ENERGETICS
Movement is everywhere; there is no such thing as immobility; the very idea
of rest is itself an illusion. Immobility is only apparent and relative,
and disappears under closer examination. All terrestrial objects are driven
with prodigious velocity around the sun, and the dwellers on the earth's
equator travel each day around the 40,000 kilometres of its circumference.
All objects on the globe are in motion, the inanimate as well as the
living. The waters rise in vapour from the sea, float over mountain and
valley, and return down the rivers to the sea again. Still more marvellous
is the current of water which flows eternally from dew and rain, through
the sap of plants and the blood of animals to the mineral world again. The
very mountains crumble and their substance is washed down into the plains;
the winds move the air and raise the waves of the sea, whilst the strong
ocean currents are produced by variations of temperature in different
parts. This agitation, this incessant and universal motion, has been a
favourite subject of poetic contemplation. Heraclitus writes: "There is a
perpetual flow, all is one universal current; nothing remains as it was,
change alone is eternal." Ovid writes in his _Metamorphoses_: "Believe me,
nothing perishes in this vast universe, but all varies, and changes its
figure. I think that nothing endures long under the same appearance. What
was solid earth has become sea, and solid ground has issued from the bosom
of the waters."
The French poetess Mme. Ackermann has expressed the same idea in beautiful
verse:--
"Ainsi, jamais d'arret. L'immortelle matiere,
Un seul instant encore n'a pu se reposer.
La Nature ne fait, patiente ouvriere,
Que defaire et recomposer.
{98}
Tout se metamorphose entre ses mains actives;
Partout le mouvement incessant et divers,
Dans le cercle eternel des formes fugitives,
Agitant l'immense univers."
It was only towards the middle of last century that mankind in the long
search after unity in nature began to realize that all the movements of the
universe are the manifestations of a single agent, which we call energy. In
reality all the phenomena of nature may be conceived as diverse forms of
motion, and the word "energy" is the common expression applied to all the
various modes of motion in the universe. It was by the study of heat, and
more especially of thermodynamics, that we obtained our conceptions of the
science of energetics.
It was in Munich in 1798 that the English engineer Count Rumford first
observed that in the operation of boring a cannon the copper was heated to
such a degree that the shavings became red-hot. This suggested his famous
experiment, in which a heavy iron pestle was turned by horse power in a
metal mortar filled with water. The water boiled, and when more water was
added this also became heated to ebullition, and so on indefinitely.
Rumford argued that the heat thus obtained in an indefinite quantity could
not be a material substance; that motion was the only thing added to the
water without limit, and that therefore heat must be motion.
While Rumford's experiment showed the transformation of motion into heat,
the steam engine was soon afterwards to demonstrate the opposite
transformation, viz. that of heat into motion.
The actual state of our knowledge with regard to the science of energy
rests on two principles, that of Mayer and that of Carnot.
The first principle was defined by J. R. Mayer, a medical practitioner of
Heilbronn, whose work, _Bemerkungen ueber die Kraefte der unbelebten
Natur_, was published in 1842. "All physical phenomena," says Mayer,
"whether vital or chemical, are forms of motion. All these forms of motion
are susceptible of change into one another, and in all the transformations
the {99} quantity of mechanical work represented by different modes of
motion remains invariable."
The energy of a given body is the amount of transferable motion stored up
in that body, and is measured by its capacity of producing mechanical work.
Ostwald thus defines energy: "Energy is work, all that can be obtained from
work, and all that can be changed into work." Different forms of energy may
be measured in different ways, but all forms of energy can be measured
either in units of mechanical work or in units of heat, in
kilogramme-metres or foot-pounds or in calories, according as the energy in
question is transformed into mechanical work or into heat. The first
principle of energetics, the conservation of energy, may be thus expressed:
"Energy is eternal; none is ever created, and none is ever lost. The
quantity of energy in the universe is invariable, and is conserved for ever
in its integrity."
The unit by which we measure quantities of heat is the calory, the amount
of heat required to raise the temperature of one kilogramme of water one
degree Centigrade.
The practical unit of mechanical work is the kilogramme-metre, the work
required to raise the weight of one kilogramme to the height of one metre.
The theoretical unit of work is one erg, the work required to move a mass
of one gramme through one centimetre against a force of one dyne.
