PERIODICITY
_Periodic Precipitation._--A phenomenon is said to be periodic when it
varies in time and space and is identically reproduced at equal intervals.
We are surrounded on all sides by periodic phenomena; summer and winter,
day and night, sleep and waking, rhythm and rhyme, flux and reflux, the
movements of respiration and the beating of the heart, all are periodic.
Our first sorrows were appeased by the periodic rhythm of the cradle, and
in our later years the periodic swing of the rocking-chair and the hammock
still soothe the infirmities of old age.
Sound is a periodic movement of the atmosphere which brings to us harmony
and melody. Light consists of periodic undulations of the ether which
convey to us the beauty of form and colour. Periodic ethereal waves waft to
us the wireless message through terrestrial space and the radiant energy of
the sun and stars.
It is therefore not to be wondered at that the phenomena of diffusion are
also periodic. According to Professor Quinke of Heidelberg, the first
mention of the periodic formation of chemical precipitates must be
attributed to Runge in 1885. Since that time these precipitates have been
studied by a number of authors, and particularly by R. Liesegang of
Duesseldorf, who in 1907 published a work on the subject, entitled _On
Stratification by Diffusion_.
In 1901 I presented to the Congress of Ajaccio a number of preparations
showing concentric rings, alternately transparent and opaque, obtained by
diffusing a drop of potassium ferrocyanide solution in gelatine containing
a trace of ferric {68} sulphate. At the Congress of Rheims in 1907 I
exhibited the result of some further experiments on the same subject.
These periodic precipitates may be obtained from a great number of
different chemical substances. The following is the best method of
demonstrating the phenomenon. A glass lantern slide is carefully cleaned
and placed absolutely level. We then take 5 c.c. of a 10 per cent. solution
of gelatine and add to it one drop of a concentrated solution of sodium
arsenate. This is poured over the glass plate whilst hot, and as soon as it
is quite set, but before it can dry, we allow a drop of silver nitrate
solution containing a trace of nitric acid to fall on it from a pipette.
The drop slowly spreads in the gelatine, and we thus obtain magnificent
rings of periodic precipitates of arsenate of silver, with which any one
may easily repeat the experiments detailed in this chapter.
[Illustration: FIG. 12.--Lines of diffusion precipitate, showing the
simultaneous propagation of "undulations of different wave-length.]
_Circular Waves of Precipitation._--The wave-front of the periodic rings of
precipitates is always perpendicular to the rays of diffusion. The distance
between the rings depends on the concentration of the diffusing solution.
The greater the fall of concentration, the less is the interval between the
rings. Each ring represents an equipotential line in the field of
diffusion. These equipotential lines of diffusion give us the best and most
concrete reproduction of the mode of propagation of periodic waves in
space. They are, in fact, a visible diagram of the propagation of the waves
of light and sound. Occasionally we may observe in the gelatine the
simultaneous propagation of undulations of different wave-length, just as
we have them in the ether and the air. These diffusion wavelets {69} give
us a very beautiful representation of the simultaneous propagation of
undulations of different wave-length in the same medium.
[Illustration: FIG. 13.--Waves of diffusion refracted at a plane surface on
passing from a less concentrated into a more concentrated solution. The
refracted wave-front is flattened, the wave-length being less in the denser
medium.]
Like waves of light and sound, these waves of diffusion are refracted when
they pass from one medium into another of a different density, where they
have a different velocity. When, for instance, a diffusion wave passes from
a 5 per cent. solution of gelatine into a 10 per cent. solution, the
wave-front is retarded, the retardation being proportional to the length of
the path through the denser medium. Hence the wave-front is flattened, the
curvature of the refracted wave being less than that of the original wave
of diffusion. The contrary is the case when the wave-front passes into a
medium where its velocity is greater. The middle of the wave-front now
travels faster than the flanks, and the curvature is increased.
[Illustration: FIG. 14.--Transformation of a spherical wave-front into a
plane wave-front by a convergent diopter.]
These diffusion rings furnish us with most excellent diagrams of refraction
at a "diopter," _i.e._ a spherical surface separating two media of
different densities. Fig. 14 shows the refraction at a convergent diopter,
_i.e_. a surface where the denser medium is convex. The diffusion waves in
this case emanate from the principal focus of the diopter, and therefore
become plane on passing through the convex surface of the denser gelatine.
These periodic diffusion rings also illustrate the phenomena of colour
diffraction. Diffusion waves of different {70} wavelength are unequally
refracted by a gelatine lens. Hence rings of different wave-length which,
originating at the same spot, are at first concentric, are no longer
parallel after passing through a gelatine lens. A convergent lens which
will change the long spherical incident waves into shorter plane waves,
will transform the short incident waves into concave waves whose curvature
is opposite to that of the original waves, _i.e._ it will transform a
divergent into a convergent beam. This is an illustration of what is called
the aberration of refrangibility.
In the same way we may demonstrate the course of diffusion waves through a
gelatine prism, showing the refraction on their incidence and again on
emergence. The prism is made of a stronger gelatine solution, which is more
refractive than the gelatine around it. The waves of diffusion whilst
traversing the prism are retarded, and this retardation is greatest at the
base where the passage is longer. Hence the wave-front is tilted towards
the base of the prism, and this tilting is repeated when the wave-front
leaves the prism.
If we examine diffusion waves of different wave-length on their emergence
from the gelatine prism, we shall see that they cut one another. With a
dense prism, the wave-front of the shorter waves is more tilted towards the
base than the wave-front of the longer waves. For diffusion as for light
the shorter waves are the most refracted. Both refraction and dispersion
are due to the unequal resistances of the medium to undulatory movements of
different periodicity.
[Illustration: FIG. 15.--Diffraction of diffusion waves on passing through
a narrow aperture.]
_Diffraction._--When light traverses a minute orifice, instead {71} of
passing on in a straight line, it spreads out like a fan, forming a
diverging cone of light, just as if the orifice were itself a luminous
point. This is the phenomenon of diffraction which has hitherto been
considered incompatible with the emission theory of light. Diffusion waves
may also be made to pass through a narrow orifice, when they will behave
exactly like the waves of light. The new waves radiate from the orifice
like a fan, instead of giving a cone of waves bounded by lines passing
through the circumference of the orifice and the original centre of
radiation. Thus on passing through a small orifice diffusion waves exhibit
the phenomenon of diffraction just as light waves do.
[Illustration: FIG. 16.--Interference of diffusion waves.]
_Interference._--The phenomenon of interference may also be illustrated by
waves of diffusion. If on a gelatine plate we produce two series of
diffusion waves from two separate centres, we get at certain points an
appearance corresponding to the interference of two sets of light waves.
This appearance is best shown by sowing on the gelatine film a straight row
of drops equidistant from one another. It should be remarked that this
phenomenon of the production of circles of precipitate separated by
transparent spaces, although periodic, is not of necessity vibratory or
undulatory. It would thus appear that periodic phenomena may be propagated
through space without vibratory or oscillatory motion. If we submit to a
critical examination the various experiments which have established the
undulatory theory of light, we find that they do indeed demonstrate the
periodic nature of light, but in no wise prove that light is a vibratory
movement of the ether. {72} On the contrary, the hypothesis that light is
propagated by vibratory movements is open to many objections. Even the
Zeeman effect, although it may tend to establish the fact that light is
produced by vibratory movement, by no means proves that it is propagated in
the same manner. When the theory was accepted that the transmission of
light was periodic it was supposed that this periodic transmission could
only be vibratory or undulatory in character, since waves or vibrations
were the only periodic phenomena known at that time. We now know that there
are other means of periodic transmission which are apparently not
undulatory. The periodic precipitates produced by diffusion show us the
transmission of spherical waves through space, which follow the laws of
light, although the periodic phenomenon is apparently emissive rather than
vibratory.
It will be remembered that Newton considered light to be produced by
projectile-like particles emanating from a centre, and proceeding in
straight lines in all directions. This emission theory of light was
abandoned in favour of Huygens' undulatory theory.
It was said that the phenomena of interference and diffraction could not be
explained by the theory of emission, while the undulatory theory gave a
simple explanation. The scientific mind was unable to conceive the idea of
emission and periodicity as taking part in the same phenomenon. The savants
and thinkers who have meditated on this question have always considered the
theory of emission and that of periodicity as incompatible. Nevertheless,
we are here in presence of a phenomenon in which emission and periodicity
exist simultaneously. The molecules emanating from our drop are diffused in
straight radiating lines, and yet produce periodic precipitates which are
subject to interference and diffraction like the undulations of Huygens.
The phenomena associated with the pressure of light, the {73} discovery of
the cathode rays and the radiations of radium, together with the
introduction of the electron theory of electricity, all seem to have
brought again into greater prominence Newton's original conception of the
emissionary nature of light.
Some of the phenomena of radiation can be explained only by the emission
theory, and others by the undulatory theory of light. All these
difficulties would be solved if we admitted the hypothesis that radiating
bodies project electrons, which produce in the ether periodic waves similar
to those formed in our gelatine films by the molecules of diffusion.
These diffusion films are of the greatest possible service in the practical
teaching of optics. They place before the eye of the student a working
model as it were of the undulations of light. When projected on the screen,
they give excellent pictures of the phenomena of refraction, diffraction,
and interference, and the simultaneous propagation of undulation of
different wave-lengths, and they show in a visible manner the changes of
wave-length in media of different densities.
Diffusion waves differ greatly in length, varying from several millimetres
to 2 [mu]. Many are even shorter than this, too short to be separately
distinguished even under the highest power of the microscope, when they
give the effect of moire or mother-of-pearl.
It is easy to construct a spectroscopic grating in this way with fine lines
whose distance apart is of the order of a micron, separated by clear
spaces. Every physical laboratory may thus produce its own spectroscopic
gratings, rectilinear, circular, or of any desired form.
The most beautiful colour effects may be produced with these diffusion
gratings, as we have shown at the Congress of Rheims in 1907. We have a
considerable collection of these diffusion gratings, some with very fine
lines, giving a very extended spectrum, and others with coarser striations
which give a large number of small spectra.
This study of periodic precipitates is of the highest interest when we come
to investigate the production of colour in natural objects, such as the
wings of insects or the plumage of {74} birds. Many tissues have this lined
or striated structure and exhibit interference colours like those of the
periodic precipitates, their structure showing alternate transparent and
opaque lines, whose width is of the order of a micron. This is the
structure of muscle, and to this striated surface is also attributable many
of the most beautiful colours of nature, the gleam of tendon and
aponeurosis, the fire of scarab and beetle, the colours of the peacock, and
the iridescence of the mollusc and the pearl. The study of liquid diffusion
has given us an idea of the physical mechanism by which these striated
tissues are produced, a mechanism which up to the present time has not been
even suspected. Our experiments show how readily such striped or ruled
structures may be produced in a colloidal solution by the simple diffusion
of salts such as are found in every living organism.
[Illustration: FIG. 17.--Photomicrograph of striated structure of a
periodic precipitate of carbonate and phosphate of lime (magnified 500
times).]
