certain substance. For if we examine its production, we find that
here on earth it is principally fire and flame which engender it,
both of which contain beyond doubt bodies which are in rapid
movement, since they dissolve and destroy many other bodies more
solid than they: while if we regard its effects, we see that when
light is accumulated, say by concave mirrors, it has the property
of combustion just as fire has, that is to say, it disunites the
parts of bodies, which is assuredly a proof of _motion_, at least
in the _true philosophy_, in which the causes of all natural
effects are conceived as _mechanical_ causes. Which in my judgment
must be accomplished or all hope of ever understanding physics
renounced."[52]
S. Carnot,[53] in introducing the principle of excluded perpetual motion
into the theory of heat, makes the following apology:
"It will be objected here, perhaps, that a perpetual motion proved
impossible for _purely mechanical actions_, is perhaps not so when
the influence of _heat_ or of electricity is employed. But can
phenomena of heat or electricity be thought of as due to anything
else than to _certain motions of bodies_, and as such must they not
be subject to the general laws of mechanics?"[54]
These examples, which might be multiplied by quotations from recent
literature indefinitely, show that a tendency to explain all things
mechanically actually exists. This tendency is also intelligible.
Mechanical events as simple motions in space and time best admit of
observation and pursuit by the help of our highly organised senses. We
reproduce mechanical processes almost without effort in our imagination.
Pressure as a circumstance that produces motion is very familiar to us
from daily experience. All changes which the individual personally
produces in his environment, or humanity brings about by means of the
arts in the world, are effected through the instrumentality of
_motions_. Almost of necessity, therefore, motion appears to us as the
most important physical factor. Moreover, mechanical properties may be
discovered in all physical events. The sounding bell trembles, the
heated body expands, the electrified body attracts other bodies. Why,
therefore, should we not attempt to grasp all events under their
mechanical aspect, since that is so easily apprehended and most
accessible to observation and measurement? In fact, no objection _is_ to
be made to the attempt to elucidate the properties of physical events by
mechanical _analogies_.
But modern physics has proceeded _very far_ in this direction. The point
of view which Wundt represents in his excellent treatise _On the
Physical Axioms_ is probably shared by the majority of physicists. The
axioms of physics which Wundt sets up are as follows:
1. All natural causes are motional causes.
2. Every motional cause lies outside the object moved.
3. All motional causes act in the direction of the straight line of
junction, and so forth.
4. The effect of every cause persists.
5. Every effect involves an equal countereffect.
6. Every effect is equivalent to its cause.
These principles might be studied properly enough as fundamental
principles of mechanics. But when they are set up as axioms of physics,
their enunciation is simply tantamount to a negation of all events
except motion.
According to Wundt, all changes of nature are mere changes of place. All
causes are motional causes (page 26). Any discussion of the
philosophical grounds on which Wundt supports his theory would lead us
deep into the speculations of the Eleatics and the Herbartians. Change
of place, Wundt holds, is the _only_ change of a thing in which a thing
remains identical with itself. If a thing changed _qualitatively_, we
should be obliged to imagine that something was annihilated and
something else created in its place, which is not to be reconciled with
our idea of the identity of the object observed and of the
indestructibility of matter. But we have only to remember that the
Eleatics encountered difficulties of exactly the same sort in motion.
Can we not also imagine that a thing is destroyed in _one_ place and in
_another_ an exactly similar thing created? After all, do we really know
_more_ why a body leaves one place and appears in another, than why a
_cold_ body grows _warm_? Granted that we had a perfect knowledge of the
mechanical processes of nature, could we and should we, for that reason,
_put out of the world_ all other processes that we do not understand? On
this principle it would really be the simplest course to deny the
existence of the whole world. This is the point at which the Eleatics
ultimately arrived, and the school of Herbart stopped little short of
the same goal.
Physics treated in this sense supplies us simply with a diagram of the
world, in which we do not know reality again. It happens, in fact, to
men who give themselves up to this view for many years, that the world
of sense from which they start as a province of the greatest
familiarity, suddenly becomes, in their eyes, the supreme
"world-riddle."
