Produced by Jon Richfield
FRAGMENTS OF SCIENCE:
A Series of Detached
ESSAYS, ADDRESSES, AND REVIEWS.
BY
JOHN TYNDALL, F.R.S.
Printed By Spottiswoode AND CO.
NEW-STREET SQUARE
PARLIAMENT STREET
SIXTH EDITION,
VOL. 1.
LONDON: LONGMANS, GREEN, AND CO.
1879.
All rights reserved.
PREFACE TO THE SIXTH EDITION.
VOL. I. INORGANIC NATURE.
I. THE CONSTITUTION OF NATURE.
II. RADIATION.
1. Visible and Invisible Radiation.
2. Origin and Character of Radiation. The Aether.
3. The Atomic Theory in reference to the Aether.
4. Absorption of Radiant Heat by Gases.
5. Formation of Invisible Foci.
6. Visible and Invisible Rays of the Electric Light.
Figure 1 Spectrum of Electric Light.
7. Combustion by Invisible Rays.
8. Transmutation of Rays: Calorescence.
9. Deadness of the Optic Nerve to the Calorific Rays.
10. Persistence of Rays.
11. Absorption of Radiant Heat by Vapours and Odours.
12. Aqueous Vapour in relation to the Terrestrial Temperatures.
13. Liquids and their Vapours in relation to Radiant Heat.
14. Reciprocity of Radiation and Absorption.
15. Influence of Vibrating Period and Molecular Form.
Physical Analysis of the Human Breath.
16. Summary and Conclusion.
III. ON RADIANT HEAT IN RELATION TO THE COLOUR AND
CHEMICAL CONSTITUTION OF BODIES.
IV. NEW CHEMICAL REACTIONS PRODUCED BY LIGHT.
1. DECOMPOSITION BY LIGHT.
Physical Considerations.
Production of Sky-blue by the Decomposition of Nitrite of Amyl.
2. ON THE BLUE COLOUR OF THE SKY, & THE POLARISATION OF SKYLIGHT.
3. THE SKY OF THE ALPS.
V. ON DUST AND DISEASE.
Experiments on Dusty Air.
The Germ Theory of Contagious Disease.
Parasitic Diseases of Silkworms. Pasteur's Researches.
Origin and Propagation of Contagious Matter.
The Germ Theory applied to Surgery.
The Luminous beam as a means of Research.
The Floating Matter of the Air.
Dr. Bennett's Experiments.
Application of Luminous beams to Water.
Chalk-water. Clark's Softening Process.
Cotton-wool Respirator.
Fireman's Respirator.
Helmholtz on Hay Fever.
VI. VOYAGE TO ALGERIA TO OBSERVE THE ECLIPSE.
VII. NIAGARA.
VIII THE PARALLEL ROADS OF GLEN ROY.
IX. ALPINE SCULPTURE.
X. RECENT EXPERIMENTS ON FOG-SIGNALS.
XI. ON THE STUDY OF PHYSICS.
XII. ON CRYSTALLINE AND SLATY CLEAVAGE.
XIII. ON PARAMAGNETIC AND DIAMAGNETIC FORCES.
XIV. PHYSICAL BASIS OF SOLAR CHEMISTRY.
XV. ELEMENTARY MAGNETISM.
XVI. ON FORCE.
XVII. CONTRIBUTIONS TO MOLECULAR PHYSICS.
XVIII. LIFE, AND LETTERS OF FARADAY.
XIX. THE COPLEY MEDALIST OF 1870.
XX. THE COPLEY MEDALIST OF 1871.
XXI. DEATH BY LIGHTNING.
XXII. SCIENCE AND THE 'SPIRITS'.
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VOL. II.
I. REFLECTIONS ON PRAYER AND NATURAL LAW.
II MIRACLES AND SPECIAL PROVIDENCES.
ADDITIONAL REMARKS ON MIRACLES.
III ON PRAYER AS A FORM OF PHYSICAL ENERGY.
IV. VITALITY.
V. MATTER AND FORCE.
VI. SCIENTIFIC MATERIALISM.
VII. AN ADDRESS TO STUDENTS.
VIII. SCIENTIFIC USE OF THE IMAGINATION.
IX. THE BELFAST ADDRESS.
X. APOLOGY FOR THE BELFAST ADDRESS.
XI. THE REV. JAMES MARTINEAU AND THE BELFAST ADDRESS.
XII. FERMENTATION, & ITS BEARINGS ON SURGERY & MEDICINE.
XIII. SPONTANEOUS GENERATION.
XIV. SCIENCE AND MAN.
XV. PROFESSOR VIRCHOW AND EVOLUTION.
XVI. THE ELECTRIC LIGHT.
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PREFACE TO THE SIXTH EDITION.
TO AVOID unwieldiness of bulk this edition of the 'Fragments' is
published in two volumes, instead of, as heretofore, in one.
The first volume deals almost exclusively with the laws and phenomena
of matter. The second trenches upon questions in which the phenomena
of matter interlace more or less with those of mind.
New Essays have been added, while old ones have been revised, and in
part recast. To be clear, without being superficial, has been my aim
throughout.
