Contemporary Problems of Molecular Physics1).

Academician P. P. Lazarev.

A substantial feature of contemporary physics is the striving to pass from a continuous representation of the substrate of physical phenomena to images and models closer to reality, consisting of separate parts not connected with one another. Atomism, having come down from antiquity, received, thanks to the works of Clausius, Boltzmann, and Maxwell, significant development first in the theory of gases; later van der Waals applied atomistic views to the theory of the continuity of the transition of a gas into a liquid and gave a brilliant theory of this phenomenon, which remains of essential importance up to the present time. At the end of the nineties and the beginning of the nineteen-hundreds, thanks to the works of Lorentz and J. J. Thomson, atomism penetrates into the theory of electricity, giving rise to the modern theory of electrons, and into the theory of energy, thanks to the investigations of Planck, which laid the foundation of the theory of quanta. As always happens with the rapid development of a complex and extensive scientific field, many phenomena cannot at once be connected into one coherent whole; many facts lead to entirely opposite interpretations; finally, experimental data are found that apparently contradict one another. But as our knowledge deepens, the missing connections appear, generalizations arise that establish a strict regularity among the observed facts, and new broad problems of experimental investigation arise. All molecular physics is at present in a period of rapid reconstruction, and in my report I intend to give an account of a number of my still unpublished theoretical investigations, which are to form the basis of a series of works proposed for execution in the Physical Laboratory of the Academy of Sciences and in the Physical Institute of the Moscow Scientific Institute.

1) Speech at a public meeting of the Council of the Moscow Scientific Institute, February 4, 1918.

The creation of the kinetic theory of gases, which at first operated with a system of material points—molecules possessing identical velocities and not bound to one another by forces of attraction—made it possible at once to solve the question of the simplest laws taking place in a gaseous medium. The theory not only connected the specific volume \(v\) and the pressure \(p\) in the form of the Boyle–Mariotte law, but also made it possible to determine the constant in the form

\[ \mathrm{Const.}=pv=\frac{Dc^{2}}{3}, \]

where \(D\) is the density of the gas, and \(c\) is the velocity of motion of its molecules. This same theory showed that, at a given temperature, we must regard the kinetic energy of a molecule as proportional to the absolute temperature of the medium. In further applications of the theory to the explanation of phenomena, however, difficulties arose, and the theory had to be complicated by new corrections. First of all, it is necessary to admit the extension of atoms and molecules, since otherwise, at a high velocity of their motion, it is impossible to explain the slow diffusion of one gas into another, the poor thermal conductivity of gases, etc.; and this assumption at once leads to the result that molecules cannot, without mutual collision, traverse any considerable path and that, if at first we were to impart to all molecules a completely identical velocity, then after a more or less short time there would result a new, so-called Maxwellian, distribution of the velocities of molecules in a gaseous medium, in which at every velocity at any given moment there corresponds a definite number of molecules; moreover, the relation between the magnitude of the velocity \(c\), the number of molecules \(dN\) having velocities lying between \(c\) and \(c+dc\), and the total number of molecules \(N_{0}\), is expressed by the relation

\[ dN=N_{0}\frac{4}{\sqrt{\pi\alpha^{3}}}\,c^{2}e^{-\frac{c^{2}}{\alpha^{2}}}\,dc, \]

where \(\alpha\) is a constant.

Colliding with one another during motion, the molecules traverse, depending on accidental causes, different distances, but the mean free path of a molecule \(\lambda\) between its two collisions is a quantity quite definite for each gas, and the coefficient of internal friction makes it possible to calculate the dimensions of the mean free path.

We can thus determine the magnitude of the mean free path by an indirect method, and this was done by a number of investigators. However, it is possible to find another, more direct method as well, by studying the course of the temperature inside a gas during thermal conduction and measur-

that near the wall, over the extent of the mean free path, there must be a temperature variation different from that in the free gas. As we have been able to show, in this way a direct method can be obtained for the free path, and checking it by indirect methods of investigation will make it possible fully to resolve the question of the mean path.

