Jean Baptiste Perrin – Nobel Lecture
Nobel Lecture, December 11, 1926
Discontinuous Structure of Matter
Since I have the great honour to have to
summarize here the work which has enabled me to receive the high
international distinction awarded by the Swedish Academy of
Sciences, I shall speak of the "discontinuous structure of
matter".
Introduction
A fluid such as air or water seems to us at
first glance to be perfectly homogeneous and continuous; we can
put more water or less water into this glass, and the experiment
seems to suggest to us that the amount of water contained in it
can vary by an infinitely small amount, which is the same as
saying that water is "indefinitely divisible". Similarly, a
sphere of glass or of quartz, a crystal of alum, are received by
our senses as being perfectly continuous, and particularly when
we see this alum crystal growing in a supersaturated solution,
each of the planes bounding the crystal moves parallel to itself
in a continuous manner.
However, this can be taken for granted only
up to the degree of subtlety reached by the resolving power of
our senses which, for example, would certainly be unable to
distinguish between two positions of the crystal face one
millionth of a millimetre apart. Beyond the things which our
senses separate in this manner, our imagination remains free, and
ever since ancient times, just as the philosophers who started
from the " full" or the "void", has hesitated between two
hypotheses.
For the former, matter remains continuous:
"full", not only (as is reasonable and probable) a little beyond
this domain on our scale where our senses make it appear as such,
but indefinitely.
For the latter, who were the first
atomists, all matter consists of minute grains separated by empty
gaps; not any hypothesis has been formulated for the structure of
these grains themselves, atoms, which were considered as
indestructible constituent elements of the Universe.
Lastly, and doubtless always, but
particularly at the end of the last century, certain scholars
considered that since the appearances on our scale were finally
the only important ones for us, there was no point in seeking
what might exist in an inaccessible domain. I find it very
difficult to understand this point of view since what is
inaccessible today may becomes accessible tomorrow (as has
happened by the invention of the microscope), and also because
coherent assumptions on what is still invisible may increase our
understanding of the visible.
Indeed, increasingly numerous and strong
reasons have come to support a growing probability, and it can
finally be said the certainty, in favour of the hypothesis of the
atomists.
There is, first of all, the familiar
observation of solutions; we all say, for example, that sugar and
water are present in sugar water, although it is impossible to
distinguish the different parts in it. And similarly, we
recognize quite simply bromine in chloroform. This can be
understood if the bromine and the chloroform are formed
respectively by very small particles in continuous movement which
can intermingle with one another without losing their
individuality. Those elementary constituent particles, those
molecules, are probably of the same kind, like articles
made in series, for each pure substance (defined by its
resistance to the fractionation test) or even more surely for
each definite chemical species (experiment proves that it
is never necessary to consider a continuous sequence of chemical
species), and we come to formulate the molecular hypothesis by
saying that for a sufficient magnification any fluid appears to
us as formed by molecules in continuous movement which impinge
ceaselessly upon one another, and of which there are as many
distinct varieties as chemical species can be recognized in the
fluid under consideration.
These molecules which exist in the mixtures
are not indestructible since they must disappear (or appear) when
a chemical reaction causes the chemical species which they
constitute to disappear (or appear); when a mixture of hydrogen
and oxygen explodes to give water, the molecules of hydrogen and
oxygen certainly have to disappear at the same time as the water
molecules appear. But we know that the decomposition of chemical
species, when carried out as far as possible, has led to the
experimental definition of a small number of simple bodies
which can always be recovered, without any change in their
nature, and without loss or gain of mass, from combinations in
which they have been introduced. It is then very difficult not to
assume that, for example, one and the same substance "exists" in
all the chemical species from which the simple substance hydrogen
can be regained and which passes, disguised but indestructible,
through our various reactions. Dalton supposed, and this is the
essential point of the atomic hypothesis, that this substance is
formed by a definite variety of particles which are all identical
and which cannot be cut into pieces in the reactions which we can
produce, and which for this reason are called atoms. There
are, therefore, one or several atoms of hydrogen in each molecule
of a hydrogenated chemical species.
The fundamental laws of chemistry which are
well known to you and which are laws of discontinuity
(discontinuity between chemical species, and discontinuous
variation according to the " multiple proportions" in the
composition of species made from the same simple bodies) then
become immediately clear: they are imposed solely by the
condition that the molecule constituting a compound contains a
necessarily whole number of atoms of each of the simple bodies
combined in this compound. And I do not need to tell you that if
one admits that " analogous " bodies (alkali halides, for
example) must have analogous formulae, simple chemical analysis
will give for the elements of the same " family" the ratios of
the weights of the atoms, or "atomic weights", of these
elements.
But in order to pass from one family to
another, from hydrogen to oxygen for example, it was necessary to
have the gas laws and Avogadro's hypothesis or law which I recall
because my researches are based on it: when one of those cases
occurs where the ratios of the weights of the molecules of the
two compounds are known, it is found that masses proportional to
these masses (which must, therefore, contain the same number of
molecules) occupy equal volumes in the gaseous state under the
same conditions of temperature and pressure. This means that as
far as these substances are concerned, equal numbers of heavy or
light molecules develop equal pressures at the same temperature
and in equal volumes. Since the mass of a molecule, and not its
nature, must affect the impact of the molecule upon the wall, I
see here a justification (not yet agreed, I must say) of the
following proposition known as Avogadro's postulate, or
hypothesis:
When gaseous masses, at the same
temperature and pressure, occupy equal volumes, they all contain
the same number of molecules.
These "equimolecular" masses are determined
for the various chemical species, as soon as one of them has been
chosen. They are called gram-molecules when the masses in
the gaseous state occupy, at the same temperature and pressure,
the same volume as 32 grams of oxygen. The number N of the
molecules constituting any gram-molecule is Avogadro's
number. For each simple substance the gram-molecule of a
compound contains as many gram-atoms as the molecule contains
atoms of this simple substance, and the gram-atom is the product
of the mass of the atom and Avogadro's number N.
In short, if molecules and atoms exist,
their relative weights are known to us, and their absolute
weights would be known at the same time as Avogadro's number.
You also know how - particularly for
understanding substitutions - it was assumed that the atoms of a
molecule are held together by valences of which each
unites only two atoms, a kind of bolt holding rigidly together
two bars or protuberances which pre-exist on the two atoms. A new
detail is thus introduced here to the concept of the atom, but
once this new hypothesis is accepted, the structural formulae can
be determined for an enormous number of compounds, and with such
success in regard to forecasting the properties that it could be
said that the hundreds of thousands of structural formulae set up
by the organic chemists constitute just as many arguments in
favour of the atomic theory.
These brilliant successes tell us,
otherwise, nothing about the absolute weights of the atoms. If
they all became at the same time a thousand times smaller, a
milliard times smaller, infinitesimal in the mathematical sense
of the word, with matter becoming again continuous at each
reduction, our chemical laws and our formulae would be unchanged,
and the idea of the atom, then driven back infinitely far beyond
all experimental reach, would lose its interest and its
reality.
