making this determination, we may point out that if a weight be raised a
certain height, the work which is done in raising it will be given out
by the weight in its descent. If you carry a 1 lb. weight to the top of
the London Monument, which is 200 ft. high, you perform 200 units of
work. When the weight is at the top, the work is not lost; for let the
weight be attached to a cord passing over a pulley, and it will, as it
descends, draw up to the top another 1 lb. weight.[21] If you drop the
weight so that it falls freely, it descends with a continually
increasing velocity, strikes the pavement, and comes to rest. Still your
work is not lost. The collision of the weight and the pavement develops
_heat_, just as in the case of the experiment depicted on page 168, but
to a less degree—the increase of temperature might not be sensible to
the touch, but could be recognized by delicate instruments. Your work,
then, has now changed into the form of heat—the weight and the pavement
are hotter than before. This heat is carried off by contiguous
substances. But still your work is not lost, for it has made the earth
warmer. The heat, however, soon flows away by radiation from the earth,
and is diffused into space. The final result of your work is, then, that
a certain _measurable_ quantity of heat has been sent off into space. Is
your work now finally lost? Not so: in reality, it is only diffused
throughout the universe in the form of radiant heat of low intensity.
Yet it is lost for ever for useful purposes; for from this final form of
diffused heat there is no known or conceivable process by which heat can
be gathered up again.
Footnote 21:
See Note B, at the end.
Dr. Joule arranged paddles of brass or iron, so that they could turn
freely in a circular box containing water or quicksilver. From the sides
of the box partitions projected inwards, which contained openings that
permitted the divided arms of the paddle to pass, and preventing the
liquid from moving _en masse_, thus caused a churning action when the
paddle was turned. Now, every one who has worked a rotatory churn knows
that a considerable resistance is offered to this action; but every one
does not know that under these circumstances the liquid becomes warmer.
It was Dr. Joule’s object to discover how much the temperature of his
liquid was raised by a measured quantity of work. He used very delicate
thermometers, and had to take a number of precautions which need not
here be described; and he obtained the definite quantity of work by the
descent of a known weight through a known distance, a cord attached to
the weight being wound on a drum, which communicated motion to the
paddle. The experiments were conducted with varying circumstances, to
avoid chances of error, and were repeated very many times until uniform
and consistent indications were always obtained. The result of the
experiments showed that 772 units of work (foot-pounds) furnished heat
which would raise the temperature of 1 lb. of water from 32° to 33° F.,
which is the unit of heat. This number, 772, is a constant of the
greatest importance in scientific and practical calculations, and is
called “_the mechanical equivalent of heat_.” The amount of _work_ it
represents is sometimes called a “Joule,” and is always represented in
algebraical formulæ by “J.” Mr. Joule’s first paper appeared in 1843,
and soon afterwards various branches of the subject of “The Equivalence
and Persistence of Forces” were taken up by a number of able men, who
have advanced its principles along various lines of inquiry. Among the
most noted contributors to this question we find the names of Sir
William Thomson, Helmholtz, James Thomson, Rankin, Clausius, Tait,
Andrews, and Maxwell.
In the steam engine the case is the inverse of that presented by the
above-named experiment of Dr. Joule’s. Here we have heat producing work.