For the characterization of the properties of a gas, the investigation of the specific heats of a gas at constant pressure and constant volume, \(\gamma_p\) and \(\gamma_v\), carried out so that these two quantities can be obtained independently of one another, is of very great interest. In this respect, a method being developed by us at the Physical Institute may be of importance, and is a modification of Nernst’s calorimetric method. By determining the heating of a gas placed in a cylinder, either at constant pressure or at constant volume, one can easily, knowing the expended electrical energy and the rise in temperature, find the specific heats. The development of this method will make it possible indirectly to determine the mean path lengths from the coefficients of thermal conductivity. Knowing the values \(\gamma_p\) and \(\gamma_v\), one can separately find their ratio \(\frac{\gamma_p}{\gamma_v}\).

The study of the quantity \(\frac{\gamma_p}{\gamma_v}\) is important, among other things, in that it can give an idea of the form of the molecules, since the ratio \(\frac{\gamma_p}{\gamma_v}\), depending on the diameter of the molecule, must be different according as we are dealing with spherical or elongated molecules. And here it appears possible to decide the question whether a complex molecule—for example, a hydrocarbon of the fatty series, having a row of carbon atoms connected with one another in the form of an extended chain—moves with the chain extended, or whether this molecule curls up into a small ball. To study this phenomenon we use Kundt’s method of acoustic waves, which makes it possible directly to measure \(\frac{\gamma_p}{\gamma_v}\).

In connection with the mean free path of the molecule, the question of extremely short acoustic waves is worth raising. As Lebedev showed, by reducing the dimensions of an acoustic wave to an insignificant magnitude comparable with \(\lambda\), one can easily discover a peculiar attenuation of sound, depending on the transition of acoustic vibrations into thermal motions; and the study of the propagation of short waves in gases of different nature is of undoubted interest.

We now pass to the second fundamental question of the theory of gases—the law of Maxwell’s distribution of velocities. The only method for studying this phenomenon up to the present has been the method

of the broadening of spectral bands with heating. Rayleigh showed that the broadening of spectral bands can be explained, if the emission of the molecule is assumed to be monochromatic, by the Doppler phenomenon; and the distribution of brightness in the spectral band agreed rather well with the distribution assumed by Maxwell.

I have shown that another method may be used to study the phenomenon of distribution. Suppose we have two vessels separated by a wall. Let one contain gas under a certain pressure, and the other contain a vacuum. If the velocities of all the molecules in the vessel were the same, and for a certain time the two vessels were connected by an opening, then some of the molecules would pass into the vacuum and would be distributed throughout the whole vessel, still possessing the same velocities as before. The temperature, proportional to the kinetic energy of motion of the molecule, should not, with equality of velocities, change after the vessels are connected; meanwhile, as experiment reveals, there is an increase of temperature in the vessel where there had been a vacuum and a decrease of it in the vessel with the gas. An explanation of this phenomenon can be obtained if one assumes that the velocities of the molecules are distributed according to Maxwell’s law. In this case, when the stopcock connecting the vessels is opened, the faster molecules outrun the slower ones, and a relatively larger number of molecules with greater velocities pass into the vacuum, whence the temperature of the gas in the vessel from which it is flowing out decreases. For the experimental study of this phenomenon I have constructed a pendulum which, during its oscillation, opens for a definite time an orifice releasing gas into a vacuum, and with this apparatus investigations are now being carried out at the Scientific Institute. In working with gases, in order to avoid the influence of the Joule–Thomson effect, which depends on molecular forces and is also manifested by cooling of the vessel from which the gas flows out, it is necessary to use perfect gases. When easily liquefied gases are used, the same apparatus, on the contrary, makes it possible to study also the Joule–Thomson effect, and this brings us to the next part of the problem—to the study of molecular forces in substances.

