THE VARIOUS STATES OF MATTER
§ 1. THE STATICS OF FLUIDS
The division of bodies into gaseous, liquid, and solid, and the
distinction established for the same substance between the three
states, retain a great importance for the applications and usages of
daily life, but have long since lost their absolute value from the
scientific point of view.
So far as concerns the liquid and gaseous states particularly, the
already antiquated researches of Andrews confirmed the ideas of
Cagniard de la Tour and established the continuity of the two states.
A group of physical studies has thus been constituted on what may be
called the statics of fluids, in which we examine the relations
existing between the pressure, the volume, and the temperature of
bodies, and in which are comprised, under the term fluid, gases as
well as liquids.
These researches deserve attention by their interest and the
generality of the results to which they have led. They also give a
remarkable example of the happy effects which may be obtained by the
combined employment of the various methods of investigation used in
exploring the domain of nature. Thermodynamics has, in fact, allowed
us to obtain numerical relations between the various coefficients, and
atomic hypotheses have led to the establishment of one capital
relation, the characteristic equation of fluids; while, on the other
hand, experiment in which the progress made in the art of measurement
has been utilized, has furnished the most valuable information on all
the laws of compressibility and dilatation.
The classical work of Andrews was not very wide. Andrews did not go
much beyond pressures close to the normal and ordinary temperatures.
Of late years several very interesting and peculiar cases have been
examined by MM. Cailletet, Mathias, Batelli, Leduc, P. Chappuis, and
other physicists. Sir W. Ramsay and Mr S. Young have made known the
isothermal diagrams[6] of a certain number of liquid bodies at the
ordinary temperature. They have thus been able, while keeping to
somewhat restricted limits of temperature and pressure, to touch upon
the most important questions, since they found themselves in the
region of the saturation curve and of the critical point.
[Footnote 6: By isothermal diagram is meant the pattern or complex
formed when the isothermal lines are arranged in curves of which the
pressure is the ordinate and the volume the abscissa.--ED.]
But the most complete and systematic body of researches is due to M.
Amagat, who undertook the study of a certain number of bodies, some
liquid and some gaseous, extending the scope of his experiments so as
to embrace the different phases of the phenomena and to compare
together, not only the results relating to the same bodies, but also
those concerning different bodies which happen to be in the same
conditions of temperature and pressure, but in very different
conditions as regards their critical points.
From the experimental point of view, M. Amagat has been able, with
extreme skill, to conquer the most serious difficulties. He has
managed to measure with precision pressures amounting to 3000
atmospheres, and also the very small volumes then occupied by the
fluid mass under consideration. This last measurement, which
necessitates numerous corrections, is the most delicate part of the
operation. These researches have dealt with a certain number of
different bodies. Those relating to carbonic acid and ethylene take in
the critical point. Others, on hydrogen and nitrogen, for instance,
are very extended. Others, again, such as the study of the
compressibility of water, have a special interest, on account of the
peculiar properties of this substance. M. Amagat, by a very concise
discussion of the experiments, has also been able to definitely
establish the laws of compressibility and dilatation of fluids under
constant pressure, and to determine the value of the various
coefficients as well as their variations. It ought to be possible to
condense all these results into a single formula representing the
volume, the temperature, and the pressure. Rankin and, subsequently,
Recknagel, and then Hirn, formerly proposed formulas of that kind; but
the most famous, the one which first appeared to contain in a
satisfactory manner all the facts which experiments brought to light
and led to the production of many others, was the celebrated equation
of Van der Waals.
Professor Van der Waals arrived at this relation by relying upon
considerations derived from the kinetic theory of gases. If we keep to
the simple idea at the bottom of this theory, we at once demonstrate
that the gas ought to obey the laws of Mariotte and of Gay-Lussac, so
that the characteristic equation would be obtained by the statement
that the product of the number which is the measure of the volume by
that which is the measure of the pressure is equal to a constant
coefficient multiplied by the degree of the absolute temperature. But
to get at this result we neglect two important factors.
We do not take into account, in fact, the attraction which the
molecules must exercise on each other. Now, this attraction, which is
never absolutely non-existent, may become considerable when the
molecules are drawn closer together; that is to say, when the
compressed gaseous mass occupies a more and more restricted volume. On
the other hand, we assimilate the molecules, as a first approximation,
to material points without dimensions; in the evaluation of the path
traversed by each molecule no notice is taken of the fact that, at the
moment of the shock, their centres of gravity are still separated by a
distance equal to twice the radius of the molecule.
M. Van der Waals has sought out the modifications which must be
introduced into the simple characteristic equation to bring it nearer
to reality. He extends to the case of gases the considerations by
which Laplace, in his famous theory of capillarity, reduced the effect
of the molecular attraction to a perpendicular pressure exercised on
the surface of a liquid. This leads him to add to the external
pressure, that due to the reciprocal attractions of the gaseous
particles. On the other hand, when we attribute finite dimensions to
these particles, we must give a higher value to the number of shocks
produced in a given time, since the effect of these dimensions is to
diminish the mean path they traverse in the time which elapses between
two consecutive shocks.
The calculation thus pursued leads to our adding to the pressure in
the simple equation a term which is designated the internal pressure,
and which is the quotient of a constant by the square of the volume;
also to our deducting from the volume a constant which is the
quadruple of the total and invariable volume which the gaseous
molecules would occupy did they touch one another.