In neither volume have I aspired to sit in the seat of the scornful,
but rather to treat the questions touched upon with a tolerance, if
not a reverence, befitting their difficulty and weight.
Holding, as I do, the nebular hypothesis, I am logically bound to
deduce the life of the world from forces inherent in the nebula. With
this view, which is set forth in the second volume, it seemed but fair
to associate the reasons which cause me to conclude that every attempt
made in our day to generate life independently of antecedent life has
utterly broken down.
A discourse on the Electric Light winds up the Second volume. The
incongruity of its position is to be referred to the lateness of its
delivery.
********************
VOL. I. INORGANIC NATURE.
I. THE CONSTITUTION OF NATURE.
[Footnote: 'Fortnightly Review,' 1865, vol. iii. p. 129.]
WE cannot think of space as finite, for wherever in imagination we
erect a boundary, we are compelled to think of space as existing
beyond it. Thus by the incessant dissolution of limits we arrive at a
more or less adequate idea of the infinity of space. But, though
compelled to think of space as unbounded, there is no mental necessity
compelling us to think of it either as filled or empty; whether it is
so or not must be decided by experiment and observation. That it is
not entirely void, the starry heavens declare; but the question still
remains, Are the stars themselves hung in vacuo? Are the vast
regions which surround them, and across which their light is
propagated, absolutely empty? A century ago the answer to this
question, founded on the Newtonian theory, would have been, 'No, for
particles of light are incessantly shot through space.' The reply of
modern science is also negative, but on different grounds. It has the
best possible reasons for rejecting the idea of luminiferous
particles; but, in support of the conclusion that the celestial spaces
are occupied by matter, it is able to offer proofs almost as cogent as
those which can be adduced of the existence of an atmosphere round the
earth. Men's minds, indeed, rose to a conception of the celestial and
universal atmosphere through the study of the terrestrial and local
one. From the phenomena of sound, as displayed in the air, they
ascended to the phenomena of light, as displayed in the _aether_; which
is the name given to the interstellar medium.
The notion of this medium must not be considered as a vague or
fanciful conception on the part of scientific men. Of its reality
most of them are as convinced as they are of the existence of the sun
and moon. The luminiferous aether has definite mechanical properties.
It is almost infinitely more attenuated than any known gas, but its
properties are those of a solid rather than of a gas. It resembles
jelly rather than air. This was not the first conception of the
aether, but it is that forced upon us by a more complete knowledge of
its phenomena. A body thus constituted may have its boundaries; but,
although the aether may not be co-extensive with space, it must at all
events extend as far as the most distant visible stars. In fact it is
the vehicle of their light, and without it they could not be seen.
This all-pervading substance takes up their molecular tremors, and
conveys them with inconceivable rapidity to our organs of vision. It
is the transported shiver of bodies countless millions of miles
distant, which translates itself in human consciousness into the
splendour of the firmament at night.
If the aether have a boundary, masses of ponderable matter might be
conceived to exist beyond it, but they could emit no light. Beyond
the aether dark suns might burn; there, under proper conditions,
combustion might be carried on; fuel might consume unseen, and metals
be fused in invisible fires. A body, moreover, once heated there,
would continue for ever heated; a sun or planet once molten, would
continue for ever molten. For, the loss of heat being simply the
abstraction of molecular motion by the aether, where this medium is
absent no cooling could occur. A sentient being on approaching a
heated body in this region, would be conscious of no augmentation of
temperature. The gradations of warmth dependent on the laws of
radiation would not exist, and actual contact would first reveal the
heat of an extra ethereal sun.
Imagine a paddle-wheel placed in water and caused to rotate. From it,
as a centre, waves would issue in all directions, and a wader as he
approached the place of disturbance would be met by stronger and
stronger waves. This gradual augmentation of the impression made upon
the wader is exactly analogous to the augmentation of light when we
approach a luminous source. In the one case, however, the coarse
common nerves of the body suffice; for the other we must have the
finer optic nerve. But suppose the water withdrawn; the action at a
distance would then cease, and, as far as the sense of touch is
concerned, the wader would be first rendered conscious of the motion
of the wheel by the blow of the paddles. The transference of motion
from the paddles to the water is mechanically similar to the
transference of molecular motion from the heated body to the aether;
and the propagation of waves through the liquid is mechanically
similar to the propagation of light and radiant heat.
As far as our knowledge of space extends, we are to conceive it as the
holder of the luminiferous aether, through which are interspersed, at
enormous distances apart, the ponderous nuclei of the stars.
Associated with the star that most concerns us we have a group of dark
planetary masses revolving at various distances round it, each again
rotating on its own axis; and, finally, associated with some of these
planets we have dark bodies of minor note--the moons. Whether the
other fixed stars have similar planetary companions or not is to us a
matter of pure conjecture, which may or may not enter into our
conception of the universe. But probably every thoughtful person
believes, with regard to those distant suns, that there is, in space,
something besides our system on which they shine.