First of all we must mention that, if in perfect gases we may entirely neglect molecular forces, then in liquefied gases one must admit, especially if the gases are strongly compressed, considerable forces, which become still greater upon liquefaction of the substance. In a liquid, molecules can move about near one another, being, however, all the time held within the sphere of mutual action, and only at the surface is the tearing away of individual molecules observed, these passing into vapor. When the velocities of motion of the particles of a liquid are diminished upon its cooling, we ultimately transform the liquid into a solid body, in which the mo-

molecules must be fixed in definite positions and can oscillate only about a definite point.

As for the nature of molecular forces, at the present time these forces may be regarded as forces of two kinds. First, between the charged parts of atoms, or molecules, there must act forces of an electrostatic character; second, oscillating electrons produce ponderomotive phenomena owing to electromagnetic actions.

Forces of the first kind do not depend on temperature, varying strongly with the dielectric constant of the medium, whereas forces of the second kind increase with temperature and do not depend on the dielectric constant. All phenomena in a substance are composed of the interplay of both kinds of forces, and in molecular interactions we have a very complex picture of the phenomena of attraction and repulsion. In view of the complexity of the structure of the atom, consisting of a positive nucleus and of rings of electrons rotating around it, we must expect a definite distribution in space of the fields of forces, manifested especially strongly at short distances. In gases and liquids the character of the field has little influence on the phenomena of attraction because of the rotation of the molecules, and in this case we may represent the forces of interaction as the mean of the magnitudes of the forces over a certain interval of time, and regard them, as Boltzmann and van der Waals do, as depending only on the distance between the molecules.

The same may be assumed in solid amorphous bodies, where the field of forces around a molecule must be completely uniform and depend only on the distance. In crystalline substances, on the contrary, the field of the molecules must be nonuniform and depend on the directions from which the given molecule is considered.

Since the field of a molecule is symmetric with respect to certain axes in the molecule, it can be shown that for each substance, in the general case, several positions of equilibrium are possible for definite positions of the field axes, when the potential energy reaches a minimum. These positions, depending on the change of electrodynamic forces with temperature, can change; and we obtain, in this way, an explanation of the existence of allotropic modifications. In the transformation of one modification into another, the potential energy must change discontinuously, and this is reflected in the appearance of a thermal effect.

As for the question of the law of action of the forces and of its variation with distance, for amorphous substances we have succeeded in solving this question in a very simple form, by showing that the laws of these actions may be taken to be identical for all substances. In

in this assumption we obtain proportionality between the number of atoms in a unit volume and the hardness of the body, determined by the force required to tear one molecule away from the remaining mass of the substance. In Fig. 1 we give the empirically discovered relation, by Bottone, Turner, and Benedicks, between atomic weight (axis of abscissas), hardness (dotted line), and the number of atoms in a unit volume (solid line), which shows that, at least in a first approximation, the relation we have derived may be recognized as correct.

Fig. 1.

The derivation of the relation between the number of atoms in a unit volume \(N\) and the hardness \(H\) may be made as follows: suppose that we have a solid amorphous body bounded by a plane on which there is situated a molecule of the substance \(A\); let the plane of the body be the plane \(xy\), and let the axis \(z\) pass through the molecule downward (Fig. 2). Let us take in the body a small volume

\[ dv = r^2 \operatorname{Cos}\alpha . d\alpha\, d\varphi\, dr, \]

where the angle \(\alpha\) is the angle between the plane \(xy\) and the radius vector drawn from the molecule, and the angle \(\varphi\) is the angle between the axis \(x\) and the plane passing through the axis \(z\) and the molecule. Then, assuming symmetry of the field of forces, the interaction of one molecule of volume \(dv\) and the molecule \(A\) is expressed as follows:

\[ df = f(r) \]

where \(f(r)\) is a function of the distance \(r\) of the molecule \(A\) from \(dv\); the total number of molecules in the volume \(dv\) is \(N\,dv\), and, consequently, the interaction of the whole volume

Fig. 2.