The experiments fit in fairly well with the formula of Van der Waals,
but considerable discrepancies occur when we extend its limits,
particularly when the pressures throughout a rather wider interval are
considered; so that other and rather more complex formulas, on which
there is no advantage in dwelling, have been proposed, and, in certain
cases, better represent the facts.
But the most remarkable result of M. Van der Waals' calculations is
the discovery of corresponding states. For a long time physicists
spoke of bodies taken in a comparable state. Dalton, for example,
pointed out that liquids have vapour-pressures equal to the
temperatures equally distant from their boiling-point; but that if, in
this particular property, liquids were comparable under these
conditions of temperature, as regards other properties the parallelism
was no longer to be verified. No general rule was found until M. Van
der Waals first enunciated a primary law, viz., that if the pressure,
the volume, and the temperature are estimated by taking as units the
critical quantities, the constants special to each body disappear in
the characteristic equation, which thus becomes the same for all
fluids.
The words corresponding states thus take a perfectly precise
signification. Corresponding states are those for which the numerical
values of the pressure, volume, and temperature, expressed by taking
as units the values corresponding to the critical point, are equal;
and, in corresponding states any two fluids have exactly the same
properties.
M. Natanson, and subsequently P. Curie and M. Meslin, have shown by
various considerations that the same result may be arrived at by
choosing units which correspond to any corresponding states; it has
also been shown that the theorem of corresponding states in no way
implies the exactitude of Van der Waals' formula. In reality, this is
simply due to the fact that the characteristic equation only contains
three constants.
The philosophical importance and the practical interest of the
discovery nevertheless remain considerable. As was to be expected,
numbers of experimenters have sought whether these consequences are
duly verified in reality. M. Amagat, particularly, has made use for
this purpose of a most original and simple method. He remarks that, in
all its generality, the law may be translated thus: If the isothermal
diagrams of two substances be drawn to the same scale, taking as unit
of volume and of pressure the values of the critical constants, the
two diagrams should coincide; that is to say, their superposition
should present the aspect of one diagram appertaining to a single
substance. Further, if we possess the diagrams of two bodies drawn to
any scales and referable to any units whatever, as the changes of
units mean changes in the scale of the axes, we ought to make one of
the diagrams similar to the other by lengthening or shortening it in
the direction of one of the axes. M. Amagat then photographs two
isothermal diagrams, leaving one fixed, but arranging the other so
that it may be free to turn round each axis of the co-ordinates; and
by projecting, by means of a magic lantern, the second on the first,
he arrives in certain cases at an almost complete coincidence.
This mechanical means of proof thus dispenses with laborious
calculations, but its sensibility is unequally distributed over the
different regions of the diagram. M. Raveau has pointed out an equally
simple way of verifying the law, by remarking that if the logarithms
of the pressure and volume are taken as co-ordinates, the co-ordinates
of two corresponding points differ by two constant quantities, and the
corresponding curves are identical.
From these comparisons, and from other important researches, among
which should be particularly mentioned those of Mr S. Young and M.
Mathias, it results that the laws of corresponding states have not,
unfortunately, the degree of generality which we at first attributed
to them, but that they are satisfactory when applied to certain groups
of bodies.[7]
[Footnote 7: Mr Preston thus puts it: "The law [of corresponding
states] seems to be not quite, but very nearly true for these
substances [_i.e._ the halogen derivatives of benzene]; but in the
case of the other substances examined, the majority of these
generalizations were either only roughly true or altogether departed
from" (_Theory of Heat_, London, 1904, p. 514.)--ED.]
If in the study of the statics of a simple fluid the experimental
results are already complex, we ought to expect much greater
difficulties when we come to deal with mixtures; still the problem has
been approached, and many points are already cleared up.
Mixed fluids may first of all be regarded as composed of a large
number of invariable particles. In this particularly simple case M.
Van der Waals has established a characteristic equation of the
mixtures which is founded on mechanical considerations. Various
verifications of this formula have been effected, and it has, in
particular, been the object of very important remarks by M. Daniel
Berthelot.
It is interesting to note that thermodynamics seems powerless to
determine this equation, for it does not trouble itself about the
nature of the bodies obedient to its laws; but, on the other hand, it
intervenes to determine the properties of coexisting phases. If we
examine the conditions of equilibrium of a mixture which is not
subjected to external forces, it will be demonstrated that the
distribution must come back to a juxtaposition of homogeneous phases;
in a given volume, matter ought so to arrange itself that the total
sum of free energy has a minimum value. Thus, in order to elucidate
all questions relating to the number and qualities of the phases into
which the substance divides itself, we are led to regard the
geometrical surface which for a given temperature represents the free
energy.
I am unable to enter here into the detail of the questions connected
with the theories of Gibbs, which have been the object of numerous
theoretical studies, and also of a series, ever more and more
abundant, of experimental researches. M. Duhem, in particular, has
published, on the subject, memoirs of the highest importance, and a
great number of experimenters, mostly scholars working in the physical
laboratory of Leyden under the guidance of the Director, Mr Kamerlingh
Onnes, have endeavoured to verify the anticipations of the theory.