From this general view of the present condition of space, and of the
bodies contained in it, we pass to the enquiry whether things were so
created at the beginning. Was space furnished at once, by the fiat of
Omnipotence, with these burning orbs? In presence of the revelations
of science this view is fading more and more. Behind the orbs, we now
discern the nebulae from which they have been condensed. And without
going so far back as the nebulae, the man of science can prove that
out of common non-luminous matter this whole pomp of stars might have
been evolved.
The law of gravitation enunciated by Newton is, that every particle of
matter in the universe attracts every other particle with a force
which diminishes as the square of the distance increases. Thus the
sun and the earth mutually pull each other; thus the earth and the
moon are kept in company, the force which holds every respective pair
of masses together being the integrated force of their component
parts. Under the operation of this force a stone falls to the ground
and is warmed by the shock; under its operation meteors plunge into
our atmosphere and rise to incandescence. Showers of such meteors
doubtless fall incessantly upon the sun. Acted on by this force, the
earth, were it stopped in its orbit to-morrow, would rush towards, and
finally combine with, the sun. Heat would also be developed by this
collision. Mayer first, and Helmholtz and Thomson afterwards, have
calculated its amount. It would equal that produced by the combustion
of more than 5,000 worlds of solid coal, all this heat being generated
at the instant of collision. In the attraction of gravity, therefore,
acting upon non-luminous matter, we have a source of heat more
powerful than could be derived from any terrestrial combustion. And
were the matter of the universe thrown in cold detached fragments into
space, and there abandoned to the mutual gravitation of its own parts,
the collision of the fragments would in the end produce the fires of
the stars.
The action of gravity upon matter originally cold may, in fact, be the
origin of all light and heat, and also the proximate source of such
other powers as are generated by light and heat. But we have now to
enquire what is the light and what is the heat thus produced? This
question has already been answered in a general way. Both light and
heat are modes of motion. Two planets clash and come to rest; their
motion, considered as that of masses, is destroyed, but it is in great
part continued as a motion of their ultimate particles. It is this
latter motion, taken up by the aether, and propagated through it with
a velocity of 186,000 miles a second, that comes to us as the light
and heat of suns and stars. The atoms of a hot body swing with
inconceivable rapidity--billions of times in a second--but this power
of vibration necessarily implies the operation of forces between the
atoms themselves. It reveals to us that while they are held together
by one force, they are kept asunder by another, their position at any
moment depending on the equilibrium of attraction and repulsion. The
atoms behave as if connected by elastic springs, which oppose at the
same time their approach and their retreat, but which tolerate the
vibration called heat. The molecular vibration once set up is
instantly shared with the aether, and diffused by it throughout space.
We on the earth's surface live night and day in the midst of aethereal
commotion. The medium is never still. The cloud canopy above us may
be thick enough to shut out the light of the stars; but this canopy is
itself a warm body, which radiates its thermal motion through the
aether. The earth also is warm, and sends its heat-pulses incessantly
forth. It is the waste of its molecular motion in space that chills
the earth upon a clear night; it is the return of thermal motion from
the clouds which prevents the earth's temperature, on a cloudy night,
from falling so low. To the conception of space being filled, we must
therefore add the conception of its being in a state of incessant
tremor.
The sources of this vibration are the ponderable masses of the
universe. Let us take a sample of these and examine it in detail.
When we look to our planet, we find it to be an aggregate of solids,
liquids, and gases. Subjected to a sufficiently low temperature, the
two last, would also assume the solid form. When we look at any one
of these, we generally find it composed of still more elementary
parts. We learn, for example, that the water of our rivers is formed
by the union, in definite proportions, of two gases, oxygen and
hydrogen. We know how to bring these constituents together, so as to
form water: we also know how to analyse the water, and recover from it
its two constituents. So, likewise, as regards the solid portions of
the earth. Our chalk hills, for example, are formed by a combination
of carbon, oxygen, and calcium. These are the so-called elements the
union of which, in definite proportions, has resulted in the formation
of chalk. The flints within the chalk we know to be a compound of
oxygen and silicium, called silica; and our ordinary clay is, for the
most part, formed by the union of silicium, oxygen, and the well-known
light metal, aluminium. By far the greater portion of the earth's
crust is compounded of the elementary substances mentioned in these
few lines.
The principle of gravitation has been already described as an
attraction which every particle of matter, however small, exerts on
every other particle. With gravity there is no selection; no
particular atoms choose, by preference, other particular atoms as
objects of attraction; the attraction of gravitation is proportional
simply to the quantity of the attracting matter, regardless of its
quality. But in the molecular world which we have now entered matters
are otherwise arranged. Here we have atoms between which a strong
attraction is exercised, and also atoms between which a weak
attraction is exercised. One atom can jostle another out of its place,
in virtue of a superior force of attraction. But, though the amount
of force exerted varies thus from atom to atom, it is still an
attraction of the same mechanical quality, if I may use the term, as
that of gravity itself. Its intensity might be measured in the same
way, namely by the amount of motion which it can generate in a certain
time. Thus the attraction of gravity at the earth's surface is
expressed by the number 32; because, when acting freely on a body for
a second of time, gravity imparts to the body a velocity of thirty-two
feet a second. In like manner the mutual attraction of oxygen and
hydrogen might be measured by the velocity imparted to the atoms in
their rushing together. Of course such a unit of time as a second is
not here to be thought of, the whole interval required by the atoms to
cross the minute spaces which separate them amounting only to an
inconceivably small fraction of a second.
