which the power of an animal, as far as energy is
concerned, is not creative, but only directive. It was seen that, in
order to do work, an animal must be fed; and, even at a still earlier
period, Count Rumford remarked that a ton of hay will be administered
more economically by feeding a horse with it, and then getting work out
of the horse, than by burning it as fuel in an engine.

225. In this chapter, the same line of thought has been carried
out a little further. We have seen that life is associated with
delicately-constructed machines, so that whenever a transmutation of
energy is brought about by a living being, could we trace the event
back, we should find that the physical antecedent was probably a much
less transmutation, while again the antecedent of this would probably
be found still less, and so on, as far as we could trace it.

226. But with all this, we do not pretend to have discovered the true
nature of life itself, or even the true nature of its relation to the
material universe.

What we have ventured is the assertion that, as far as we can judge,
life is always associated with machinery of a certain kind, in virtue
of which an extremely delicate directive touch is ultimately magnified
into a very considerable transmutation of energy. Indeed, we can hardly
imagine the freedom of motion implied in life to exist apart from
machinery possessed of very great delicacy of construction.

In fine, we have not succeeded in solving the problem as to the true
nature of life, but have only driven the difficulty into a borderland
of thick darkness, into which the light of knowledge has not yet been
able to penetrate.


_Organized Tissues are subject to Decay._

227. We have thus learned two things, for, in the first place, we
have learned that life is associated with delicacy of construction,
and in the next (Art. 220), that delicacy of construction implies
an unstable arrangement of natural forces. We have now to remark
that the particular force which is thus used by living beings is
chemical affinity. Our bodies are, in truth, examples of an unstable
arrangement of chemical forces, and the materials which composed them,
if not liable to sudden explosion, like fulminating powder, are yet
preeminently the subjects of decay.

228. Now, this is more than a mere general statement; it is a truth
that admits of degrees, and in virtue of which those parts of our
bodies which have, during life, the noblest and most delicate office to
perform, are the very first to perish when life is extinct.

  “Oh! o’er the eye death most exerts his might,
  And hurls the spirit from her throne of light;
  Sinks those blue orbs in their long last eclipse,
  But spares us yet the charm around the lips.”

So speaks the poet, and we have here an aspect of things in which the
lament of the poet becomes the true interpretation of nature.


_Difference between Animals and Inanimate Machines._

229. We are now able to recognize the difference between the relations
to energy of a living being, such as man, and a machine, such as a
steam-engine.

There are many points in common between the two. Both require to be
fed, and in both there is the transmutation of the energy of chemical
separation implied in fuel and food into that of heat and visible
motion.

But while the one--the engine--requires for its maintenance only
carbon, or some other variety of chemical separation, the other--the
living being--demands to be supplied with organized tissue. In fact,
that delicacy of construction which is so essential to our well-being,
is not something which we can elaborate internally in our own
frames--all that we can do is to appropriate and assimilate that which
comes to us from without; it is already present in the food which we
eat.


_Ultimate Dependence of Life upon the Sun._

230. We have already (Art. 203) been led to recognize the sun as the
ultimate material source of all the energy which we possess, and we
must now regard him as the source likewise of all our delicacy of
construction. It requires the energy of his high temperature rays so to
wield and manipulate the powerful forces of chemical affinity; so to
balance these various forces against each other, as to produce in the
vegetable something which will afford our frames, not only energy, but
also delicacy of construction.

Low temperature heat would be utterly unable to accomplish this; it
consists of ethereal vibrations which are not sufficiently rapid, and
of waves that are not sufficiently short, for the purpose of shaking
asunder the constituents of compound molecules.

231. It thus appears that animals are, in more ways than one,
pensioners upon the sun’s bounty; and those instances, which at first
sight appear to be exceptions, will, if studied sufficiently, only
serve to confirm the rule.

Thus the recent researches of Dr. Carpenter and Professor Wyville
Thomson have disclosed to us the existence of minute living beings in
the deepest parts of the ocean, into which we may be almost sure no
solar ray can penetrate. How, then, do these minute creatures obtain
that energy and delicacy of construction without which they cannot
live? in other words, how are they fed?

Now, the same naturalists who discovered the existence of these
creatures, have recently furnished us with a very probable explanation
of the mystery. They think it highly probable that the whole ocean
contains in it organic matter to a very small but yet perceptible
extent, forming, as they express it, a sort of diluted soup, which thus
becomes the food of these minute creatures.

232. In conclusion, we are dependent upon the sun and centre of our
system, not only for the mere energy of our frames, but also for our
delicacy of construction--the future of our race depends upon the sun’s
future. But we have seen that the sun must have had a beginning, and
that he will have an end.

We are thus induced to generalize still further, and regard, not only
our own system, but the whole material universe when viewed with
respect to serviceable energy, as essentially evanescent, and as
embracing a succession of physical events which cannot go on for ever
as they are.

But here at length we come to matters beyond our grasp; for physical
science cannot inform us what must have been before the beginning, nor
yet can it tell us what will take place after the end.


FOOTNOTES:

[10] _See_ an article on “The Position of Life,” by the author of this
work, in conjunction with Mr. J. N. Lockyer, “Macmillan’s Magazine,”
September, 1868; also a lecture on “The Recent Developments of Cosmical
Physics,” by the author of this work.




  APPENDIX.

  CORRELATION OF VITAL WITH CHEMICAL AND
  PHYSICAL FORCES.

  BY JOSEPH LE CONTE,

  PROFESSOR OF GEOLOGY AND NATURAL HISTORY IN THE
  UNIVERSITY OF CALIFORNIA.




CORRELATION OF VITAL WITH CHEMICAL AND PHYSICAL FORCES.


Vital force; whence is it derived? What is its relation to the other
forces of Nature? The answer of modern science to these questions is:
It is derived from the lower forces of Nature; it is related to other
forces much as these are related to each other--it is correlated with
chemical and physical forces.

At one time matter was supposed to be destructible. By combustion or
by evaporation matter seemed to be consumed--to pass out of existence;
but now we know it only changes its form from the solid or liquid to
the gaseous condition--from the visible to the invisible--and that,
amid all these changes, the same quantity of matter remains. Creation
or destruction of matter, increase or diminution of matter, lies beyond
the domain of Science; her domain is confined entirely to the changes
of matter. Now, it is the doctrine of modern science that the same is
true of force. Force seems often to be annihilated. Two cannon-balls
of equal size and velocity meet each other and fall motionless. The
immense energy of these moving bodies seems to pass out of existence.
But not so; it is changed into heat, and the exact amount of heat may
be calculated; moreover, an equal amount of heat may be changed back
again into an equal amount of momentum. Here, therefore, force is not
lost, but is changed from a visible to an invisible form. Motion is
changed from bodily motion into molecular motion. Thus heat, light,
electricity, magnetism, chemical affinity, and mechanical force, are
transmutable into each other, back and forth; but, amid all these
changes, the amount of force remains unchanged. Force is incapable of
destruction, except by the same power which created it. The domain
of Science lies within the limits of these changes--creation and
annihilation lie outside of her domain.

The mutual convertibility of forces into each other is called
_correlation of forces_; the persistence of the same amount, amid all
these protean forms, is called _conservation of force_.[11]

The correlation of physical forces with each other and with chemical
force is now universally acknowledged and somewhat clearly conceived.
The correlation of vital force with these is not universally
acknowledged, and, where acknowledged, is only imperfectly conceived.
In 1859 I published a paper[12] in which I attempted to put the idea of
correlation of vital force with chemical and physical forces in a more
definite and scientific form. The views expressed in that paper have
been generally adopted by physiologists. Since the publication of the
paper referred to, the subject has lain in my mind, and grown at least
somewhat. I propose, therefore, now to reëmbody my views in a more
popular form, with such additions as have occurred to me since.

There are four planes of material existence, which may be represented
as raised one above another. These are: 1. The plane of elementary
existence; 2. The plane of chemical compounds, or mineral kingdom;
3. The plane of vegetable existence; and, 4. The plane of animal
existence. Their relations to each other are truly expressed by writing
them one above the other, thus:

 I may sometimes use the word energy instead. If any one should charge
 me with want of precision in language, my answer is: Our language
 cannot be more precise until our ideas in this department are far
 clearer than now.

  4. _Animal Kingdom._
  3. _Vegetable Kingdom._
  2. _Mineral Kingdom._
  1. _Elements._

Now, it is a remarkable fact that there is a special force, whose
function it is to raise matter from each plane to the plane above,
and to execute movements on the latter. Thus, it is the function
of chemical affinity alone to raise matter from No. 1 to No. 2, as
well as to execute all the movements, back and forth, by action and
reaction; in a word, to produce all the phenomena on No. 2 which
together constitute the science of chemistry. It is the prerogative
of vegetable life-force alone to lift matter from No. 2 to No. 3, as
well as to execute all the movements on that plane, which together
constitute the science of vegetable physiology. It is the prerogative
of animal life-force alone to lift matter from No. 3 to No. 4, and to
preside over the movements on this plane, which together constitute the
science of animal physiology. But there is no force in Nature capable
of raising matter at once from No. 1 to No. 3, or from No. 2 to No. 4,
without stopping and receiving an accession of force, of a different
kind, on the intermediate plane. Plants cannot feed upon elements, but
only on chemical compounds; animals cannot feed on minerals, but only
on vegetables. We shall see in the sequel that this is the necessary
result of the principle of conservation of force in vital phenomena.

It is well known that atoms, in a nascent state--i. e., at the moment
of their separation from previous combination--are endowed with
peculiar and powerful affinity. Oxygen and nitrogen, nitrogen and
hydrogen, hydrogen and carbon, which show no affinity for each other
under ordinary circumstances, readily unite when one or both are in a
nascent condition. The reason seems to be that, when the elements of
a compound are torn asunder, the chemical affinity which previously
bound them together is set free, ready and eager to unite the nascent
elements with whatever they come in contact with. This state of exalted
chemical energy is retained but a little while, because it is liable
to be changed into some other form of force, probably heat, and is
therefore no longer chemical energy. To illustrate by the planes:
matter falling down from No. 2 to No. 1 generates force by which matter
is lifted from No. 1 to No. 2. Decomposition generates the force by
which combination is effected. This principle underlies every thing I
shall further say.