It will be noted that the laws of
crystallography, which are laws of discontinuity just as
the fundamental laws of chemistry, lead to similar considerations
in regard to the dimensions of an elementary cell which is
repeated periodically along the three dimensions of a
parallelepipedic lattice and should constitute the crystal which
is homogeneous in appearance on our scale. Only in this way can
one understand how the symmetries of crystals are soley those of
reticular systems (for example, never symmetry axes of the order
of 5), and explain at the same time the law of rational indices
(a kind of laws of multiple proportions which describe what
discontinuities separate the possible faces), a law which
requires the three dimensions of the elementary parallelepiped to
be in definite ratios. Here again the grain of matter could
become infinitely small without the laws having to be
changed.
In short, in order really to establish the
Atomic Theory, it was necessary to obtain the weights and
dimensions of the atoms and not only their ratios. A remarkably
successful attempt to do this was made about fifty years ago by
the physicists who created the kinetic theory of gases by
assuming that gases are made of elastic molecules which are on
the average fairly widely separated from one another so that,
between two collisions, each molecule can move in a straight
line, the duration of the collision being negligible in relation
to that of the free path.
Furthermore, if it is agreed that the
pressure of a gas on a wall is solely due to the impacts of the
molecules upon this wall, and if we write that this (known)
pressure must consequently be numerically equal to the impulse
exerted perpendicularly on the wall by the molecules impinging
against unit surface in unit time, an equation is obtained which
shows the mean velocity of the gas molecules.
It is also known that if, in a gas, a rigid
plane is made to slide parallel to a fixed plane at a distance
D and with a constant velocity V, each intermediate
layer at a distance d from the fixed plane is involved
with a velocity equal to V(d/D), and that the fixed
and moving planes are drawn in opposite directions by forces (per
unit surface) equal to the product of the velocity gradient
V/D and a fixed factor for each gas, the latter measuring
the viscosity of this gas (at the temperature of the
experiment). This is readily understood from the kinetic theory:
the unit surface of the fixed plane is drawn in the direction of
the movement by a force numerically equal to the total excess
impulse received in this direction, this excess being
proportional to the number of impinging molecules (in other
words, both to the density and to the mean molecular velocity
which we can determine), and proportional to the mean excess
impulse of each impinging molecule; this individual mean excess
is itself proportional to the distance of the layer in which the
molecule was at the time of the previous impact, and consequently
to the mean free path. In this way it is seen how Maxwell
was able to deduce this mean free path from the
experimental determination of the viscosity.
Now, as Clausius observed, the molecules
are all the smaller as the mean free path (now known) becomes
greater (if the molecules were reduced to points, they would
never collide with one another). And it is seen, therefore, that
if the free path is known, it is possible to calculate the
total surface of the molecules which form a given mass of
gas. The total volume of these same molecules is probably
little different from the volume occupied by this mass if it were
solidified. Finally, from two obvious equations we derive both
the number and the diameter of the molecules which constitute,
let us say, a gram-molecule of the gas.
Depending on the gas, the diameters found
in this way are graded between 2 and 5 ten-millionths of a
millimetre; and the values found for Avogadro's number are
between 40 x 1022 and 120 x 1022. The
uncertainty is largely 100 per cent, both because of the
inaccuracy of certain measurements and especially because the
calculations have been simplified by making assumptions which can
only be approximate. But the order of magnitude is achieved: an
atom vanishes in our substance almost as the latter would vanish
in the sun
The sequence of reasonings which I have
just summarized deserves our profound admiration; however, they
were not sufficient to carry conviction owing to the uncertainty
which in spite of everything existed not only in the simplifying
assumptions (sphericalness of the molecules, for example), but in
the very hypotheses on which the reasoning is based. This
conviction will without doubt come to life if entirely different
paths lead us to the same values for the molecular sizes.
The Brownian movement
Let us consider a liquid in equilibrium:
the water contained in this glass, for example. It appears to us
homogeneous and continuous, and immobile in all its parts. If we
place in it a denser object, it falls, and we know quite well
that once it has arrived at the bottom of the glass, it stays
there and is unlikely to ascend again "by itself".
We could have observed this water before it
reached equilibrium, and to see how it reached it, at the moment
when we filled this glass; then we should have been able to find
(by observing the visible indicator dust which was specially
mixed with the water) that the movement of the various parts of
the water which were coordinated at first in parallel movements,
became more and more uncoordinated by scattering in all
directions between smaller and smaller parts until the whole
appeared completely immobile (nothing prevents us as yet from
assuming that this scattering will continue without limit).
It is very remarkable that these so
familiar ideas become false on the scale of the observations
which we can make under a microscope: each microscopic particle
placed in water (or any other liquid), instead of falling in a
regular manner exhibits a continuous and perfectly irregular
agitation. It goes to and fro whilst turning about, it rises,
falls, rises again, without tending in any way towards repose,
and maintaining indefinitely the same mean state of agitation.
This phenomenon which was predicted by Lucretius, suspected by
Buffon, and established with certainty by Brown, constitutes the
Brownian movement.
The nature of the grains is not important,
but the smaller a grain is, the more violently does it become
agitated. There is also complete independence between the
movements of two grains, even if they are very close together,
which excludes the hypothesis of collective convection produced
by the impacts or temperature differences. We are, finally,
forced to think that each grain only follows the portion of
liquid surrounding it, in the same way that an indicating buoy
indicates and analyses the movement all the better if it is
smaller: a float follows the movement of the sea more faithfully
than a battleship.
We obtain from this an essential property
of what is called a liquid in equilibrium: its repose is only
an illusion due to the imperfection of our senses, and what we
call equilibrium is a certain well-defined permanent system of a
perfectly irregular agitation. This is an experimental fact
in which no hypothesis plays any part.
Since this agitation remains on an average
constant (it would be possible to make this "impression" accurate
by measurements), the movement possessed by a part of the liquid
does not scatter without limit in all directions between smaller
and smaller parts, in spite of what observations made on our
scale suggest to us; this spreading does not go beyond a certain
limit for which, at each moment, just as much movement is
coordinated as becomes uncoordinated.
This is explainable if the liquid consists
of elastic grains, and I do not see how it can be understood if
the structure is continuous. Moreover, it is seen that the
agitation for a given observable particle must increase with the
size of the molecules: the magnitude of the Brownian movement,
therefore, will probably enable us to calculate the molecular
sizes.*
In short, the Brownian movement (an
experimental fact) leads us to the hypothesis of the molecules;
and we then understand quite well how each particle that is
situated in a liquid and is being bombarded ceaselessly by
neighbouring molecules, receives shocks which on the whole have
all the less change of coming to equilibrium as the particle
becomes smaller, with the result that this particle must be
tossed to and fro irregularly.