\(dv\) is \(dF = N f(r) dv = N f(r) r^2 \operatorname{Cos}\alpha\, d\alpha\, d\varphi\, dr\). Projecting this force onto the axis \(z\) and integrating over the hemisphere of molecular action, we have the force acting on one molecule into the body along the vertical, equal to

\[ F_z = \int_{0}^{R} \int_{0}^{2\pi} \int_{0}^{\frac{\pi}{2}} \operatorname{Sin}\alpha\, \operatorname{Cos}\alpha . d\alpha d\varphi N f(r) r^2 dr. \]

or

\[ F_z=\pi N\int_{0}^{R} f(r)r^{2}\,dr=NF(R),\ \text{where} \]

\(R\) is the radius of the sphere of molecular action, and \(F(R)\) is a function of \(R\). Knowing the magnitude of the force \(F_z\), equal to the force necessary to remove one molecule \(A\) from the surface, we obtain an idea of the hardness \(H\), which increases with increasing force \(F_z\), and this force, like the magnitude of the hardness, increases proportionally to \(N\); whence we have that the hardness \(H=\beta \tilde{N}\), where \(\beta\) is a constant depending on the form of the function \(F(R)\).

We may make the simplest assumption about the form of \(F(R)\) by putting \(F(R)=\mathrm{Const.}\), which corresponds to the supposition that the law of action of molecular forces does not depend on the nature of the substance; then the hardness \(H\) is proportional to \(N\), as follows in the first approximation from the empirical data of Turner and Benedicks.

In crystalline substances possessing molecules with symmetrically arranged fields, as is readily understood, we cannot adopt such a simple relation between force and distance, and the law of proportionality between the hardness of a body and the concentration of atoms in it can no longer have the strict significance that is in fact observed.

Passing to liquids, it is necessary to distinguish the conditions of equilibrium of molecules at the surface and inside the liquid. Whereas inside the liquid the molecules perform quite disordered motions and are in a sphere of a field of force that is continuously changing in all directions, at the surface, owing to the difference in the magnitudes of the forces acting on one side and on the other side of the surface, an oriented position of the molecules of liquids is possible, such that their long diameter is situated perpendicular to the free surface. At the surface of a liquid we have an arrangement of molecules resembling a solid crystalline body and, if the molecules have the shape of elongated rods, it is possible to imagine that optical properties, e.g., double refraction, will be observed in such a liquid film to the same extent as in a solid crystalline body.

Such relations may be observed in liquid crystals, which, according to our theory, should be regarded as droplets of one homogeneous liquid in another, likewise homogeneous one. All optical phenomena in droplets of liquid crystals are excellently explained by admitting an orientation of the molecules of the boundary layer, which, for the liquid-crystalline substances investigated, must indeed have an elongated form. Attempts to find, for water at the boundary with air, a layer with double refraction have not given us

up to the present time have not yielded positive results, and this may be explained by the small magnitude of the double refraction that may be expected in water.

The study of capillary forces at a surface has allowed us to establish theoretically the relation, previously derived by Eötvös and connecting the specific volume \(v\), the capillary constant \(\alpha\), and the temperature \(T\) in the form:

\[ \frac{v^{\frac{2}{3}}\alpha}{T}=\mathrm{Const}. \]

In connection with the dielectric constant of a liquid stands the mobility of the electrons in the molecule; as this mobility increases, the dielectric constant also increases, and this creates more favorable conditions for attraction in the charged parts of the molecules. Two molecules that come into contact with their parts bearing opposite charges are held more firmly when the electrons are readily mobile than when the electrons are of low mobility, all other conditions being the same. We must therefore expect in liquids with a large dielectric constant a considerable association of molecules, bound by electrostatic forces into large aggregates.

The theory we are developing makes it possible to determine readily the work of removing one molecule of a liquid from its surface, that is, the latent heat of evaporation. Since the forces binding the molecules depend on the dielectric constant, it becomes clear that this latter quantity must be connected with the latent heat of vaporization, as was found experimentally by Tereshin.

