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The work discussed in this paper was begun in 1924 in London, and was later on resumed in Durham. It forms part of an investigation which began eight years ago, of which the purpose was to gain information from a new quarter about intermolecular action; and the first part was published in 1923 by Masson and Dolley. In that part of the work, which dealt with the compressibilities of argon, of oxygen, of ethylene, and of a number of mixtures of each pair of these gases, a systematic study was made of deviations from Dalton’s law of partial pressures. It was possible to exhibit the cohesion of the molecules of one gas with those of another gas; and to prove, without using any special theory, that this type of cohesion is neither caused nor influenced by the possibility of chemical action between the atoms composing two colliding molecules. Thus this kind of cohesion differs from that which gives rise to unimolecular films, where the cohesion is chiefly traceable to the specific action of some particular atom within one molecule upon a particular atom in another, or in a surface. The bearing of this distinction has been discussed elsewhere, and thermodynamic aspects of the first paper have been recently dealt with by other authors. Meanwhile, it becomes clear from the results of that paper that any theory, proposed to explain the van der Waal’s cohesion between molecules of two different chemical kinds, need not invoke any types of force beyond those that could explain cohesion in a single pure gas. The present paper deals experimentally and theoretically with such forces. The first stage of the present experiments (1924) with helium and hydrogen indicated a new property in gases; for the data showed a certain range of mixtures of these two as being more incompressible than either constituent; a maximum being suggested at about 30 per cent, of helium in the mixture. Incidentally, this displaced hydrogen from its position as the least compressible gas. The effects were, however, slight; and, chiefly in order to test their genuineness, we resumed the work in 1926, and improved the methods in various ways. One result has been to confirm the new property, though the effect is very small; and meanwhile, Lennard Jones has independently noticed a similar effect in the experimental data of Holborn for a mixture of neon and helium; and in his recent theoretical work on gaseous mixtures he has been able to show it as a special case of the general properties of gases. The same general treatment proves to be applicable to the work we have done, as will be shown.

The quantum theory has provided a means of calculating the interaction energies of two atoms by a perturbation method. It appears that, the short range interaction forces are due mainly to electron exchange phenomena between the two atoms, while the van der Waals forces arise from mutual polarization effects. The theory gives the first of these forces in the first approximation, while the van der Waals forces appear only in the second approximation, At large distances, where the interaction is small, it is somewhat surprising that the first approximation is not sufficient, and one is led to doubt the accuracy of the method when applied at distances at which the first and second approximations give comparable results. At these distances the mutual potential energy is comparable with the mean kinetic energy of a gas atom at ordinary temperatures, and it is therefore clear that a study of gas-kinetic collision phenomena should provide a satisfactory test of the validity of the perturbation method in this region. It is the object of this paper to carry out a number of calculations with this aim in view. In a previous paper the quantum theory of collisions was applied to gas-kinetic collisions, and it was shown that, although the classical theory can be used with accuracy to determine the law of force from viscosity and diffusion phenomena associated with heavy gases, it cannot he applied with safety to hydrogen and helium. The method to he used in such cases was given, and it was also shown that the existence of a definite total collision area—a feature of the quantum theory of scattering by a centre of force, the potential of which falls of more rapidly than r -2 at large distances—provides a further means of determining the law of force. As this collision area can now be directly measured with accuracy by molecular ray experiments, the range of applicability of tins method is considerably greater than that of methods based on transport phenomena.

1. In a recent note I have called attention to the degree of correspondence between W. L. Bragg’s estimates (based on X-ray crystal measurements) of the dimensions of certain atoms, and those deduced by means of the kinetic theory of gases from determinations of viscosity. I was not then fully aware of the modern work of Chapman‡ in relation to the latter subject, and made calculations by means of a formula which has been definitely superseded. The result was that the comparison gave only qualitative agreement. A closer examination of the data, in the light of Chapman’s results, together with a new aspect of the matter which forms the main subject of the present paper, reveals certain interesting facts regarding the probable arrangement of atoms in molecules, and, in addition, leads to substantial quantitative agreement with Bragg’s values. 2. From the very close agreement between the values of the atomic radius calculated by means of Chapman’s formula, and from van der Waal’s law, there appears now to be no room for doubt that, in the case of monatomic gases, at any rate, the atoms, when in thermal agitation, behave like hard spheres which exert mutual attraction on one another. It is also evident that the absolute diameters of these spheres are now known with considerable accuracy, sufficient to justify quoting to three significant figures. They are given for four monatomic gases in column 3 of Table I for comparison with Bragg’s values, which appear in column 2. They differ to a slight extent from those calculated by Chapman himself, owing to the adoption in the present calculation of Millikan’s|| recent value 2.705 x 10 19 for the number of molecules per cubic centimetre at N. T. P. This differs by about 2 per cent, from that used by Chapman, and the substitution results in an increase of about 1 per cent, in the estimated atomic diameter.