This applies to absolutely whatever kind of
particle. If it has been possible to bring into suspension in a
liquid a large number of particles all of the same nature, we say
that an emulsion has been produced. This emulsion is stable if
the particles in suspension do not stick together when the
hazards of the Brownian movement bring them into contact, and if
they re-enter the liquid when these hazards bring them against
the walls or to the surface. From this two-fold point of view
such a stable emulsion is comparable to a solution.
It is precisely by pursuing this analogy that I have been able to
obtain a simple determination of the molecular sizes.
Extension of the gas laws to emulsions
I must, first of all, recall how the gas
laws and particularly Avogadro's law came to be regarded, thanks
to Van 't Hoff, as applicable to dilute solutions.
The pressure exerted by a gas on the walls
limiting its expansion becomes, for a dissolved substance, the
osmotic pressure exerted on semi-permeable walls
which allow the solvent to pass, but hold back this dissolved
substance. Such is a membrane of copper ferrocyanide which
separates sugared water from pure water.
Now, the measurements of Pfeffer show that
in fact the equilibrium exists only if there is a certain excess
pressure from the side on which the sugar is, and Van 't Hoff has
pointed out that the value of this excess pressure or osmotic
pressure is precisely that of the pressure which would be
exerted, in accordance with Avogadro's law, on the wall of the
container containing the sugared water if the sugar present could
occupy the entire container alone and in the gaseous state. It is
then probable that the same would occur with every dissolved
substance, but we do not need to recall the thermodynamic
reasoning with which Van 't Hoff justified this generalization
nor to make other measurements of the osmotic pressure: Arrhenius
has indeed shown that every substance which, in solution,
confirms the well-known Raoult laws through its freezing
temperature and its vapour pressure, necessarily exerts through
this very fact the pressure predicted by Van 't Hoff on every
wall which halts it without halting the solvent. In short, the
Raoult laws which were established by a very large number of
measurements, are logically equivalent to the law of Van't Hoff
which consists in the extension of Avogadro's law to solutions,
and we can now say:
Equal numbers of molecules, regardless
of the kind, in the gaseous state or dissolved, exert - at the
same temperature and in equal volumes - equal pressures on the
walls detaining them.
This law applies equally to heavy or light
molecules, in such manner that, for example, the molecule of
quinine which contains more than one hundred atoms, has neither a
greater nor a lesser effect when it impinges against the wall
than the light molecule of hydrogen which contains two atoms.
I have thought that it was perhaps valid
for stable emulsions with visible grains, in such manner that
each of these grains which is agitated by the Brownian movement,
counts as a molecule when it collides with a wall.
Let us assume then that we can measure the
osmotic pressure which equal grains exert, through their Brownian
movement, against a unit of a wall which holds them up and allows
water to pass (let us say blotting paper). Let us also assume
that we can count these grains in the immediate vicinity of the
wall unit, that is to say that we know the "abundance" of the
grains per unit volume near this wall unit. This number n
also measures the abundance of molecules in any gas (let us say
hydrogen) which would exert the same pressure on the walls of the
container in which it would be enclosed. If, for example, the
osmotic pressure measured is the hundred-millionth of a barye, we
shall know that a cubic centimetre of hydrogen under normal
conditions (pressure equal to a million baryes) contains 100
million million times n molecules (1014 n). And
the gram-molecule (22,412 c.c. in the gaseous state under normal
conditions) will contain 22,412 times more molecules: this number
will be Avogadro's number.
This is very simple; but how to measure the
stupendously weak osmotic pressure that an emulsion exerts?
This will, in fact, not be necessary nor,
as we have just explained, will it be necessary to measure the
osmotic pressure of a solution to make sure that this solution
obeys the gas laws. And it will be sufficient for us to find an
experimentally accessible property for emulsions which would be
logically equivalent to the gas laws.
I found such a property (1908) by extending
to emulsions the fact that is qualitatively well known to you,
that in a vertical column of a gas in equilibrium the density
decreases as the altitude increases.
Law of the vertical distribution of an emulsion
We all know that air is more rarefied at
the top of a mountain than at sea level and, generally speaking,
he pressure of air has to diminish as one goes higher since this
pressure has then to carry only a smaller part of the atmosphere
which applies its weight against the earth.
If we specify this slightly vague reasoning
in the Laplace manner, we shall say that each horizontal slice of
a gas in equilibrium in a large vertical pump would remain in
equilibrium if it were imprisoned between two rigid pistons
(which would no longer allow exchange of molecules between this
slice and the neighbouring slices of the gas) and these pistons
would exert respectively the pressures existing at the lower face
and at the upper face of the slice; with the result that, per
unit surface, the difference of these pressures is equal to the
weight of the gas supported. That is to say that if the thickness
dh of the slice is sufficiently small so that the
abundance of molecules near the upper face differs little from
the abundance n near the lower face, the pressure
difference dp between the two faces will be equal to
n p dh, where
p denotes the weight of a
molecule.
This very simple equation expresses two
important facts: first of all, as the abundance n of
molecules is proportional to the pressure p at each given
temperature, we see that for a column of a given gas (for a given
p) and of uniform temperature, the
relative reduction of the pressure dp/p, or also the
relative reduction of the abundance dn/n which can be said
to measure the rarefaction, always has the same value for the
same difference in level dh, whatever this level may be.
For example, each time that you climb a flight of stairs, the
pressure in the air (or the abundance of molecules) is reduced by
one forty-thousandth of its value. Adding these effects for each
step, we see that at whatever level we were originally, each time
we ascend by the same height, the pressure (or the density) in
air at a uniform temperature will be divided by the same number;
for example, in oxygen at 0° the rarefaction will be doubled
for each rise of 5 kilometres.
The other fact which emerges immediately
from our equation relates to the weight p of the molecule; for the same value of level
dh, the rarefaction dp/p (or dn/n) varies in
inverse ratio with the weight of the molecule. Adding here again
the effects for each step, we see that in two different gases at
the same temperature, the rises producing the same rarefaction
are in inverse ratio to the molecular weights. For example, as we
know that the oxygen molecule (if it exists, and in accordance
with the laws summarized above) must weigh 16 times more than the
hydrogen molecule, it is necessary to rise 16 times higher in
hydrogen than in oxygen, i.e. 80 kilometres, for the rarefaction
to be doubled.
You can appreciate the influence of the
altitude, and of the molecular weight, on the rarefaction by
looking at this schematic picture where I have drawn three
gigantic vertical test tubes (the highest is 300 kilometers)
containing equal numbers of hydrogen molecules, helium molecules,
and oxygen molecules. At a uniform temperature the molecules
would be distributed as shown in the drawing, being more numerous
near the bottom as they increase in weight.
Let us now admit that Avogadro's law
applies to emulsions as it does to gases.
We assume, therefore, that we have a stable
emulsion made of equal grains which is left to itself at a
constant temperature, being only under the influence of its own
weight. We can repeat the previous reasoning with the only change
that the intergranular space, instead of being void, is now a
liquid which exerts on each grain, in an opposite direction to
its weight, a push in accordance with Archimedes' principle.