There are, therefore, two ideas or principles underlying this paper:
1. The correlation of vital with physical and chemical forces; 2.
That in all cases _vital force is produced by decomposition_--is
transformed nascent affinity. Neither of these is new. Grove, many
years ago, brought out, in a vague manner, the idea that vital force
was correlated with chemical and physical forces.[13] In 1848 Dr.
Freke, M. R. I. A., of Dublin, first advanced the idea that vital force
of animal life was generated by decomposition. In 1851 the same idea
was brought out again by Dr. Watters, of St. Louis. These papers were
unknown to me when I wrote my article. They have been sent to me in the
last few years by their respective authors. Neither of these authors,
however, extends this principle to vegetation, the most fundamental
and most important phenomenon of life. In 1857 the same idea was again
brought out by Prof. Henry, of the Smithsonian Institution, and by him
extended to vegetation. I do not, therefore, now claim to have first
advanced this idea, but I do claim to have in some measure rescued it
from vagueness, and given it a clearer and more scientific form.

I wish now to apply these principles in the explanation of the most
important phenomena of vegetable and animal life:

1. VEGETATION.--The most important phenomenon in the life-history of
a plant--in fact, the starting-point of all life, both vegetable and
animal--is the formation of organic matter in the leaves. The necessary
conditions for this wonderful change of mineral into organic matter
seem to be, sunlight, chlorophyl, and living protoplasm, or bioplasm.
This is the phenomenon I wish now to discuss.

The plastic matters of which vegetable structure is built are of
two kinds--amyloids and albuminoids. The amyloids, or starch and
sugar groups, consist of C, H, and O; the albuminoids of C, H, O,
N, and a little S and P. The quantity of sulphur and phosphorus is
very small, and we will neglect them in this discussion. The food
out of which these substances are elaborated are, CO₂, H₂O,
and H_{3}N--carbonic acid, water, and ammonia. Now, by the agency of
sunlight in the presence of chlorophyl and bioplasm, these chemical
compounds (CO₂, H₂O, and H_{3}N) are torn asunder, or shaken
asunder, or decomposed; the excess of O, or of O and H, is rejected,
and the remaining elements in a nascent condition combine to form
organic matter. To form the amyloids--starch, dextrine, sugar,
cellulose--only CO₂ and H₂O are decomposed, and excess of O
rejected. To form albuminoids, or protoplasm, CO₂, H₂O, and
H_{3}N, are decomposed, and excess of O and H rejected.

It would seem in this case, therefore, that physical force (light)
is changed into nascent chemical force, and this nascent chemical
force, under the peculiar conditions present, forms organic matter,
and reappears as vital force. Light falling on living green leaves is
destroyed or consumed in doing the work of decomposition; disappears
as light, to reappear as nascent chemical energy; and this in its
turn disappears in forming organic matter, to reappear as the vital
force of the organic matter thus formed. The light which disappears is
proportioned to the O, or the O and H rejected; is proportioned also to
the quantity of organic matter formed, and also to the amount of vital
force resulting. To illustrate: In the case of amyloids, oxygen-excess
falling or running down from plane No. 2 to plane No. 1 generates force
to raise C, H, and O, from plane No. 2 to plane No. 3. In the case of
albuminoids, oxygen-excess and hydrogen-excess running down from No. 2
to No. 1 generate force to raise C, H, O, and N, from No. 2 to No. 3.
To illustrate again: As sun-heat falling upon water disappears as heat,
to reappear as mechanical power, raising the water into the clouds, so
sunlight falling upon green leaves disappears as light, to reappear as
vital force lifting matter from the mineral into the organic kingdom.

2. GERMINATION.--Growing plants, it is seen, take their life-force
from the sun; but seeds germinate and commence to grow in the dark.
Evidently there must be some other source from which they draw their
supply of force. They cannot draw force from the sun. This fact is
intimately connected with another fact, viz., that they do not draw
their food from the mineral kingdom. The seed in germination feeds
entirely upon a supply of organic matter laid up for it by the
mother-plant. It is the decomposition of this organic matter which
supplies the force of germination. Chemical compounds are comparatively
stable--it requires sunlight to tear them asunder; but organic matter
is more easily decomposed--it is almost spontaneously decomposed.
It may be that heat (a necessary condition of germination) is the
force which determines the decomposition. However this may be, it
is certain that a portion of the organic matter laid up in the seed
is decomposed, burned up, to form CO₂ and H₂O, and that this
combustion furnishes the force by which the mason-work of tissue-making
is accomplished. In other words, of the food laid up in the form of
starch, dextrine, protoplasm, a portion is decomposed to furnish the
force by which the remainder is organized. Hence the seed always loses
weight in germination; it cannot develop unless it is in part consumed;
“it is not quickened except it die.” This self-consumption continues
until the leaves and roots are formed; then it begins to draw force
from the sun, and food from the mineral kingdom.

To illustrate: In germination, matter running down from plane No. 3
to plane No. 2 generates force by which other similar matter is moved
about and raised to a somewhat higher position on plane No. 3. As
water raised by the sun may be stored in reservoirs, and in running
down from these may do work, so matter raised by sun-force into the
organic kingdom by one generation is stored as force to do the work of
germination of the next generation. Again, as, in water running through
an hydraulic ram, a portion runs to waste, in order to generate force
to lift the remainder to a higher level, so, of organic matter stored
in the seed, a portion runs to waste to create force to organize the
remainder.

Thus, then, it will be seen that three things, viz., the absence
of sunlight, the use of organic food, and the loss of weight, are
indissolubly connected in germination, and all explained by the
principle of conservation of force.

3. STARTING OF BUDS.--Deciduous trees are entirely destitute of leaves
during the winter. The buds must start to grow in the spring without
leaves, and therefore without drawing force from the sun. Hence,
also, food in the organic form must be, and is, laid up from the
previous year in the body of the tree. A portion of this is consumed
with the formation of CO₂ and H₂O, in order to create force for
the development of the buds. So soon as by this means the leaves are
formed, the plant begins to draw force from the sun, and food from the
mineral kingdom.

4. PALE PLANTS.--Fungi and etiolated plants have no chlorophyl,
therefore cannot draw their force from the sun, nor make organic
matters from inorganic. Hence these also must feed on organic matter;
not, indeed, on starch, dextrine, and protoplasm, but on decaying
organic matter. In these plants the organic matter is taken up in some
form intermediate between the planes No. 3 and No. 2. The matter thus
taken up is, a portion of it, consumed with the formation of CO₂ and
H₂O, in order to create force necessary to organize the remainder.
To illustrate: Matter falling from some intermediate point between No.
2 and No. 3 to No. 2, produces force sufficient to raise matter from
the same intermediate point to No. 3; a portion runs to waste downward,
and creates force to push the remainder upward.

5. GROWTH OF GREEN PLANTS AT NIGHT.--It is well known that almost all
plants grow at night as well as in the day. It is also known that
plants at night exhale CO₂. These two facts have not, however, as
far as I know, been connected with one another, and with the principle
of conservation of force. It is usually supposed that in the night
the decomposition of CO₂ and exhalation of oxygen are checked by
withdrawal of sun light, and some of the CO₂ in the ascending sap is
exhaled by a physical law. But this does not account for the growth. It
is evident that, in the absence of sun light, the force required for
the work of tissue-building can be derived only from the decomposition
and combustion of organic matter. There are two views as to the source
of this organic matter, either or both of which may be correct: First.
There seems to be no doubt that most plants, especially those grown in
soils rich in _humus_, take up a portion of their food in the form of
semi-organic matter, or soluble _humus_. The combustion of a portion of
this in every part of the plant, by means of oxygen also absorbed by
the roots, and the formation of CO₂, undoubtedly creates a supply of
force night and day, independently of sunlight. The force thus produced
by the combustion of a portion might be used to raise the remainder
into starch, dextrine, etc., or might be used in tissue-building.
During the day, the CO₂ thus produced would be again decomposed in
the leaves by sunlight, and thus create an additional supply of force.
During the night, the CO₂ would be exhaled.[14]

Again: It is possible that more organic matter is made by sunlight
during the day than is used up in tissue-building. Some of this excess
is again consumed, and forms CO₂ and H₂O, in order to continue
the tissue-building process during the night. Thus the plant during the
day stores up sun-force sufficient to do its work during the night.
It has been suggested by Dr. J. C. Draper,[15] though not proved, or
even rendered probable, that the force of tissue-building (_force
plastique_) is always derived from decomposition, or combustion of
organic matter. In that case, the force of organic-matter formation
is derived from the sun, while the force of tissue-building (which is
relatively small) is derived from the combustion of organic matter thus
previously formed.

6. FERMENTATION.--The plastic matters out of which vegetable tissue
is built, and which are formed by sunlight in the leaves, are of
two kinds, viz., amyloids (dextrine, sugar, starch, cellulose), and
albuminoids, or protoplasm. Now, the amyloids are comparatively
stable, and do not spontaneously decompose; but the albuminoids not
only decompose spontaneously themselves, but drag down the amyloids
with which they are associated into concurrent decomposition--not only
change themselves, but propagate a change into amyloids. Albuminoids,
in various stages and kinds of decomposition, are called ferments. The
propagated change in amyloids is called fermentation. By various kinds
of ferments, amyloids are thus dragged down step by step to the mineral
kingdom, viz., to CO₂ and H₂O. The accompanying table exhibits
the various stages of the descent of starch, and the ferments by which
they are effected:

  1. Starch             }
  2. Dextrine           } Diastase.
  3. Sugar              }
  4. Alcohol and CO₂   Yeast.
  5. Acetic acid          Mother of vinegar.
  6. CO₂ and H₂O    Mould.

By appropriate means, the process of descent may be stopped on any one
of these planes. By far too much is, unfortunately, stopped on the
fourth plane. The manufacturer and chemist may determine the downward
change through all the planes, and the chemist has recently succeeded
in ascending again to No. 4; but the plant ascends and descends the
scale at pleasure (avoiding, however, the fourth and fifth), and even
passes at one step from the lowest to the highest.

Now, it will be seen by the table that, connected with each of
these descensive changes, there is a peculiar ferment associated.
Diastase determines the change from starch to dextrine and
sugar--saccharification; yeast, the change from sugar to
alcohol--fermentation; mother of vinegar, the change from alcohol to
acetic acid--acetification; and a peculiar mould, the change from
acetic acid to CO₂ and water. But what is far more wonderful and
significant is, that, associated with each of these ferments, except
diastase, and therefore with each of these descensive changes, except
the change from starch to sugar, or saccharification, there is a
peculiar form of life. Associated with alcoholic fermentation, there
is the yeast-plant; with acetification, the vinegar-plant; and with the
decomposition of vinegar, a peculiar kind of mould. We will take the
one which is best understood, viz., yeast-plant (saccharomyce), and its
relation to alcoholic fermentation.