We are a little less advanced as regards abnormal substances; that is
to say, those composed of molecules, partly simple and partly complex,
and either dissociated or associated. These cases must naturally be
governed by very complex laws. Recent researches by MM. Van der Waals,
Alexeif, Rothmund, Künen, Lehfeld, etc., throw, however, some light on
the question.
The daily more numerous applications of the laws of corresponding
states have rendered highly important the determination of the
critical constants which permit these states to be defined. In the
case of homogeneous bodies the critical elements have a simple, clear,
and precise sense; the critical temperature is that of the single
isothermal line which presents a point of inflexion at a horizontal
tangent; the critical pressure and the critical volume are the two
co-ordinates of this point of inflexion.
The three critical constants may be determined, as Mr S. Young and M.
Amagat have shown, by a direct method based on the consideration of
the saturated states. Results, perhaps more precise, may also be
obtained if one keeps to two constants or even to a single one--
temperature, for example--by employing various special methods. Many
others, MM. Cailletet and Colardeau, M. Young, M.J. Chappuis, etc.,
have proceeded thus.
The case of mixtures is much more complicated. A binary mixture has a
critical space instead of a critical point. This space is comprised
between two extreme temperatures, the lower corresponding to what is
called the folding point, the higher to that which we call the point
of contact of the mixture. Between these two temperatures an
isothermal compression yields a quantity of liquid which increases,
then reaches a maximum, diminishes, and disappears. This is the
phenomenon of retrograde condensation. We may say that the properties
of the critical point of a homogeneous substance are, in a way,
divided, when it is a question of a binary mixture, between the two
points mentioned.
Calculation has enabled M. Van der Waals, by the application of his
kinetic theories, and M. Duhem, by means of thermodynamics, to foresee
most of the results which have since been verified by experiment. All
these facts have been admirably set forth and systematically
co-ordinated by M. Mathias, who, by his own researches, moreover, has
made contributions of the highest value to the study of questions
regarding the continuity of the liquid and gaseous states.
The further knowledge of critical elements has allowed the laws of
corresponding states to be more closely examined in the case of
homogeneous substances. It has shown that, as I have already said,
bodies must be arranged in groups, and this fact clearly proves that
the properties of a given fluid are not determined by its critical
constants alone, and that it is necessary to add to them some other
specific parameters; M. Mathias and M. D. Berthelot have indicated
some which seem to play a considerable part.
It results also from this that the characteristic equation of a fluid
cannot yet be considered perfectly known. Neither the equation of Van
der Waals nor the more complicated formulas which have been proposed
by various authors are in perfect conformity with reality. We may
think that researches of this kind will only be successful if
attention is concentrated, not only on the phenomena of
compressibility and dilatation, but also on the calorimetric
properties of bodies. Thermodynamics indeed establishes relations
between those properties and other constants, but does not allow
everything to be foreseen.
Several physicists have effected very interesting calorimetric
measurements, either, like M. Perot, in order to verify Clapeyron's
formula regarding the heat of vaporization, or to ascertain the values
of specific heats and their variations when the temperature or the
pressure happens to change. M. Mathias has even succeeded in
completely determining the specific heats of liquefied gases and of
their saturated vapours, as well as the heat of internal and external
vaporization.
§ 2. THE LIQUEFACTION OF GASES, AND THE PROPERTIES OF BODIES AT A
LOW TEMPERATURE
The scientific advantages of all these researches have been great,
and, as nearly always happens, the practical consequences derived from
them have also been most important. It is owing to the more complete
knowledge of the general properties of fluids that immense progress
has been made these last few years in the methods of liquefying gases.
From a theoretical point of view the new processes of liquefaction can
be classed in two categories. Linde's machine and those resembling it
utilize, as is known, expansion without any notable production of
external work. This expansion, nevertheless, causes a fall in the
temperature, because the gas in the experiment is not a perfect gas,
and, by an ingenious process, the refrigerations produced are made
cumulative.
Several physicists have proposed to employ a method whereby
liquefaction should be obtained by expansion with recuperable external
work. This method, proposed as long ago as 1860 by Siemens, would
offer considerable advantages. Theoretically, the liquefaction would
be more rapid, and obtained much more economically; but unfortunately
in the experiment serious obstacles are met with, especially from the
difficulty of obtaining a suitable lubricant under intense cold for
those parts of the machine which have to be in movement if the
apparatus is to work.
M. Claude has recently made great progress on this point by the use,
during the running of the machine, of the ether of petrol, which is
uncongealable, and a good lubricant for the moving parts. When once
the desired region of cold is reached, air itself is used, which
moistens the metals but does not completely avoid friction; so that
the results would have remained only middling, had not this ingenious
physicist devised a new improvement which has some analogy with
superheating of steam in steam engines. He slightly varies the initial
temperature of the compressed air on the verge of liquefaction so as
to avoid a zone of deep perturbations in the properties of fluids,
which would make the work of expansion very feeble and the cold
produced consequently slight. This improvement, simple as it is in
appearance, presents several other advantages which immediately treble
the output.