Consequently, the effective weight z of the gram to which this
reasoning is applied, is its actual weight reduced by this
push.
If now our generalization is justified,
once the emulsion is in equilibrium it will produce a
miniature atmosphere of visible molecules where equal rises
will be accompanied by equal rarefactions. But if, for example,
the rise in the emulsion to double the rarefaction is a milliard
times less than in oxygen, it means that the effective weight of
the grain is a milliard times greater than that of the oxygen
molecule. It will, therefore, be sufficient to determine the
effective weight of the visible grain (which forms links between
the magnitudes on our scale and the molecular magnitudes) in
order to obtain by a simple ratio the weight of any molecule, and
consequently Avogadro's number.
It is in this sense that I carried out my
experiments which I was able to do successfully.
I first prepared stable emulsions made from
solid (vitreous) spheres of various resins in suspension in a
liquid (generally water). This was done by dissolving the resin
in alcohol and adding to this limpid solution a large amount of
water. The resin is quite insoluble in the water and is then
precipitated as microscopic spherules of all sizes. By means of
prolonged centrifuging similar to those in which the red blood
corpuscles are separated from the blood serum, it is possible to
collect these grains as a consistent deposit which splits up
again as a stable emulsion of distinct spherules when it is
agitated in the pure water after the supernatant alcohol solution
has been removed.
It was then necessary, starting with an
emulsion where the grains are of very different size, to succeed
in separating these grains according to size in order to have
uniform emulsions (consisting of equal grains). The
process which I used can be compared with fractional
distillation: just as, in a distillation, the fractions which
come off first are richer in the most volatile constituents, so
in a centrifuging of a pure emulsion (spherules of the
same substance), the parts which settle out first are richer in
coarse grains, and this is a method of separating the grains
according to size by proceeding according to rules which it would
be unnecessary to elaborate here. It is also necessary to be
patient: I treated in my most careful fractionation one kilogram
of gamboge and obtained after several months of daily operations
a fraction containing several decigrams of grains with a diameter
of approximately three-quarters of a thousandth of a millimetre
which was appreciably equal to what I had wanted to obtain.
If a droplet of a very dilute emulsion made
with such equal grains is allowed to evaporate on the slide under
a microscope, the grains are seen, when the evaporation is almost
complete (and doubtless as a result of capillary action), to run
and join together in regular lines just as cannon-balls in a
horizontal row of a pile of cannon-balls.
You can see this on the photograph which is
now projected. And you will understand how it is possible
simultaneously to obtain a successful centrifuging and to measure
the mean diameter of the grain of the emulsion. (Other processes
are, moreover, possible.)
On the other hand, there is no difficulty
in determining the density of the glass constituting the
spherules (several processes: the most correct consists in
suspending the grains in a solution which is just so dense that
the centrifuging cannot separate the grains).
We then know everything necessary for
calculating the effective weight of the grain of the
emulsion.
On the other hand, we shall have studied
the equilibrium distribution of the emulsion under the action of
gravity. For this we imprison a drop of the emulsion in a
well-closed dish (evaporation must be impossible) arranged for
microscopic observation. The distribution of the grains is at
first uniform, but it is found that the grains accumulate
progressively in the lower layers until a limiting distribution
is reached with reversible settling or expansion depending on
whether the temperature is lowered or raised. There are two
possible methods of observation, as shown in the drawing
projected here. In one method (the horizontal microscope) the
rarefaction of the emulsion is obtained immediately from the
height, and the resemblance to a miniature atmosphere is
extremely striking, precise measurements being possible from
instantaneous photographs. But it is then difficult to give the
emulsion a height lower than, shall we say, one millimetre, and
the time needed for establishing a permanent state becomes long
(several days) which involves complications and difficulties.
In the other method of observation the
microscope is vertical, and the emulsion imprisoned between the
slide and the cover-glass has now a thickness only of the order
of a tenth of a millimetre. We take an objective of high
magnifying power and weak focal depth so that a very thin
horizontal layer of the emulsion (of the order of 2 microns) is
clearly seen, and an instantaneous photograph is taken. We thus
have the abundance at a certain level (as an aviator could take
the density of air at every level). The abundances at different
levels are then compared at our leisure.
The success is complete. Before insisting
that it is so, I can show a cinematographic film on which you
will see for yourselves the equilibrium distribution of an
emulsion formed from spherules which are agitated by the Brownian
movement.
The observations and the countings which
this film summarizes for you prove that the laws of ideal gases
apply to dilute emulsions. This generalization was predicted as a
consequence of the molecular hypothesis by such simple reasoning
that its verification definitely constitutes a very strong
argument in favour of the existence of molecules. In particular,
it was necessary - it can be verified effectively, and it is very
remarkable - that the various emulsions studied lead, within the
limit of the possible errors, to the same value for Avogadro's
number. In fact, I changed (with the valuable assistance of
Bjerrum, Dabrovski, and Bruhat) the mass of the grains (from 1 to
50), their nature (gamboge, mastic), their density (1.20 to
1.06), the nature of the intergranular liquid (water, strongly
sugared water, glycerol in the upper layers of which the grains
of mastic, being lighter, accumulated) and lastly the temperature
(from -9° to +60°). My most careful measurements made
with an emulsion the rarefaction of which doubled with each rise
of 6 microns, gave a value for N of 68 X
1022.
The accuracy of such determinations, so far
of several hundredths, can certainly be improved: the same does
not apply to values obtained from the kinetic theory of gases,
because here perfecting the measurements would not diminish the
uncertainties inherent in the simplifying assumptions which were
introduced to facilitate the calculations.
Non-diluted emulsions
Proceeding then further in tracing the
similarities between liquids and emulsions, I was able to show
(1913) that a non-diluted emulsion is comparable to a compressed
liquid of which the molecules would be visible.
For this purpose it was necessary to
determine the osmotic pressure as a function of the concentration
when the gas laws cease to be applicable. Let us, therefore,
consider a vertical column of emulsion which extends upwards
practically without limit. At each level the osmotic pressure can
be regarded as supporting the whole of the grains above it, and
we shall, therefore, know it by counting all these grains. The
emulsion will be imprisoned between two vertical plate glasses
only several microns apart so that all the grains can be taken by
an instantaneous photograph. The concentration of the grams at
each level is, on the other hand, fixed by the known number of
grains present in a small known volume near this level. In short,
we shall in this way know the pressure corresponding to a known
concentration: this will give experimentally the law of
compressibility which can then be compared with Van der Waals'
law.
Rene Costantin made these measurements
under my direction and confirmed that Van der Waals' law applies
to emulsions which are already too concentrated to conform to the
gas laws. The resulting value for Avogadro's number is 62 x
1022.
Even Van der Waals' law is no longer
suitable for concentrations above 3 per cent, but the
compressibility remains measurable, consequently the law of
compressibility remains known empirically.