It has been stated that when a body falls to the earth it is warmed by
the shock. Here, to use the terminology of Mayer, we have a
_mechanical_ combination of the earth and the body. Let us suffer the
falling body and the earth to dwindle in imagination to the size of
atoms, and for the attraction of gravity let us substitute that of
chemical affinity; we have then what is called a chemical combination.
The effect of the union in this case also is the development of heat,
and from the amount of heat generated we can infer the intensity of
the atomic pull. Measured by ordinary mechanical standards, this is
enormous. Mix eight pounds of oxygen with one of hydrogen, and pass a
spark through the mixture; the gases instantly combine, their atoms
rushing over the little distances which separate them. Take a weight
of 47,000 pounds to an elevation of 1,000 feet above the earth's
surface, and let it fall; the energy with which it will strike the
earth will not exceed that of the eight pounds of oxygen atoms, as
they dash against one pound of hydrogen atoms to form water.
It is sometimes stated that gravity is distinguished from all other
forces by the fact of its resisting conversion into other forms of
force. Chemical affinity, it is said, can be converted into heat and
light, and these again into magnetism and electricity: but gravity
refuses to be so converted; being a force maintaining itself under all
circumstances, and not capable of disappearing to give place to
another. The statement arises from vagueness of thought. If by it be
meant that a particle of matter can never be deprived of its weight,
the assertion is correct; but the law which affirms the convertibility
of natural forces was never intended, in the minds of those who
understood it, to affirm that such a conversion as that here implied
occurs in any case whatever. As regards convertibility into heat,
gravity and chemical affinity stand on precisely the same footing.
The attraction in the one case is as indestructible as in the other.
Nobody affirms that when a stone rests upon the surface of the earth,
the mutual attraction of the earth and stone is abolished; nobody
means to affirm that the mutual attraction of oxygen for hydrogen
ceases, after the atoms have combined to form water. What is meant,
in the case of chemical affinity, is, that the pull of that affinity,
acting through a certain space, imparts a motion of translation of the
one atom towards the other. This motion is not heat, nor is the force
that produces it heat. But when the atoms strike and recoil, the
motion of translation is converted into a motion of vibration, which
is heat. The vibration, however, so far from causing the extinction
of the original attraction, is in part carried on by that attraction.
The atoms recoil, in virtue of the elastic force which opposes actual
contact, and in the recoil they are driven too far back. The original
attraction then triumphs over the force of recoil, and urges the atoms
once more together. Thus, like a pendulum, they oscillate, until
their motion is imparted to the surrounding aether; or, in other
words, until their heat becomes radiant heat.
In this sense, and in this sense only, is chemical affinity converted
into heat. There is, first of all, the attraction between the atoms;
there is, secondly, space between them. Across this space the
attraction urges them. They collide, they recoil, they oscillate.
There is here a change in the form of the motion, but there is no real
loss. It is so with the attraction of gravity. To produce motion by
gravity space must also intervene between the attracting bodies. When
they strike together motion is apparently destroyed, but in reality
there is no destruction. Their atoms are suddenly urged together by
the shock; by their own perfect elasticity these atoms recoil; and
thus is set up the molecular oscillation which, when communicated to
the proper nerves, announces itself as heat.
It was formerly universally supposed that by the collision of
unelastic bodies force was destroyed. Men saw, for example, that when
two spheres of clay, painter's putty, or lead for example, were urged
together, the motion possessed by the masses, prior to impact, was
more or less annihilated. They believed in an absolute destruction of
the force of impact. Until recent times, indeed, no difficulty was
experienced in believing this, whereas, at present, the ideas of force
and its destruction refuse to be united in most philosophic minds. In
the collision of elastic bodies, on the contrary, it was observed that
the motion with which they clashed together was in great part restored
by the resiliency of the masses, the more perfect the elasticity the
more complete being the restitution. This led to the idea of
perfectly elastic bodies--bodies competent to restore by their recoil
the whole of the motion which they possessed before impact--and this
again to the idea of the _conservation_ of force, as opposed to that
destruction of force which was supposed to occur when unelastic bodies
met in collision.
We now know that the principle of conservation holds equally good with
elastic and unelastic bodies. Perfectly elastic bodies would develop
no heat on collision. They would retain their motion afterwards,
though its direction might be changed; and it is only when sensible
motion is wholly or partly destroyed, that heat is generated. This
always occurs in unelastic collision, the heat developed being the
exact equivalent of the sensible motion extinguished. This heat
virtually declares that the property of elasticity, denied to the
masses, exists among their atoms; by the recoil and oscillation of
which the principle of conservation is vindicated.
But ambiguity in the use of the term 'force' makes itself more and
more felt as we proceed. We have called the attraction of gravity a
force, without any reference to motion. A body resting on a shelf is
as much pulled by gravity as when, after having been pushed off the
shelf, it falls towards the earth. We applied the term force also to
that molecular attraction which we called chemical affinity. When,
however, we spoke of the conservation of force, in the case of elastic
collision, we meant neither a pull nor a push, which, as just
indicated, might be exerted upon inert matter, but we meant force
invested in motion--the _vis viva_, as it is called, of the colliding
masses.