It is well known that, in connection with alcoholic fermentation,
there is a peculiar unicelled plant which grows and multiplies.
Fermentation never takes place without the presence of this plant; this
plant never grows without producing fermentation, and the rapidity
of the fermentation is in exact proportion to the rapidity of the
growth of the plant. But, as far as I know, the fact has not been
distinctly brought out that the decomposition of the sugar into alcohol
and carbonic acid furnishes the force by which the plant grows and
multiplies. If the growing cells of the yeast-plant be observed under
the microscope, it will be seen that the carbonic-acid bubbles form,
and therefore probably the decomposition of sugar takes place only in
contact with the surface of the yeast-cells. The yeast-plant not only
assimilates matter, but also force. It decomposes the sugar in order
that it may assimilate the chemical force set free.

We have already said that the change from starch to sugar, determined
by diastase (saccharification), is the only one in connection with
which there is no life. Now, it is a most significant fact, in this
connection, that this is also the only change which is not, in a proper
sense, descensive, or, at least, where there is no decomposition.

We now pass from the phenomena of vegetable to the phenomena of animal
life.

7. DEVELOPMENT OF THE EGG IN INCUBATION.--The development of the egg
in incubation is very similar to the germination of a seed. An egg
consists of albuminous and fatty matters, so inclosed that, while
oxygen of the air is admitted, nutrient matters are excluded. During
incubation the egg changes into an embryo; it passes from an almost
unorganized to a highly-organized condition, from a lower to a higher
condition. There is work done: there must be expenditure of force;
but, as we have already seen, vital force is always derived from
decomposition. But, as the matters to be decomposed are not taken _ab
extra_, the egg must consume itself; that it does so, is proved by
the fact that in incubation the egg absorbs oxygen, eliminates CO₂
and probably H₂O, and loses weight. As in the seed, a portion of
the matters contained in the egg is consumed in order to create force
to organize the remainder. Matter runs down from plane No. 4 to plane
No. 2, and generates force to do the work of organization on plane No.
4. The amount of CO₂ and H₂O formed, and therefore the loss of
weight, is a measure of the amount of plastic work done.

8. DEVELOPMENT WITHIN THE CHRYSALIS SHELL.--It is well known that many
insects emerge from the egg not in their final form, but in a wormlike
form, called a larva. After this they pass into a second passive state,
in which they are again covered with a kind of shell--a sort of second
egg-state, called the chrysalis. From this they again emerge as the
perfect insect. The butterfly is the most familiar, as well as the
best, illustration of these changes. The larva or caterpillar eats with
enormous voracity, and grows very rapidly. When its growth is complete,
it covers itself with a shell, and remains perfectly passive and almost
immovable for many days or weeks. During this period of quiescence of
animal functions there are, however, the most important changes going
on within. The wings and legs are formed, the muscles are aggregated in
bundles for moving these appendages, the nervous system is more highly
developed, the mouth-organs and alimentary canal are greatly changed
and more highly organized, the simple eyes are changed into compound
eyes. Now, all this requires expenditure of force, and therefore
decomposition of matter; but no food is taken, therefore the chrysalis
must consume its own substance, and therefore lose weight. It does so;
the weight of the emerging butterfly is in many cases not one-tenth
that of the caterpillar. Force is stored up in the form of organic
matter only to be consumed in doing plastic work.

9. MATURE ANIMALS.--Whence do animals derive their vital force? I
answer, from the decomposition of their food and the decomposition of
their tissues.

Plants, as we have seen, derive their vital force from the
decomposition of their mineral food. But the chemical compounds on
which plants feed are very stable. Their decomposition requires a
peculiar and complex contrivance for the reception and utilization of
sunlight. These conditions are wanting in animals. Animals, therefore,
cannot feed on chemical compounds of the mineral kingdom; they must
have organic food which easily runs into decomposition; they must feed
on the vegetable kingdom.

Animals are distinguished from vegetables by incessant decay in
every tissue--a decay which is proportional to animal activity. This
incessant decay necessitates incessant repair, so that the animal body
has been likened to a temple on which two opposite forces are at work
in every part, the one tearing down, the other repairing the breach as
fast as made. In vegetables no such incessant decay has ever been made
out. If it exists, it must be very trifling in comparison. Protoplasm,
it is true, is taken up from the older parts of vegetables, and these
parts die; but the protoplasm does not seem to decompose, but is used
again for tissue-building. Thus the internal activity of animals is of
two kinds, tissue-destroying and tissue-building; while that of plants
seems to be, principally, at least, of one kind, tissue-building.
Animals use food for force and repair and growth, and in the mature
animal only for force and repair. Plants, except in reproduction, use
food almost wholly for growth--they never stop growing.

Now, the food of animals is of two kinds, amyloids and albuminoids. The
carnivora feed entirely on albuminoids; herbivora on both amyloids and
albuminoids. All this food comes from the vegetable kingdom, directly
in the case of herbivora, indirectly in the case of carnivora. Animals
cannot make organic matter. Now, the tissues of animals are wholly
albuminoid. It is obvious, therefore, that for the repair of the
tissues the food must be albuminoid. The amyloid food, therefore (and,
as we shall see in carnivora, much of the albuminoid), must be used
wholly for force. As coal or wood, burned in a steam-engine, changes
chemical into mechanical energy, so food, in excess of what is used
for repair, is burned up to produce animal activity. Let us trace more
accurately the origin of animal force by examples.

10. CARNIVORA.--The food of carnivora is entirely albuminoid. The idea
of the older physiologists, in regard to the use of this food, seems
to have been as follows: Albuminoid matter is exceedingly unstable; it
is matter raised, with much difficulty and against chemical forces,
high, and delicately balanced on a pinnacle, in a state of unstable
equilibrium, for a brief time, and then rushes down again into the
mineral kingdom. The animal tissues, being formed of albuminoid matter,
are short-lived; the parts are constantly dying and decomposing; the
law of death necessitates the law of reproduction; decomposition
necessitates repair, and therefore food for repair. But the force by
which repair is effected was for them, and for many physiologists now,
underived, innate. But the doctrine maintained by me in the paper
referred to is, that the decomposition of the tissues creates not only
the necessity, but also the force, of repair.

Suppose, in the first place, a carnivorous animal uses just enough
food to repair the tissues, and no more--say an ounce. Then I say the
ounce of tissue decayed not only necessitates the ounce of albuminous
food for repair, but the decomposition sets free the force by which
the repair is effected. But it will be perhaps objected that the force
would all be consumed in repair, and none left for animal activity of
all kinds. I answer: it would not all be used up in repair, for, the
food being already albuminoid, there is probably little expenditure of
force necessary to change it into tissue; while, on the other hand, the
force generated by the decomposition of tissue into CO₂, H₂O,
and urea, is very great--the ascensive change is small, the descensive
change is great. The decomposition of one ounce of albuminous tissue
into CO₂, H₂O, and urea, would therefore create force sufficient
not only to change one ounce of albuminous matter into tissue, but
also leave a considerable amount for animal activities of all kinds. A
certain quantity of matter, running down from plane No. 4 to plane No.
2, creates force enough not only to move the same quantity of matter
about on plane No. 4, but also to do much other work besides. It is
probable, however, that the wants of animal activity are so immediate
and urgent that, under these conditions, much food would be burned for
this purpose, and would not reach the tissues, and the tissues would be
imperfectly repaired, and would therefore waste.

Take, next, the carnivorous animal full fed. In this case there can
be no doubt that, while a portion of the food goes to repair the
tissues, by far the larger portion is consumed in the blood, and
passes away partly as CO₂ and H₂O through the lungs, and partly
as urea through the kidneys. This part is used, and can be of use
only, to create force. The food of carnivora, therefore, goes partly
to tissue-building, and partly to create heat and force. The force of
carnivorous animals is derived partly from decomposing tissues and
partly from food-excess consumed in the blood.

11. HERBIVORA.--The food of herbivora and of man is mixed--partly
albuminoid and partly amyloid. In man, doubtless, the albuminoids
are usually in excess of what is required for tissue-building; but
in herbivora, probably, the albuminoids are not in excess of the
requirements of the decomposing tissues. In this case, therefore, the
whole of the albuminoids is used for tissue-making, and the whole of
the amyloids for force-making. In this class, therefore, these two
classes of food may be called tissue-food and force-food. The force of
these animals, therefore, is derived partly from the decomposition of
the tissues, but principally from the decomposition and combustion of
the amyloids and fats.

Some physiologists speak of the amyloid and fat food as being burned
to keep up the animal heat; but it is evident that the prime object
in the body, as in the steam-engine, is not heat, but force. Heat is
a mere condition and perhaps a necessary concomitant of the change,
but evidently not the prime object. In tropical regions the heat is
not wanted. In the steam-engine, chemical energy is first changed into
heat, and heat into mechanical energy; in the body the change is,
probably, much of it direct, and not through the intermediation of heat.

12. We see at once, from the above, why it is that plants cannot feed
on elements, viz., because their food must be decomposed in order to
create the organic matter out of which all organisms are built. This
elevation of matter, which takes place in the green leaves of plants,
is the starting-point of life; upon it alone is based the possibility
of the existence of the organic kingdom. The running down of the
matter there raised determines the vital phenomena of germination, of
pale plants, and even of some of the vital phenomena of green plants,
and all the vital phenomena of the animal kingdom. The stability of
chemical compounds, usable as plant-food, is such that a peculiar
contrivance and peculiar conditions found only in the green leaves of
plants are necessary for their decomposition. We see, therefore, also,
why animals as well as pale plants cannot feed on mineral matter.

We easily see also why the animal activity of carnivora is greater
than that of herbivora, for the amount of force necessary for the
assimilation of their albuminoid food is small, and therefore a larger
amount is left over for animal activity. Their food is already on plane
No. 4; assimilation, therefore, is little more than a _shifting_ on the
plane No. 4 from a liquid to a solid condition--from liquid albuminoid
of the blood to solid albuminoid of the tissues.