We shall now pass to the conditions of equilibrium of a liquid and a solid body, and let us imagine at the surface of a solid body \(LL\) (Fig. 3) a molecule of liquid \(A\), which will experience, from the side of the liquid, an action \(A_1\), directed upward and composed of the actions of all the molecules of the liquid contained in the hemisphere described with the radius of molecular action. From the side of the solid body, a similar force \(A_2\) acts on the same molecule, acting in the opposite direction. We represent the radii for the solid body and for the liquid as different. If the force \(A_1>A_2\), then the molecules of the solid body at the surface will be torn away and pass into solution, at the same time decreasing the magnitude of the acting forces in the direction toward the liquid, \(A_1'\). Dissolution will cease when \(A_1'=A_2\), and this relation makes it possible to establish the laws of dissolution.

Fig. 3.

Using methods analogous to that which makes it possible to establish the connection between the hardness of a solid and the concentration of atoms, it is easy to show that, since the forces of attraction of a molecule \(A\) by a liquid depend on the dielectric constant, the solubility of a solid is a definite function of the dielectric constant of the solvent. Similar relations had already been discovered experimentally by P. I. Walden, and the theory, explaining the existence of Walden’s law of dissolution, makes it possible to understand cases of deviation from it.

Since the electrodynamic phenomena in molecules, manifested by attractions, must depend on temperature, the connection between solubility and temperature becomes clear.

By changing the form of the surface separating the solid and the liquid and thereby changing the ratio \(\dfrac{A_1}{A_2}\), one can substantially change the rate of dissolution. A change in the rate must also occur if, instead of a thick layer of solid, the finest powder is taken for dissolution, forming grains whose thickness is less than the radius of the sphere of molecular action: in this case the thickness of the dissolving grain corresponds to the part of the solid \(S\) between the surface and the dotted line \(p\) (Fig. 3).

A change in the form of the surface and the formation of the finest recesses, pockets with cavities, where the curvature is commensurable with or even smaller than the radius of molecular action, may lead to an enormous increase in the forces of attraction of the solid and to an accumulation of molecules of liquid or gas in the corresponding parts of the surface—to adsorption. The accumulation of gas molecules, causing a change in their mobility and bringing the gas closer to a liquefied state, must be accompanied by thermal effects. The layer in which adsorption is observed must, for a liquid, be small and commensurable with the radius of the sphere of molecular action. For gases, the adsorbed layer, in which the concentration changes its magnitude, must extend over the length of the mean free path of the molecule and, consequently, at low pressures may occupy a considerable thickness; the study of adsorption from this point of view, already begun by me in my laboratory, appears to be a matter attainable with modern technical means.

By heating a salt in the presence of a solvent and transferring an excess of the salt into solution, we can, by decanting it and cooling to the former temperature, obtain a solvent supersaturated with the salt. In this case a molecule of the salt, situated at the center of the sphere of molecular action, experiences on all sides identical forces of attraction, which, owing to the presence of molecules of dissolved salt, are smaller than the attraction of the solvent and, at a certain

salt content is less than the attraction of the solid body. When a crystal of the solid salt is placed in a supersaturated solution, we shall at once cause the excess salt to crystallize out, since on each molecule at the surface of the solid salt two forces will act: from the side of the solution, \(A_1\), and from the side of the solid body, \(A_2\), of which \(A_2 > A_1\); as a result, the salt from the solution will be deposited on the solid salt. Since in crystals having the same crystalline form the fields of force may be quite identical, the fact becomes understandable that salt is precipitated from solutions not only by the same salt itself, but also by a number of other salts having the same crystalline structure as it.

If we layer an aqueous solution of a substance with water, then for a molecule or ion of the substance situated at the boundary of the solution and pure water the same conditions are created as at the boundary of a solid body and a liquid. From the side of the pure water an attractive force \(A_1\) acts on the molecule, and from the side of the solution \(A_2\). The first force must, according to the preceding, be greater than the second, since the salt dissolves in water, and we have a force that tends to move the dissolved molecule into the pure solvent. In the same way it can be shown that the motion of salt, with a known concentration gradient, toward the side of lower concentration proceeds according to a law analogous to Fick’s law of diffusion.