Joule of Manchester was the first to verify Mayer's law quantitatively. By
an experiment analogous to that of Rumford, he transformed work into heat,
arranging his apparatus so that he might measure the amount of heat
produced and the work expended. On dividing the quantity of work that had
disappeared by the quantity of heat which had been disengaged, he found
that 424 kilogramme-metres of work had been expended for each calory of
heat produced.
Hirn of Colmar measured the ratio of work to heat in the steam engine. He
found that for each calory of heat which had disappeared there were
produced 425 kilogramme-metres of work. {100}
This number 425 has therefore been accepted as representing in calories and
kilogramme-metres the transformation of work into heat, and of heat into
work.
Further measurements on the transformations of other forms of energy,
chemical energy and electrical energy, have shown that Joule's law of
equivalents is general, and that the quantity of mechanical work
represented by any form of energy remains undiminished after
transformation, whatever the nature of that transformation.
Energy presents itself to us under two forms, potential and actual.
Potential energy is slumbering energy, energy localized or locked up in the
body. In order to transform potential energy into actual energy, there is
required the intervention of an additional awakening, stimulating, or
exciting energy from without. This stimulating energy may be almost
infinitesimal in amount and bears no quantitative relation to the amount of
energy transformed. It is the small amount of work required to turn the key
which liberates an indeterminate quantity of potential energy.
Actual energy, on the other hand, is energy in movement, awake and alert,
ready to be transformed into any other form of energy without the
intervention of any such external stimulating force.
The passage of a given quantity of energy from the potential into the
actual state is effected gradually, and during the time of transformation
the sum of the actual and the potential energy remains constant.
A weight suspended by a cord possesses a quantity of potential energy equal
to the product of its weight into the height through which it can fall.
This energy is locked up in a certain space, it cannot be transformed
without the intervention of some external energy to cut the cord. During
the falling of the weight, at the middle of its path, half of this
slumbering energy has become kinetic, and is represented by the _vis viva_
of the weight, while the other half is still potential and is equivalent to
the work which the weight will accomplish during the second half of its
fall. At any moment the sum of these two energies, the sleeping and the
waking {101} energies, represents the total potential energy of the weight
before it began to fall.
So with the powder in a gun. The potential energy of the powder cannot
become actual without some stimulus, some exciting force from without to
set it free. It is the external work of pressing the trigger that liberates
the potential energy of the powder, transforming it into the actual energy
of combustion, and the kinetic energy of the projectile.
Since energy is work, and work is a function of motion, there is in reality
no such thing as energy in repose. Matter according to our modern
conception is a complex of molecules, atoms, and electrons; we conceive the
molecules of matter as always in movement, animated with cyclic or
vibratory motion, these oscillatory or rotatory movements representing the
potential energy of the body in question. Potential energy is thus the
expression of molecular motion without translation of the molecules as a
whole in space.
When this potential energy is transformed into actual energy by the
intervention of some external force, we get a current of energy, a
transference of the molecules in space. Thus, when an external force has
released the weight, the molecular orbits in the falling body change in
form, and the potential energy of the molecular motion becomes the kinetic
energy of the falling body. Similarly in the conduction of heat, the energy
of the hot body is transferred to a colder body by transmission of the
vibratory motion from molecule to molecule. So again with chemical energy,
the molecular motion of combustion may be transformed into the radiant
energy of the ethereal waves.
Actual energy may be regarded as a current of molecular motion. To make the
matter clearer, let a mass of matter be represented by a regiment of
soldiers. Then each soldier will represent an electron, a company will be
an atom, and a battalion will be a molecule. As long as the soldiers mark
time, turn, or otherwise exercise without advancing, we have simply an
accumulation of potential energy. The word of command, "March," is the
exciting force which suddenly transforms this potential into kinetic
energy. The marching {102} regiment is a representation of a body
possessing kinetic energy. Potential energy is energy confined to a certain
point in space, whereas actual energy is a current of energy, continually
changing its place or form. Energy is like water-power--potential in the
lake, actual in the waterfall or river.
Any mechanism capable of causing one form of energy to pass into another is
a transformer of energy. A steam engine is a transformer of energy,
changing caloric energy into mechanical work. An electrical machine is a
transformer of energy, converting mechanical motion into a current of
electricity, whilst an electro-motor changes the movement of electrons into
mechanical movement. Every living being, and even man himself, is but a
transformer of energy, changing the energy derived from the earth and air
and sun into mechanical motion, nervous energy, and heat.