We see also why the internal activity of plants may conceivably be
only of one kind; for, drawing their force from the sun, tissue-making
is not necessarily dependent on tissue-decay. While, on the other
hand, the internal activity of animals must be of two kinds, decay and
repair; for animals always draw a portion of their force, and starving
animals the whole of their force, from decaying tissue.

13. There are several general thoughts suggested by this subject, which
I wish to present in conclusion:

_a._ We have said there are four planes of matter raised one above the
other: 1. Elements; 2. Chemical compounds; 3. Vegetables; 4. Animals.
Their relative position is truly represented thus:

  4. _Animals._
  3. _Plants._
  2. _Chemical compounds._
  1. _Elements._

Now, there are also four planes of force similarly related to each
other, viz., physical force, chemical force, vitality, and will. On the
first plane of matter operates physical force only; for chemical force
immediately raises matter into the second plane. On the second plane
operates, in addition to physical, also chemical force. On the third
plane operates, in addition to physical and chemical, also vital force.
On the fourth plane, in addition to physical, chemical, and vital,
also the force characteristic of animals, viz., will.[16] With each
elevation there is a peculiar force added to the already existing,
and a peculiar group of phenomena is the result. As matter only rises
step by step from plane to plane, and never two steps at a time, so
also force, in its transformation into higher forms of force, rises
only step by step. Physical force does not become vital except through
chemical force, and chemical force does not become will except through
vital force.

Again, we have compared the various grades of matter, not to a
gradually rising inclined plane, but to successive planes raised one
above the other. There are, no doubt, some intermediate conditions;
but, as a broad, general fact, the changes from plane to plane are
sudden. Now, the same is true also of the forces operating on these
planes--of the different grades of force, and their corresponding
groups of phenomena. The change from one grade to another, as from
physical to chemical, or from chemical to vital, is not, as far as we
can see, by sliding scale, but suddenly. The groups of phenomena which
we call physical, chemical, vital, animal, rational, and moral, do not
merge into each other by insensible gradations. In the ascensive scale
of forces, in the evolution of the higher forces from the lower, there
are places of rapid, paroxysmal change.

_b._ Vital force is transformed into physical and chemical forces; but
it is not on that account identical with physical and chemical force,
and therefore we ought not, as some would have us, discard the term
vital force. There are two opposite errors on this subject: one is the
old error of regarding vital force as something innate, underived,
having no relation to the other forces of Nature; the other is the
new error of regarding the forces of the living body as nothing but
ordinary physical and chemical forces, and therefore insisting that
the use of the term vital force is absurd and injurious to science.
The old error is still prevalent in the popular mind, and still
haunts the minds of many physiologists; the new error is apparently
a revulsion from the other, and is therefore common among the most
advanced scientific minds. There are many of the best scientists who
ridicule the use of the term vital force, or vitality, as a remnant
of superstition; and yet the same men use the words gravity, magnetic
force, chemical force, physical force, etc. Vital force is not
underived--is not unrelated to other forces--is, in fact, correlated
with them; but it is nevertheless a distinct form of force, far more
distinct than any other form, unless it be still higher forms, and
therefore better entitled to a distinct name than any lower form. Each
form of force gives rise to a peculiar group of phenomena, and the
study of these to a peculiar department of science. Now, the group of
phenomena called vital is more peculiar, and more different from other
groups, than these are from each other; and the science of physiology
is a more distinct department than either physics or chemistry; and
therefore the form of force which determines these phenomena is more
distinct, and better entitled to a distinct name, than either physical
or chemical forces. De Candolle, in a recent paper,[17] suggests the
term vital movement instead of vital force; but can we conceive of
movement without force? And, if the movement is peculiar, so also is
the form of force.

_c._ Vital is transformed physical and chemical forces; true, but the
necessary and very peculiar condition of this transformation is the
previous existence then and there of living matter. There is something
so wonderful in this peculiarity of vital force that I must dwell on it
a little.

Elements brought in contact with each other under certain physical
conditions--perhaps heat or electricity--unite and rise into the second
plane, i. e., of chemical compounds; so also several elements, C, H, O,
and N, etc., brought in contact with each other under certain physical
or chemical conditions, such as light, nascency, etc., unite and rise
into plane No. 3, i. e., form organic matter. In both cases there is
chemical union under certain physical conditions; but in the latter
there is one unique condition, viz., the previous existence then and
there of organic matter, under the guidance of which the transformation
of matter takes place. In a word, organic matter is necessary
to produce organic matter; there is here a law of like producing
like--there is an assimilation of matter.

Again, physical force changes into other forms of physical force,
or into chemical force, under certain physical conditions; so also
physical and chemical forces are changed into vital force under certain
physical conditions. But, in addition, there is one altogether unique
condition of the latter change, viz., the previous existence then and
there of vital force. Here, again, like produces like--here, again,
there is assimilation of force.

This law of like producing like--this law of assimilation of matter
and force--runs throughout all vital phenomena, even to the minutest
details. It is a universal law of generation, and determines the
existence of species; it is the law of formation of organic matter and
organic force; it determines all the varieties of organic matter which
we call tissues and organs, and all the varieties of organic force
which we call functions. The same nutrient pabulum, endowed with the
same properties and powers, carried to all parts of a complex organism
by this wonderful law of like producing like, is changed into the
most various forms and endowed with the most various powers. There
are certainly limits and exceptions to this law, however; otherwise
differentiation of tissues, organs, and functions, could not take
place in embryonic development; but the limits and exceptions are
themselves subject to a law even more wonderful than the law of like
producing like itself, viz., the law of evolution. There is in all
organic nature, whether organic kingdom, organic individual, or organic
tissues, a law of variation, strongest in the early stages, limited
very strictly by another law--the law of inheritance, of like producing
like.

_d._ We have seen that all development takes place at the expense of
decay--all elevation of one thing, in one place, at the expense of
corresponding running down of something else in another place. Force is
only transferred and transformed. The plant draws its force from the
sun, and therefore what the plant gains the sun loses. Animals draw
from plants, and therefore what the animal kingdom gains the vegetable
kingdom loses. Again, an egg, a seed, or a chrysalis, developing to a
higher condition, and yet taking nothing _ab extra_, must lose weight.
Some part must run down, in order that the remainder should be raised
to a higher condition. The amount of evolution is measured by the loss
of weight. By the law of conservation of force, it is inconceivable
that it should be otherwise. Evidently, therefore, in the universe,
taken as a whole, evolution of one part must be at the expense of
some other part. The evolution or development of the whole cosmos--of
the whole universe of matter--as a unit, by forces within itself,
according to the doctrine of conservation of force, is inconceivable.
If there be any such evolution, at all comparable with any known form
of evolution, it can only take place by a constant increase of the
whole sum of energy, i. e., by a constant influx of divine energy--for
the same quantity of matter in a higher condition must embody a greater
amount of energy.

_e._ Finally, as organic matter is so much matter taken from the
common fund of matter of earth and air, embodied for a brief space,
to be again by death and decomposition returned to that common fund,
so also it would seem that the organic forces of the living bodies of
plants and animals may be regarded as so much force drawn from the
common fund of physical and chemical forces, to be again all refunded
by death and decomposition. Yes, by decomposition; we can understand
this. But death! can we detect any thing returned by simple death?
What is the nature of the difference between the living organism and
a dead organism? We can detect none, physical or chemical. All the
physical and chemical forces withdrawn from the common fund of Nature,
and embodied in the living organism, seem to be still embodied in the
dead until little by little it is returned by decomposition. Yet the
difference is immense, is inconceivably great. What is the nature of
this difference expressed in the formula of material science? What is
it that is gone, and whither is it gone? There is something here which
science cannot yet understand. Yet it is just this loss which takes
place in death, and before decomposition, which is in the highest sense
vital force.

Let no one from the above views, or from similar views expressed by
others, draw hasty conclusions in favor of a pure materialism. Force
and matter, or spirit and matter, or God and Nature, these are the
opposite poles of philosophy--they are the opposite poles of thought.
There is no clear thinking without them. Not only religion and virtue,
but science and philosophy, cannot even exist without them. The belief
in spirit, like the belief in matter, rests on its own basis of
phenomena. The true domain of philosophy is to reconcile these with
each other.


FOOTNOTES:

[11] In recent works the word _energy_ is used to designate active or
working force as distinguished from passive or non-working force. It is
in this working condition only that force is conserved, and therefore
_conservation of energy_ is the proper expression. Nevertheless, since
the distinction between force and energy is imperfectly or not at all
defined in the higher forms of force, and especially in the domain of
life, I have preferred in this article to use the word _force_ in the
general sense usual until recently.

[12] _American Journal of Science_, November, 1859. _Philadelphia
Magazine_, vol. xix., p. 133.

[13] In 1845 Dr. J. R. Mayer published a paper on “Organic Motion and
Nutrition.” I have not seen it.

[14] For more full account, see my paper, _American Journal of
Science_, November, 1859, sixth and seventh heads.

[15] _American Journal of Science_, November, 1872. The experiments
of Dr. Draper are inconclusive, because they are made on _seedlings_,
which, until their supply of organic food is exhausted, are independent
of sunlight.

[16] I might add still another plane and another force, viz., the human
plane, on which operate, in addition to all the lower forces, also
free-will and reason. I do not speak of these, only because they lie
beyond the present ken of inductive science.

[17] _Archives des Sciences_, vol. xlv., p. 345, December, 1872.




CORRELATION OF NERVOUS AND MENTAL FORCES.

BY ALEXANDER BAIN, LL. D.,

PROFESSOR OF LOGIC AND MENTAL PHILOSOPHY IN THE UNIVERSITY OF
ABERDEEN.




THE CORRELATION OF NERVOUS AND MENTAL FORCES.


The doctrine called the correlation, persistence, equivalence,
transmutability, indestructibility of force, or the conservation of
energy, is a generality of such compass that no single form of words
seems capable of fully expressing it; and different persons may prefer
different statements of it. My understanding of the doctrine is, that
there are five chief powers or forces in Nature: one _mechanical_,
or _molar_, the momentum of moving matter; the others _molecular_,
or embodied in the molecules, also supposed in motion--these are,
heat, light, chemical force, electricity. To these powers, which are
unquestionable and distinct, it is usual to add vital force, of which,
however, it is difficult to speak as a whole; but one member of our
vital energies, the nerve-force, allied to electricity, fully deserves
to rank in the correlation.