Intelligible as it is, therefore, that the efforts of thinkers have
always been bent upon the "reduction of all physical processes to the
motions of atoms," it must yet be affirmed that this is a chimerical
ideal. This ideal has often played an effective part in popular
lectures, but in the workshop of the serious inquirer it has discharged
scarcely the least function. What has really been achieved in mechanical
physics is either the _elucidation_ of physical processes by more
familiar _mechanical analogies_, (for example, the theories of light and
of electricity,) or the exact _quantitative_ ascertainment of the
connexion of mechanical processes with other physical processes, for
example, the results of thermodynamics.
III. THE PRINCIPLE OF ENERGY IN PHYSICS.
We can know only from _experience_ that mechanical processes produce
other physical transformations, or _vice versa_. The attention was first
directed to the connexion of mechanical processes, especially the
performance of work, with changes of thermal conditions by the invention
of the steam-engine, and by its great technical importance. Technical
interests and the need of scientific lucidity meeting in the mind of S.
Carnot led to the remarkable development from which thermodynamics
flowed. It is simply _an accident of history_ that the development in
question was not connected with the practical applications of
_electricity_.
In the determination of the maximum quantity of _work_ that, generally,
a heat-machine, or, to take a special case, a steam-engine, can perform
with the expenditure of a _given_ amount of heat of combustion, Carnot
is guided by mechanical analogies. A body can do work on being heated,
by expanding under pressure. But to do this the body must receive heat
from a _hotter_ body. Heat, therefore, to do work, must pass from a
hotter body to a colder body, just as water must fall from a higher
level to a lower level to put a mill-wheel in motion. Differences of
temperature, accordingly, represent forces able to do work exactly as do
differences of height in heavy bodies. Carnot pictures to himself an
ideal process in which no heat flows away unused, that is, without doing
work. With a given expenditure of heat, accordingly, this process
furnishes the maximum of work. An analogue of the process would be a
mill-wheel which scooping its water out of a higher level would slowly
carry it to a lower level without the loss of a drop. A peculiar
property of the process is, that with the expenditure of the same work
the water can be raised again exactly to its original level. This
property of _reversibility_ is also shared by the process of Carnot. His
process also can be reversed by the expenditure of the same amount of
work, and the heat again brought back to its original temperature level.
Suppose, now, we had _two_ different reversible processes _A_, _B_, such
that in _A_ a quantity of heat, _Q_, flowing off from the temperature
_t₁_ to the lower temperature _t₂_ should perform the work _W_, but in
_B_ under the same circumstances it should perform a greater quantity of
work _W_ + _W'_; then, we could join _B_ in the sense assigned and _A_
in the reverse sense into a _single_ process. Here _A_ would reverse the
transformation of heat produced by _B_ and would leave a surplus of work
_W'_, produced, so to speak, from nothing. The combination would present
a perpetual motion.
With the feeling, now, that it makes little difference whether the
mechanical laws are broken directly or indirectly (by processes of
heat), and convinced of the existence of a _universal_ law-ruled
connexion of nature, Carnot here excludes for the first time from the
province of _general_ physics the possibility of a perpetual motion.
_But it follows, then, that the quantity of work W, produced by the
passage of a quantity of heat Q from a temperature t₁ to a temperature
t₂, is independent of the nature of the substances as also of the
character of the process, so far as that is unaccompanied by loss, but
is wholly dependent upon the temperature t₁, t₂.
This important principle has been fully confirmed by the special
researches of Carnot himself (1824), of Clapeyron (1834), and of Sir
William Thomson (1849), now Lord Kelvin. The principle was reached
_without any assumption whatever_ concerning the nature of heat, simply
by the exclusion of a perpetual motion. Carnot, it is true, was an
adherent of the theory of Black, according to which the sum-total of the
quantity of heat in the world is constant, but so far as his
investigations have been hitherto considered the decision on this point
is of no consequence. Carnot's principle led to the most remarkable
results. W. Thomson (1848) founded upon it the ingenious idea of an
"absolute" scale of temperature. James Thomson (1849) conceived a Carnot
process to take place with water freezing under pressure and, therefore,
performing work. He discovered, thus, that the freezing point is lowered
0·0075° Celsius by every additional atmosphere of pressure. This is
mentioned merely as an example.