The special object of M. Claude was to obtain oxygen in a practical
manner by the actual distillation of liquid air. Since nitrogen boils
at -194° and oxygen at -180.5° C., if liquid air be evaporated, the
nitrogen escapes, especially at the commencement of the evaporation,
while the oxygen concentrates in the residual liquid, which finally
consists of pure oxygen, while at the same time the temperature rises
to the boiling-point (-180.5° C.) of oxygen. But liquid air is costly,
and if one were content to evaporate it for the purpose of collecting
a part of the oxygen in the residuum, the process would have a very
poor result from the commercial point of view. As early as 1892, Mr
Parkinson thought of improving the output by recovering the cold
produced by liquid air during its evaporation; but an incorrect idea,
which seems to have resulted from certain experiments of Dewar--the
idea that the phenomenon of the liquefaction of air would not be,
owing to certain peculiarities, the exact converse of that of
vaporization--led to the employment of very imperfect apparatus. M.
Claude, however, by making use of a method which he calls the
reversal[8] method, obtains a complete rectification in a remarkably
simple manner and under extremely advantageous economic conditions.
Apparatus, of surprisingly reduced dimensions but of great efficiency,
is now in daily work, which easily enables more than a thousand cubic
metres of oxygen to be obtained at the rate, per horse-power, of more
than a cubic metre per hour.
[Footnote 8: Methode avec retour en arriere.--ED]
It is in England, thanks to the skill of Sir James Dewar and his
pupils--thanks also, it must be said, to the generosity of the Royal
Institution, which has devoted considerable sums to these costly
experiments--that the most numerous and systematic researches have
been effected on the production of intense cold. I shall here note
only the more important results, especially those relating to the
properties of bodies at low temperatures.
Their electrical properties, in particular, undergo some interesting
modifications. The order which metals assume in point of conductivity
is no longer the same as at ordinary temperatures. Thus at -200° C.
copper is a better conductor than silver. The resistance diminishes
with the temperature, and, down to about -200°, this diminution is
almost linear, and it would seem that the resistance tends towards
zero when the temperature approaches the absolute zero. But, after
-200°, the pattern of the curves changes, and it is easy to foresee
that at absolute zero the resistivities of all metals would still
have, contrary to what was formerly supposed, a notable value.
Solidified electrolytes which, at temperatures far below their fusion
point, still retain a very appreciable conductivity, become, on the
contrary, perfect insulators at low temperatures. Their dielectric
constants assume relatively high values. MM. Curie and Compan, who
have studied this question from their own point of view, have noted,
moreover, that the specific inductive capacity changes considerably
with the temperature.
In the same way, magnetic properties have been studied. A very
interesting result is that found in oxygen: the magnetic
susceptibility of this body increases at the moment of liquefaction.
Nevertheless, this increase, which is enormous (since the
susceptibility becomes sixteen hundred times greater than it was at
first), if we take it in connection with equal volumes, is much less
considerable if taken in equal masses. It must be concluded from this
fact that the magnetic properties apparently do not belong to the
molecules themselves, but depend on their state of aggregation.
The mechanical properties of bodies also undergo important
modifications. In general, their cohesion is greatly increased, and
the dilatation produced by slight changes of temperature is
considerable. Sir James Dewar has effected careful measurements of the
dilatation of certain bodies at low temperatures: for example, of ice.
Changes in colour occur, and vermilion and iodide of mercury pass into
pale orange. Phosphorescence becomes more intense, and most bodies of
complex structure--milk, eggs, feathers, cotton, and flowers--become
phosphorescent. The same is the case with certain simple bodies, such
as oxygen, which is transformed into ozone and emits a white light in
the process.
Chemical affinity is almost put an end to; phosphorus and potassium
remain inert in liquid oxygen. It should, however, be noted, and this
remark has doubtless some interest for the theories of photographic
action, that photographic substances retain, even at the temperature
of liquid hydrogen, a very considerable part of their sensitiveness to
light.
Sir James Dewar has made some important applications of low
temperatures in chemical analysis; he also utilizes them to create a
vacuum. His researches have, in fact, proved that the pressure of air
congealed by liquid hydrogen cannot exceed the millionth of an
atmosphere. We have, then, in this process, an original and rapid
means of creating an excellent vacuum in apparatus of very different
kinds--a means which, in certain cases, may be particularly
convenient.[9]
[Footnote 9: Professor Soddy, in a paper read before the Royal Society
on the 15th November 1906, warns experimenters against vacua created
by charcoal cooled in liquid air (the method referred-to in the text),
unless as much of the air as possible is first removed with a pump and
replaced by some argon-free gas. According to him, neither helium nor
argon is absorbed by charcoal. By the use of electrically-heated
calcium, he claims to have produced an almost perfect vacuum.--ED.]
Thanks to these studies, a considerable field has been opened up for
biological research, but in this, which is not our subject, I shall
notice one point only. It has been proved that vital germs--bacteria,
for example--may be kept for seven days at -190°C. without their
vitality being modified. Phosphorescent organisms cease, it is true,
to shine at the temperature of liquid air, but this fact is simply due
to the oxidations and other chemical reactions which keep up the
phosphorescence being then suspended, for phosphorescent activity
reappears so soon as the temperature is again sufficiently raised. An
important conclusion has been drawn from these experiments which
affects cosmogonical theories: since the cold of space could not kill
the germs of life, it is in no way absurd to suppose that, under
proper conditions, a germ may be transmitted from one planet to
another.