Taking the one mechanical force, and those three of the molecular
named heat, chemical force, electricity, there has now been established
a definite rate of commutation, or exchange, when any one passes into
any other. The mechanical equivalent of heat, the 772 foot-pounds of
Joule, expresses the rate of exchange between mechanical momentum
and heat: the equivalent or exchange of heat and chemical force is
given (through the researches of Andrews and others) in the figures
expressing the heat of combinations; for example, one pound of carbon
burnt evolves heat enough to raise 8,080 pounds of water one degree, C.
The combination of these to equivalents would show that the consumption
of half a pound of carbon would raise a man of average weight to the
highest summit of the Himalayas.

It is an essential part of the doctrine, that force is never absolutely
created, and never absolutely destroyed, but merely transmuted in form
or manifestation.

As applied to living bodies, the following are the usual positions. In
the growth of plants, the forces of the solar ray--heat and light--are
expended in decomposing (or deoxidizing) carbonic acid and water, and
in building up the living tissues from the liberated carbon and the
other elements; all which force is given up when these tissues are
consumed, either as fuel in ordinary combustion, or as food in animal
combustion.

It is this animal combustion of the matter of plants, and of animals
(fed on plants)--namely, the reoxidation of carbon, hydrogen,
etc.--that yields all the manifestations of power in the animal frame.
And, in particular, it maintains (1) a certain warmth or temperature
of the whole mass, against the cooling power of surrounding space; it
maintains (2) mechanical energy, as muscular power; and it maintains
(3) nervous power, or a certain flow of the influence circulating
through the nerves, which circulation of influence, besides reacting
on the other animal processes--muscular, glandular, etc.--has for its
distinguishing concomitant the MIND.

The extension of the correlation of force to mind, if at all competent,
must be made through the nerve-force, a genuine member of the
correlated group. Very serious difficulties beset the proposal, but
they are not insuperable.

The history of the doctrines relating to mind, as connected with body,
is in the highest degree curious and instructive, but, for the purpose
of the present paper, we shall notice only certain leading stages of
the speculation.[18]

Not the least important position is the Aristotelian; a position
in some respects sounder than what followed and grew out of it. In
Aristotle, we have a kind of gradation from the life of plants to the
highest form of human intelligence. In the following diagram, the
continuous lines may represent the material substance, and the dotted
lines the immaterial:


 A. _Soul of Plants._

  ---- Without consciousness.


 B. _Animal Soul._

  ---- Body and mind inseparable.
  ....


 C. _Human Soul_--NOUS--_Intellect_.

 I. Passive intellect.

  ----  Body and mind inseparable.
  ....

 II. Active intellect--cognition of the highest principles.

 .... Pure form; detached from matter; the prime mover of all; immortal.

All the phases of life and mind are inseparably interwoven with the
body (which inseparability is Aristotle’s definition of the soul)
except the last, the active _nous_, or intellect, which is detached
from corporeal matter, self-subsisting, the essence of Deity, and an
immortal substance, although the immortality is not personal to the
individual. (The immateriality of this higher intellectual agent was
net, however, that thorough-going negation of all material attributes
which we now understand by the word “immaterial.”) How such a
self-subsisting and purely spiritual soul could hold communication with
the body-leagued souls, Aristotle was at a loss to say--the difficulty
reappeared after him, and has never been got over. That there should
be an agency totally apart from, and entirely transcending, any known
powers of inert matter, involves no difficulty--for who is to limit
the possibilities of existence? The perplexity arises only when this
radically new and superior principle is made to be, as it were, off
and on with the material principle; performing some of its functions
in pure isolation, and others of an analogous kind by the aid of the
lower principle. The difference between the active and the passive
reason of Aristotle is a mere difference of gradation; the supporting
agencies assumed by him are a total contrast in kind--wide as the poles
asunder. There is no breach of continuity in the phenomena, there is an
impassable chasm between their respective foundations.

Fifteen centuries after Aristotle, we reach what may be called the
modern settlement of the relations of mind and body, effected by Thomas
Aquinas. He extended the domain of the independent immaterial principle
from the highest intellectual soul of Aristotle to all the three souls
recognized by him--the vegetable or plant soul (without consciousness),
the animal soul (with consciousness), and the intellect throughout. The
two lower souls--the vegetable and the animal--need the coöperation of
the body in this life; the intellect works without any bodily organ,
except that it makes use of the perceptions of the senses.


 A. _Vegetable or Nutritive Soul._

  ---- Incorporates an immaterial part, although unconscious.
  ....


 B. _Animal Soul._

  ---- Has an immaterial part, with consciousness.
  ....


 C. _Intellect._

 .... Purely immaterial.

The animal soul, B, contains sensation, appetite, and emotion, and is a
mixed or two-sided entity; but the intellect, C, is a purely one-sided
entity, the immaterial. This does not relieve our perplexities; the
phenomena are still generically allied and continuous--sensation passes
into intellect without any breach of continuity; but as regards the
agencies, the transition from a mixed or united material and immaterial
substance to an immaterial substance apart, is a transition to a
differently constituted world, to a transcendental sphere of existence.

The settlement of Aquinas governed all the schools and all the
religious creeds, until quite recent times; it is, for example,
substantially the view of Bishop Butler. At the instance of modern
physiology, however, it has undergone modifications. The dependence
of purely intellectual operations, as memory, upon the material
processes, has been reluctantly admitted by the partisans of an
immaterial principle; an admission incompatible with the isolation of
the intellect in Aristotle and in Aquinas. This more thorough-going
connection of the mental and the physical has led to a new form of
expressing the relationship, which is nearer the truth, without being,
in my judgment, quite accurate. It is now often said _the mind and the
body act upon each other_; that neither is allowed, so to speak, to
pursue its course alone--there is a constant interference, a mutual
influence between the two. This view is liable to the following
objections:

1. In the first place, it assumes that we are entitled to speak of
mind apart from body, and to affirm its powers and properties in that
separate capacity. But of mind apart from body we have no direct
experience, and absolutely no knowledge. The wind may act upon the sea,
and the waves may react upon the wind; but the agents are known in
separation--they are seen to exist apart before the shock of collision;
but we are not permitted to see a mind acting apart from its material
companion.

2. In the second place, we have every reason for believing that there
is an unbroken material succession, side by side with all our mental
processes. From the ingress of a sensation, to the outgoing responses
in action, the mental succession is not for an instant dissevered from
a physical succession. A new prospect bursts upon the view; there is a
mental result of sensations, emotion, thought, terminating in outward
displays of speech or gesture. Parallel to this mental series is the
physical series of facts, the successive agitation of the physical
organs, called the eye, the retina, the optic nerve, optic centres,
cerebral hemispheres, outgoing nerves, muscles, etc. There is an
unbroken physical circle of effects, maintained while we go the round
of the mental circle of sensation, emotion, and thought. It would be
incompatible with every thing we know of the cerebral action to suppose
that the physical chain ends abruptly in a physical void, occupied by
an immaterial substance; which immaterial substance, after working
alone, imparts its results to the other edge of the physical break,
and determines the active response--two shores of the material with an
intervening ocean of the immaterial. There is, in fact, no rupture of
nervous continuity. The only tenable supposition is, that mental and
physical proceed together, as individual twins. When, therefore, we
speak of a mental cause, a mental agency, we have always a two-sided
cause; the effect produced is not the effect of mind alone, but of mind
in company with body. That mind should have operated on the body, is
as much as to say that a two-sided phenomenon, one side being bodily,
can influence the body; it is, after all, body acting upon body. When
a shock of fear paralyzes digestion, it is not the emotion of fear,
in the abstract, or as a pure mental existence, that does the harm;
it is the emotion in company with a peculiarly excited condition of
the brain and nervous system; and it is this condition of the brain
that deranges the stomach. When physical nourishment, or physical
stimulant, acting through the blood, quiets the mental irritation, and
restores a cheerful tone, it is not a bodily fact causing a mental
fact by a direct line of causation: the nourishment and the stimulus
determine the circulation of blood to the brain, give a new direction
to the nerve-currents, and the mental condition corresponding to
this particular mode of cerebral action henceforth manifests itself.
The line of mental sequence is thus, not mind causing body, and body
causing mind, but mind-body giving birth to mind-body; a much more
intelligible position. For this double or conjoint causation, we can
produce evidence; for the single-handed causation we have no evidence.

If it were not my peculiar province to endeavor to clear up the
specially metaphysical difficulties of the relationship of mind and
body, I would pass over what is to me the most puzzling circumstance of
the relationship, and indeed the only real difficulty in the question.

I say the real difficulty, for factitious difficulties in abundance
have been made out of the subject. It is made a mystery how mental
functions and bodily functions should be allied together at all. That,
however, is no business of ours; we accept this alliance, as we do any
other alliance, such as gravity with inert matter, or light with heat.
As a fact of the universe, the union is, properly speaking, just as
acceptable, and as intelligible, as the separation would be, if that
were the fact. The real difficulty is quite another thing.

What I have in view is this: when I speak of mind as allied with
body--with a brain and its nerve-currents--I can scarcely avoid
_localizing_ the mind, giving it a local habitation. I am thereupon
asked to explain what always puzzled the schoolmen, namely, whether the
mind is all in every part, or only all in the whole; whether in tapping
any point I may come at consciousness, or whether the whole mechanism
is wanted for the smallest portion of consciousness. One might perhaps
turn the question by the analogy of the telegraph wire, or the electric
circuit, and say that a complete circle of action is necessary to any
mental manifestation; which is probably true. But this does not meet
the case. The fact is that, all this time we are speaking of nerves
and wires, we are not speaking of mind, properly so called, at all; we
are putting forward physical facts that go along with it, but these
physical facts are not the mental fact, and they even preclude us from
thinking of the mental fact. We are in this fix: mental states and
bodily states are utterly contrasted; they cannot be compared, they
have nothing in common except the most general of all attributes,
degree, and order in time; when engaged with one we must be oblivious
of all that distinguishes the other. When I am studying a brain
and nerve communicating, I am engrossed with properties exclusively
belonging to the object or material world; I am at that moment (except
by very rapid transitions or alternations) unable to conceive a truly
mental fact, my truly mental consciousness. Our mental experience, our
feelings and thoughts, have no extension, no place, no form or outline,
no mechanical division of parts; and we are incapable of attending to
any thing mental until we shut off the view of all that. Walking in the
country in spring, our mind is occupied with the foliage, the bloom,
and the grassy meads, all purely objective things; we are suddenly and
strongly arrested by the odor of the May-blossom; we give way for a
moment to the sensation of sweetness: for that moment the objective
regards cease; we think of nothing extended; we are in a state where
extension has no footing; there is, to us, place no longer. Such states
are of short duration, mere fits, glimpses; they are constantly shifted
and alternated with object states, but while they last and have their
full power we are in a different world; the material world is blotted
out, eclipsed, for the instant unthinkable. These subject-moments are
studied to advantage in bursts of intense pleasure, or intense pain, in
fits of engrossed reflection, especially reflection upon mental facts;
but they are seldom sustained in purity beyond a very short interval;
we are constantly returning to the object-side of things--to the world
where extension and place have their being.