Force in this form has a definite mechanical measure, in the amount of
work that it can perform. The simplest form of work is the raising of
a weight. A man walking up-hill, or up-stairs, with a pound weight in
his hand, to an elevation say of sixteen feet, performs a certain
amount of work, over and above the lifting of his own body. If he
carries the pound to a height of thirty-two feet, he does twice the
work; if to a height of forty-eight feet, he does three times the
work; if to sixty-four feet, he does four times the work, and so on.
If, moreover, he carries up two pounds instead of one, other things
being equal, he does twice the work; if three, four, or five pounds,
he does three, four, or five times the work. In fact, it is plain
that the work performed depends on two factors, the weight raised and
the height to which it is raised. It is expressed by the product of
these two factors.
But a body may be caused to reach a certain elevation in opposition to
the force of gravity, without being actually carried up. If a hodman,
for example, wished to land a brick at an elevation of sixteen feet
above the place where he stood, he would probably pitch it up to the
bricklayer. He would thus impart, by a sudden effort, a velocity to
the brick sufficient to raise it to the required height; the work
accomplished by that effort being precisely the same as if he had
slowly carried up the brick. The initial velocity to be imparted, in
this case, is well known. To reach a height of sixteen feet, the
brick must quit the man's hand with a velocity of thirty-two feet a
second. It is needless to say, that a body starting with any
velocity, would, if wholly unopposed or unaided, continue to move for
ever with the same velocity. But when, as in the case before us, the
body is thrown upwards, it moves in opposition to gravity, which
incessantly retards its motion, and finally brings it to rest at an
elevation of sixteen feet. If not here caught by the bricklayer, it
would return to the hodman with an accelerated motion, and reach his
hand with the precise velocity it possessed on quitting it.
An important relation between velocity and work is here to be pointed
out. Supposing the hodman competent to impart to the brick, at
starting, a velocity of sixty-four feet a second, or twice its former
velocity, would the amount of work performed be twice what it was in
the first instance? No; it would be four times that quantity; for a
body starting with twice the velocity of another, will rise to four
times the height. In like manner, a three-fold velocity will give a
nine-fold elevation, a four-fold velocity will give a sixteen-fold
elevation, and so on. The height attained, then, is not proportional
to the initial velocity, but to the square of the velocity. As
before, the work is also proportional to the weight elevated. Hence
the work which any moving mass whatever is competent to perform, in
virtue of the motion which it at any moment possesses, is jointly
proportional to its weight and the square of its velocity. Here,
then, we have a second measure of work, in which we simply translate
the idea of height into its equivalent idea of motion.
In mechanics, the product of the mass of a moving body into the square
of its velocity, expresses what is called the _vis viva_, or living
force. It is also sometimes called the 'mechanical effect.' If, for
example, a cannon pointed to the zenith urge a ball upwards with twice
the velocity imparted to a second ball, the former will rise to four
times the height attained by the latter. If directed against a
target, it will also do four times the execution. Hence the
importance of imparting a high velocity to projectiles in war. Having
thus cleared our way to a perfectly definite conception of the _vis
viva_ of moving masses, we are prepared for the announcement that the
heat generated by the shock of a falling body against the earth is
proportional to the _vis viva_ annihilated. The heat is proportional to
the square of the velocity. In the case, therefore, of two
cannon-balls of equal weight, if one strike a target with twice the
velocity of the other, it will generate four times the heat, if with
three times the velocity, it will generate nine times the heat, and so
on.
Mr. Joule has shown that a pound weight falling from a height of 772
feet, or 772 pounds falling through one foot, will generate by its
collision with the earth an amount of heat sufficient to raise a pound
of water one degree Fahrenheit in temperature. 772 "foot-pounds"
constitute the mechanical equivalent of heat. Now, a body falling
from a height of 772 feet, has, upon striking the earth, a velocity of
223 feet a second; and if this velocity were imparted to the body, by
any other means, the quantity of heat generated by the stoppage of its
motion would be that stated above. Six times that velocity, or 1,338
feet, would not be an inordinate one for a cannon-ball as it quits the
gun. Hence, a cannon-ball moving with a velocity of 1,338 feet a
second, would, by collision, generate an amount of heat competent to
raise its own weight of water 36 degrees Fahrenheit in temperature. If
composed of iron, and if all the heat generated were concentrated in
the ball itself, its temperature would be raised about 360 degrees
Fahrenheit; because one degree in the case of water is equivalent to
about ten degrees in the case of iron. In artillery practice, the
heat generated is usually concentrated upon the front of the bolt, and
on the portion of the target first struck. By this concentration the
heat developed becomes sufficiently intense to raise the dust of the
metal to incandescence, a flash of light often accompanying collision
with the target.