Among the discoveries made with the new processes, the one which most
strikingly interested public attention is that of new gases in the
atmosphere. We know how Sir William Ramsay and Dr. Travers first
observed by means of the spectroscope the characteristics of the
_companions_ of argon in the least volatile part of the atmosphere.
Sir James Dewar on the one hand, and Sir William Ramsay on the other,
subsequently separated in addition to argon and helium, crypton,
xenon, and neon. The process employed consists essentially in first
solidifying the least volatile part of the air and then causing it to
evaporate with extreme slowness. A tube with electrodes enables the
spectrum of the gas in process of distillation to be observed. In this
manner, the spectra of the various gases may be seen following one
another in the inverse order of their volatility. All these gases are
monoatomic, like mercury; that is to say, they are in the most simple
state, they possess no internal molecular energy (unless it is that
which heat is capable of supplying), and they even seem to have no
chemical energy. Everything leads to the belief that they show the
existence on the earth of an earlier state of things now vanished. It
may be supposed, for instance, that helium and neon, of which the
molecular mass is very slight, were formerly more abundant on our
planet; but at an epoch when the temperature of the globe was higher,
the very speed of their molecules may have reached a considerable
value, exceeding, for instance, eleven kilometres per second, which
suffices to explain why they should have left our atmosphere. Crypton
and neon, which have a density four times greater than oxygen, may, on
the contrary, have partly disappeared by solution at the bottom of the
sea, where it is not absurd to suppose that considerable quantities
would be found liquefied at great depths.[10]
[Footnote 10: Another view, viz. that these inert gases are a kind of
waste product of radioactive changes, is also gaining ground. The
discovery of the radioactive mineral malacone, which gives off both
helium and argon, goes to support this. See Messrs Ketchin and
Winterson's paper on the subject at the Chemical Society, 18th October
1906.--ED.]
It is probable, moreover, that the higher regions of the atmosphere
are not composed of the same air as that around us. Sir James Dewar
points out that Dalton's law demands that every gas composing the
atmosphere should have, at all heights and temperatures, the same
pressure as if it were alone, the pressure decreasing the less
quickly, all things being equal, as its density becomes less. It
results from this that the temperature becoming gradually lower as we
rise in the atmosphere, at a certain altitude there can no longer
remain any traces of oxygen or nitrogen, which no doubt liquefy, and
the atmosphere must be almost exclusively composed of the most
volatile gases, including hydrogen, which M.A. Gautier has, like Lord
Rayleigh and Sir William Ramsay, proved to exist in the air. The
spectrum of the _Aurora borealis_, in which are found the lines of
those parts of the atmosphere which cannot be liquefied in liquid
hydrogen, together with the lines of argon, crypton, and xenon, is
quite in conformity with this point of view. It is, however, singular
that it should be the spectrum of crypton, that is to say, of the
heaviest gas of the group, which appears most clearly in the upper
regions of the atmosphere.
Among the gases most difficult to liquefy, hydrogen has been the
object of particular research and of really quantitative experiments.
Its properties in a liquid state are now very clearly known. Its
boiling-point, measured with a helium thermometer which has been
compared with thermometers of oxygen and hydrogen, is -252°; its
critical temperature is -241° C.; its critical pressure, 15
atmospheres. It is four times lighter than water, it does not present
any absorption spectrum, and its specific heat is the greatest known.
It is not a conductor of electricity. Solidified at 15° absolute, it
is far from reminding one by its aspect of a metal; it rather
resembles a piece of perfectly pure ice, and Dr Travers attributes to
it a crystalline structure. The last gas which has resisted
liquefaction, helium, has recently been obtained in a liquid state; it
appears to have its boiling-point in the neighbourhood of 6°
absolute.[11]
[Footnote 11: M. Poincaré is here in error. Helium has never been
liquefied.--ED.]
§ 3. SOLIDS AND LIQUIDS
The interest of the results to which the researches on the continuity
between the liquid and the gaseous states have led is so great, that
numbers of scholars have naturally been induced to inquire whether
something analogous might not be found in the case of liquids and
solids. We might think that a similar continuity ought to be there met
with, that the universal character of the properties of matter forbade
all real discontinuity between two different states, and that, in
truth, the solid was a prolongation of the liquid state.
To discover whether this supposition is correct, it concerns us to
compare the properties of liquids and solids. If we find that all
properties are common to the two states we have the right to believe,
even if they presented themselves in different degrees, that, by a
continuous series of intermediary bodies, the two classes might yet be
connected. If, on the other hand, we discover that there exists in
these two classes some quality of a different nature, we must
necessarily conclude that there is a discontinuity which nothing can
remove.
The distinction established, from the point of view of daily custom,
between solids and liquids, proceeds especially from the difficulty
that we meet with in the one case, and the facility in the other, when
we wish to change their form temporarily or permanently by the action
of mechanical force. This distinction only corresponds, however, in
reality, to a difference in the value of certain coefficients. It is
impossible to discover by this means any absolute characteristic which
establishes a separation between the two classes. Modern researches
prove this clearly. It is not without use, in order to well understand
them, to state precisely the meaning of a few terms generally rather
loosely employed.