By causing a solution to diffuse in a narrow capillary space and observing the influence of the walls, it can be shown, both theoretically and experimentally, that diffusion is considerably accelerated owing to the influence of adsorption by the walls. Such experiments were carried out in our laboratory and undoubtedly established the phenomenon of acceleration. On the other hand, by changing the shape of the interface between the solvent and the solution and making it spherical, so that the convexity is directed toward the solution, it is easy to show that the solution must diffuse more rapidly, since the number of molecules attracted into the solution in this case will be smaller than if the surface were plane; such conditions were indeed realized in our laboratory and showed agreement between theory and experiment.

The dissolution of gases must proceed much more simply than the dissolution of solid bodies, and for gases having no chemical affinity for the solvent we may represent the phenomenon as follows: a gas molecule, flying up to the surface of the liquid, pushes apart the molecules of the surface capillary layer and, losing part of its kinetic energy, continues to move inside the solvent; sometimes the molecule may, in its motion in the liquid, pass again into the gas, bypassing the surface. The greater the concentration of gas above the liquid,

the greater will also be the number of gas particles passing into the liquid. In this way we can derive the law of absorption of a gas by a liquid—the law of Henry-Dalton. The surface capillary layer must, in our view, play an essential role in the penetration of gas particles into the liquid. If the surface tension is increased, then the separation of the liquid molecules is accomplished with greater difficulty, and the gas must dissolve in the liquid in a smaller quantity than before. As Sechenov’s experiments have shown, we do indeed have this regularity in the phenomenon of dissolution, and thus the theory is confirmed here as well.

If a porous vessel is placed in water and a salt solution is poured inside the vessel, then the dimensions of the pores can be chosen so that the solvent molecules pass freely through them, while the molecules of the dissolved substance cannot pass through them. In this case the dissolved substance will attract the solvent into the porous vessel, increasing the pressure, which rises proportionally to the concentration. In this way the quantitative laws of osmotic pressure can be explained.

Proceeding from the same principles, I have explained and obtained the theoretical laws for the case of the motion of a substance between two solvents, and also for the change in the boiling points due to the dissolution of substances.

In conclusion, it can be shown that the considerations developed above make it possible to understand the existence of a connection between the dielectric constant of a solvent and its ionizing action on salt molecules. Each salt molecule we may imagine as consisting of two charged parts—ions—bound by electrostatic forces. If a salt molecule is introduced into a solvent, and a solvent molecule approaches it, then an interaction begins between the charged parts of the molecules, which changes depending on the mobility of the electrons in the solvent molecule, that is, depending on the dielectric constant. If, under the influence of a certain field produced by the salt molecule, the displacement of the electrons is large, then it may turn out that the bond between the solvent molecule and one of the salt ions is greater than the interionic bond, and then the salt molecule will be transformed into two ions, which are immediately surrounded by the corresponding solvent molecules, turned toward the ion with the side that has the opposite charge. Since in this case the attraction between the ion and the solvent molecule must be greater than between two solvent molecules, around each ion there must form a cluster of solvent molecules, constituting a group denser in concentration than the free solvent. Such an action

of the solvent is the more considerable, the lower the concentration of the salt molecules. In this way one can understand the change of ionization with concentration and the influence on the ionizing power of the solvent of the dielectric constant.

A rise in temperature, making the bond between the two ions of the salt less strong, also increases the degree of dissociation of the salt.

We shall conclude our review of the theoretical views developed by us in this series of investigations by indicating certain problems planned for realization in our laboratories and concerning the conception of the structure of the molecules of a solid body.