Let us now fix our attention for a moment on the gunpowder which urges
the cannon-ball. This is composed of combustible matter, which if
burnt in the open air would yield a certain amount of heat. It will
not yield this amount if it perform the work of urging a ball. The
heat then generated by the gunpowder will fall short of that produced
in the open air, by an amount equivalent to the _vis viva_ of the ball;
and this exact amount is restored by the ball on its collision with
the target. In this perfect way are heat and mechanical motion
connected.
Broadly enunciated, the principle of the conservation of force
asserts, that the quantity of force in the universe is as unalterable
as the quantity of matter; that it is alike impossible to create force
and to annihilate it. But in what sense are we to understand this
assertion? It would be manifestly inapplicable to the force of
gravity as defined by Newton; for this is a force varying inversely as
the square of the distance; and to affirm the constancy of a varying
force would be self-contradictory. Yet, when the question is properly
understood, gravity forms no exception to the law of conservation.
Following the method pursued by Helmholtz, I will here attempt an
elementary exposition of this law. Though destined in its
applications to produce momentous changes in human thought, it is not
difficult of comprehension.
For the sake of simplicity we will consider a particle of matter,
which we may call F, to be perfectly fixed, and a second movable
particle, D, placed at a distance from F. We will assume that these
two particles attract each other according to the Newtonian law. At a
certain distance, the attraction is of a certain definite amount,
which might be determined by means of a spring balance. At half this
distance the attraction would be augmented four times; at a third of
the distance, nine times; at one-fourth of the distance, sixteen
times, and so on. In every case, the attraction might be measured by
determining, with the spring balance, the amount of tension just
sufficient to prevent D from moving towards F. Thus far we have
nothing whatever to do with motion; we deal with statics, not with
dynamics. We simply take into account the _distance_ of D from F, and
the _pull_ exerted by gravity at that distance.
It is customary in mechanics to represent the magnitude of a force by
a line of a certain length, a force of double magnitude being
represented by a line of double length, and so on. Placing then the
particle D at a distance from F, we can, in imagination, draw a
straight line from D to F, and at D erect a perpendicular to this
line, which shall represent the amount of the attraction exerted on D.
If D be at a very great distance from F, the attraction will be very
small, and the perpendicular consequently very short. If the distance
be practically infinite, the attraction is practically _nil_. Let us
now suppose at every point in the line joining F and D a perpendicular
to be erected, proportional in length to the attraction exerted at
that point; we thus obtain an infinite number of perpendiculars, of
gradually increasing length, as D approaches F. Uniting the ends of
all these perpendiculars, we obtain a curve, and between this curve
and the straight line joining F and D we have an area containing all
the perpendiculars placed side by side. Each one of this infinite
series of perpendiculars representing an attraction, or tension, as it
is sometimes called, the area just referred to represents the sum of
the tensions exerted upon the particle D, during its passage from its
first position to F.
Up to the present point we have been dealing with tensions, not with
motion. Thus far _vis viva_ has been entirely foreign to our
contemplation of D and F. Let us now suppose D placed at a
practically infinite distance from F; here, as stated, the pull of
gravity would be infinitely small, and the perpendicular representing
it would dwindle almost to a point. In this position the sum of the
tensions capable of being exerted on D would be a maximum. Let D now
begin to move in obedience to the infinitesimal attraction exerted
upon it. Motion being once set up, the idea of _vis viva_ arises. In
moving towards F the particle D consumes, as it were, the tensions.
Let us fix our attention on D, at any point of the path over which it
is moving. Between that point and F there is a quantity of unused
tensions; beyond that point the tensions have been all consumed, but
we have in their place an equivalent quantity of _vis viva_. After D
has passed any point, the tension previously in store at that point
disappears, but not without having added, during the infinitely small
duration of its action, a due amount of motion to that previously
possessed by D. The nearer D approaches to F, the smaller is the sum
of the tensions remaining, but the greater is the _vis viva_; the
farther D is from F, the greater is the sum of the unconsumed
tensions, and the less is the living force. Now the principle of
conservation affirms _not_ the constancy of the value of the tensions of
gravity, nor yet the constancy of the _vis viva_, taken separately, but
the absolute constancy of the value of both taken together. At the
beginning the _vis viva_ was zero, and the tension area was a maximum;
close to F the _vis viva_ is a maximum, while the tension area is zero.
At every other point, the work-producing power of the particle D
consists in part of _vis viva_, and in part of tensions.
If gravity, instead of being attraction, were repulsion, then, with
the particles in contact, the sum of the tensions between D and F
would be a maximum, and the _vis viva_ zero. If, in obedience to the
repulsion, D moved away from F, _vis viva_ would be generated; and the
farther D retreated from F the greater would be its _vis viva_, and the
less the amount of tension still available for producing motion.
Taking repulsion as well as attraction into account, the principle of
the conservation of force affirms that the mechanical value of the
_tensions_ and _vires vivae_ of the material universe, so far as we know
it, is a constant quantity. The universe, in short, possesses two
kinds of property which are mutually convertible. The diminution of
either carries with it the enhancement of the other, the total value
of the property remaining unchanged.