The first law of energetics, that of the conservation of energy, is
analogous to Lavoisier's principle in chemistry, the conservation of
matter. The sign of equality which unites the terms of a chemical equation
expresses the fact that after every chemical reaction the same total mass
of matter is present as before the transformation. This is also true of
energy; after every transformation we find exactly the same total quantity
of energy as before it. This, however, tells us nothing as to the
conditions of the transformation, or the causes, _i.e._ the anterior
phenomena, which determined such transformation.
The second principle of energetics, that of Carnot, enunciated in 1824,
deals with the conditions under which a transformation of energy is
possible. A mass of water at a certain height represents a quantity of
potential energy equal to the product of its weight by its height; but this
energy cannot produce mechanical work unless the water is allowed to fall.
Consider two lakes at the same altitude and of the same capacity, one of
which is entirely landlocked, while the other has an open channel leading
to the sea. Each lake represents the same quantity of potential energy, but
the energy of the landlocked lake is useless, it cannot be {103}
transformed; whereas the other lake whose water can run into the sea
realizes the conditions necessary for utilization, viz. the
transformability of its energy. The same may be said of all forms of
energy; a heat engine can only act as a transformer, change heat into work,
if there is a difference of temperature between its source and its sink; an
electric motor can only work if there is a fall of potential between the
entrance and the exit of the electric current.
Energy presents itself to us as the product of two factors, weight and
height in the waterfall, quantity and temperature in the heat engine,
current intensity and potential in the electric motor.
In considering these two factors we may note that one factor is always a
quantity (Q) and the other an intensity (I). This latter expresses some
sort of difference of position or condition, the height of the weight, a
difference of temperature in the heat engine, of pressure in the gas
engine, or of electric potential in the dynamo or electric furnace. There
can be no current of energy without this difference of potential, and
therefore no transformation from one form of energy to another.
The second law of thermodynamics, Carnot's law, may therefore be enunciated
thus: "Energy cannot be transformed without a fall of potential."
We may also derive this principle from a consideration of the formula of
efficiency, the ratio of the work done by the transformer to the work done
on the transformer.
Efficiency = energy transformed / total energy absorbed
The total energy is the product QI, _i.e._ the product of the total
quantity by the total intensity at our disposal. The transformed energy is
Q(I - I'), the product of the total quantity by the difference of intensity
at the inlet and at the outlet of the machine. The formula for efficiency
thus becomes
Q(I - I') / QI = (I - I') / I.
If I represents a temperature, then in order that the efficiency may be
positive I' must be less than I, {104} there must be a fall of temperature
in the machine. If I' were greater than I, _i.e._ if the temperature at the
outlet were greater than that at the inlet, the efficiency would be a
negative one, and the transformer would have to borrow heat from some
external source.
_Entropy._--In every transformation of energy a certain portion of the
energy is transformed into heat: a lamp gives out useless heat as well as
light, a machine gives out useless heat as well as mechanical work. This
loss of useful energy as heat occurs in every transference or
transformation of energy; it is only in the case of heat passing from a
hotter to a colder body that there is no such transformation. When equality
of temperature is established there has been no loss of energy, but the
whole of the energy has become unutilizable, i.e. untransformable. In the
formula of efficiency the fall of intensity I - I' is now zero, and
therefore the efficiency of the machine
(I - I') / I
is also zero.
Since in all its transformations a certain fraction of the energy is
changed into heat, there is a tendency in nature for all differences of
temperature to become equalized. Hence the quantity of utilizable energy in
the universe tends to diminish. Clausius called this unutilizable energy
enmeshed in the substance of a body its entropy, and showed that in every
transformation the amount of this unutilizable energy tended to increase.
"The entropy of a system always tends towards a maximum value."
If this gradual incessant increase of entropy is universal in nature, and
if there is no compensatory mechanism, the universe must be tending towards
a definite end, when the whole of its energy shall have been transformed
into unutilizable heat with a uniform temperature. There is, however,
reason to suppose that some such compensatory mechanism does in fact exist.