About twenty years after the publication of Carnot's book a further
advance was made by J. R. Mayer and J. P. Joule. Mayer, while engaged as
a physician in the service of the Dutch, observed, during a process of
bleeding in Java, an unusual redness of the venous blood. In agreement
with Liebig's theory of animal heat he connected this fact with the
diminished loss of heat in warmer climates, and with the diminished
expenditure of organic combustibles. The total expenditure of heat of a
man at rest must be equal to the total heat of combustion. But since
_all_ organic actions, even the mechanical actions, must be set down to
the credit of the heat of combustion, some connexion must exist between
mechanical work and expenditure of heat.
Joule started from quite similar convictions concerning the galvanic
battery. A heat of association equivalent to the consumption of the zinc
can be made to appear in the galvanic cell. If a current is set up, a
part of this heat appears in the conductor of the current. The
interposition of an apparatus for the decomposition of water causes a
part of this heat to disappear, which on the burning of the explosive
gas formed, is reproduced. If the current runs an electromotor, a
portion of the heat again disappears, which, on the consumption of the
work by friction, again makes its appearance. Accordingly, both the
heat produced and the work produced, appeared to Joule also as
connected with the consumption of material. The thought was therefore
present, both to Mayer and to Joule, of regarding heat and work as
equivalent quantities, so connected with each other that what is lost in
one form universally appears in another. The result of this was a
_substantial_ conception of heat and of work, and _ultimately a
substantial conception of energy_. Here every physical change of
condition is regarded as energy, the destruction of which generates work
or equivalent heat. An electric charge, for example, is energy.
In 1842 Mayer had calculated from the physical constants then
universally accepted that by the disappearance of one kilogramme-calorie
365 kilogramme-metres of work could be performed, and _vice versa_.
Joule, on the other hand, by a long series of delicate and varied
experiments beginning in 1843 ultimately determined the mechanical
equivalent of the kilogramme-calorie, more exactly, as 425
kilogramme-metres.
If we estimate every change of physical condition by the _mechanical
work_ which can be performed upon the _disappearance_ of that condition,
and call this measure _energy_, then we can measure all physical changes
of condition, no matter how different they may be, with the same common
measure, and say: _the sum-total of all energy remains constant_. This
is the form that the principle of excluded perpetual motion received at
the hands of Mayer, Joule, Helmholtz, and W. Thomson in its extension to
the whole domain of physics.
After it had been proved that heat must _disappear_ if mechanical work
was to be done at its expense, Carnot's principle could no longer be
regarded as a complete expression of the facts. Its improved form was
first given, in 1850, by Clausius, whom Thomson followed in 1851. It
runs thus: "If a quantity of heat _Q'_ is transformed into work in a
reversible process, _another_ quantity of heat _Q_ of the absolute[55]
temperature _T₁_ is lowered to the absolute temperature _T₂_." Here
_Q'_ is dependent only on _Q_, _T₁_, _T₂_, but is independent of the
substances used and of the character of the process, so far as that is
unaccompanied by loss. Owing to this last fact, it is sufficient to find
the relation which obtains for some one well-known physical substance,
say a gas, and some definite simple process. The relation found will be
the one that holds generally. We get, thus,
_Q'/(Q' + Q) = (T₁-T₂)/T₁_ (1)
that is, the quotient of the available heat _Q'_ transformed into work
divided by the sum of the transformed and transferred heats (the total
sum used), the so-called _economical coefficient_ of the process, is,
_(T₁-T₂)/T₁_.