Now, the quantity of steam which enters the cylinder of a steam engine
may be found, and the temperature of the steam can be determined, and
from these the amount of _heat_ which passes into the cylinder per
minute, say, can be calculated. A large portion of this heat is, in an
ordinary engine, yielded up to the condensing water, and another part is
lost by conduction and radiation from the cylinder, condenser, pipes,
&c. But both these quantities can be estimated. When the amount is
compared with that entering the cylinder in the steam, a difference is
always found, which leaves a quantity of heat unaccounted for. When this
quantity is compared with the _work_ done by the engine in the same
interval (which work can be measured as described on page 10), it is
always found that for every 772 units of work a unit of heat has
disappeared from the cylinder. The numerical relation between work and
heat which is established in these two cases has been tested in many
quite different ways; and, within the limits of experimental errors,
always with the same numerical result. But equally definite quantitative
relations are known to exist among all the other forms of force; and the
manner in which these are convertible into each other has already been
indicated, although want of space prevents full illustration of this
part of the subject. It may, however, be seen that each form of force
can be mediately or immediately converted into mechanical effect, hence
each is expressible in terms of work. That is to say, we can assign to a
unit of electricity, for example, a number expressing the work which it
would do if entirely converted into work; and the same number also
expresses the work which would be required to produce the unit of
electricity. An ounce of hydrogen in combining with 8 oz. of oxygen
produces a certain measurable quantity of heat. If that heat, say = H,
were all converted into work, we now know that the work would = HJ.
Hence we can express a definite chemical action in terms of _work_. The
same is generally true of all physical forces, though in some cases,
such as light, vital action, &c., the quantitative relations have not
yet been definitely determined.
Since, then, all the forces with which we are acquainted are expressible
(though the exact relations of some have yet to be discovered) in terms
of work, it is found of great advantage to consider the power of doing
work as the common measure of doing all these. Thus, if we define
_energy_ as that which does, or that which is capable of doing, work, we
have a term extremely convenient in the description of some aspects of
our subject. Thus we can now speak of the _energies of nature_, instead
of the _forces_. And all forces, active or passive, may be summed up in
one word—_energy_. And, further, the great discovery of the conservation
of forces under definite equivalents, may be summed up very briefly in
this statement—THE AMOUNT OF ENERGY IN THE UNIVERSE IS CONSTANT. To make
this statement clear requires that a distinction between two forms of
every kind of energy be pointed out. To recur to the example before
imagined: if you carry the 1 lb. weight up the Monument, and deposit it
on the ledge at the top, it might lie there for a thousand years before
it was made to give back the work you had performed upon it. That work
has been, in a manner, _stored up_ by the _position_ you have given to
your weight. Now, in taking up the weight, you expended energy—you
really performed work: that is an instance of energy in operation, and
may be termed “actual energy.” In what form does the energy exist during
the thousand years we may suppose your weight to lie at the top of the
Monument? It is ready to yield up your work again at any moment it is
permitted to descend, and it possesses therefore during the whole period
a _potential energy_ equal in amount to the _actual energy_ you bestowed
upon it. A similar distinction between actual and potential energy
exists with regard to every form of force. If by any means you separate
an atom of carbon from an atom of oxygen, you exert actual energy. The
process is analogous to carrying up the weight. The atoms when separated
possess _potential_ energy,—they can rush together again, like the
weight to the earth, and in doing so will give out the work which was
expended on their separation. A parallel illustration might be drawn
from electrical force.
A typical example of the storing up of energy is furnished by a
crossbow. The moment a man begins to bend the bow he is doing work,
because he pulls the string in opposition to the bow’s resistance to a
change in its form; and it is plain that the amount of energy thus
expended is measurable. Suppose, now, the bow has been bent and the
string caught in the notch, from which it is released by drawing the
trigger when the discharge of the bow is desired. The bow may be
retained for an indefinite period in the bent condition, and in this
state it possesses, in the form of _potential energy_, all the work
which has been expended in bending it, and which it will, in fact, give
out, in some way or other, whenever the trigger is drawn. To fix our
ideas, let us suppose that to draw the string over the notch required a
pull of 50 lbs. over a space of 6 in.; that is equivalent to 50 × ½ = 25
units of work. Now let the bow be used to shoot an arrow weighing ¼ lb.