The considerations here applied to gravity apply equally to chemical
affinity. In a mixture of oxygen and hydrogen the atoms exist apart,
but by the application of proper means they may be caused to rush
together across that space that separates them. While this space
exists, and as long as the atoms have not begun to move towards each
other, we have tensions and nothing else. During their motion towards
each other the tensions, as in the case of gravity, are converted into
_vis viva_. After they clash we have still _vis viva_, but in another
form. It _was_ translation, it _is_ vibration. It _was_ molecular
transfer, it _is_ heat.
It is possible to reverse these processes, to unlock the combined
atoms and replace them in their first positions. But, to accomplish
this, as much heat would be required as was generated by their union.
Such reversals occur daily and hourly in nature. By the solar waves,
the oxygen of water is divorced from its hydrogen in the leaves of
plants. As molecular _vis viva_ the waves disappear, but in so doing
they re-endow the atoms of oxygen and hydrogen with tension. The
atoms are thus enabled to recombine, and when they do so they restore
the precise amount of heat consumed in their separation. The same
remarks apply to the compound of carbon and oxygen, called carbonic
acid, which is exhaled from our lungs, produced by our fires, and
found sparingly diffused everywhere throughout the air. In the leaves
of plants the sunbeams also wrench the atoms of carbonic acid asunder,
and sacrifice themselves in the act; but when the plants are burnt,
the amount of heat consumed in their production is restored.
This, then, is the rhythmic play of Nature as regards her forces.
Throughout all her regions she oscillates from tension to _vis viva_,
from _vis viva_ to tension. We have the same play in the planetary
system. The earth's orbit is an ellipse, one of the foci of which is
occupied by the sun. Imagine the earth at the most distant part of
the orbit. Her motion, and consequently her _vis viva_, is then a
minimum. The planet rounds the curve, and begins its approach to the
sun. In front it has a store of tensions, which are gradually
consumed, an equivalent amount of _vis viva_ being generated. When
nearest to the sun the motion, and consequently the _vis viva_, reach a
maximum. But here the available tensions have been used up. The
earth rounds this portion of the curve and retreats from the sun.
Tensions are now stored up, but _vis viva_ is lost, to be again restored
at the expense of the complementary force on the opposite side of the
curve. Thus beats the heart of the universe, but without increase or
diminution of its total stock of force.
I have thus far tried to steer clear amid confusion, by fixing the
mind of the reader upon things rather than upon names. But good names
are essential; and here, as yet, we are not provided with such. We
have had the force of gravity and living force--two utterly distinct
things. We have had pulls and tensions; and we might have had the
force of heat, the force of light, the force of magnetism, or the
force of electricity--all of which terms have been employed more or
less loosely by writers on physics. This confusion is happily avoided
by the introduction of the term 'energy,' which embraces both _tension_
and _vis viva_. Energy is possessed by bodies already in motion; it is
then actual, and we agree to call it actual or dynamic energy. It is
our old _vis viva_. On the other hand, energy is possible to bodies not
in motion, but which, in virtue of attraction or repulsion, possess a
power of motion which would realise itself if all hindrances were
removed. Looking, for example, at gravity; a body on the earth's
surface in a position from which it cannot fall to a lower one
possesses no energy. It has neither motion nor power of motion. But
the same body suspended at a height above the earth has a power of
motion, though it may not have exercised it. Energy is possible to
such a body, and we agree to call this potential energy. It consists
of our old tensions. We, moreover, speak of the conservation of
energy, instead of the conservation of force; and say that the sum of
the potential and dynamic energies of the material universe is a
constant quantity.
A body cast upwards consumes the actual energy of projection, and lays
up potential energy. When it reaches its utmost height all its actual
energy is consumed, its potential energy being then a maximum. When
it returns, there is a reconversion of the potential into the actual.
A pendulum at the limit of its swing possesses potential energy; at
the lowest point of its arc its energy is all actual. A patch of snow
resting on a mountain slope has potential energy; loosened, and
shooting down as an avalanche, it possesses dynamic energy. The
pine-trees growing on the Alps have potential energy; but rushing down
the _Holzrinne_ of the woodcutters they possess actual energy. The same
is true of the mountains themselves. As long as the rocks which
compose them can fall to a lower level, they possess potential energy,
which is converted into actual when the frost ruptures their cohesion
and hands them over to the action of gravity. The stone avalanches of
the Matterhorn and Weisshorn are illustrations in point. The hammer
of the great bell of Westminster, when raised before striking,
possesses potential energy; when it falls, the energy becomes dynamic;
and after the stroke, we have the rhythmic play of potential and
dynamic in the vibrations of the bell. The same holds good for the
molecular oscillations of a heated body. An atom is driven against
its neighbour, and recoils. The ultimate amplitude of the recoil
being attained, the motion of the atom in that direction is checked,
and for an instant its energy is all potential. It is then drawn
towards its neighbour with accelerated speed; thus, by attraction,
converting its potential into dynamic energy. Its motion in this
direction is also finally checked, and again, for an instant, its
energy is all potential. It once more retreats, converting, by
repulsion, its potential into dynamic energy, till the latter attains
a maximum, after which it is again changed into potential energy.
Thus, what is true of the earth, as she swings to and fro in her
yearly journey round the sun, is also true of her minutest atom. We
have wheels within wheels, and rhythm within rhythm.