Behind us stretches an infinite past, and in the future we believe that the
phenomena of nature will be unrolled in a cycle which has no end. But the
arguments derived from a study of entropy apply only to the facts and
phenomena actually under our notice, the supposed {105} impossibility,
without borrowing energy from without, of re-establishing the differences
of temperature by drawing heat from a colder in order to concentrate it in
a hotter body, and may not be absolutely identical with those obtaining in
other ages. Our ignorance of such a phenomenon and our powerlessness to
produce it in no way argue that it is impossible. It may exist for aught we
know in some other region of space, or in another time than ours. We may
perhaps some day obtain artificially the conditions which would render
possible such a phenomenon, since it may be possible to produce in the
experimental laboratory conditions which are not spontaneously realized in
nature under present conditions. The future may perchance reveal to us
absolutely new phenomena which have not hitherto been realized. In his work
on the evolution of matter and of energy Gustave le Bon gives expression to
some interesting and original ideas on this subject.
The laws of Mayer and Carnot alone are not sufficient to explain the
phenomena of life, without some consideration of the laws of stimulus.
Mayer's principle asserts the conservation of energy, and Carnot's the
conditions necessary for its transformation, but these alone cannot account
for the transformation of potential into actual energy. A weight suspended
by a cord does not fall merely because there is room for its descent. We
need the intervention of some outside force to cut the cord. In every
transformation of energy this external force is required to cut the cord,
or pull the trigger, some external force of excitation or liberation, an
energy which may be infinitesimal in amount, and which bears no proportion
to the quantity of potential energy it sets free. This intervention of an
excitatory, stimulating, or liberating energy is universal. Every
phenomenon of nature is but a transformation or a transference of energy,
determined by the intervention of a minimal quantity of energy from
without. This liberation of large quantities of potential energy by an
exceedingly small external stimulus has not hitherto received the
consideration it demands. Certain phenomena, such as those of chemical
catalysis or the action of soluble ferments, excite our astonishment
because such extremely small quantities of {106} certain substances will
determine the chemical transformations of large quantities of matter, there
being no proportion between the amount of the catalytic substance and of
the matter transformed. These phenomena are, however, only particular cases
of the general law of energetics that transformation requires a stimulus.
The catalyzer, or ferment, does not contribute matter to the reaction, but
only the minimal energy necessary to liberate the chemical potential energy
stored in the fermenting substance.
We must therefore add a third to the two laws of energetics, Mayer's law of
conservation, and Carnot's law of fall of potential. This third law is the
law of stimulus, the necessity of the intervention of an external
excitatory force capable of setting in motion the current of energy
required for a transformation. This stimulus is the primary phenomenon, the
determinant cause of such transformation.
Three conditions, then, are required for a transformation or displacement
of energy:--
1. _The cause_, the intervention of a stimulus which starts the
transformation or displacement.
2. _The possibility_, the necessary fall of potential.
3. _The condition_, the conservation of the energy concerned, since being
indestructible its total quantity cannot alter.
Every living being is a transformer of energy. The lower animals and man
himself receive from food and air the potential energy which becomes actual
under the process of oxydation. This chemical combustion is the source of
all vital energy; the ancients aptly compared life to a flame, and
Lavoisier has shown that life, like the flame, is maintained by a process
of oxydation. The energy derived from food and air is restored by the
organism to the external world in the form of heat and mechanical motion.
The celebrated experiments of Atwater show that there is an absolute
equality between the energy obtained from the oxydation of the various
aliments and the sum of the calorific and mechanical energy liberated by a
living being.
Man obtains his supply of energy either directly from the {107} vegetable
world, or indirectly from vegetables which have passed through the flesh of
animals. Vegetables in their turn obtain their substance from the mineral
world and their energy from the sun. The salts, the water, and the carbonic
acid absorbed by plants possess no store of potential energy. Whence then
can they obtain the potential energy which they transmit to animals and
man, if not from the sun? The energy of the solar radiations is absorbed by
the chlorophyll of the leaves, and stored up in the organic carbohydrates
formed by the synthesis of water and carbon. Chlorophyll has the peculiar
property of reducing carbonic acid, and uniting the carbon with water in
different proportions to form sugar and starch, whilst fats and vegetable
albumens are also formed by an analogous reaction. All these complex bodies
are stores of energy; the vital processes of oxydation do but liberate in
the human body the energy which the chlorophyll of plants has absorbed from
the solar rays.