If a conjunction of forces acting on a homogeneous material mass
happens to deform it without compressing or dilating it, two very
distinct kinds of reactions may appear which oppose themselves to the
effort exercised. During the time of deformation, and during that time
only, the first make their influence felt. They depend essentially on
the greater or less rapidity of the deformation, they cease with the
movement, and could not, in any case, bring the body back to its
pristine state of equilibrium. The existence of these reactions leads
us to the idea of viscosity or internal friction.
The second kind of reactions are of a different nature. They continue
to act when the deformation remains stationary, and, if the external
forces happen to disappear, they are capable of causing the body to
return to its initial form, provided a certain limit has not been
exceeded. These last constitute rigidity.
At first sight a solid body appears to have a finite rigidity and an
infinite viscosity; a liquid, on the contrary, presents a certain
viscosity, but no rigidity. But if we examine the matter more closely,
beginning either with the solids or with the liquids, we see this
distinction vanish.
Tresca showed long ago that internal friction is not infinite in a
solid; certain bodies can, so to speak, at once flow and be moulded.
M.W. Spring has given many examples of such phenomena. On the other
hand, viscosity in liquids is never non-existent; for were it so for
water, for example, in the celebrated experiment effected by Joule for
the determination of the mechanical equivalent of the caloric, the
liquid borne along by the floats would slide without friction on the
surrounding liquid, and the work done by movement would be the same
whether the floats did or did not plunge into the liquid mass.
In certain cases observed long ago with what are called pasty bodies,
this viscosity attains a value almost comparable to that observed by
M. Spring in some solids. Nor does rigidity allow us to establish a
barrier between the two states. Notwithstanding the extreme mobility
of their particles, liquids contain, in fact, vestiges of the property
which we formerly wished to consider the special characteristic of
solids.
Maxwell before succeeded in rendering the existence of this rigidity
very probable by examining the optical properties of a deformed layer
of liquid. But a Russian physicist, M. Schwedoff, has gone further,
and has been able by direct experiments to show that a sheath of
liquid set between two solid cylinders tends, when one of the
cylinders is subjected to a slight rotation, to return to its original
position, and gives a measurable torsion to a thread upholding the
cylinder. From the knowledge of this torsion the rigidity can be
deduced. In the case of a solution containing 1/2 per cent. of
gelatine, it is found that this rigidity, enormous compared with that
of water, is still, however, one trillion eight hundred and forty
billion times less than that of steel.
This figure, exact within a few billions, proves that the rigidity is
very slight, but exists; and that suffices for a characteristic
distinction to be founded on this property. In a general way, M.
Spring has also established that we meet in solids, in a degree more
or less marked, with the properties of liquids. When they are placed
in suitable conditions of pressure and time, they flow through
orifices, transmit pressure in all directions, diffuse and dissolve
one into the other, and react chemically on each other. They may be
soldered together by compression; by the same means alloys may be
produced; and further, which seems to clearly prove that matter in a
solid state is not deprived of all molecular mobility, it is possible
to realise suitable limited reactions and equilibria between solid
salts, and these equilibria obey the fundamental laws of
thermodynamics.
Thus the definition of a solid cannot be drawn from its mechanical
properties. It cannot be said, after what we have just seen, that
solid bodies retain their form, nor that they have a limited
elasticity, for M. Spring has made known a case where the elasticity
of solids is without any limit.
It was thought that in the case of a different phenomenon--that of
crystallization--we might arrive at a clear distinction, because here
we should he dealing with a specific quality; and that crystallized
bodies would be the true solids, amorphous bodies being at that time
regarded as liquids viscous in the extreme.
But the studies of a German physicist, Professor O. Lehmann, seem to
prove that even this means is not infallible. Professor Lehmann has
succeeded, in fact, in obtaining with certain organic compounds--
oleate of potassium, for instance--under certain conditions some
peculiar states to which he has given the name of semi-fluid and
liquid crystals. These singular phenomena can only be observed and
studied by means of a microscope, and the Carlsruhe Professor had to
devise an ingenious apparatus which enabled him to bring the
preparation at the required temperature on to the very plate of the
microscope.
It is thus made evident that these bodies act on polarized light in
the manner of a crystal. Those that M. Lehmann terms semi-liquid still
present traces of polyhedric delimitation, but with the peaks and
angles rounded by surface-tension, while the others tend to a strictly
spherical form. The optical examination of the first-named bodies is
very difficult, because appearances may be produced which are due to
the phenomena of refraction and imitate those of polarization. For the
other kind, which are often as mobile as water, the fact that they
polarize light is absolutely unquestionable.
Unfortunately, all these liquids are turbid, and it may be objected
that they are not homogeneous. This want of homogeneity may, according
to M. Quincke, be due to the existence of particles suspended in a
liquid in contact with another liquid miscible with it and enveloping
it as might a membrane, and the phenomena of polarization would thus
be quite naturally explained.[12]
[Footnote 12: Professor Quincke's last hypothesis is that all liquids
on solidifying pass through a stage intermediate between solid and
liquid, in which they form what he calls "foam-cells," and assume a
viscous structure resembling that of jelly. See _Proc. Roy. Soc. A._,
23rd July 1906.--ED.]
