CHAPTER VI
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 Düsseldorf, 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
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.
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
give us a very beautiful representation of the simultaneous propagation of undulations of different wave-length in the same medium.
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.
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
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.
Diffraction.—When light traverses a minute orifice, instead
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.
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.
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
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 μ. 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 moiré 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
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.
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
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 (Na2CO3) to one of dibasic sodium phosphate (Na2HPO4). 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
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."
A slight alkalinity of the liquid is necessary to start the phenomenon. This explains the retardation at the beginning
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.