IV. THE CONCEPTIONS OF HEAT.
When a cold body is put in contact with a warm body it is observed that
the first body is warmed and that the second body is cooled. We may say
that the first body is warmed _at the expense of_ the second body. This
suggests the notion of a thing, or heat-substance, which passes from the
one body to the other. If two masses of water _m_, _m'_, of unequal
temperatures, be put together, it will be found, upon the rapid
equalisation of the temperatures, that the respective changes of
temperatures _u_ and _u'_ are inversely proportional to the masses and
of opposite signs, so that the algebraical sum of the products is,
_mu + m'u' = 0_.
Black called the products _mu_, _m'u'_, which are decisive for our
knowledge of the process, _quantities of heat_. We may form a very clear
_picture_ of these products by conceiving them with Black as measures of
the quantities of some substance. But the essential thing is not this
picture but the _constancy_ of the sum of these products in simple
processes of conduction. If a quantity of heat disappears at one point,
an equally large quantity will make its appearance at some other point.
The retention of this idea leads to the discovery of specific heat.
Black, finally, perceives that also something else may appear for a
vanished quantity of heat, namely: the fusion or vaporisation of a
definite quantity of matter. He adheres here still to this favorite
view, though with some freedom, and considers the vanished quantity of
heat as still present, but as _latent_.
The generally accepted notion of a caloric, or heat-stuff, was strongly
shaken by the work of Mayer and Joule. If the quantity of heat can be
increased and diminished, people said, heat cannot be a substance, but
must be a _motion_. The subordinate part of this statement has become
much more popular than all the rest of the doctrine of energy. But we
may convince ourselves that the motional conception of heat is now as
unessential as was formerly its conception as a substance. Both ideas
were favored or impeded solely by accidental historical circumstances.
It does not follow that heat is not a substance from the fact that a
mechanical equivalent exists for quantity of heat. We will make this
clear by the following question which bright students have sometimes put
to me. Is there a mechanical equivalent of electricity as there is a
mechanical equivalent of heat? Yes, and no. There is no mechanical
equivalent of _quantity_ of electricity as there is an equivalent of
_quantity_ of heat, because the same quantity of electricity has a very
different capacity for work, according to the circumstances in which it
is placed; but there _is_ a mechanical equivalent of electrical energy.
Let us ask another question. Is there a mechanical equivalent of water?
No, there is no mechanical equivalent of quantity of water, but there is
a mechanical equivalent of weight of water multiplied by its distance
of descent.
When a Leyden jar is discharged and work thereby performed, we do not
picture to ourselves that the quantity of electricity disappears as work
is done, but we simply assume that the electricities come into different
positions, equal quantities of positive and negative electricity being
united with one another.
What, now, is the reason of this difference of view in our treatment of
heat and of electricity? The reason is purely historical, wholly
conventional, and, what is still more important, is wholly indifferent.
I may be allowed to establish this assertion.
In 1785 Coulomb constructed his torsion balance, by which he was enabled
to measure the repulsion of electrified bodies. Suppose we have two
small balls, _A_, _B_, which over their whole extent are similarly
electrified. These two balls will exert on one another, at a certain
distance _r_ of their centres, a certain repulsion _p_. We bring into
contact with _B_ now a ball _C_, suffer both to be equally electrified,
and then measure the repulsion of _B_ from _A_ and of _C_ from _A_ at
the same distance _r_. The sum of these repulsions is again _p_.
Accordingly something has remained constant. If we ascribe this effect
to a substance, then we infer naturally its constancy. But the essential
point of the exposition is the divisibility of the electric force _p_
and not the simile of substance.
In 1838 Riess constructed his electrical air-thermometer (the
thermoelectrometer). This gives a measure of the quantity of heat
produced by the discharge of jars. This quantity of heat is not
proportional to the quantity of electricity contained in the jar by
Coulomb's measure, but if _Q_ be this quantity and _C_ be the capacity,
is proportional to _Q_²/2_C_, or, more simply still, to the energy of
the charged jar. If, now, we discharge the jar completely through the
thermometer, we obtain a certain quantity of heat, _W_. But if we make
the discharge through the thermometer into a second jar, we obtain a
quantity less than _W_. But we may obtain the remainder by completely
discharging both jars through the air-thermometer, when it will again be
proportional to the energy of the two jars. On the first, incomplete
discharge, accordingly, a part of the electricity's capacity for work
was lost.