This enables - and this idea was due
entirely to René Costantin who died for France in 1915 - a
theory of Smoluchovski to be checked on the density fluctuations
which the molecular agitation should produce in a liquid in
equilibrium. According to this theory, the fluctuation
(n'-n)/n in a volume containing accidentally n'
molecules whilst it should contain only n if the
distribution were uniform, has a mean value which can be
calculated if the compressibility of the liquid is known, and
which includes Avogadro's number.
For our emulsions of equal grains,
considered as fluids with visible molecules, the measurements of
osmotic compressibility, carried out as far as a content of 7 per
cent, have confirmed Smoluchovski's theory by giving
approximately 60 X 1022 for Avogadro's number.
Measurements of the Brownian movement
The equilibrium distribution of an emulsion
is due to the Brownian movement, and the more rapidly as this
movement is more active. But this rapidity is not important for
the final distribution. In fact, as we have just seen, I also
studied the distribution first on the permanent state without
making any measurement on the Brownian movement. But by means of
such measurements it is possible, though in a less obvious
manner, to demonstrate the discontinuous structure of matter and
to obtain a determination of Avogadro's number.
It is due to Einstein and
Smoluchovski that we have a kinetic theory of the Brownian
movement which lends itself to verification.
Without being disturbed by the intricate
path described by a grain within a given time, these physicists
characterize the agitation by the rectilinear segment joining the
point of departure with the point of arrival, the segment being
on an average greater as the agitation is livelier. This segment
will be the displacement of the grain during the time
considered.
If we then admit that the Brownian movement
is perfectly irregular at right angles to the vertical, we
prove that the mean horizontal displacement of a grain is doubled
when the duration of the displacement is quadrupled, and is
tenfold if that duration becomes a hundredfold, and so forth.
This means that the mean square of the horizontal displacement is
proportional to the duration t of this displacement. This can
easily be verified.
Now, this mean square is equal to twice the
mean square 
of the projection of the displacement on an arbitrary horizontal
axis. Consequently, the mean value of the quotient  for a given grain
remains constant. Obviously, since it increases as the grain is
more agitated, this mean quotient characterizes the activity
of the Brownian movement.
Having said this, there must be a
diffusion for the grains of an emulsion just as for the
molecules of a solution; Einstein shows that the coefficient of
diffusion should be equal to the half of the number which
measures the activity of the agitation.
On the other hand, the steady state in a
vertical column of emulsion is produced and maintained by the
interplay of two opposing actions, gravity and the Brownian
movement; this can be expressed by writing that at each level the
flow through diffusion towards the poor regions is equal to that
which gravity produces towards the rich regions.
In order to calculate the flow by diffusion
it must be admitted, as we have done, that grains or molecules
are equivalent to each other in regard to the osmotic pressures;
in order to calculate the flow produced by gravity, in the case
of spherules of radius a, it must be admitted, though at
first it appeared uncertain, that the (very weak) mean velocity
of fall of a grain animated by a very active Brownian movement
can still be calculated by "Stokes' law" which applies to the
uniform fall in a viscous liquid of a large sphere which is
practically not animated by a Brownian movement. In fact, I have
since shown experimentally that this is so.
Having admitted this hypothesis, Einstein
finds that the diffusion coefficient  is equal to (RT/N)
(6paz)-1 (R
being the gas constant, T the absolute temperature, and
z the viscosity).
So far we have thought of the
translational Brownian movement only. Now a grain rotates
at the same time as it is displaced. Einstein was able to show
that if 
denotes the mean square in a time t of the component of
the angle of rotation around an axis, the agitation coefficient
of rotation 
is fixed for the same grain and should be equal to (RT/N)
(4pa3z)-1. His
reasoning implies equality between the mean energy of
translation and the mean energy of rotation which was
predicted by Boltzmann and which we shall make more probable if
we succeed in confirming this equation.
These theories can be judged by experiment
if we know how to prepare spherules of a measurable
radius. I was, therefore, in a position to attempt this check
as soon as I knew, thanks to Langevin, of the work of
Einstein.
I must say that, right at the beginning,
Einstein and Smoluchovski had pointed out that the order of
magnitude of the Brownian movement seemed to correspond to their
predictions. And this approximate agreement gave already much
force to the kinetic theory of the phenomenon, at least in broad
outline.
It was impossible to say anything more
precise so long as spherules of known size had not been prepared.
Having such grains, I was able to check Einstein's formulae by
seeing whether they led always to the same value for Avogadro's
number and whether it was appreciably equal to the value already
found.
This is obtained for the displacements by
noting on the camera lucida (magnification known) the horizontal
projections of the same grain at the beginning and at the end of
an interval of time equal to the duration chosen, in such a
manner as to measure a large number of displacements, for example
in one minute.
In several series of measurements I varied,
with the aid of several collaborators, the size of the grains (in
the ratio of I to 70,000) as well as the nature of the liquid
(water, solutions of sugar or urea, glycerol) and its viscosity
(in the ratio of 1 to 125). They gave values between 55 x
1022 and 72 x 1022, with differences which
could be explained by experimental errors. The agreement is such
that it is impossible to doubt the correctness of the kinetic
theory of the translational Brownian movement.
It must otherwise be observed that although
it is didactically of comparable difficulty to the kinetic theory
of the viscosity of gases, Einstein's theory does not introduce
simplifying approximations and, like the measurement of height
distribution, lends itself to a precise determination of
Avogadro's number.
My most careful measurements which gave me
N equal to 69 x 1022 had been made on grains
which, for reasons which are no longer of interest, had their
initial position at 6 µ from the bottom of the
preparation. In the course of the verifications which I had asked
René Costantin to make on preparations which were only
several microns thick, he found that the vicinity of a wall
slowed down the Brownian movement. The measurements made at a
distance from the walls gave a value for N of 64 x
1022.
With regard to the rotational
Brownian movement, Einstein's formula predicts a mean rotation of
approximately 8° per hundredth of a second for spheres of 1
µ diameter, a rotation which is too rapid to be
perceived and which - with greater reason - escapes measurement.
And, in fact, this rotation had not been made the subject of any
experimental study, at least not quantitatively. (Einstein did
not suppose that his formula could be verified.)
I overcame the difficulty by preparing
large spherules of mastic. I arrived at them by making pure water
pass slowly under an alcohol solution of resin. A passage zone is
produced where the grains form which then have generally a
diameter of some twelve microns. They are limpid spheres, like
glass balls. They frequently seem to be perfect, and then their
rotation is not observable. But they also frequently contain
small vacuoles, guide marks by means of which the rotational
Brownian movement is easily perceived.
But the weight of these large grains keeps
them very close to the bottom which disturbs their Brownian
movement. I, therefore, tried to give the intergranular liquid
the density of the grains by dissolving suitable substances in
it. A complication soon arose in that at the amount necessary for
keeping the grains suspended between the two waters, almost all
these substances agglutinated the grains into bunches of
grapes, showing thus in the nicest way possible the
phenomenon of coagulation which is not easy to obtain on
ordinary suspensions or colloidal solutions (of ultramicroscopic
grains). Coagulation failed to occur in a single substance,
urea.