M. Tamman is of opinion that it is more a question of an emulsion,
and, on this hypothesis, the action on light would actually be that
which has been observed. Various experimenters have endeavoured of
recent years to elucidate this question. It cannot be considered
absolutely settled, but these very curious experiments, pursued with
great patience and remarkable ingenuity, allow us to think that there
really exist certain intermediary forms between crystals and liquids
in which bodies still retain a peculiar structure, and consequently
act on light, but nevertheless possess considerable plasticity.
Let us note that the question of the continuity of the liquid and
solid states is not quite the same as the question of knowing whether
there exist bodies intermediate in all respects between the solids and
liquids. These two problems are often wrongly confused. The gap
between the two classes of bodies may be filled by certain substances
with intermediate properties, such as pasty bodies and bodies liquid
but still crystallized, because they have not yet completely lost
their peculiar structure. Yet the transition is not necessarily
established in a continuous fashion when we are dealing with the
passage of one and the same determinate substance from the liquid to
the solid form. We conceive that this change may take place by
insensible degrees in the case of an amorphous body. But it seems
hardly possible to consider the case of a crystal, in which molecular
movements must be essentially regular, as a natural sequence to the
case of the liquid where we are, on the contrary, in presence of an
extremely disordered state of movement.
M. Tamman has demonstrated that amorphous solids may very well, in
fact, be regarded as superposed liquids endowed with very great
viscosity. But it is no longer the same thing when the solid is once
in the crystallized state. There is then a solution of continuity of
the various properties of the substance, and the two phases may
co-exist.
We might presume also, by analogy with what happens with liquids and
gases, that if we followed the curve of transformation of the
crystalline into the liquid phase, we might arrive at a kind of
critical point at which the discontinuity of their properties would
vanish.
Professor Poynting, and after him Professor Planck and Professor
Ostwald, supposed this to be the case, but more recently M. Tamman has
shown that such a point does not exist, and that the region of
stability of the crystallized state is limited on all sides. All along
the curve of transformation the two states may exist in equilibrium,
but we may assert that it is impossible to realize a continuous series
of intermediaries between these two states. There will always be a
more or less marked discontinuity in some of the properties.
In the course of his researches M. Tamman has been led to certain very
important observations, and has met with fresh allotropic
modifications in nearly all substances, which singularly complicate
the question. In the case of water, for instance, he finds that
ordinary ice transforms itself, under a given pressure, at the
temperature of -80° C. into another crystalline variety which is
denser than water.
The statics of solids under high pressure is as yet, therefore, hardly
drafted, but it seems to promise results which will not be identical
with those obtained for the statics of fluids, though it will present
at least an equal interest.
§ 4. THE DEFORMATIONS OF SOLIDS
If the mechanical properties of the bodies intermediate between solids
and liquids have only lately been the object of systematic studies,
admittedly solid substances have been studied for a long time. Yet,
notwithstanding the abundance of researches published on elasticity by
theorists and experimenters, numerous questions with regard to them
still remain in suspense.
We only propose to briefly indicate here a few problems recently
examined, without going into the details of questions which belong
more to the domain of mechanics than to that of pure physics.
The deformations produced in solid bodies by increasing efforts
arrange themselves in two distinct periods. If the efforts are weak,
the deformations produced are also very weak and disappear when the
effort ceases. They are then termed elastic. If the efforts exceed a
certain value, a part only of these deformations disappear, and a part
are permanent.
The purity of the note emitted by a sound has been often invoked as a
proof of the perfect isochronism of the oscillation, and,
consequently, as a demonstration _a posteriori_ of the correctness of
the early law of Hoocke governing elastic deformations. This law has,
however, during some years been frequently disputed. Certain
mechanicians or physicists freely admit it to be incorrect, especially
as regards extremely weak deformations. According to a theory in some
favour, especially in Germany, i.e. the theory of Bach, the law which
connects the elastic deformations with the efforts would be an
exponential one. Recent experiments by Professors Kohlrausch and
Gruncisen, executed under varied and precise conditions on brass, cast
iron, slate, and wrought iron, do not appear to confirm Bach's law.
Nothing, in point of fact, authorises the rejection of the law of
Hoocke, which presents itself as the most natural and most simple
approximation to reality.
The phenomena of permanent deformation are very complex, and it
certainly seems that they cannot be explained by the older theories
which insisted that the molecules only acted along the straight line
which joined their centres. It becomes necessary, then, to construct
more complete hypotheses, as the MM. Cosserat have done in some
excellent memoirs, and we may then succeed in grouping together the
facts resulting from new experiments. Among the experiments of which
every theory must take account may be mentioned those by which Colonel
Hartmann has placed in evidence the importance of the lines which are
produced on the surface of metals when the limit of elasticity is
exceeded.
It is to questions of the same order that the minute and patient
researches of M. Bouasse have been directed. This physicist, as
ingenious as he is profound, has pursued for several years experiments
on the most delicate points relating to the theory of elasticity, and
he has succeeded in defining with a precision not always attained even
in the best esteemed works, the deformations to which a body must be
subjected in order to obtain comparable experiments. With regard to
the slight oscillations of torsion which he has specially studied, M.
Bouasse arrives at the conclusion, in an acute discussion, that we
hardly know anything more than was proclaimed a hundred years ago by
Coulomb. We see, by this example, that admirable as is the progress
accomplished in certain regions of physics, there still exist many
over-neglected regions which remain in painful darkness. The skill
shown by M. Bouasse authorises us to hope that, thanks to his
researches, a strong light will some day illumine these unknown
corners.