vertically upwards. The height in feet to which the arrow will rise
multiplied into its weight in pounds will be the work done upon it by
the bow. Now, we say that experiment proves that in the case supposed
the arrow would rise just 100 ft., so that the work done _by_ the bow (¼
× 100 = 25) would be precisely that done _upon it_. For the sake of
simplicity, we keep this illustration free from the mention of
interfering causes, which have to be considered and allowed for when the
matter is put to the real test of quantitative experiment. The instance
of the crossbow brings into notice a highly instructive circumstance,
which is this: the bow, which it may have taken the strength of a
Hercules to bend, will shoot its bolt by the mere touch of a child on
the trigger. In the same way, when a man fires a gun, he merely permits
the _potential_ energy contained in the charge to convert itself into
_actual_, or _kinetic_, energy. The real source of the energy, in the
case of the child discharging the crossbow, is the muscular power of the
man who drew it; the real source of the energy in exploding gunpowder is
the separation of carbon atoms from oxygen atoms, and that has been done
by the sun’s rays, as truly as the string was pulled away from the bow
by muscular power. If we turn our attention to nitro-glycerine or to
nitro-cellulose, we can, by following the chemical actions giving rise
to these substances, in like manner trace their energies to our great
luminary. The unstable union by which oxygen and nitrogen atoms are
locked up in the solid and liquid forms of nitro-cellulose and
nitro-glycerine is also the work of the sun; for nitrogen acids, or
rather nitrates, are produced naturally under certain electrical and
other conditions of the atmosphere, which are due, directly or
indirectly, to the sun’s action; and they cannot be formed artificially,
except by imitating the natural conditions, as by passing electric
sparks through air, &c.
It will now be understood, as regards the wonderful relations between
animal and vegetable life, which have already been alluded to more than
once, how the sun, by expending actual energy, separates atoms of carbon
from atoms of oxygen in the leaves of plants, and confers upon these a
position of advantage, _i.e._, potential energy; and how animals,
absorbing the separated carbon in the form of food, and inhaling the
separated oxygen in the air they breathe, cause the conversion of the
potential into actual energy, which appears in the heat, movements, and
vital functions of the animal body. In coal we have the energy which
plants absorbed from the sun ages ago, stored up in a potential form.
The carbon atoms are ready to rush into union with oxygen atoms, and
convert their energy of position into the energies developed by chemical
action, viz., heat, light, &c. Energy is thus constantly shifting its
form from actual to potential, and _vice versâ_, and exhibiting itself
under the various transformations of force, as when sun-force changes to
chemical action, chemical action to heat, heat to electricity, &c.
Energy is, indeed, the real modern PROTEUS—constantly assuming different
shapes, difficult to grasp if not held in fetters; now taking on the
form of a lion, now of a flame of fire, a whirlwind, a rushing stream.
As sober, literal matter of fact we catch glimpses of energy under these
very forms.
The greatest discovery of the age has, as already indicated, immediate
and important practical bearings. The amount of thought which, even in
the present day, is devoted by unscientific mechanics to the old problem
of perpetual motion is far greater than is generally supposed. The
principle of the conservation of energy shows that this is an
impossibility; that the inventor who seeks to create force might just as
well try to create matter; that the production of a perpetually moving
self-sustaining machine is as far removed from human power as the
bringing into existence of a new planet. In force, as in matter, the law
is inexorable—_ex nihilo nihil fit_. Again, knowing the definite amount
of energy obtainable from the combustion of a pound of coal, we can
compare the amount we actually procure from it in our steam engines with
this theoretical quantity as the limit towards which our improvements
should bring us continually nearer, but which we can never exceed, or,
indeed, even reach. The schemers of perpetual motion are not the only
class of speculators who pursue objects which are incompatible with our
principle. There are many who seek to accomplish desirable ends by
inadequate means: who, for example, are aiming perhaps to accomplish the
reduction of ores by a quantity of fuel less than that mechanically
equivalent to the work, or who conceive that by adding to coal some
substance which itself is unchanged, an indefinitely greater amount of
heat may be liberated by the combustion.