In water containing 27 per cent urea I was,
therefore, able to follow the agitation of the grains and to
measure their rotation. For this I noted at equal intervals of
time the successive positions of certain vacuoles from which it
was then possible, at one's leisure, to find again the
orientation of the sphere at each of these moments and to
calculate its rotation from one moment to the next. The
calculations were made on approximately 200 (fairly rough) gl an
e measurements on spheres having a diameter of 13 µ,
and gave me for N the value of 65 x 1022 This
agreement with the previous . determinations is all the more
striking as even the order of magnitude of the phenomenon was not
known (1910).
The molecular reality
Briefly, and in spite of the variety of
experimental conditions and techniques, the study of the
emulsions gave me for Avogadro's number:
68 x 1022 by means of the
distribution of emulsions analogous to gases;
62 x 1022 by means of that of emulsions analogous to
liquids;
60 x 1022 by means of the fluctuations in
concentrated emulsions;
64 x 1022 by means of the translational Brownian
movement;
65 x 1022 by means of the rotational Brownian
movement;
or, as a crude average, 64 x
1022.
I can recall here that on the other hand,
considering gases as consisting of molecules which diffract light
(Rayleigh,
Smoluchovski, Einstein) it was possible to obtain (somewhat after
my first experiments) Avogadro's number by means of measurements
relating to the critical opalescence (Keesom: 75 x
1022 ), the blueness of the sky (Bauer and L.
Brillouin, then Fowler: 65 x 1022), and relating in a
particularly precise manner to light that was laterally diffused
by gases (Cabannes: 65 x 1022; 1921).
The theory of black-body radiation, where
the reasoning is allied to that of the kinetic theory, gives
again the same value (64 x 1022).
Along other lines, the measurements of the
electric charges of charged microscopic dust, which should be
whole multiples of the elementary charge of ions, led - by stages
with Townsend, J.J.
Thomson, Harold A. Wilson, Ehrenhaft, and finally Millikan (1909) - to the
same result (61 x 1022).
Lastly, radioactivity which enables the
atoms forming a given mass of helium to be counted one by one,
has given in a totally different manner proofs of the
discontinuity of matter by imposing once again the same value (62
x 1022 to 70 x 1022) on Avogadro's
number.
Such a collection of agreements between the
various pieces of evidence according to which the molecular
structure is translated to the scale of our observations, creates
a certitude at least equal to that which we attribute to the
principles of thermodynamics. The objective reality of
molecules and atoms which was doubted twenty years ago, can
today be accepted as a principle the consequences of which
can always be proved.
Nevertheless, however sure this new
principle may be, it would still be a great step forward in our
knowledge of matter, and for all that a certitude of a different
order, if we could perceive directly these molecules the
existence of which has been demonstrated.
Without having arrived there, I have at
least been able to observe a phenomenon where the discontinuous
structure of matter can be seen directly.
Monomolecular films
I encountered this phenomenon (1913) by
observing under the microscope small laminae of "soapy water",
and in such simple conditions that it is surprising it was not
discovered earlier.
You know the properties of thin
laminae: each ray reflected from such a lamina is formed by
the superposition of a ray reflected from the front side of the
lamina on a ray reflected from the rear side. For each elementary
colour these rays add together or subtract from one another
according to a classical formula, depending on whether they are
in phase or out of phase; in particular, there is extinction when
the thickness of the lamina is an even multiple of one quarter of
the wavelength, and there is maximum reflection when it is an odd
multiple.
If, therefore, white light strikes a lamina
which has a thickness increasing continuously from zero, the
reflected light is at first non-existent (black lamina), then
weak (grey lamina), then lively and still almost white, becoming
successively straw yellow, orange yellow, red, violet, blue
(tints of the first order), then again (but with different tints)
yellow, red, violet, blue, green (second order); and so on, the
reflected colour becoming continuously more complex and more
off-white up to the "white of a higher order" (the spectrum is
furrowed with black grooves the number of which increases with
the thickness of the lamina). All these tints will be present at
the same time on a lamina which has not a uniform thickness and
which will be black or grey in its thinnest region, straw yellow
in a thicker region, red in an even thicker region, and so
forth.
It is the same with ordinary soap bubbles,
with their magnificent colours. The gradation of these colours
seems to us perfectly continuous, from the lowest part of the
bubble where the wall is thicker, to its upper part, which
thinning progressively, becomes white and then grey, after
passing through the "first-order" tints. At that moment, just
before the bubble bursts, this thin region: begins to show one or
several black spots, quite round, which contrast strongly
with the neighbouring grey tone (I mistook them for holes when I
was a child) and the very sharp edge of which marks a strong
discontinuity in the thickness. In fact, they are not completely
black, but reflect so little light that their thickness is
certainly small in relation to the wavelengths of white light. In
an enclosed space that is free from dust, these black spots may
extend over areas of the order of one square decimetre, and
remain for several months (Dewar).
A more careful examination has long since
shown that in the first black spot may form even blacker circles,
therefore thinner ones, again with a sharp periphery. In
measurements which were at the time very remarkable, although not
very accurate, Reinold and Rücker, and then Johonnott had
shown that the darkest spot could have a thickness of 6
mµ (milli-microns), and the other roughly twice this.
No interpretation had been given: it was simply thought that the
surface tension which is variable below a certain thickness,
became equal again for the thickness of the two black spots to
what it is for large thicknesses. In the light of subsequent
observations we shall understand that the black spot represents a
kind of carpet formed by two layers or perhaps even by a single
layer of molecules held together parallel with one another.
Without indicating here the intermediate
stages which I passed through, let us say straightaway that, by
observing in the microscope in bright light a small horizontal
lamina of a given soapy water (approximately 5 per cent pure
alkali oleate), I have seen the discontinuities multiplying of
which the black spots were the first example.
The observation is made as for a metal
surface: the light emitted through a lateral aperture in the tube
of the microscope and reflected towards the objective, passes it
and is reflected on the thin lamina, returning to the eye through
the objective and the eye-piece to give a clear image of the
lamina.
We then see, first of all, the colours in
continuous gradation of the ordinary laminae of soapy water; then
the lamina quivers; liquid gathers together in globules; at the
same time, uniform bands, with flat tints separated from one
another by arcs of a circle, appear in the whole lamina which
becomes a kind of mosaic. These arcs terminate at the globules
around which they radiate like stars. Once this stratification is
organized, a very slow evolution takes place by displacement of
the contours and the globules, giving (according to circumstances
over which I had no control) more or less importance to one band
or the other or a series of bands which is the reason for the
extraordinary variety of stepped laminae which are observed. Very
frequently kinds of flat bulges are seen protruding from the
globules or from the non-stratified peripheral liquid and
spreading over bands which have already formed.