A particularly interesting chapter on elasticity is that relating to
the study of crystals; and in the last few years it has been the
object of remarkable researches on the part of M. Voigt. These
researches have permitted a few controversial questions between
theorists and experimenters to be solved: in particular, M. Voigt has
verified the consequences of the calculations, taking care not to
make, like Cauchy and Poisson, the hypothesis of central forces a mere
function of distance, and has recognized a potential which depends on
the relative orientation of the molecules. These considerations also
apply to quasi-isotropic bodies which are, in fact, networks of
crystals.
Certain occasional deformations which are produced and disappear
slowly may be considered as intermediate between elastic and permanent
deformations. Of these, the thermal deformation of glass which
manifests itself by the displacement of the zero of a thermometer is
an example. So also the modifications which the phenomena of magnetic
hysteresis or the variations of resistivity have just demonstrated.
Many theorists have taken in hand these difficult questions. M.
Brillouin endeavours to interpret these various phenomena by the
molecular hypothesis. The attempt may seem bold, since these phenomena
are, for the most part, essentially irreversible, and seem,
consequently, not adaptable to mechanics. But M. Brillouin makes a
point of showing that, under certain conditions, irreversible
phenomena may be created between two material points, the actions of
which depend solely on their distance; and he furnishes striking
instances which appear to prove that a great number of irreversible
physical and chemical phenomena may be ascribed to the existence of
states of unstable equilibria.
M. Duhem has approached the problem from another side, and endeavours
to bring it within the range of thermodynamics. Yet ordinary
thermodynamics could not account for experimentally realizable states
of equilibrium in the phenomena of viscosity and friction, since this
science declares them to be impossible. M. Duhem, however, arrives at
the idea that the establishment of the equations of thermodynamics
presupposes, among other hypotheses, one which is entirely arbitrary,
namely: that when the state of the system is given, external actions
capable of maintaining it in that state are determined without
ambiguity, by equations termed conditions of equilibrium of the
system. If we reject this hypothesis, it will then be allowable to
introduce into thermodynamics laws previously excluded, and it will be
possible to construct, as M. Duhem has done, a much more comprehensive
theory.
The ideas of M. Duhem have been illustrated by remarkable experimental
work. M. Marchis, for example, guided by these ideas, has studied the
permanent modifications produced in glass by an oscillation of
temperature. These modifications, which may be called phenomena of the
hysteresis of dilatation, may be followed in very appreciable fashion
by means of a glass thermometer. The general results are quite in
accord with the previsions of M. Duhem. M. Lenoble in researches on
the traction of metallic wires, and M. Chevalier in experiments on the
permanent variations of the electrical resistance of wires of an alloy
of platinum and silver when submitted to periodical variations of
temperature, have likewise afforded verifications of the theory
propounded by M. Duhem.
In this theory, the representative system is considered dependent on
the temperature of one or several other variables, such as, for
example, a chemical variable. A similar idea has been developed in a
very fine set of memoirs on nickel steel, by M. Ch. Ed. Guillaume. The
eminent physicist, who, by his earlier researches, has greatly
contributed to the light thrown on the analogous question of the
displacement of the zero in thermometers, concludes, from fresh
researches, that the residual phenomena are due to chemical
variations, and that the return to the primary chemical state causes
the variation to disappear. He applies his ideas not only to the
phenomena presented by irreversible steels, but also to very different
facts; for example, to phosphorescence, certain particularities of
which may be interpreted in an analogous manner.
Nickel steels present the most curious properties, and I have already
pointed out the paramount importance of one of them, hardly capable of
perceptible dilatation, for its application to metrology and
chronometry.[13] Others, also discovered by M. Guillaume in the course
of studies conducted with rare success and remarkable ingenuity, may
render great services, because it is possible to regulate, so to
speak, at will their mechanical or magnetic properties.
[Footnote 13: The metal known as "invar."--ED.]
The study of alloys in general is, moreover, one of those in which the
introduction of the methods of physics has produced the greatest
effects. By the microscopic examination of a polished surface or of
one indented by a reagent, by the determination of the electromotive
force of elements of which an alloy forms one of the poles, and by the
measurement of the resistivities, the densities, and the differences
of potential or contact, the most valuable indications as to their
constitution are obtained. M. Le Chatelier, M. Charpy, M. Dumas, M.
Osmond, in France; Sir W. Roberts Austen and Mr. Stansfield, in
England, have given manifold examples of the fertility of these
methods. The question, moreover, has had a new light thrown upon it by
the application of the principles of thermodynamics and of the phase
rule.
Alloys are generally known in the two states of solid and liquid.
Fused alloys consist of one or several solutions of the component
metals and of a certain number of definite combinations. Their
composition may thus be very complex: but Gibbs' rule gives us at once
important information on the point, since it indicates that there
cannot exist, in general, more than two distinct solutions in an alloy
of two metals.
Solid alloys may be classed like liquid ones. Two metals or more
dissolve one into the other, and form a solid solution quite analogous
to the liquid solution. But the study of these solid solutions is
rendered singularly difficult by the fact that the equilibrium so
rapidly reached in the case of liquids in this case takes days and, in
certain cases, perhaps even centuries to become established.