Enough has been said to show that the energies of animal life can be
traced to the sun as their source. The sun builds up the plant,
separating oxygen from carbon. The animal—directly or mediately by
devouring other animals—takes the carbonaceous matter of the plant, and
reunites it with oxygen. In the plant the sun winds up the spring which
gives life to the animal mechanism; for the winding-up of a spring and
the separation of the atoms having chemical affinities are alike
instances of supplying potential energy. In the animal there is a
running-down of the potential into actual energy. It is plain also that
of the total energy radiated from the sun in every direction, the earth
receives but a very small part (1/2300000000). By far the larger part is
diffused into space, where, for all such purposes as those with which we
are concerned, it is lost. The heat which the sun sends out in a year is
calculated to be equal to that which would be produced by the combustion
of a layer of coal 17 miles thick over the whole surface of the
luminary. Is the sun, then, a flaming fire? By no means. Combustion is
not possible at its temperature; and as we know the substances which
enter into its composition are the same as those we find in the earth,
we know that the chemical energies of such substances could not supply
the sun’s expenditure. Passing over as unsatisfactory an explanation
which might occur to some minds—namely, that the sun was created hot at
the beginning, and has so continued—there are two theories which attempt
to account for the sun’s heat. One is that of Meyer, who supposes the
heat is due to the continual impact of meteorites drawn to the sun by
its gravity; and the other is that of Helmholtz, who attributes the heat
to the continual condensation of the substance of the sun. Helmholtz
calculates that a shrinking of the sun’s diameter by only 1/10000th of
its present amount, would supply heat to last for two thousand years;
while the condensation of the substance of the sun to the density of the
earth would cover the sun’s expenditure for 17,000,000 of years. There
is great probability that both theories may be correct, and that the
cause of the sun’s heat may be considered as due in general terms to
aggregation of matter, by which the original potential energy of
position is converted into the actual energy of heat and light. Now,
however immense may be our planetary system, the sun being continually
throwing off this energy into space, there must come a time when the
supplies of meteorites will fail, and when the great globe of the sun
will have shrunk to its smallest dimensions. We see, then, that heat and
light are produced by the aggregation of matter; the heat and light are
radiated into space; the small fraction intercepted by our globe is the
source of almost every movement—the original stuff, so to speak, out of
which all terrestrial forces are made. The sun produces the winds, the
thunderstorms, the electric currents of the Aurora, the phenomena of
terrestrial magnetism, and is the source of vegetable and animal life.
The waves, the rains, the mountain torrents, the flowing rivers, are the
work of the sun’s emanations.
In the illustration of the energy expended on raising a weight
afterwards dropped, we traced that energy into the final form of heat of
a low temperature radiated into space. It would be easy to show that all
energy ultimately takes the same form. Now, although it is easy to
convert work into heat, there is no conceivable process by which
uniformly-diffused heat can again be made to do any kind of work. The
case may be compared to water, which in moving down from a higher to a
lower level may be made to perform any variety of work. But when all the
water has passed down from the higher level to the lower, it can no
longer do any work. Whenever work is done by the agency of heat, there
is always a passing from a higher temperature to a lower—a transference
of heat from a hotter body to a colder. If the condenser of the steam
engine had the same temperature as the steam, the machine would not
work. Not only do all the energies in operation on the face of the earth
continually run down into the form of radiant heat sent off by the earth
into space; but our sun’s energy, and that of the suns of other systems,
are also continually passing off into space; and the final effect must
be a uniform diffusion of heat in a universe in which none of the varied
forms of energy we now behold in operation will be possible, because all
will have run down to the same dead level of uniformly-diffused heat.
This startling corollary from the principle of the conservation of
energy has been worked out by Sir W. Thomson under the title of “The
Dissipation of Energy.” It leads us to contemplate a state of things in
which all light and life will have passed away from the universe—a
condition which the poet’s terrible dream of darkness, “which was not
all a dream,” seems to shadow forth—
“The bright sun was extinguished, and the stars
Did wander darkling in the eternal space,
Rayless and pathless; and the icy earth
Swung blind and blackening in the moonless air.