We thus observe, in order of increasing
thickness, black bands which do not seem to differ from the "
black spots" which we just mentioned; then grey, white, yellow,
red, blue bands; and then bands having second-order tints, and so
on, up to higher-order white. Each band has a uniform colour
standing out clearly and discontinuously against adjacent bands.
The richness of the colours can be extreme as you see from the
colour photographs (Lumiere autochrome plates) which are here
projected. The richness pertaining partly to a transitional tint
- e.g. some purple - represented by an insignificant region on a
lamina of ordinary soap, may extend here as a flat tint over an
important area.
These bands are definitely liquids; this is
shown by the existence of exactly circular contours (when
solidification occurs, the areas become like dried skins with a
dentated contour), by the mobility of these contours which change
by blowing without breaking the lamina, by the existence finally
of a " two-dimensional " Brownian movement which is found (for
droplets, or for small flat discs, pieces detached from the
bands), on grey or coloured bands (the Brownian movement is all
the less lively when these bands are thicker which is natural in
view of the fact that the frictions then become more
important).
Let me add that I have also been able to
obtain such stepped laminae with alkali oleate in glycerol, and
also with alkali colophonates and resinates in water.
Having examined a large number of
stratified laminae, it occurred to me, before I made any
measurement, that the difference in thickness between two
adjacent bands cannot fall below a certain value and that this
elementary minimum difference, a kind of "step of a staircase",
is included a whole number of times in each band. Similarly, if
we throw playing-cards on the table, the thickness at each point
is that of a whole number of cards, without all possible
thicknesses being necessarily present, since two or three cards
may remain stuck together. The stratified liquid strips would,
therefore, be formed by the piling up of identical sheets, more
or less overlapping each other, their liquid state imposing on
the free contours the form of arcs of a circle (which are fixed
at their extremities on globules or on the non-stratified
periphery, according to conditions so far unknown).
The measurements confirmed this impression.
From 1913 onwards I found a value ranging between 4.2 and 5.5
mµ. And since then, precise photometric
determinations made under my direction in 1921 by P.V. Wells, who
otherwise had to overcome serious experimental difficulties, have
fully established what we can call a law of multiple
thicknesses.
We first of all applied simply the
classical relationship between the thickness of the lamina and
the intensity of the reflected light, using monochromatic
lighting.
On the first-order band 120 measurements
were made, giving thicknesses grouped according to the law of
chances around 4.4 mµ. It is certainly the best
measurement made so far of the thickness of the "black spot " for
which Johonnott gave 6 mµ. The extreme thinness of
this band, the faintness of the reflected light, and the
difficulties due to parasitic lights make this determination
particularly interesting.
The set of the measurements for the first
fifteen bands give similarly thicknesses which are, within
several hundredths, of the successive multiples of 4.5
mµ.
As this elementary thickness is not known
with a precision greater than 4 per cent, it seems impossible to
verify the law above a certain thickness. For example, at this
accuracy any thickness greater than 120 mµ would be a
multiple of 4.5 mµ. But if the law exists, the
thickness should always vary in the same way between two adjacent
areas; or again the "step of the stairs" should remain the same,
and this can be verified.
This is, in fact, what Wells saw, operating
this time in white light and using a method which René
Marcelin had suggested to me in 1914, by obtaining tints
identical to those of the lamina by means of a quartz compensator
of variable thickness which was placed between crossed nicols.
(The difference between the thicknesses of quartz which gave the
tints of the two adjacent liquid bands, determines the difference
in thickness of these bands.) He obtained in this way 4.2
mµ near the first-order violet and 4.3 near the
second-order violet.
In short, the "step of the staircase" has
the same value near the first, the fiftieth or the hundredth
band, i.e. approximately 4.4 mµ; and we can be sure
that:
In a stratified liquid lamina the
thickness of each band is a whole multiple of the same elementary
thickness;
in other words, it is very probable
that:
The bands of the stratified laminae are
formed by the overlapping, in any number, of identical
fundamental "sheets".
This is how a "discontinuous and periodic
structure" of matter is perceived quite directly, at least in a
certain group of cases.
Similar experiments, suggested precisely by
these observations of stratified laminae of soapy water, were
made on mica at the beginning of 1914 by René Marcelin (who
died for France in 1914). We know that if we pour selenium on to
mica, and if we try to tear off this mica, thin laminae of mica
remain adhering to the selenium. These laminae exhibit bright
colourations which are divided into completely flat tints
separated by clear rectilinear contours which mark
discontinuities of thickness. The minimum difference of thickness
measured with the Michel Levy comparator was found to be equal to
0.7 mµ which would, therefore, be the thickness of a
monomolecular layer in the crystal. But the measuring accuracy
becomes low for such a small thickness.
Let us return to the stratified laminae of
soapy water for which the size of the discontinuities is such
that we have readily accessible the elementary sheet the periodic
repetition of which forms the bands. We shall want to know what
this elementary sheet is. I see in it a monomolecular film of
hydrated bioleate.
We know, in fact (Rayleigh, A. Marcelin,
Langmuir) that water on which float globules of oleic acid, is
covered between these globules with a veil of oleic acid 1.9
mµ thick. According to its known density, this veil
can be formed only by a single layer of molecules arranged
perpendicularly to the surface and probably glued to the water by
their (hygroscopic) acid groups. The surface of a soapy water is
greasy (low surface tension, arrest of the movements of camphor);
it is, therefore, covered at least by a similar layer of oleic
acid or oleate, as can be shown by analysing a known quantity of
soapy water drawn in the form of laminae having a known total
surface area (Jean Perrin, Mouquin). The black spot corresponding
to the maximum possible thinning would, therefore, be a kind of
sandwich containing a layer of water molecules against each side
of which, and glued to it by their acid groups, parallel
molecules of oleic acid or oleate are arranged, the whole forming
an anisotropic lamina or liquid crystalline sheet. The piling-up
of such sheets, easily sliding over each other - with weak
cohesion forces existing between them - would give the successive
bands.
In remarkable agreement with this
conception is the fact that the molecular length as calculated
for oleic acid from X-ray diffraction measurements recently made
in the laboratories of Bragg and Friedel agrees with the
thickness of our fundamental sheet.
I do not think that there is any more to be
said, at the moment, on the direct visibility of molecules.
The discontinuous structure of the atom
Even whilst evidence continued to
accumulate on the still disputed atomic reality, a start was made
to penetrate the interior structure of these atoms, a research in
which Rutherford and
Bohr obtained
marvellous results, as we know. And I must summarize here my
contribution to this research.
It was known that when an electric
discharge passes in a glass tube through a sufficiently rarefied
gas, the part facing the cathode is illuminated by a fluorescence
on which the shadow of any obstacle placed in front of the
cathode is outlined; and that the cathode rays definable
in this way, are deflected by the magnetic field, describing a
circular trajectory when they are thrown at right angles to a
uniform field (Hittorf). Crookes had had the intuition that these
rays were trajectories of negative particles emitted by the
cathode and violently repelled by it (1886), but he did not
succeed in establishing this electrification. And this emission
theory was abandoned when Hertz on the one hand
failed in his attempts to manifest the negative electricity of
the rays, and on the other hand showed that they were able to
pass through glass foil or aluminium foil several microns thick.