This, then, as it appears to me, is the only real difficulty of the
physical and mental relationship. There is an alliance with matter,
with the object, or extended world; but the thing allied, the mind
proper, has itself no extension, and cannot be joined in local union.
Now, we have no form of language, no familiar analogy, suited to this
unique conjunction; in comparison with all ordinary unions, it is a
paradox or a contradiction. We understand union in the sense of local
connection; here is a union where local connection is irrelevant,
unsuitable, contradictory, for we cannot think of mind without putting
ourselves out of the world of place. When, as in pure feeling--pleasure
or pain--we change to the subject attitude from the object attitude,
we have undergone a change not to be expressed by place; the fact is
not properly described by the transition from the _external_ to the
_internal_, for that is still a change in the region of the extended.
The only adequate expression is a _change of state_: a change from the
state of the extended cognition to a state of unextended cognition.
By various theologians, heaven has been spoken of us not a place,
but a _state_; and this is the only phrase that I can find suitable
to describe the vast, though familiar and easy, transition from the
material or extended, to the immaterial or unextended side of the
universe of being.

When, therefore, we talk of incorporating mind with brain, we must be
held as speaking under an important reserve or qualification. Asserting
the union in the strongest manner, we must yet deprive it of the almost
invincible association of union in place. An extended organism is the
condition of our passing into a state where there is no extension. A
human being is an extended and material thing, attached to which is the
power of becoming alive to feeling and thought, the extreme remove from
all that is material; a condition of _trance_ wherein, while it lasts,
the material drops out of view--so much so, that we have not the power
to represent the two extremes as lying side by side, as container and
contained, or in any other mode of local conjunction. The condition
of our existing thoroughly in the one, is the momentary eclipse or
extinction of the other.

The only mode of union that is not contradictory is the union of close
succession in _time_; or of position in a continued thread of conscious
life. We are entitled to say that the same being is, by alternate fits,
object and subject, under extended and under unextended consciousness;
and that without the extended consciousness the unextended would not
arise. Without certain peculiar modes of the extended--what we call
a cerebral organization, and so on--we could not have those times of
trance, our pleasures, our pains, and our ideas, which at present we
undergo fitfully and alternately with our extended consciousness.

Having thus called attention to the metaphysical difficulty of
assigning the relative position of mind and matter, I will now state
briefly what I think the mode of dealing with mind in correlation with
the other forces. That there is a definite equivalence between mental
manifestations and physical forces, the same as between the physical
forces themselves, is, I think, conformable to all the facts, although
liable to peculiar difficulties in the way of decisive proof:

I. The mental manifestations are in exact proportion to their physical
supports.

If the doctrine of the thorough-going connection of mind and body
is good for any thing, it must go this length. There must be a
numerically-proportioned rise and fall of the two together. I believe
that all the unequivocal facts bear out this proportion.

Take first the more obvious illustrations. In the employment of
external agents, as warmth and food, all will admit that the sensation
rises exactly as the stimulant rises, until a certain point is reached,
when the agency changes its character; too great heat destroying the
tissues, and too much food impeding digestion. There is, although we
may not have the power to fix it, a _sensational equivalent_ of heat,
of food, of exercise, of sound, of light; there is a definite change
of feeling, an accession of pleasure or of pain, corresponding to a
rise of temperature in the air of 10°, 20°, or 30°. And so with regard
to every other agent operating upon the human sensibility: there is,
in each set of circumstances, a sensational equivalent of alcohol, of
odors, of music, of spectacle.

It is this definite relation between outward agents and the human
feelings that renders it possible to discuss human interests from the
objective side, the only accessible side. We cannot read the feelings
of our fellows; we merely presume that like agents will affect them all
in nearly the same way. It is thus that we measure men’s fortunes and
felicity by the numerical amount of certain agents, as money, and by
the absence or low degree of certain other agents, the causes of pain
and the depressors of vitality. And, although the estimate is somewhat
rough, this is not owing to the indefiniteness of the sensational
equivalent, but to the complications of the human system, and chiefly
to the narrowness of the line that everywhere divides the wholesome
from the unwholesome degrees of all stimulants.

Let us next represent the equivalence under vital or physiological
action. The chief organ concerned is the brain; of which we know that
it is a system of myriads of connecting threads, ramifying, uniting,
and crossing at innumerable points; that these threads are actuated
or made alive with a current influence called the nerve force; that
this nerve-force is a member of the group of correlating forces;
that it is immediately derived from the changes in the blood, and in
the last resort from oxidation, or combustion, of the materials of
the food, of which combustion it is a definite equivalent. We know,
further, that there can be no feeling, no volition, no intellect,
without a proper supply of blood, containing both oxygen and the
material to be oxidized; that, as the blood is richer in quality in
regard to these constituents, and more abundant in quantity, the mental
processes are more intense, more vivid. We know also that there are
means of increasing the circulation in one organ, and drawing it off
from another, chiefly by calling the one into greater exercise, as
when we exert the muscles or convey food to the stomach; and that,
when mental processes are more than usually intensified, the blood is
proportionally drawn to the brain; the oxidizing process is there in
excess, with corresponding defect and detriment in other organs. In
high mental excitement, digestion is stopped; muscular vigor is abated
except in the one form of giving vent to the feelings, thoughts, and
purposes; the general nutrition languishes; and, if the state were long
continued or oft repeated, the physical powers, strictly so called,
would rapidly deteriorate. We know, on the other extreme, that sleep
is accompanied by reduced circulation in the brain; there is in fact a
reduced circulation generally; while of that reduced amount more goes
to the nutritive functions than to the cerebral.

In listening to Dr. Frankland’s lecture on “Muscular Power,” delivered
at the Royal Institution of London, I noticed that, in accounting for
the various items of expenditure of the food, he gave “mental work” as
one heading, but declined to make an entry thereinunder. I can imagine
two reasons for this reserve, the statement of which will further
illustrate the general position. In the first place, it might be
supposed that mind is a phenomenon so anomalous, uncertain, so remote
from the chain of material cause and effect, that it is not even to be
mentioned in that connection.

To which I should say, that mind is indeed, as a phenomenon, widely
different from the physical forces, but, nevertheless, rises and falls
in strict numerical concomitance with these: so that it still enters,
if not directly, at least indirectly, into the circle of the correlated
forces. Or, secondly, the lecturer may have held that, though a
definite amount of the mental manifestations accompanies a definite
amount of oxidation in the special organs of mind, there is no means
of reducing this to a measure, even in an approximate way. To this I
answer, that the thing is difficult but not entirely impracticable.
There is a possibility of giving, approximately at least, the amount of
blood circulating in the brain, in the ordinary waking state; and, as
during a period of intense excitement we know that there is a general
reduction, almost to paralysis, of the collective vital functions,
we could not be far mistaken in saying that, in that case, perhaps
one-half or one-third of all the oxidation of the body was expended in
keeping up the cerebral fires.

It is a very serious drawback in any department of knowledge, where
there are relations of quantity, to be unable to reduce them to
numerical precision. This is the case with mind in a great degree,
although not with it alone; many physical qualities are in the same
state of unprecise measurement. We cannot reduce to numbers the
statement of a man’s constitutional vigor, so as to say how much he
has lost by fatigue, by disease, by age, or how much he has gained by
a certain healthy regimen. Undoubtedly, however, it is in mind that
the difficulties of attaining the numerical statement are greatest if
not nearly insuperable. When we say that one man is more courageous,
more loving, more irascible than another, we apply a scale of degree,
existing in our own mind, but so vague that we may apply it differently
at different times, while we can hardly communicate it to others
exactly as it stands to ourselves. The consequence is, that a great
margin of allowance must always be made in those statements; we can
never run a close argument, or contend for a nice shade of distinction.
Between the extremes of timidity and courage of character the best
observer could not entertain above seven or eight varieties of
gradation, while two different persons consulting together could hardly
agree upon so minute a subdivision as that. The phrenologists, in their
scale of qualities, had the advantage of an external indication of
size, but they must have felt the uselessness of graduating this beyond
the delicacy of discriminating the subjective side of character; and
their extreme scale included twenty steps or interpolations.

Making allowance for this inevitable defect, I will endeavor to present
a series of illustrations of the principle of correlation as applied
to mind, in the manner explained. I deal not with mind directly, but
with its material side, with whose activity, measured exactly as we
measure the other physical forces, true mental activity has a definite
correspondence.

Let us suppose, then, a human being with average physical constitution,
in respect of nutritive vigor, and fairly supplied with food and with
air, or oxygen. The result of the oxidation of the food is a definite
total of force, which may be variously distributed. The demand made
by the brain, to sustain the purely mental functions, may be below
average, or above average; there will be a corresponding, but inverse,
variation of the remainder available for the more strictly physical
processes, as muscular power, digestive power, animal heat, and so on.

In the first case supposed, the case of a small demand for mental work
and excitement, we look for, and we find, a better _physique_--greater
muscular power and endurance, more vigor of digestion, rendering a
coarser food sufficient for nourishment, more resistance to excesses of
cold and heat; in short, a constitution adapted to physical drudgery
and physical hardship.

Take, now, the other extreme. Let there be a great demand for mental
work. The oxidation must now be disproportionately expended in the
brain; less is given to the muscles, the stomach, the lungs, the skin,
and secreting organs generally. There is a reduction of the possible
muscular work, and of the ability to subsist on coarser food, and
to endure hardship. Experience confirms this inference; the common
observation of mankind has recognized the fact--although in a vague,
unsteady form--that the head-worker is not equally fitted to be a
hand-worker. The master, mistress, or overseer has each more delicacy
of sense, more management, more resource, than the manual operatives,
but to these belongs the superiority of muscular power and persistence.