* * * * *
The world was void,
The populous and the powerful was a lump,
Seasonless, herbless, treeless, manless, lifeless—
A lump of death—a chaos of hard clay.
The rivers, lakes, and ocean all stood still,
And nothing stirred within their silent depths.
* * * * *
The waves were dead; the tides were in their grave,
The Moon, their mistress, had expired before;
The winds were withered in the stagnant air,
And the clouds perished; Darkness had no need
Of aid from them—She was the Universe.”
The doctrine of this persistence and dissipation of energy completely
harmonizes with the grand speculation termed the “nebular hypothesis,”
which regards the universe as having originally consisted of uniformly
diffused matter, which, being endowed with the power of gravitation,
aggregated round certain centres. This process is still going on; and,
according to modern speculations, light and life and motion are but
manifestations of this primæval potential energy being converted into
actual energy, and degrading ultimately into the form of
universally-diffused heat. To quote the closing sentences of the
eloquent passage in which Professor Tyndall concludes the work mentioned
above, “To nature nothing can be added, from nature nothing can be taken
away; the sum of her energies is constant, and the utmost man can do in
the pursuit of physical truth, or in the applications of physical
knowledge, is to shift the constituents of the never-varying total. The
law of conservation rigidly excludes both creation and annihilation.
Waves may change to ripples, and ripples to waves; magnitude may be
substituted for number, and number for magnitude; asteroids may
aggregate to suns, suns may resolve themselves into floræ and faunæ, and
floræ and faunæ melt in air: the flux of power is eternally the same. It
rolls in music through the ages, and all terrestrial energy—the
manifestations of life as well as the display of phenomena—are but the
modulations of its rhythm.”
The discoveries to which we have here endeavoured to attract the
reader’s attention thus give rise to conceptions of the utmost grandeur
and interest. We see that the sum of Nature’s energies is constant; that
all the manifestations of force are but the transference of power from
one position to another. And we have recognized the material source of
all our terrestrial energies in the sun. Two theories have already been
mentioned by which it is sought to account for the sun’s heat—the
meteoric theory of Meyer and Thomson, and the shrinkage theory of
Helmholtz. These both assume gravitation as the primal force from which
the supply of heat and other energies must be drawn, and they assume
also that the laws of radiation and of the degradation of temperature in
the transformation of heat into other forces, as we find them operating
at the earth’s surface, are equally in action in every region of space.
Hence is deduced that conception of the final state of the universe as
one of merely equally diffused temperature admitting of no further
transformation. This speculation presents the _universe_ in the aspect
of a clock, now indeed going, but when once run down, incapable of ever
being again wound up. There seems in this view a want of symmetry, so to
speak; we miss the feeling of harmonious _rhythm_ to which Tyndall
refers. There is, however, another cosmic theory, well supported by
accumulating facts, which assigns to gravitation a less important part
in the production of solar heat and in the evolution of worlds, and it
is one which supplies also a basis for the explanation of such phenomena
as aerolites, comets, variable stars, the inclination of planets’ axes
to their orbits, the proper motion of our sun, and that of the so called
fixed stars, of all of which the nebular hypothesis fails to give any
account; while, on the other hand, the _impact theory_, as it has been
named, includes the other, and goes beyond it. The reader who desires to
pursue this subject may be referred to Croll’s book on Stellar
Evolution.
In the last few paragraphs we have been dealing with speculations as
much as with discoveries. But indeed the former are the offspring of the
latter, as certainly as one invention becomes the parent of others. The
human mind never rests contented with the knowledge and mastery of
nature actually gained, but ever seeks to pass beyond and attain still
greater power. The volume we are now bringing to a close has given but
brief and imperfect indications of specimens, taken here and there, of
what has been done during the short period of one century. We may draw
an augury for the future of man’s dominion from the powers his
Promethean spirit has already grasped: