THE PHYSICAL SCIENCES
=42. General.= In the formal sciences we began the specialization of the
object from the most general concept of thing conceivable, possessing no
other characteristic attribute than its capability of being
distinguished from other things; and we carried the specialization so
far that we could follow in its movements an object definite as to time
and space. This object, to be sure, was defined only in that it occupied
a definite space, and accordingly had a definite form. As a matter of
fact, the spacial thing of geometry and phoronomy reveals no further
attributes.
It is here that the physical sciences enter into their dominion one
after the other, and fill the empty space of the geometric thing with
definite attributes. These are the secondary qualities of Locke, of
which he assumed that they do not belong so much to the bodies
themselves as that they merely appear to us so on account of the nature
of our human sense organs. Now that our knowledge concerning the nature
of those properties as well as the structure of our sense organs is
much more thorough, we have more definite ideas also of the subjective
part of the corresponding experiences, and in a large measure are able
to separate it from the objective part.
All properties which physical bodies in contradistinction to geometric
bodies possess can be traced back to a fundamental concept, which, in
conjunction with the concepts explained in the former chapter, serves to
characterize and distinguish the physical structure. For example, the
fact that we can distinguish cubes of equal size but of different
material, different temperature, and different luminosity, can be traced
back always and entirely to the different kinds of energy acting in the
geometric space in question. The concept of energy, therefore, plays
approximately the same rôle in the physical sciences as the concept of
thing in the formal sciences, and the essentials of this new field of
science are the comprehensive knowledge and development of this concept.
Because of its great importance it has long been known and applied in
individual forms. But the systematization of the physical sciences
relative to energy is a matter of only recent date.
=43. Mechanics.= Recently many scientists have taken exception to the
traditional division of mechanics into _statics_, or the science of
equilibrium, and _dynamics_, or the science of motion, because it does
not correspond to the essence of the thing, equilibrium being only the
limit-case of motion. However, the classic presentations of this
science are based on that division, so that it must express an essential
difference. This difference we can clearly recognize through the
application of the concept of energy to mechanics. We then learn that
statics is the science of work, or the energy of position, and that
dynamics is the science of living force, or of the energy of motion.
By _work_ in the mechanical sense we mean the expenditure of force
required for the locomotion of physical bodies. While a cube of lead is
geometrically equal to a cube of glass, we experience a great difference
between them when we lift them from the floor to a table. We call the
cube of lead heavier than the glass cube, and we find it requires more
work to raise the former than the latter. For psychologic reasons this
judgment becomes especially clear when the work required to lift the
lead cube marks the limit of our physical capacity.
Work depends not only upon the difference described above, but also upon
the distance through which it is exerted. It increases in proportion as
the distance increases. In mechanics work is proportional both to the
distance and to that peculiar property which in the given example we
call _weight_. But a more general concept has been formed for that
property in the mechanical sense, called _force_, of which weight
constitutes but a special instance. Whenever there is a resistance
combined with a change of place we speak of a force, _and the product
of the force and the distance we call work_.
The cause of this kind of concept formation is the following: There are
a great number of different machines, all of them possessing the
peculiarity that work can be put into them at a definite place and taken
out at another place. Now, centuries of experience have shown that it is
impossible to obtain more work from such mechanical machines than has
been put into them. As a matter of fact, the work obtained is always
less than the work put in, and the two approach equality as the machine
approaches perfection. It is to such ideal machines, therefore, that
_the law of the conservation of work_ applies. This law states that,
though a given quantity of work may be changed in the most manifold ways
as to direction, force, etc., it is impossible to change its _quantity_.
The reason we can judge of this fact with such certainty is because for
many centuries a number of the ablest mechanicians have sought for a
solution of the problem of perpetual motion, that is, for the
construction of a machine from which more work can be gotten than is put
into it. All such attempts have failed. But the positive result secured
from these apparently futile efforts is the law of the conservation of
work. The greatness and importance of this result will become apparent
in the further course of our study.
Here for the first time we meet with a law expressing the
_quantitative_ conservation of a thing, which may none the less undergo
the most varied qualitative changes. With the knowledge of this fact we
involuntarily combine the notion that it is the "same" thing that passes
through all these transformations, and that it only changes its outward
form without being changed in its essence. Such ideas, it is true, are
widespread, but they have a very doubtful side to them, since they
correspond to no distinct concept. If we want to call the quantitative
magnitude of the product of the force and distance the "essence" of
work, and the determination of the force and the distance according to
magnitude and direction, which come under consideration for each special
value, as its "form," then, of course, there is no objection to be made
to mere nomenclature. But we must bear in mind that the difference
obtaining here lies exclusively in the fact that the amount of work
measured quantitatively remains unchanged, while its factors undergo
simultaneous and opposite changes.
This discovery, that there is a magnitude which can be quantitatively
determined, and which, as experience shows, remains unchanged, however
much its factors may change, invariably results not only in a very
simple and clear formulation of the corresponding natural law, but also
corresponds to the general tendency of the human mind to work out
conceptually "the permanent in change." If, in accordance with the
word-sense, we denote everything which persists under changing
conditions by the name of _substance, we encounter in work the first
substance_ of which we have attained knowledge in our scientific
journeys. In the history of the evolution of human thought this
substance has been preceded by others, especially by the weight and mass
of ponderable bodies (which are also subject to a law of conservation),
so that at present we are inclined to connect with the word substance a
tacit secondary sense of ponderability. But this is a remnant of the
still very widely spread mechanistic theory of the universe, which,
though it has almost finished its rôle in physics, will presumably
continue to persist for a long time to come in the popularly scientific
consciousness in accordance with the laws of collective thought.
=44. Kinetic Energy.= The law of the conservation of work is by no means
true of all cases in which work is expended or converted, but, as has
been said, only of _ideal_ machines, that is, of such cases which do not
exist in reality. But while in imperfect machines there is at least an
approximation to this law, there are besides countless normal cases in
which we cannot even speak of an approximation. When, for example, a
stone falls to the ground from a certain height, a certain quantity of
work is expended, which is equal to that by means of which the stone can
be raised again to its original height. This quantity of work apparently
disappears entirely when the stone remains lying on the ground. We
shall discuss this case later. Or the falling of the stone can be so
guided that it can lift itself again. This happens, for instance, when,
by fastening the stone to a thread, it is forced to move in a curved
path, or to perform pendular oscillations. In that case, it is true, the
stone will fall to the lowest point which the thread permits, and so
will there have lost its work without having done any other work in the
meantime. But it has entered a condition by virtue of which it raises
itself again, so that (as before, only in the ideal limit-case) it
reaches its former height, and so has lost no work. For this moment,
too, then, the law of the conservation of work obtains. But in the
meantime new relations have arisen.
What distinguishes the stone moving like a pendulum from the stone which
simply falls is, that at its lowest point it has not remained lying
still, but possesses a certain velocity. By means of this it lifts
itself again, and after it has reached its former height, it has lost
its velocity. _Therefore, there is a reciprocal relation between the
work which it loses and the velocity which it gains_, and the question
may therefore be put, How can this relation be represented
mathematically? Experience teaches that in every such case a function of
the velocity and of another property of the body, called _mass_, can be
established in such a way that this function, called the _kinetic
energy_ of the body, increases precisely as much as the amount of work
the body has expended, and _vice versa_. The sum of the kinetic energy
of the body and of the _work_ is therefore _constant_, and the clearest
mode of conceiving of this relation is by assuming _that work can be
transformed into kinetic energy and vice versa_ in such a way that given
amounts of the two magnitudes are equal or equivalent to one another.
Naturally, this is only an abbreviated way of expressing the actual
relations, for it might just as well be assumed that the work really
disappears and the kinetic energy really originates anew, and that the
disappearance of the one substance only happens regularly to coincide
with the origin of the other. But it is this regular conjunction of
phenomena that constitutes the sole ground of every _causal_ relation,
and in such a sense we are justified _in regarding the disappearing work
as the cause of the kinetic energy that arises_, and to designate this
relation summarily as a transformation.
By the inclusion of cases in which work is converted into kinetic energy
the law of the conservation of work therefore becomes _the law of the
conservation of the sum of work and kinetic energy_. We are thereby
compelled to extend the concept of substance, which at first contains
only work, to the sum of both magnitudes, and to introduce a new name
for this enlarged concept.
It will soon appear that all cases of imperfect machines, in which work
disappears without giving rise to an equivalent amount of kinetic
energy, can, with a corresponding enlargement of the concept, be
likewise included in the law of conservation. For experience has shown
that in such cases something else arises, heat, light, or electric
force, etc. This generalized concept, which embraces all natural
processes and permits the sum of all corresponding values to be
expressed by a law of conservation, we call _energy_. The law in
question, therefore, is:
_In all processes the sum of the existing energies remains unchanged._
The principle of the conservation of work in perfect machines proves to
be an ideal special instance of this general law. A perfect machine is
one in which work changes into nothing but _work_ of another kind, and
not into a different kind of energy. Then each side of the equation
which expresses the general law of energy, namely,
Energy that has disappeared = energy that has arisen,
contains only the magnitude of the work, and expresses the law of the
conservation of work. If, on the other hand, as in the case of the
pendulum, the work increasingly changes part by part into kinetic
energy, and _vice versa_, the equation during the first period is:
Work that has disappeared = kinetic energy that has arisen,
and during the second period in which the pendulum rises again,
Kinetic energy that has disappeared = work that has arisen.
Thus, while work can be called a substance only in a limited sense,
since its conservation is limited only to perfect machines, we may call
energy a substance unqualifiedly, since in every instance of which we
know the principle has been maintained _that a quantity of any energy
never disappears unless an equivalent quantity of another energy
arises_. Accordingly, this law of the conservation of energy must be
taken as a fundamental law of the physical sciences. But not only do all
the phenomena of physics, including chemistry, occur within the limits
of the law of conservation, but until the contrary is proved the law of
conservation must also be regarded as operative in all the later
sciences, that is, in all the activities of organisms, so that all the
phenomena of life must also take place within the limits of the law of
conservation. This corresponds to the general fact, which I have
emphasized a number of times, that all the laws of a former science find
application in all the following sciences, since the latter can only
contain concepts which by specialization, that is, by the addition of
further characteristics, have sprung from the concepts of the former or
more general sciences.
=45. Mass and Matter.= It has been noted above that kinetic energy
depends upon another magnitude beside velocity. A conception of its
nature can be obtained when we try to put different bodies in motion.
In doing so the muscles of the arm perform certain quantities of work,
and we feel whether the quantities are greater or smaller. In this way
we obtain a clear consciousness of the fact that different bodies
require quite different quantities of work for the same velocity. The
property which comes into play here is called _mass_, and mass is
proportional to the work which the various bodies require to attain the
same velocity. Since the work and the velocity can be measured very
accurately by appropriate means, mass also lends itself to a
correspondingly accurate measurement.
All known ponderable bodies have mass. That means there is a regular
connection between the property which makes a body tend to the earth
with a certain definite force (called weight) and the property by virtue
of which a body assumes certain velocities under the influences of
motive causes. We can readily conceive that it is possible for us to
learn only of such bodies as are heavy, that is, bodies which are _held_
by the earth, since the others, if they exist at all, would naturally
have left the earth long ago. That all these bodies also have mass is to
be explained in a similar way. For a body of mass zero would at each
impulse assume infinitely great velocity, and could therefore never be
the object of our observation. Consequently, by reason of the physical
conditions obtaining on the earth's surface, the bodies known to us must
combine both properties, mass and weight.
The name given to this concept of the combined presence of mass and
weight in space is _matter_. Experience shows that there is a law of
_conservation_ for these magnitudes also, according to which _whatever
changes we may produce in bodies possessing weight and mass, no change
will occur in the sum of their weight and mass_. According to the
nomenclature previously introduced we must therefore call weight and
mass substances, since they remain the same as to quantity, no matter
what changes they may undergo. However, it is usual to apply the name
substance to the concept of matter composed of mass and weight. In fact,
scientists often go so far as to limit the name to this single instance
of the various laws of conservation, and to take substance to mean
exclusively the combination of mass and weight. This is connected with
the conception which we are about to discuss, that all natural phenomena
can ultimately be conceived as the motion of matter. Through the greater
part of the nineteenth century this conception, called _scientific
materialism_, was accepted almost without opposition. At present it is
being more and more recognized that it was only an unproved assumption,
which the development of science daily proves to be more untenable.
=46. Energetic Mechanics.= In the light of our previous observations the
branch of science traditionally known as mechanics appears as the
science of work and of kinetic energy. Furthermore, statics is shown to
be the science of work, while dynamics, besides treating of kinetic
energy in itself, also treats of the phenomena of the change of work
into kinetic energy, and _vice versa_. We shall find the same relation
again later, only in more manifold forms. Every branch of physics proves
to be the science of a special kind of energy, and to the knowledge of
each kind of energy must be added the knowledge of the relations by
which it changes to the other forms of energy and _vice versa_. It is
true that in the traditional division of physics this system has not
been strictly carried out, since an additional and very influential
motive for classification has been the regard paid to the various human
sense organs.
Nevertheless this ground does not lie in the field of physics, but in
that of physiology, and must, therefore, be abandoned in the interest of
strict systematization.
Of the physical sciences mechanics was the first to develop in the
course of historical evolution. A number of factors contributed to this
end--the wide distribution of mechanical phenomena, their significance
to human life, and the comparative simplicity of the principles of
mechanics, which made it possible to discover them at an early date.
Most to be noted is, that of all departments of physics mechanics is the
first which lent itself to comprehensive _mathematical_ treatment. It is
true that the mathematical treatment of mechanics was possible only
after idealizing assumptions had been made--perfect machines and the
like--so that the results of this mathematical treatment not
infrequently had very little to do with reality. The mistake of losing
sight of the physical problem and of making mechanics a chapter of
mathematics has not always been avoided, and it is only in most recent
times that the consciousness has again arisen that the classical
mechanics, in arbitrarily limiting itself to extreme idealized cases,
sometimes runs the risk of losing sight of the aim of science.
=47. The Mechanistic Theories.= Because the evolution of mechanics
antedates that of the other branches of physics, mechanics has largely
served as a model for the formal organization of the other physical
sciences, just as geometry, which has been handed down to us from
antiquity in the very elaborate form of Euclid, has largely been used as
a model for scientific work in general. Such methods of analogy prove to
be extremely useful at first because they serve as a guide to indicate
when and where new sciences, in which all possibilities are open, can be
got hold of. But later on such analogies are apt to be harmful. For each
new science soon requires new methods, by reason of the peculiar
manifoldness which it has to deal with, and the finding and the
introduction of these new methods are easily delayed, and, as a matter
of fact, often have been delayed, because scientists could not free
themselves soon enough from the old analogy.
By its being based upon memory the human mind is so constructed that it
cannot assimilate something entirely new. The new must in some way be
connected with the known in order that it may be organically embodied in
the aggregate of concepts. Therefore, it is the first involuntary
impulse of our mind, in the presence of new experiences or thoughts, to
look about for such points at which a linking of the unknown to the
known seems possible. In the case of mechanics this necessity for
finding connecting links has acted in such a way that the attempt has
been made, and is still being made, to conceive and represent all
physical phenomena as mechanical.
The impulse to this was first given by the extraordinary successes which
mechanics has attained in the generalization and prediction of the
_motions of the heavenly bodies_. The names of Copernicus, Kepler, and
Newton mark the individual steps in the mechanization of astronomy. The
cause of this lies in the fact that the heavenly bodies actually
approximate very closely the ideal of the purely mechanical form with
which classical mechanics deals. These successes encourage the attempt
to apply these mental instruments that were productive of such rich
results to all other natural phenomena. An old theory, according to
which all physical things are composed of the most minute solid
particles of matter called _atoms_, supported these tendencies and
invited the attempt to regard the little world of atoms as subject to
the same laws as had been found to apply so successfully to the great
world of the stars.
Thus we see how this mechanistic hypothesis, the assumption that all
natural phenomena can be reduced to mechanical phenomena, comes as if it
were a self-understood matter, and with its claim to be a profound
interpretation of nature it scarcely permits the question as to its
justification to be raised at all. And the effects here have been the
same as I described above in cases in which inferences from analogy are
accepted too extensively or too credulously. While it is true, no doubt,
that the mechanical hypothesis at first was fruitful of results in
special research, because it facilitated the putting of the
question--for example, we need think only of the atomic hypothesis in
chemistry--later, the efforts to find further hypothetic help for the
inadequacies of the hypothesis that gradually came to light, have not
infrequently led scientific research to pseudo-problems, that is, to
questions which are questions only in hypothesis, but to which no actual
reality can be shown to correspond. Such problems, therefore, are by
their very nature _insoluble_, and constitute an inexhaustible source of
differences of scientific opinion.
The most flagrant of the injurious consequences of the mechanistic
hypothesis appear in the scientific treatment of the mental phenomena.
Ready as scientists were to represent all other life phenomena, such as
digestion, assimilation, and even generation and propagation, as the
consequence of an extremely complicated play of certain atoms, their
courage never went so far as to apply this principle to mental life and
to consider that by mechanics the last word had been said on the
subject.
It is because of this hesitancy to bring mental phenomena under the same
mechanistic principle as all the other phenomena that the philosophical
systems had to search for some other means to connect the mental world
with the mechanical, and the efforts of the philosophers to bring about
this end have been most varied. Of the various doctrines that have come
down to us, that of the _pre-established harmony_ proposed by Leibnitz
is in the ascendant in our day, and is now called the theory of the
_psycho-physical parallelism_. According to this theory it is assumed
that the mental world exists alongside, and quite independent of, the
mechanical, but that the things have been so prearranged that mental
processes take place simultaneously with certain mechanical processes
(according to some, with all mechanical processes) in such a way that,
although the two series do not influence each other in the least, they
always correspond to each other precisely. How such a relation has come
about and how it is maintained remains unsaid, or is left to future
explanation.
We need only think of the content of this hypothesis with an unbiased
mind to lose all relish for it at once. In fact, it has no other _raison
d'être_ than the presumption that the mental and the mechanical world
are opposed to each other. As soon as we abandon the thesis that the
non-mental world is exclusively mechanical, we acquire the possibility
again of finding for the theory of mental phenomena a constant and
regular connection with the theories of all other phenomena, especially
with the phenomena of life. Therefore it will be found most expedient in
every respect, instead of rendering scientific research one-sided and
almost blind to nonconforming facts by preconceived hypotheses, such as
the mechanistic hypothesis, to seek, as hitherto, from step to step, the
new elements of manifoldness which must be taken account of in the
progressive upbuilding of science and to limit ourselves faithfully to
them in the formation of general ideas.
=48. Complementary Branches of Mechanics.= The field of pure or
classical mechanics is limited to the above two kinds of energy, work
and kinetic energy, though these do not exhaust the manifoldness of the
mechanical energies. Accordingly, other branches of mechanics dealing
with the corresponding phenomena are added to the classical mechanics
described above.
If by mechanical energies we understand all energies in which _changes
of space are connected with changes of energy_, there are as many
different forms as there are spacial concepts that seem applicable.
_Form_, _Volume_, and _Surface_ of bodies in space are especially
recognizable as the field of action for energy, which shows different
properties or manifoldnesses according to each of these relations.
The _energy of form_ is manifested in bodies (solid or rigid bodies)
that maintain a definite shape because every change of shape is
connected with work or with the expenditure of some other energy. If the
changes are small, the bodies are of such a nature that they return to
their former condition of their own accord after the force exerted upon
them has ceased to act. This property is called _elasticity_. However,
the theory of elasticity, which has been extensively and rationally
developed, is regarded as belonging rather to mathematical physics in
general than to mechanics in particular. In greater changes of shape the
energy of form, or elastic energy, passes into other forms, and the body
does not return to its former shape after the force has been removed.
Other bodies have no energy of form (or only in an infinitesimally
slight degree), so that they allow of changes of form without the
expenditure of work, but their volume can be changed only by work. These
are divided into two classes. First, the _liquids_, which have a
definite volume (corresponding to the definite shape of solids), the
changes of which in _every_ sense, both compression and expansion,
require work. Secondly, the _gases_ with volume energy in only one sense
of the word, in which only the compression of volume requires work,
while in expansion a certain amount of work is thrown off. Such bodies
can exist only so long as the expenditure of their volume energy by
spontaneous expansion is prevented by the presence of a counter energy,
as, for example, the elasticity of the walls of a vessel. This tendency
is called _pressure_.
Finally, there are energy qualities at the surfaces between various
kinds of bodies which come into play at the change of these surfaces.
They always lie in such a direction that the enlargement of the surfaces
requires work, and hence, by reason of the law of conservation of
energy, cannot proceed by itself. In cases where there has been an
inverse kind of energy present, that is, one which diminishes with
increasing surface, it also has been active as a rule, thus bringing
about the disappearance of the existing boundaries.
Since the seat of this kind of energy is in the surfaces (or
superficies), it is called _surface-energy_. The phenomena depending
upon it manifest themselves most clearly at the surface boundaries
between _liquids_ and _gases_. They are called _capillary phenomena_.
This strange name, derived from the word _capilla_, hair, has its origin
in the fact that because of surface-energy liquids rise in tubes which
they wet, and the narrower the tube the higher they rise. If the lumen
of the tube is as fine as a _hair_, a considerable rise can be observed.
This is the entire connection between the name and the thing.
The mechanics of liquids is called _hydromechanics_, that of gases,
_aeromechanics_, after the most familiar liquid, water, and the most
familiar gas, air. The study of surface-energy under the name of the
capillary theory forms part of theoretical physics. While formerly this
branch, too, was regarded as a working part, or, rather, as a playing
part, of mathematical problems, in more recent times extensive
experimental research has made its entry in this province also, and has
demonstrated the necessity of passing from the former abstractions or
idealizations, which were carried altogether too far, to a better and
profounder regard for the actually existing complexities.
=49. The Theory of Heat.= The various forms of energies the aggregate of
which is comprehended in physics, have very different special
characters. A systematic investigation has not yet been made of the
characters of manifoldness by which, for example, work is distinguished
from heat, electrical energy from kinetic energy, etc., nor of what are
the essential properties peculiar to each individual energy. We feel
certain that differences do exist, for otherwise the energies could not
be distinguished, and we feel certain that these differences are very
important, for doubt seldom arises as to the kind of energy to which a
certain phenomenon is to be assigned. But just as we have no systematic
table of the elementary concepts, so we are still without a systematic
natural history of the forms of energy in which the peculiarities of
every species are characterized, and in which the entire material is so
arranged according to these characteristics that we can take a general
survey of it.
As regards heat energy, its foremost and most striking characteristic is
its physiological effect. In our skin there are organs for the
perception of heat as well as of cold, that is, for temperatures above
and below the temperature of the skin. However, the temperature that
these organs can bear without injury to themselves is of a very small
range, beyond which physical apparatuses of all kinds must be used, such
as "thermometers."
Heat is the simplest kind of energy from the point of view of
manifoldness. Every heat quantity is marked by a temperature, just as a
kinetic energy is marked by velocity. But while a velocity is determined
in space so that velocities of equal magnitude have in addition a
threefold infinite manifoldness in reference to direction, a temperature
is characterized completely and unambiguously by a simple number, the
degree of temperature. Two temperatures of equal degree can in no wise
be distinguished, since temperature possesses no other possible
manifoldness than degree.
The same property is found in heat energy itself. In heat energy we
measure the quantity of energy itself and call it the _heat quantity_,
while in some of the other kinds of energy, only the factors into which
they can be divided are measured, and no habitual conception of the
energy itself is developed. A heat quantity is likewise fully indicated
by its measure number.
That heat is an energy, that is, that it is developed in equal
quantities from other kinds of energy, and can change back again into
them, is a discovery which, despite its fundamental and general
character, was not made before the forties of the nineteenth century. As
often happens in cases of important scientific advances, the same idea
came simultaneously to a number of investigators. The first to grasp and
fully comprehend this idea was _Julius Robert Mayer_ of Heilbronn, who
published his results in 1842. Mayer not only showed that the imperfect
machines (p. 134), which limit the validity of the law of the
conservation of work, owe this peculiarity to the fact that they
transform a part of the work into _heat_, and that when we take account
of this part, the law of conservation holds perfectly good, but he also
calculated, with extraordinary acumen, the mechanical equivalent of heat
from the then existing data of physics. That is to say, he determined
how many units of heat (in the measure then in use) correspond to a unit
of work (in its specific measure) in the change from one to the other,
and back. And this fundamental knowledge of the existence of a
quantitatively unchangeable substance, arising from work, and capable of
being transformed into it, Mayer did not limit in its application merely
to heat. He was the first to construct a table, which he made as
complete as possible, of all the forms of energy then known, and to
assert and prove the possibility of their reciprocal change into each
other.
In view of this relation of the quantitative equivalent of the various
forms of energy when transformed into one another, an attempt is being
made at present to measure them all with the _same unit_. That is, some
easily obtained quantity of energy is arbitrarily chosen as a unit and
it is determined that in every other form of energy the unit shall be
equal to the quantity obtained from that unit on its transformation into
the energy in question. For formal reasons the kinetic energy of a mass
of two grams which moves with the velocity of one centimeter in a second
has been chosen as the unit. It is called _erg_, an abbreviation of
energy. The amount is very small, and for technical reasons 10^{10}
times greater unit is used. To raise the temperature of a gram of water
one degree a quantity of energy equal to 41,830,000 ergs is required.
=50. The Second Fundamental Principle.= Another fundamental discovery
has been made in connection with the heat form of energy, which, like
the law of conservation, relates to all forms of energy, but has found
its first and most important application in heat. While the law of
conservation answers the question, how much of the new form of energy is
developed if a given quantity of energy changes, but gives no clue as to
when such a change occurs, this second law asserts the condition under
which such changes arise, and is therefore called the _second
fundamental principle_.
The discovery of this law antedates _Mayer's_ discovery of the law of
conservation by about twenty years, and was made by a French military
engineer, _Sadi Carnot_, who died soon afterward without having lived to
see the recognition his great work obtained. _Carnot_ asked himself the
question, Upon what does the action of the steam engine, which had just
then come into use, depend? This led him first to the more general
question of the action of heat engines in general. He found that no heat
engine could work unless the heat dropped from a higher to a lower
temperature, just as no water wheel can work unless the water flows from
a higher to a lower level, and he determined the conditions which an
_ideal heat engine_ must fulfil, that is, a machine in which the
greatest possible value in work is obtained from heat. However, an ideal
machine of this nature can be constructed in very different ways, and
Carnot's discovery consists in the recognition of the fact _that the
quantity of work obtained from the heat unit does not at all depend upon
the peculiar construction of the ideal machine, but is determined solely
by the temperature between which the heat transition takes place_. This
follows from the following considerations:
In the first place an ideal engine must be _reversible_, that is, it
must be capable of working both ways, changing heat into work and work
back into heat. Now, if we have two ideal engines between the same
temperatures, and if we assume that engine A produces more work from the
same quantity of heat than engine B, then let A move one way and let B
move the other way with the work obtained from A. Since B produces less
work from a given amount of heat, hence more heat from an equal amount
of work, there will in the end be more heat at the higher temperature
than was originally there. But experience teaches _that there is no
means in nature by which heat in the absence of concomitant change could
be caused to rise to a higher temperature_. Therefore an engine so
constructed as to produce this result is impossible, And B cannot be of
such a nature as to produce less work from the same quantity of heat
than A.
The reverse is also impossible. For then we need merely couple the
engines in the reverse way in order to obtain the same effect.
Therefore, since B can do neither less nor more work than A, the two
must do the same amount of work--which was to be proved.
It is obvious that this process of proof is similar to that by which the
law of conservation was established. Because the arbitrary creation of
energy from nothing is impossible there must be definite and immutable
relations of change between the forms of energy. Because energy at rest
does not spontaneously pass into conditions in which it can do work,
the efficiencies of the machines must have definite and unchangeable
values. If, for example, we could cause heat of its own accord to rise
to a higher temperature, we could also construct a perpetual motion
machine which would always yield work at no expense. But this perpetual
motion would not be one that creates work out of nothing, but one that
extracts it from energy at rest. A perpetual motion machine of this
nature, too, is, according to our experience, impossible, and this
impossibility forms the content of the second fundamental principle.
On the face of it this apparently "self-evident" proposition does not
reveal how fruitful of results it is when applied to the discovery of
simple but not obvious relations. It can only be said here that the
deductions from this principle form the chief content of the extensive
science of thermodynamics, which deals with the changes of heat into
other forms of energy. We must only emphasize the fact that the
application of this law, as was already observed in stating it, is not
confined to the changes of heat alone. It is a law rather which finds
application in _all_ the forms of energy. For in every form of energy
there is a property which corresponds to temperature in heat, and upon
the equality or the inequality of which depends whether the energy in
question is at rest or ready for transformations. This property is
called the _intensity_ of the energy. In work, for instance, it is
_force_, in volume-energy it is _pressure_. If once the intensity in a
body is equal, its energy is at rest, and it never again moves of its
own accord.
Another form in which to present these relations is to make a
distinction between _free_ energy and energy _at rest_. If we have a
heat quantity the temperature of which is higher than that of the
surrounding objects, it can be used to do work only until its
temperature has dropped to that of the surrounding objects. Although
energy in abundance is still present, there is no longer any energy
_capable of change_, or _free_ energy. Since differences of temperature,
like other differences of intensity, have a constant tendency to
diminish, the amount of free energy on earth is constantly decreasing,
and yet it is only this free energy that has value. For since all
phenomena depend upon change of energy, and change of energy is possible
only through free energy, _free energy is the condition of all
phenomena_.
=51. Electricity and Magnetism.= While the knowledge of heat energy goes
back to the most ancient periods of civilization, electrical and
magnetic energies are relatively young acquisitions. The highly
developed technical application of both with the rich harvests they have
yielded belongs exclusively to most recent times.
Both these forms of energy, like those discussed above, are connected in
the main with ponderable "matter," but in a much slighter and less
regular measure. While it is not possible as yet to render any given
body free of heat (although lately the absolute zero point has been
considerably approximated), freedom from electrical and magnetic energy
is the normal condition of most bodies. This is connected with the
peculiarity that electrical and magnetic properties are decidedly
bi-symmetrical or _polar_. This property is not found in any other form
of energy, and can serve as the special scientific characteristic of
electricity and magnetism. This peculiarity shows itself in the concepts
of positive and negative magnetism, and positive and negative
electricity, and is due to the fact that two equal opposite quantities
of electricity or magnetism, when added together, do not produce double
their value, but nullify each other.[G]
[G] For the sake of the layman it must be observed that those
"quantities" are not energy magnitudes but factors of the electrical and
magnetic energies. Energy itself in its various forms is an _exclusively
positive magnitude_, and the result of the additions of their various
amounts is always the sum, never the difference, of their numerical
values. By the negative sign is understood the energy _expended_ in
contradistinction to the energy _received_. It is therefore nothing more
than the indication of a mathematical operation.
The fact that electrical and magnetic energies generally exist only in a
transitory state (with the notable exception of the magnetic condition
of the earth) is probably the cause of our not having developed a sense
organ for them, especially since their phenomena as they occur in nature
have only occasionally and in very rare instances (thunderstorms) an
influence upon us. On the other hand, the modern development of
electrotechnics is based upon that property of electrical energy by
virtue of which large quantities of it can be conducted along a thin
wire over great distances without any considerable loss, and at the
point desired can be easily changed into any other forms of energy. But
since the collection and conservation of large quantities of electrical
energy is hardly possible technically, the electrical apparatus must be
so constructed that the quantities each time required should be produced
at the moment they are used. The chief source of electricity is the
chemical energy of coal, which is first transformed into heat, then into
mechanical energy, and finally into electrical energy. This extremely
roundabout process is necessary because a method technically practicable
of transforming the chemical energy of coal directly into electrical
energy has not yet been invented. On the other hand, mechanical energy
can be easily and completely changed into electrical energy. Upon this
is based the exploitation of much "water power," the energy of which
could not be utilized but for the great capacity for change of the
electrical form.
=52. Light.= The case of light in our day seems to be similar to that of
sound, which, although it has its special sense organ in man, is yet no
particular form of energy, but has been found to be a combination of
mechanical energies in an oscillatory or mutually changing state. It
seems highly probable that light, too, is not a special form of energy,
but a peculiar oscillatory combination of electrical and magnetic
energies. It is true that the circle of proof is not yet quite closed,
but the gaps have become so small that the above conclusion may at any
rate be accepted as highly probable.
However that may be, light is an energy which, according to the known
laws, travels through space with tremendous rapidity. We will call it
_radiant energy_, since the part optically visible, to which alone the
name light in its original sense belongs, represents an extremely small
portion of a vast field, the properties of which change quite
continuously from one end to the other.
Radiant energy is characterized as an oscillatory or wave-like process.
So long as this fact was unknown (up to the beginning of the nineteenth
century) it was thought that light consisted of minute spherical
particles, which shot through space in a straight line with the
tremendous velocity mentioned above. Later, in order to "explain" its
wave nature, which in the meantime has come to be recognized, it was
assumed to be due to the elastic vibrations of an all-pervading thing
called _ether_, of which we know nothing else. This elastic undulatory
theory has been abandoned in our time in favor of an _electromagnetic_
theory supported by quite considerable experiential grounds. Whether it
will be spared the fate that has overtaken the older theories (or rather
hypotheses) of light cannot as yet be predicted with any degree of
certainty.
Radiant energy is of very marked importance in human relations. As light
it serves, with the aid of the corresponding receiving organs, the eyes,
as a more manifold means of intercommunication between our bodies and
the outer world than any other form of energy. The energy quantities
penetrating to us from the extreme limits of the world space mark the
outermost limits of which we have knowledge in any way whatsoever, and
finally the energy quantities radiating to us from the sun constitute
the supply of free energy at the expense of which all organic life on
earth is maintained. Even the chemical energy stored up in coal
represents nothing else than accumulations of former sun radiation,
which had been transformed by the plants into the permanent form of
chemical energy.
Very recently other newly discovered forms of radiant energy have been
added to light. They are produced in manifold circumstances, and some
bodies emit them constantly. The scientific elaboration of these
extremely manifold and unusual phenomena has not yet been carried so far
that they can be reduced to a doubt-free system. But so much, it seems,
is already apparent, that they are presumably not purely new forms of
energy, but rather very composite phenomena which may yield one or more
new energies as component parts. But despite the peculiarity of these
new rays, nothing certain has as yet been proved against the law of
conservation itself.
=53. Chemical Energy.= Since chemical energy is only one of several
forms of energy, there seems to be no justification for allotting it to
a special science, since all the other forms of energy must be
incorporated in physics.
But the actual existence of chemistry as a special science which has
already many subdivisions is justified in the first place by the
external fact that in practical life and in industry chemistry occupies
a very wide field comparable, if not superior, to that of the whole of
physics. In the next place, from the psychological point of view, it is
found that the chemist's methods of reasoning and working are so
different from those of the physicist that a division seems to be in
order for that reason also. Finally, there is in the nature of chemical
energy itself an important distinction which marks it off from the other
forms.
While, for example, there is only one form of heat or of kinetic energy,
and in electricity there are only the two forms of polar opposites,
chemistry, even after the greatest theoretical reduction, possesses at
least about eighty forms. That is, it possesses as many forms as there
are _chemical elements_. The experiential law, that the elements cannot
be changed into one another,[H] also limits the corresponding changes
of the chemical energies into one another, and thus characterizes the
independence of these various forms. From this results a
disproportionately greater manifoldness of relations, which find their
expression in the many thousands of the individualized chemical
substances or combinations.
[H] Lately changes of elements into one another have been observed in
individual instances, but in such peculiar circumstances that for the
present we need not consider these discoveries, which have only just
begun.
This great manifoldness and the slight regularity hitherto found in
connection with the properties and reciprocal relations of the numerous
chemical elements renders modern chemistry more a descriptive than a
rational science. It was no more than twenty years ago that an earnest
and successful attempt was begun to apply the stricter methods of
physics to the investigation of chemical phenomena. These labors, so far
as they have gone, have yielded a great many far-reaching and
comprehensive principles.
The significance of chemistry in human life is twofold. In the first
place the energy of the human body, just as that of all other living
organisms, depends chiefly upon the action of chemical energies in the
most manifold forms. Of all the physical sciences, therefore, chemistry
is the most important for biology, particularly for physiology. In the
second place, as I have emphasized a number of times, it possesses the
peculiar property which enables it to be _preserved_ for a long time
without passing into other forms and being dissipated. Furthermore,
energy in this form permits of the most powerful _concentration_. More
of chemical energy can be stored in a given space than of any other form
of energy. Both these properties, then, may be considered as the reason
why organic beings are constituted chiefly by means of chemical energy.
At any rate, it is due to these two peculiarities that chemical energy
serves as the primary source for almost all the energy used in industry.
Further, the manifoldness of chemical energy is the cause of the
peculiar manner in which it is transformed into other forms. In the
other forms of energy the transformation can be effected by the body
itself. Nothing else is required. If a stone is thrown and it hits
against a wall, it loses its kinetic energy, the greater part of which
changes into heat. But in order to liberate the _chemical_ energy of,
say, coal, the coal _alone_ is not sufficient; _another_ chemical
substance is required, the oxygen of the air. The interaction of the two
substances produces a new substance, and it is only during this process
that a corresponding part of the chemical energy is liberated. There are
a few chemical processes also (allotropic and isomeric changes) in which
a single substance without the co-agency of another substance can give
off energy. But the quantity of energy thus obtained is infinitely
small as compared to that liberated by the interaction of two or more
substances. Because of the necessity of two or more substances to
co-operate in giving off chemical energy, the opportunity for the
transformation of chemical energy is less than for the transformation of
the other forms of energy, and this is the main reason why it can be
conserved so long and so easily. All that is necessary is to prevent
contact with another substance. This is a problem, it is true, which
from the point of view of strict theoretical rigor it is almost
impossible to solve. In practice, however, it can be easily solved for
periods of time long enough at least to require special means to enable
us to recognize that it is only a temporary and not a fundamental
solution. Scientifically expressed, the cause of this is that the
_diffusion_ of the various substances in one another can theoretically
never be completely eliminated, while on the other hand the velocity of
the diffusion over distances measured only by decimeters is extremely
low.