As the extensive investigations of Coblentz and the excellent work of V. Henri on absorption in the infrared part of the spectrum show, the vibrating constituent element in this region of electromagnetic waves is either a group of atoms having the character of a chemical radical, e.g. \(CH_3\), \(C_2H_5\), \(C_6H_5\), \(COOH\), etc., or whole molecules. The study of absorption bands in the infrared region for rock salt (\(NaCl\)) and sylvine (\(KCl\)) made it possible for Rubens and Hollnagel to discover bands characteristic of these substances and belonging, as one may think from the foregoing, to the vibrations of the molecules of these substances. The calculation from these optical observations of the specific heat of \(NaCl\) and \(KCl\) gave Nernst results excellently agreeing with the experimental values of the specific heat obtained by him; and since, when a solid body is heated, we may expect the appearance of vibrations of its molecules—consequently, of \(KCl\) and \(NaCl\) molecules—then the agreement of the results obtained from optical observations and from calorimetric experiments becomes understandable. Meanwhile, experiments with the diffraction of X-rays in crystals allowed Bragg to assert that in solid crystalline formations we are dealing not with groups of molecules, but with atoms of the elements entering into the composition of the crystals and arranged in a definite crystal lattice.

In this case the concept of the molecule is lost and the crystal consists of regular rows of atoms. Reflecting on the concepts molecule and atom, it is easy to understand that the picture given by the X-ray photograph represents only the distribution of atoms in space, representing only the geometry of the crystal. This picture lacks knowledge of the molecular forces, which, at equal distances, can give different magnitudes of attraction if the attracted atoms are different.

The concept of the molecule in this sense is a dynamic concept1. If, by heating a body, we cause a certain group of ato-

can oscillate together with chlorine and potassium, this means that the bonds of the atoms of these elements are so great that, despite the proximity of adjacent homogeneous groups of atoms, the complex of chlorine and potassium oscillates as a whole, and we must regard it as a molecule. On the other hand, the structure of the diamond molecule is very complex, but the molecular bonds as well as the interatomic bonds that unite the individual carbon atoms into one whole must be of the same order of magnitude; therefore, when diamond is heated, we observe a picture of the oscillation of individual atoms. The simultaneous study of the properties of crystals in the infrared part of the spectrum, of their melting temperatures, which according to Lindemann make it possible to find the magnitude of the oscillating mass, of X-ray photographs, and of the variation of their specific heat with temperature will undoubtedly make it possible to elucidate the fundamental questions of molecular physics and makes this field one of the most interesting branches of science.

The views just set forth have been developed by us in a series of studies that are to appear in the near future in the Proceedings of the Academy of Sciences and in the Archives des Sciences physiques; verification of all the consequences of the theory has been undertaken in a whole series of works, some already carried out at the Physics Institute of the Scientific Institute, and some planned for execution in the same institution and in the Physical Laboratory of the Academy of Sciences.

In concluding our survey, we should like to draw attention to the position occupied by molecular physics in Russia. From the time of the founding of the Academy of Sciences, a number of outstanding investigators have devoted their labors to this branch of science. It is known that the founder of the modern kinetic theory of gases, D. Bernoulli, was for a time an academician in Petrograd; later M. V. Lomonosov produced remarkable studies, which have retained their significance to the present day, on the mechanics of the gaseous state of matter; Petrov carried out brilliant investigations on the electrolysis of salts and solutions, and his work was continued by Lenz, who was the first to study dilute solutions; Parrot is credited with the discovery of the phenomena of osmosis.

Researchers of a later period also introduced much that was new and very substantial into molecular physics. One need only mention the hydrate theory of solutions of D. I. Mendeleev, his famous periodic law, and the extensive work on solutions of D. P. Konovalov and P. I. Walden, the works of G. A. Tammann, N. S. Kurnakov, V. N. Ipatiev, the investigations of E. S. Fedorov in the field of crystal physics, and, finally, the works of P. N. Lebe—

ology and Ethnography, were published by me in the middle of 1917 in the journal Priroda.

[Lebe]dev’s work on the laws governing the interaction of resonators, on dielectric constants, and his works on the pressure of light, in order to understand that the field of molecular physics has found outstanding representatives in Russian physical science; and we may wish that, hand in hand with the oldest physics laboratory in Russia—the Laboratory of the Academy of Sciences—the youngest research laboratory as well—the Physical Institute of the Scientific Institute—may proceed along the path on which the creative work of Russian investigators has already yielded brilliant results.

1. Similar views, developed by me as early as 1915–1916 in a series of reports in the Chemical Section of the Society of Lovers of Natural Science, Anthro- ↩