We must look, then, to the sun as the direct source of all the energy which
animates the surface of the earth. The sun looses the winds, and raises the
waters of the sea to the mountain-tops, to form the rivers and torrents
which return again to the sea; the sun warms our hearths, drives our ships,
and works our steam engines. There is no sign of life or movement on our
planet which does not come directly or indirectly from the solar rays.
It may be asked by what path does the chemical energy of the living
organism pass into the mechanical energy of motion. It would appear that
the intermediary step cannot be heat, as in the steam engine, since the
necessary temperature would be quite incompatible with life.
The formula for the efficiency of a thermic transformer is
(T - T') / T,
the ratio of the difference of the absolute temperatures at the source and
at the sink, to the absolute temperature at the source. Calorimetric
measurements have shown that the efficiency of the human machine is about
one-fifth, _i.e._ it can transform 20 per cent. of the energy absorbed. The
ordinary temperature of muscle is 38deg C., or 311deg absolute. We have
{108} therefore (T - 311) / T = .20, or T = 388.75deg absolute, _i.e._
115.75deg C. Thus, in order to obtain an efficiency of 20 per cent. with an
ordinary thermic transformer, having a temperature of 38deg at the sink, we
should need a temperature of over 115deg C. at the source. Such a
temperature would be quite incompatible with the integrity of living
tissues, and we may therefore conclude that the human organism is not a
heat engine.
We are indeed completely ignorant of the mode of transformation of chemical
into kinetic energy in the living organism; we know only that muscular
contraction is accompanied by a change of form; at the moment of
transformation the combustion of the muscle is increased, and during
contraction the stretched muscular fibre tends to acquire a spherical
shape. It is this shortening of the muscular fibre which produces the
mechanical movement. The step which we do not as yet fully understand is
the physical phenomenon which intervenes between the disengagement of
chemical energy and the occurrence of muscular contraction. Professor
d'Arsonval supposes that this missing step is a variation in the surface
tension of the liquid in the muscular fibre. The surface tension of a
liquid is due to the unbalanced forces of cohesion acting on the surface
layer of molecules. Under the attraction of cohesion the molecules within
the liquid are in a state of equilibrium, being equally attracted in all
directions, but those at the surface of the liquid are drawn towards the
centre. The resultant of these attractive forces is a pressure normal to
the surface, which is mechanically equivalent to an elastic tension tending
to diminish the surface. In consequence of this surface tension the liquid
has a tendency to assume the form in which its surface area is a minimum,
_i.e._ the spherical form. If such a sphere is stretched into a cylinder or
fibre by mechanical tension, it will shorten itself when released; and if
by any means we increase the surface tension of such a liquid fibre it will
tend to assume a spherical form and contract just as a muscular fibre does.
The surface tension of a liquid varies with its chemical composition; the
slightest chemical modification of a liquid alters the force of {109} this
tension. We may therefore explain the mechanism of muscular contraction by
supposing that a nervous impulse alters in some way the rate of combustion
in a muscular fibre, that this alteration produces a momentary change in
the chemical composition of the muscular cell, and that this change of
chemical composition increases the surface tension of the cell sufficiently
to provoke its contraction into a more spherical form.
Ostwald has introduced a very useful conception for the study of this
question of surface energy. A liquid surface contains a quantity of energy
equal to its surface tension multiplied by its area, hence any variation
either of area or of tension corresponds to a variation of its energy. This
novel conception constitutes a valuable addition to the experimental study
of the physiology of muscular action, since it gives us some idea of the
mechanism by which chemical energy may be transformed into muscular
contraction.
Whatever the mechanism of transformation in the animal machine, we have to
consider the same quantities as in other motor machines. These are: (1) the
efficiency; (2) the potential energy; (3) the power; (4) the energy given
up to the medium under the form of heat; (5) the temperature.
Muscles, then, are merely transformers which change chemical energy into
mechanical work, the diminution of stored-up energy in a muscle being
expressed by the sensation of fatigue. A muscle may be studied in four
different phases: (1) in repose; (2) in a state of tension; (3) when doing
positive work; (4) when work is being done on it.
When a muscle is in a state of tension, as when a weight is sustained by
the outstretched arm, the muscle is producing no external work. The entire
work done is converted into heat; just as it is in a dynamo or steam engine
which is prevented from turning by a brake. Muscular contraction produces
fatigue even when it does no external work. It is impossible for the muscle
to support even the weight of the outstretched arm itself for any
considerable time.