There is nothing incompatible with the principle in allowing the
possibility of combining, under certain favorable conditions, both
physical and mental exertion in considerable amount. In fact, the
principle teaches us exactly how the thing may be done. Improve the
quality and increase the quantity of the food; increase the supply
of oxygen by healthy residence; let the habitual muscular exertion
be such as to strengthen and not impair the functions; abate as much
as possible all excesses and irregularities, bodily and mental; add
the enormous economy of an educated disposal of the forces; and you
will develop a higher being, a _greater aggregate_ of power. You
will then have more to spare for all kinds of expenditure--for the
physico-mental, as well as for the strictly physical. What other
explanation is needed of the military superiority of the officer over
the common soldier? of the general efficiency of the man nourished, but
not enervated, by worldly abundance?

It may be possible, at some future stage of scientific inquiry, to
compute the comparative amount of oxidation in the brain during severe
mental labor. Even now, from obvious facts, we must pronounce it to be
a very considerable fraction of the entire work done in the system. The
privation of the other interests during mental exertion is so apparent,
so extensive, that if the exertion should happen to be long continued,
a liberal atonement has to be made in order to stave off general
insolvency. Mental excess counts as largely as muscular excess in the
diversion of power; it would be competent to suppose either the one
or the other reducing the remaining forces of the system to one-half
of their proper amount. In both cases, the work of restoration must
be on the same simple plan of redressing the inequality, of allowing
more than the average flow of blood to the impoverished organs, for a
length of time corresponding to the period when their nourishment has
been too small. It is in this consideration that we seem to have the
reasonable, I may say the arithmetical, basis of the constitutional
treatment of chronic disease. We _repay the debt to Nature_ by allowing
the weakened organ to be better nourished and less taxed, according to
the degradation it has undergone by the opposite line of treatment. In
a large class of diseases we have obviously a species of insolvency,
to be dealt with according to the sound method of readjusting the
relations of expenditure and income. And, if such be the true theory,
it seems to follow that medication is only an inferior adjunct. Drugs,
even in their happiest application, can but guide and favor the
restorative process; just as the stirring of a fire may make it burn,
provided there be the needful fuel.

There is thus a definite, although not numerically-statable relation,
between the total of the physico-mental forces and the total of the
purely physical processes. The grand aggregate of the oxidation of the
system includes both; and, the more the force taken up by one, the
less is left to the other. Such is the statement of the correlation
of mind to the other forces of Nature. We do not deal with pure
mind--mind in the abstract; we have no experience of an entity of that
description. We deal with a compound or two-sided phenomenon--mental
on one side, physical on the other; there is a definite correspondence
in degree, although a difference of nature, between the two sides; and
the physical side is itself in full correlation with the recognized
physical forces of the world.

II. There remains another application of the doctrine, perhaps equally
interesting to contemplate, and more within my special line of study.
I mean the correlation of the mental forces among themselves (still
viewed in the conjoint arrangement). Just as we assign limits to mind
as a whole, by a reference to the grant of physical expenditure, in
oxidation, etc., for the department, so we must assign limits to the
different phases or modes of mental work--thought, feeling, and so
on--according to the share allotted to each; so that, while the mind as
a whole may be stinted by the demands of the non-mental functions, each
separate manifestation is bounded by the requirements of the others.
This is an inevitable consequence of the general principle, and equally
receives the confirmation of experience. There is the same absence of
numerical precision of estimate; our scale of quantity can have but few
divisions between the highest and the lowest degrees, and these not
well fixed.

What is required for this application of the principle is, to ascertain
the comparative cost, in the physical point of view, of the different
functions of the mind.

The great divisions of the mind are--feeling, will, and thought;
feeling, seen in our pleasures and pains; will, in our labors to
attain the one and avoid the other; thought, in our sensations, ideas,
recollections, reasonings, imaginings, and so on. Now, the forces of
the mind, with their physical supports, may be evenly or unevenly
distributed over the three functions. They may go by preference either
to feeling, to action, or to thinking; and, if more is given to one,
less must remain to the others, the entire quantity being limited.

First, as to the feelings. Every throb of pleasure costs something to
the physical system; and two throbs cost twice as much as one. If we
cannot fix a precise equivalent, it is not because the relation is not
definite, but from the difficulties of reducing degrees of pleasure to
a recognized standard. Of this, however, there can be no reasonable
doubt--namely, that a large amount of pleasure supposes a corresponding
large expenditure of blood and nerve-tissue, to the stinting, perhaps,
of the active energies and the intellectual processes. It is a matter
of practical moment to ascertain what pleasures cost least, for there
are thrifty and unthrifty modes of spending our brain and heart’s
blood. Experience probably justifies us in saying that the narcotic
stimulants are, in general, a more extravagant expenditure than the
stimulation of food, society, and fine art. One of the safest of
delights, if not very acute, is the delight of abounding physical
vigor; for, from the very supposition, the supply to the brain is not
such as to interfere with the general interests of the system. But the
theory of pleasure is incomplete without the theory of pain.

As a rule, pain is a more costly experience than pleasure, although
sometimes economical as a check to the spendthrift pleasures. Pain is
physically accompanied by an excess of blood in the brain, from at
least two causes--extreme intensity of nervous action, and conflicting
currents, both being sources of waste. The sleeplessness of the pained
condition means that the circulation is never allowed to subside from
the brain; the irritation maintains energetic currents, which bring the
blood copiously to the parts affected.

There is a possibility of excitement, of considerable amount, without
either pleasure or pain; the cost here is simply as the excitement:
mere surprises may be of this nature. Such excitement has no value,
except intellectually; it may detain the thoughts, and impress the
memory, but it is not a final end of our being, as pleasure is; and it
does not waste power to the extent that pain does. The ideally best
condition is a moderate surplus of pleasure--a gentle glow, not rising
into brilliancy or intensity, except at considerable intervals (say a
small portion of every day), falling down frequently to indifference,
but seldom sinking into pain.

Attendant on strong feeling, especially in constitutions young or
robust, there is usually a great amount of mere bodily vehemence, as
gesticulation, play of countenance, of voice, and so on. This counts as
muscular work, and is an addition to the brain-work. Properly speaking,
the cerebral currents discharge themselves in movements, and are
modified according to the scope given to those movements. Resistance
to the movements is liable to increase the conscious activity of the
brain, although a continuing resistance may suppress the entire wave.

Next as to the will, or our voluntary labors and pursuits for the great
ends of obtaining pleasure and warding off pain. This part of our
system is a compound experience of feeling and movement; the properly
mental fact being included under feeling--that is, pleasure and pain,
present or imagined. When our voluntary endeavors are successful,
a distinct throb of pleasure is the result, which counts among our
valuable enjoyments: when they fail, a painful and depressing state
ensues. The more complicated operations of the will, as in adjusting
many opposite interests, bring in the element of conflict, which is
always painful and wasting. Two strong stimulants pointing opposite
ways, as when a miser has to pay a high fee to the surgeon that saves
his eyesight, occasion a fierce struggle and severe draft upon the
physical supports of the feelings.

Although the processes of feeling all involve a manifest, and it may
be a serious, expenditure of physical power, which of course is lost
to the purely physical functions; and although the extreme degrees of
pleasure, of pain, or of neutral excitement, must be adverse to the
general vigor; yet the presumption is, that we can afford a certain
moderate share of all these without too great inroads on the other
interests. It is the thinking or intellectual part of us that involves
the heaviest item of expenditure in the physico-mental department. Any
thing like a great or general cultivation of the powers of thought, or
any occupation that severely and continuously brings them into play,
will induce such a preponderance of cerebral activity, in oxidation and
in nerve-currents, as to disturb the balance of life, and to require
special arrangements for redeeming that disturbance. This is fully
verified by all we know of the tendency of intellectual application to
exhaust the physical powers, and to bring on early decay.

A careful analysis of the operations of the intellect enables us
to distinguish the kind of exercises that involve the greatest
expenditure, from the extent and the intensity of the cerebral
occupation. I can but make a rapid selection of leading points:

First. The mere exercise of the senses, in the way of attention,
with a view to watch, to discriminate, to identify, belongs to the
intellectual function, and exhausts the powers according as it is long
continued, and according to the delicacy of the operation; the meaning
of delicacy being that an exaggerated activity of the organ is needed
to make the required discernment. To be all day on the _qui vive_ for
some very slight and barely perceptible indications to the eye or the
ear, as in catching an indistinct speaker, is an exhausting labor of
attention.

Secondly. The work of acquisition is necessarily a process of great
nervous expenditure. Unintentional imitation costs least, because there
is no forcing of reluctant attention. But a course of extensive and
various acquisitions cannot be maintained without a large supply of
blood to cement all the multifarious connections of the nerve-fibres,
constituting the physical side of acquisition. An abated support of
other mental functions, as well as of the purely physical functions,
must accompany a life devoted to mental improvement, whether arts,
languages, sciences, moral restraints, or other culture.

Of special acquisitions, languages are the most apparently voluminous;
but the memory for visible or pictorial aspects, if very high, as in
the painter and the picturesque poet, makes a prodigious demand upon
the plastic combinations of the brain.

The acquisition of science is severe, rather than multifarious; it
glories in comprehending much in little, but that little is made up of
painful abstract elements, every one of which, in the last resort, must
have at its beck a host of explanatory particulars: so that, after all,
the burden lies in the multitude. If science is easy to a select number
of minds, it is because there is a large spontaneous determination of
force to the cerebral elements that support it; which force is supplied
by the limited common fund, and leaves so much the less for other uses.

If we advert to the moral acquisitions and habits in a well-regulated
mind, we must admit the need of a large expenditure to build up the
fabric. The carefully-poised estimate of good and evil for self, the
ever-present sense of the interests of others, and the ready obedience
to all the special ordinances that make up the morality of the time,
however truly expressed in terms of high and abstract spirituality,
have their counterpart in the physical organism; they have used up
a large and definite amount of nutriment, and, had they been less
developed, there would have been a gain of power to some other
department, mental or physical.