It was assumed since then that the cathode rays were
immaterial and had a wave-like nature similar to light. This
opinion was held principally by Lenard (1894) who showed that
these rays can leave the tube where they are formed, through a
"window" made of a fairly thick foil to support the atmospheric
pressure, and that they can be studied in this way in any gas or
in an absolute vacuum.
It seemed to me, however, that the
electrified projectiles imagined by Crookes might differ
sufficiently, in size and in velocity, from ordinary molecules,
to pass through walls which were impermeable to these
molecules, and seeking to apply without complication the very
definition of the electric charge, I made cathode rays penetrate
into a "Faraday cylinder" contained inside a protective chamber.
As soon as the rays (which can, first, be drawn aside by a
magnetic field which is just strong enough to do so) enter the
cylinder, the latter presents phenomena which give precisely the
definition of a negative electric charge, and which enable it to
be measured (1895). This experiment was successful even when the
protective chamber was entirely closed, the rays penetrating it
through a thin metal foil. Almost at the same time I showed
(1896) that cathode rays are deflected by an electric field, and
that there is a method here for measuring the drop in potential
which had until then been unknown and from which they obtained
their energy.
These experiments were at once repeated,
and confirmed, by Lenard himself (whose theory they ruined), by
Wiechert, by Wien, and by J.J.
Thomson.
I had begun to make measurements which were
intended to give the velocity (obviously variable according to
the circumstances) of the cathode projectiles and the e/m ratio
of its charge to its mass, supplementing the measurement of the
drop in potential with that of the magnetic field capable of
producing a given deflection. I was anticipated here by J. J.
Thomson who in the very paper in which he published the
confirmation of my experiments showed that once the
electrification of the rays had been demonstrated, it was easy to
obtain the velocity and the charge of the projectiles from the
action of the electrical field and the magnetic field. He found
that the e/m ratio, independently of all the
circumstances, is approximately 2,000 times greater than it is
for hydrogen in electrolysis, and consequently he had the honour
of proving that the cathode projectile is much lighter than the
hydrogen atom (1897). The experimental idea of the
electron as a universal subatomic constituent was
therefore reached, and my experiments had played a certain part
in this growth of our knowledge of the manner in which matter is
discontinuous.
The problem of the structure of the atom
was immediately raised as it ceased to be the ultimate unit of
matter. J. J. Thomson assumed that whilst the atom as a whole was
neutral, it consisted of a homogeneous sphere of positive
electricity inside which the electrons were held in such
positions that the attractions and repulsions were in
equilibrium.
I was, I believe, the first to assume that
the atom had a structure reminding to that of the solar system
where the "planetary" electrons circulate around a positive
"Sun", the attraction by the centre being counterbalanced by the
force of inertia (1901). But I never tried or even saw any means
of verifying this conception. Rutherford (who had doubtless
arrived at it independently, but who also had the delicacy to
refer to the short phrase dropped during a lecture in which I had
stated it) understood that the essential difference between his
conception and that of J.J. Thomson was that there existed near
the positive and quasi-punctual Sun, enormous electrical fields
as compared with those which would exist inside or outside a
homogeneous positive sphere having the same charge, but embracing
the whole atom.
The result was that if a positive charge
which is itself quasi-punctual, is sufficiently fast to be able
to pass near such a nucleus, it will be strongly deflected just
as a comet can be deflected when it comes from the infinite and
passes near the Sun. It was in this way (1911), that Rutherford
discovered and explained that certain a rays (rays described by helium atoms projected
by radioactive substances) undergo very strong deflections when
they pass through a thin film, producing on a phosphorescent
screen, really far from the mean impact of the bundle of rays,
scintillations which mark their individual arrivals. All these
deflections are explained quantitatively on condition that the
nucleus is credited with a charge such that the number of
planetary electrons is equal to the "rank number" of the atom in
Mendeleev's series. In this way each atom consists of an
unimaginably small positive nucleus where almost the entire mass
of the atom is concentrated and around which the planetary
electrons, the presence of which determines the physical and
chemical properties of the corresponding element. revolve at
relatively colossal distances.
The nucleus itself, lastly, has been
revealed as being discontinuous and composed of hydrogen nuclei,
or protons, which are possibly "cemented " by nuclear
electrons.
As Prout had predicted, each atom can, in
fact, be regarded as resulting from the condensation on a whole
number of hydrogen atoms (the deviating elements having proved to
be mixtures of isotopes, which confirm the law
separately); the small differences which exist are explained (by
applying Einstein's law of the mass of energy) by the large
variations of internal energy which may accompany these
condensations (Langevin). And I have pointed out (1920) that the
loss of energy which must then accompany the condensation of
hydrogen into helium suffices alone to account for approximately
one hundred milliard years of solar radiation at the present rate
(the first theory to allow the understanding of the stupendous
antiquity of climatic conditions only slightly different from the
present conditions: the Helmholtz-Kelvin theory explained only a
maximum of 50 million-years, a grossly insufficient figure as far
as geology is concerned).
This led me to think that the atoms of
hydrogen, and then of helium (the only ones revealed by spectrum
analysis in the non-resolvable nebulae) condense progressively,
in the course of stellar evolution, into heavier and heavier
atoms, radioactive disintegration being the exception and atomic
integration being the rule.
However, Rutherford succeeded in proving,
in admirable experiments (1922), that when a nucleus of nitrogen,
aluminium, or phosphorus is struck forcefully by an a projectile
(sufficiently fast to "hit" it in spite of the electrical
repulsion), a proton is expelled (a
ray) with an energy which may exceed that of the a projectile,
and Rutherford interpreted this transmutation as being the
effect of an explosive disintegration (similar to that of a shell
which is exploded by an impact). I maintained, on the contrary
(1923), that there was then an integration, that the helium
nucleus at first combines with the nucleus that it has hit, to
form a radioactive atom (of a species as yet unknown) which soon
expels a proton, and that there finally remains an atom which is
three units heavier than the atom that has been hit. This has
since been confirmed by Blackett (1925) in the very laboratory of
Rutherford: three converging rays are counted (by the method of
C.T.R. Wilson) when a Rutherford transmutation occurs, instead of
the four which would exist if the striking projectile retained
its individuality after the impact.
But this refers rather to the evolution of
Matter than to its discontinuity; if I were to say any more, I
should be departing from the subject on which I came here to
speak.
*Similarly, the fact that there exists a definite
isothermal radiation for each temperature, and that even a
temperature is definable without the energy present in the form
of radiation continuously gliding towards colours of increasingly
smaller wavelengths, requires a structure to be discontinuous
(Planck).
From Nobel Lectures, Physics 1922-1941, Elsevier Publishing Company, Amsterdam, 1965
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