When a body is heated, a change of molecular arrangement always
occurs, and to produce this change heat is consumed. Hence, a portion
only of the heat communicated to the body remains as dynamic energy.
Looking back on some of the statements made at the beginning of this
article, now that our knowledge is more extensive, we see the
necessity of qualifying them. When, for example, two bodies clash,
heat is generated; but the heat, or molecular dynamic energy,
developed at the moment of collision, is not the exact equivalent of
the sensible dynamic energy destroyed. The true equivalent is this
heat, plus the potential energy conferred upon the molecules by the
placing of greater distances between them. This molecular potential
energy is afterwards, on the cooling of the body, converted into heat.
Wherever two atoms capable of uniting together by their mutual
attractions exist separately, they form a store of potential energy.
Thus our woods, forests, and coal-fields on the one hand, and our
atmospheric oxygen on the other, constitute a vast store of energy of
this kind--vast, but far from infinite. We have, besides our
coal-fields, metallic bodies more or less sparsely distributed through
the earth's crust. These bodies can be oxydised; and hence they are,
so far as they go, stores of energy. But the attractions of the great
mass of the earth's crust are already satisfied, and from them no
further energy can possibly be obtained. Ages ago the elementary
constituents of our rocks clashed together and produced the motion of
heat, which was taken up by the aether and carried away through
stellar space. It is lost for ever as far as we are concerned. In
those ages the hot conflict of carbon, oxygen, and calcium produced
the chalk and limestone hills which are now cold; and from this
carbon, oxygen, and calcium no further energy can be derived. So it
is with almost all the other constituents of the earth's crust. They
took their present form in obedience to molecular force; they turned
their potential energy into dynamic, and yielded it as radiant heat to
the universe, ages before man appeared upon this planet. For him a
residue of potential energy remains, vast, truly, in relation to the
life and wants of an individual, but exceedingly minute in comparison
with the earth's primitive store.
To sum up. The whole stock of energy or working-power in the world
consists of attractions, repulsions, and motions. If the attractions
and repulsions be so circumstanced as to be able to produce motion,
they are sources of working-power, but not otherwise. As stated a
moment ago, the attraction exerted between the earth and a body at a
distance from the earth's surface, is a source of working-power;
because the body can be moved by the attraction, and in falling can
perform work. When it rests at its lowest level it is not a source of
power or energy, because it can fall no farther. But though it has
ceased to be a source of _energy_, the attraction of gravity still acts
as a _force_, which holds the earth and weight together.
The same remarks apply to attracting atoms and molecules. As long as
distance separates them, they can move across it in obedience to the
attraction; and the motion thus produced may, by proper appliances, be
caused to perform mechanical work. When, for example, two atoms of
hydrogen unite with one of oxygen, to form water, the atoms are first
drawn towards each other--they move, they clash, and then by virtue of
their resiliency, they recoil and quiver. To this quivering motion we
give the name of heat. This atomic vibration is merely the
redistribution of the motion produced by the chemical affinity; and
this is the only sense in which chemical affinity can be said to be
converted into heat. We must not imagine the chemical attraction
destroyed, or converted into anything else. For the atoms, when
mutually clasped to form a molecule of water, are held together by the
very attraction which first drew them towards each other. That which
has really been expended is the _pull_ exerted through the space by
which the distance between the atoms has been diminished.
If this be understood, it will be at once seen that gravity, as before
insisted on, may, in this sense, be said to be convertible into heat;
that it is in reality no more an outstanding and inconvertible agent,
as it is sometimes stated to be, than is chemical affinity. By the
exertion of a certain pull through a certain space, a body is caused
to clash with a certain definite velocity against the earth. Heat is
thereby developed, and this is the only sense in which gravity can be
said to be converted into heat. In no case is the _force_, which
produces the motion annihilated or changed into anything else. The
mutual attraction of the earth and weight exists when they are in
contact, as when they were separate but the ability of that attraction
to employ itself in the production of motion does not exist.
The transformation, in this case, is easily followed by the mind's
eye. First, the weight as a whole is set in motion by the attraction
of gravity. This motion of the mass is arrested by collision with the
earth, being broken up into molecular tremors, to which we give the
name of heat.
And when we reverse the process, and employ those tremors of heat to
raise a weight--which is done through the intermediation of an elastic
fluid in the steam-engine--a certain definite portion of the molecular
motion is consumed. In this sense, and in this sense only, can the
heat be said to be converted into gravity; or, more correctly, into
potential energy of gravity. Here the destruction of the heat has
created no new attraction; but the old attraction has conferred upon
it a power of exerting a certain definite pull, between the
starting-point of the falling weight and the earth.
When, therefore, writers on the conservation of energy speak of
tensions being 'consumed' and 'generated,' they do not mean thereby
that old attractions have been annihilated, and new ones brought into
existence, but that, in the one case, the power of the attraction to
produce motion has been diminished by the shortening of the distance
between the attracting bodies, while, in the other case, the power of
producing motion has been augmented by the increase of the distance.
These remarks apply to all bodies, whether they be sensible masses or
molecules.