A muscle is doing positive work when it is raising a weight or moving a
body from one point to another. {110}
The fourth state of muscular contraction is when the muscle is doing
negative work, _i.e._ when work is being done on it, as for instance when
we go downstairs, or when a descending weight forces down the opposing arm
which attempts to support it. In this case the muscles receive a portion of
the energy lost by the descending weight, and this energy shows itself in
the muscle in the form of heat. This increase of heat in a muscle doing
negative work has been clearly demonstrated by the calorimetric experiments
of Hirn and the thermometric experiments of Beclard. Hirn's observations on
muscular calorimetry show a production of heat corresponding to 150
calories per hour when in repose, 248 calories per hour during positive
work, and 287 during negative work. Beclard's thermometric measurements
also show that the temperature of a muscle rises each time that it
contracts, and that the rise of temperature is greatest when the muscle is
doing negative work, least during positive work, and intermediate when in a
state of tension.
It is of the greatest importance in medical practice to distinguish between
these different forms of muscular activity. There is a vast physiological
difference between muscular contraction with the production of positive
work, and muscular contraction without the production of work, or with
negative work. To climb a flight of stairs is to contract the muscles with
the production of work equal to the weight of the body multiplied by the
height of the stairs. To descend the stairs is to contract the same
muscles, but with the production of negative work, and consequently a
maximum of heat. To walk on level ground is to contract the muscles with
the production of little or no external work; as in a machine turning
without friction in a vacuum.
We have seen that a fall of potential and a current of energy are the
necessary conditions for the production of any natural phenomenon. Hence we
may assume that the phenomenon of sensation is also accompanied by a fall
of potential and a current of energy. When we touch a hot body, there is a
flow of energy from the hot body to the hand. When we touch a cold body,
there is a current of energy in the opposite direction, {111} from the hand
to the body. It was formerly held, and is still held by some physiologists,
that the chief characteristic of life is the disproportion between an
excitation and the response which it invokes from the organism. Such a
doctrine can only be held by one who believes, at least implicitly, that
the phenomena of life are supernatural, or at all events different in their
nature from all other phenomena; for the disproportion between an
excitation and the response it evokes is by no means confined to living
things. This disproportion is universal in nature, and quite in conformity
with the physical laws which govern the transformation of energy. The
energy of living things is potential energy--a fact which has been too
little recognized. In the case of reflex actions it is self-evident,
because the response is immediate, and always the same for the same
stimulus. As in all other transformations, the stimulus consists in the
intervention of a minimal quantity of external energy.
Long before the discovery of the laws of energy, Lamarck had recognized and
formulated this fact. He writes: "What would vegetable life be without
excitations from without, what would be the life even of the lower animals
without this cause?" In another passage, seeking for a power capable of
exciting the action of the organism, he says: "The lower animal forms,
without nervous system, live only by the aid of excitations which they
receive from without. In the lowest forms of life this exciting force is
borrowed directly from the environment, while in the higher forms the
external exciting force is transferred to the interior of the living being
and placed at the disposal of the individual."
This remark, that the movements of living things are not communicated but
excited, that the external excitation only sets free latent or potential
energy in the organism, shows that Lamarck had penetrated more deeply than
many of the modern physiologists into the secrets of biological energy. We
seek in vain in the text-books of physiology for any conception of
potential energy in living beings, or the notion of an exciting force as
the cause of sensation. All action of a living organism is reflex action.
Every action has a cause, and {112} the cause of an organic action is an
exciting energy from without, either immediate, or stored up in the nervous
system from an external impression made at some previous epoch. Actions
which are not evidently reflex are merely delayed reflexes; we have
acquired the power of inhibiting, delaying, or modifying the response to an
external stimulus, so that the same excitation may determine responses of
very different kinds according to the mood produced by previous
impressions. When carefully investigated, no action of ours is automatic;
every movement is determined by impressions derived from without. An action
without a motive, that is without an external determining cause, would be
an action without reason.
In conclusion, we may formulate this general principle: The energy of a
living being is potential energy; sensations represent the intervention of
an external exciting energy which provokes the response, _i.e._ the
transformation of the potential energy already stored in the organism into
the actual energy of motion and vital activity.
* * * * *
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