When the charge of a jar produces heat its energy is changed and its
value by Riess's thermometer is decreased. But by Coulomb's measure the
quantity remains unaltered.
Now let us imagine that Riess's thermometer had been invented before
Coulomb's torsion balance, which is not a difficult feat, since both
inventions are independent of each other; what would be more natural
than that the "quantity" of electricity contained in a jar should be
measured by the heat produced in the thermometer? But then, this
so-called quantity of electricity would decrease on the production of
heat or on the performance of work, whereas it now remains unchanged;
in that case, therefore, electricity would not be a _substance_ but a
_motion_, whereas now it is still a substance. The reason, therefore,
why we have other notions of electricity than we have of heat, is purely
historical, accidental, and conventional.
This is also the case with other physical things. Water does not
disappear when work is done. Why? Because we measure quantity of water
with scales, just as we do electricity. But suppose the capacity of
water for work were called quantity, and had to be measured, therefore,
by a mill instead of by scales; then this quantity also would disappear
as it performed the work. It may, now, be easily conceived that many
substances are not so easily got at as water. In that case we should be
unable to carry out the one kind of measurement with the scales whilst
many other modes of measurement would still be left us.
In the case of heat, now, the historically established measure of
"quantity" is accidentally the work-value of the heat. Accordingly, its
quantity disappears when work is done. But that heat is not a substance
follows from this as little as does the opposite conclusion that it is a
substance. In Black's case the quantity of heat remains constant because
the heat passes into no _other_ form of energy.
If any one to-day should still wish to think of heat as a substance, we
might allow that person this liberty with little ado. He would only have
to assume that that which we call quantity of heat was the energy of a
substance whose quantity remained unaltered, but whose energy changed.
In point of fact we might much better say, in analogy with the other
terms of physics, energy of heat, instead of quantity of heat.
When we wonder, therefore, at the discovery that heat is motion, we
wonder at something that was never discovered. It is perfectly
indifferent and possesses not the slightest scientific value, whether we
think of heat as a substance or not. The fact is, heat behaves in some
connexions like a substance, in others not. Heat is latent in steam as
oxygen is latent in water.
V. THE CONFORMITY IN THE DEPORTMENT OF THE ENERGIES.
The foregoing reflexions will gain in lucidity from a consideration of
the conformity which obtains in the behavior of all energies, a point to
which I called attention long ago.[56]
A weight _P_ at a height _H₁_ represents an energy _W₁ = PH₁_. If we
suffer the weight to sink to a lower height _H₂_, during which work is
done, and the work done is employed in the production of living force,
heat, or an electric charge, in short, is transformed, then the energy
_W₂ = PH₂_ is still _left_. The equation subsists
_W₁/H₁ = W₂/H₂_, (2)
or, denoting the _transformed_ energy by _W' = W₁-W₂_ and the
_transferred_ energy, that transported to the lower level, by _W = W₂_,
_W'/(W' + W) = (H₁-H₂)/H₁_, (3)
an equation in all respects analogous to equation (1) at page 165. The
property in question, therefore, is by no means peculiar to heat.
Equation (2) gives the relation between the energy taken from the higher
level and that deposited on the lower level (the energy left behind); it
says that these _energies_ are proportional to the _heights of the
levels_. An equation analogous to equation (2) may be set up for _every_
form of energy; hence the equation which corresponds to equation (3),
and so to equation (1), may be regarded as valid for every form. For
electricity, for example, _H₁_, _H₂_ signify the potentials.
When we observe for the first time the agreement here indicated in the
transformative law of the energies, it appears surprising and
unexpected, for we do not perceive at once its reason. But to him who
pursues the comparative historical method that reason will not long
remain a secret.