Refraining from further detail on this head, I close the illustration
by a brief reference to one other aspect of mental expenditure, namely,
the department of intellectual production, execution, or creativeness,
to which in the end our acquired powers are ministerial. Of course,
the greater the mere continuance or amount of intellectual labor in
business, speculation, fine art, or any thing else, the greater the
demand on the _physique_. But amount is not all. There are notorious
differences of severity or laboriousness, which, when closely examined,
are summed up in one comprehensive statement--namely, the number,
the variety, and the conflicting nature of the conditions that have
to be fulfilled. By this we explain the difficulty of work, the toil
of invention, the harassment of adaptation, the worry of leadership,
the responsibility of high office, the severity of a lofty ideal,
the distraction of numerous sympathies, the meritoriousness of sound
judgment, the arduousness of any great virtue. The physical facts
underlying the mental fact are a wide-spread agitation of the cerebral
currents, a tumultuous conflict, a consumption of energy.

It is this compliance with numerous and opposing conditions that
obtains the most scanty justice in our appreciation of character.
The unknown amount of painful suppression that a cautious thinker,
a careful writer, or an artist of fine taste, has gone through,
represents a great physico-mental expenditure. The regard to evidence
is a heavy drag on the wings of speculative daring. The greater the
number of interests that a political schemer can throw overboard, the
easier his work of construction. The absence of restraints--of severe
conditions--in fine art, allows a flush and ebullience, an opulence of
production, that is often called the highest genius. The Shakespearean
profusion of images would have been reduced to one-half, if not less,
by the self-imposed restraints of Pope, Gray, or Tennyson. So, reckless
assertion is fuel to eloquence. A man of ordinary fairness of mind
would be no match for the wit and epigram of Swift.

And again. The incompatibility of diverse attributes, even in minds of
the largest compass (which supposes equally large physical resources),
belongs to the same fundamental law. A great mind may be great in many
things, because the same kind of power may have numerous applications.
The scientific mind of a high order is also the practical mind; it is
the essence of reason in every mode of its manifestation--the true
philosopher in conduct as well as in knowledge. On such a mind also,
a certain amount of artistic culture may be superinduced; its powers
of acquisition may be extended so far. But the spontaneous, exuberant,
imaginative flow, the artistic nature at the core, never was, cannot
be, included in the same individual. Aristotle could not be also a
tragic poet; nor Newton a third-rate portrait-painter. The cost of one
of the two modes of intellectual greatness is all that can be borne by
the most largely-endowed personality; any appearances to the contrary
are hollow and delusive.

Other instances could be given. Great activity and great sensibility
are extreme phases, each using a large amount of power, and therefore
scarcely to be coupled in the same system. The active, energetic man,
loving activity for its own sake, moving in every direction, wants the
delicate circumspection of another man who does not love activity for
its own sake, but is energetic only at the spur of his special ends.

And once more. Great intellect as a whole is not readily united with a
large emotional nature. The incompatibility is best seen by inquiring
whether men of overflowing sociability are deep and original thinkers,
great discoverers, accurate inquirers, great organizers in affairs; or
whether their greatness is not limited to the spheres where feeling
performs a part--poetry, eloquence, and social ascendency.


THE END.


FOOTNOTES:

[18] For the fuller elaboration of the point here referred to, see
Chapter VII., Professor Bain’s “Mind and Body”--an earlier volume in
the present series.




INDEX.


  Absorbed heat changed into chemical separation, 114.
    into actual visible energy, 105.
    into light and heat, 117.

  Acquisition, 232.

  Actinic rays, 129.

  Action and reaction equal and opposite, 8.

  Affinity, chemical, 53.

  Air and water in motion, 147.

  Albuminoids, 177, 183.

  Amber, 61.

  Ampère, 75.

  Amyloids, 177, 183.

  Ancients, their ideas not prolific, 135.

  Andrews, 141.

  Animal heat, 207.

  Animals, how they live, 188.

  Animals and inanimate machines, 165.

  Aristotle on a medium, 134.
    on mind and body, 207.

  Atmospheric circulation, 109.

  Atomic forces and heat, 58.

  Atomic or chemical separation, 80.

  Atoms and molecules, 51.

  Attention, 232.

  Attraction, molecular, 52.
    mutual, of atoms, 54.
    and repulsion of magnets, 75.
    of electric currents, 75.


  Bacon, 133, 137.

  Battery of Grove, 70.

  Budding, 180.


  Caloric, 38.

  Carnivora, 189.

  Chemical affinity, 53.
    and electrical attraction, 64.
    and heat, 58.

  Chemical combination producing heat, 119.

  Chemical instability, 156.

  Chemical separation converted into electrical separation, 122.
    into electricity in motion, 123.

  Chlorophyll, 177.

  Chrysalis, 187.

  Circulation of the atmosphere, 109.

  Clausius, 141.

  Cohesion, force of, 51.

  Cold apparently produced by the electric current, 126.

  Conduction of electricity, 61.

  Conservation, laws of, 82.
    theory of, 140.

  Crossbow and watch-spring, 25.

  Current, the electric, 69.
    and magnetism, 72.
    heating effect of, 73.
    chemical effect of, 74.

  Currents, electric, attraction and repulsion of, 74.
    induction of, 75.


  Dalton, 133.

  Davy, Sir Humphrey, 38, 137.

  Democritus on atoms, 133.

  Descartes, 136.

  Diastase, 184.

  Disease-germs, 3.

  Dissipation of energy, 141.

  Dissociation, 115.


  Egg, development of the, 186.

  Electric current, 69.
    and magnetism, 72.
    heating effect of, 73.
    chemical effect of, 74.
    induction, 65.

  Electrical attraction and chemical affinity, 64.

  Electrical separation, 81.
    when produced, 64.
    transmuted into visible motion, 124.
    into electric current, 124.

  Electro-magnetism, 72.

  Elastic forces, 50.

  Electricity, 60.
    vitreous and resinous, 63.
    negative and positive, 63.
    theory of, 63.
    in motion, 81.
    transmuted into visible motion, 124.
    into heat, 125.
    into chemical separation, 127.

  Encke’s comet, 96.

  Energies, list of, 78-82.
    natural, and their sources, 143.

  Energy, meaning of, 1-22.
    of bodies in motion proportional to their weight or mass, 14.
    proportional to the square of the velocity, 19.
    of visible motion, its transmutation, 87.
    visible, transformed into absorbed heat, 88.
    dissipation of, 141.
    transmutations of, 27.
    varies as the square of the velocity, 15.
    of motion, 24.
    transformed into electrical separation, 98.
    of position, a sort of capital, 26.

  Equilibrium, 154.

  Etiolation, 180.


  Fermentation, 183.

  Food, 145.

  Force, vital, whence derived, 171.
    physical, 194.
    chemical, 194.
    of chemical affinity, 53.
    of cohesion, 51.

  Force, mechanical or molar, 205.
    molecular, 205.

  Friction, 35.


  Heat, absorbed, changed into chemical separation, 114.
    into electrical separation, 115.
    into electricity in motion, 116.

  Heat-units of different substances, 119.

  Heat-motion, 80.

  Heat-engines, their essential conditions, 107.

  Helmholtz, 141.

  Heraclitus on energy, 133.

  Herbivora, 191.

  Heterogeneity essential in electrical development, 64.

  Huyghens, 137.

  Hydraulic press, 32.


  Inclined plane, 28.

  Incubation, 186.

  Individuals, our ignorance of, 1.

  Induction, electric, 65.
    of electric currents, 75.

  Instability, mechanical, 155.
    chemical, 156.

  Intellectual labor, 234.


  Joule, 137, 140, 141.

  Joule’s experiments on work and heat, 44.


  Kilogrammetre, 16.


  Larva, 187.

  Latent heat, 57.

  Laws of conservation, 82.

  Life depends on the sun, 165.

  Light, a perpetual, impossible, 149.

  Lime, carbonate, easily decomposed, 58.

  List of energies, 78-82.


  Machines, their true function, 33.
    animated and inanimate, 157.

  Magnets, attachment and repulsion of, 75.

  Maxwell, 141.

  Mayor, 140.

  Mechanical energy changed into heat, 23.
    equivalent of heat, 43.
    force, 205.
    instability, 155.

  Mental forces, mutual correlations of, 227-236.

  Mind, its correlations to natural forces, 218-227.
    and body, 207, 211.

  Molar force, 205.

  Molecular attraction and heat, 55.
    separation, 80.

  Molecules, ultimate, of matter, 5.
    their motions, 7.
    and atoms, 51.

  Motion changed into an electric current, 99.

  Muscular power, 207.


  Narcotic stimulants, 229.

  Negative and positive electricity, 63.

  Nerve power, 207.

  Newton, 136, 137.

  Non-conductors of electricity, 61.


  Percussion, 36.

  Perpetual motion, 139.

  Physical force, 194.

  Plants growing at night, 181.

  Positive and negative electricity, 63.

  Protoplasm, 177.

  Pulleys, their function, 30.


  Radiant energy, 81.
    converted into absorbed heat, 123.
    promoting chemical separation, 123.

  Rankine, 141.

  Resinous and vitreous electricity, 63.

  Rotation of earth retarded, 95.

  Rumford, 39, 137.


  Silver oxide readily decomposed, 58.

  Solar rays, decomposition by, 59.

  Sulphur, 146.

  Sun--a source of high-temperature heat, 148.

  Sun’s heat, origin of, 150.
    spots, auroras, and cyclones correlated, 98.


  Tait, 141.

  Temperature of dissociation, 115.

  Thermo-electricity, 116.

  Thermopile, 117.

  Thomas Aquinas, 209.

  Thomson, William and James, 140.

  Tides, 146.

  Tissues, decay of, 164.


  Universe, its probable fate, 152.

  Units of heat and work, 46.


  Vegetation, 176.

  Velocity and energy, relation between, 16.

  Virtual velocities, 34.
    principle of, its history, 137.

  Vital force, whence derived, 171.

  Vitality, 194.

  Vitreous and resinous electricity, 63.

  Voltaic current, 69.
    and magnetism, 72.
    heating effect of, 73.
    chemical effect of, 74.


  Water at high level, 24.

  Watt, 138.

  Wild’s electro-magnetic machine, 103.

  Will, 194.

  Work, definition of, 15.
    unit of, 15.
    rise of true conceptions regarding, 138.


  Yeast-plant, 185.


THE END.




Transcriber’s Notes

Errors in punctuation have been fixed.

Page 60: “heterogenous bodies” changed to “heterogeneous bodies”

Page 80: “Analagous to this” changed to “Analogous to this”

Page 82: “etherial medium” changed to “ethereal medium”

Page 157: “without occcasioned” changed to “without occasioned”

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