To make a spectroscopic grating by diffusion we proceed as follows. We take
5 c.c. of a 10 per cent. solution of gelatine, and add to it one drop of a
concentrated solution {75} of calcium nitrate. We spread the gelatine
evenly over a plain glass lantern slide and allow it to set. After it is
set, but before it dries, we place in the centre of the slide a drop of
concentrated solution containing two parts of sodium carbonate (Na_2CO_3)
to one of dibasic sodium phosphate (Na_2HPO_4). Tribasic sodium phosphate
alone without the addition of the carbonate will also give good results. If
the phosphate solution is placed on the gelatine in the form of a drop, we
obtain circular periodic precipitates. If it is desired to make a
rectilineal grating, we deposit the phosphate solution on the gelatine in a
straight line by means of two parallel glass plates. In this way we may
obtain lines of periodic precipitation to the number of 500 to 1000 per
millimetre, forming gratings which produce most beautiful spectra.
Pearls and mother-of-pearl both owe their iridescence to a similar ruled
structure, which is developed in the living tissue of a mollusc. They are,
in fact, periodic precipitates of phosphate and carbonate of lime deposited
in the colloidal organic substance of the mollusc. They have the same
structure and the same chemical composition; they have the same physical
properties, the glow, the fire, and the brilliancy of our spectroscopic
gratings. In these experiments, indeed, we have realized the synthesis of
the pearl, not only a chemical synthesis, but the synthesis of its
structure and organism.
We have been able to make these periodic precipitates by the reaction of a
great number of chemical substances, giving a bewildering variety of form
and structure. Some of these recall the form of various organisms, and
especially of insects, as may be seen in Fig. 18.
All the phenomena of life are periodic. The movement of heart and lungs,
sleep and waking, all nervous phenomena, have a regular periodicity. It is
possible that the study of these purely physical phenomena of periodic
precipitation may give us the key to the causation of rhythm and
periodicity in living beings.
Besides this periodic precipitation there appear to be other chemical
reactions which are periodic. Professor Bredig of Heidelberg has lately
described a curious phenomenon, the {76} periodic catalysis of peroxide of
hydrogen by mercury. He thus describes his experiment: "We place in a
perfectly clean test tube a few cubic centimetres of perfectly pure
mercury. Upon this we pour 10 c.c. of a 10 per cent. solution of hydrogen
peroxide. The mercury speedily becomes covered with a thin, brilliant
bronze-coloured pellicle which reflects light. Then little by little
catalysis of the hydrogen peroxide begins, with liberation of oxygen. After
some time, from five to twenty minutes, the liberation of gas at the
surface of the mercury ceases, the cloud formed by the gas bubbles
disappears, and the bronze mirror at the surface of the mercury lights up
with the glint of silver. There is a pause of one or more seconds, and then
the catalytic action begins afresh, commencing at the edges of the mirror.
The cloud is again formed and again disappears. This beautiful and
surprising rhythmic phenomenon may continue at regular intervals for an
hour or more."
[Illustration: FIG. 18.--Articulate form produced by periodic
precipitation.]
A slight alkalinity of the liquid is necessary to start the phenomenon.
This explains the retardation at the beginning {77} of the experiment,
since the rhythmic catalysis cannot begin until the hydrogen peroxide has
dissolved a little of the glass so as to render it slightly alkaline. The
catalytic process may, however, be set going at once by adding a trace of
potassium acetate to the solution.
We may even obtain a curve giving an automatic record of the periodicity of
this catalytic action. For this purpose the oxygen given off is led to a
manometer, which registers on a revolving drum the periodic variation in
pressure. The curve thus obtained presents a remarkable resemblance to a
tracing of the pulse. The frequency and character of the undulatory curve
is modified by physical and chemical influences. Like circulation or
respiration, periodic catalysis has its poisons, and exhibits signs of
fatigue, and of paralysis by cold.
The rhythmic catalysis of Bredig produces an electrical current of action
between the mercury and the water just like that produced by the rhythmic
contraction of the heart, and this current may be registered in a similar
way by means of the Einthoven galvanometer. Thus the heart-beat may be but
an instance of rhythmic catalysis, since both produce the same phenomena,
movement, chemical action, and periodic currents. In the chapter on
physiogenesis we shall return to the study of this question and consider
another rhythmic phenomenon which is the result of osmotic growth.
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