In a previous paper the author suggested that there are three hardening phenomena in Duralumin alloys, namely: (1) Primary hardening (Natural age-hardening) (2) Secondary hardening (Natural age-hardening after “Ruckbildung”) (3) Temper-hardening (Artificial age-hardening) The primary hardening may be explained by the theory of congregation (or aggregation) of solute atoms at certain selected positions on the Aluminium lattice, and the sudden reduction of the hardness on short period tempering at somewhat higher temperatures (“Ruckbildung”, “Retrogression, ” “Intermediate softening” or “De-hardening”) may be attributed to the dispersion of the aggregated solute atoms into solid solution, and the subsequent recovery of hardness at room temperature (The secondary hardening) may be attributed to reaggregation of solute atoms by the quite same process as that occurring in primary hardening. The temper hardening takes place on the basis of precipitation of so-called “intermediate” phase or of compounds, but the maximum hardness generally is attained prior to the appearance of lamellar structure under the microscope. According to the latest investigations by Preston, the formation of Cu-rich thin platelike aggregates are presumed when the Cu-Al alloy is aged at room temperature and there are diminution of aggregates when “Ruckbildung” takes place by short period tempering at 200°, but if the tempering is continued for several hours, the thin platelike aggregates are formed again, The linear dimensions of thin platelike aggregates which were formed at room temperature are far more smaller than that of aggregates which were formed at 200°. (about 40 A for the former, and about 4000 A for the latter). In the present paper the author has made a characteristic differentiation between the natural age hardening and the temper-hardening by the experimental evidence, and deduced the theory of aging. In the above mentioned explanations there are not any differences in the opinions of the present author and that of other authors to presume the formations of thin platelike aggregates which are vary in dimensions at different temperatures (the one formed at room temperature and has smaller dimensions, the other formed at higher temperature and has larger dimension). But the presentt author suggests the opinion that there are differences not only in the dimensions of the two kinds of aggregates, but also in their coaguration of atoms in the thin platelike regions of these respective cases. As the coaguration of solute atoms in the thin platelike region which was formed by natural ageing is far more weaker, so the sudden dispersion of the atoms would be expected by short period tempering, and this phenomenon corresponds to the “Ruckbildung” The thin Plate which was formed by tempering is also an aggregate of solute-atoms, but it requires an activation energy to bring about aggregation, and the “state of aggregation” is much stable than that of the former In the above explanation, the author deduced the theory of aging by applying somewhat same idea of adsorption theory, because the movements of solute in the, solid solution (i.e. the congregation and the dispersion etc.) are analogous to the case of adsorption. The relationship between the two forms of aggregations is similar to that of two forms of adsorption, namely; the van der Waals adsorption (the weaker state of adsorption) and the activated adsorption (the stronger state of adsorption). The van der Waals adsorption takes place at low temperature and removed more or less completely at somewhat higher temperatures. The activated adsorption recommences at still higher temperatures, but in a different form, as the stronger state of adsorption

The molecular exciton model has received its most extensive development and application in the field of molecular crystals1'2. More recently, numerous applications to non-crystalline molecular composite systems have been made, including van der Waals and hydrogen-bonded dimers, trimers, and higher order aggregates. Another type of composite system has also been investigated, namely the composite molecule consisting of covalently bonded molecular units, with intrinsic individual unsaturated electronic systems so isolated by single bonds that but little or insignificant electronic overlap between units may occur. It is now well established that in molecular aggregates and in composite molecules, exciton effects may be observed if sufficiently strong electronic transitions exist in the component sub-units. The result of exciton splitting of excited states in the composite molecule may be the appearance of strong spectral shifts or splittings (which may be of the order of 2000 cm—1) of the absorption bands for the component molecules. At the same time, as a consequence of the exciton splitting of the excited state manifold, an enhancement of triplet state excitation may result. The purpose of this paper is to present a summary of the various type cases for molecular dimers, trimers and double and triple molecules in the description of the molecular exciton strong-coupling model. Then it will be shown by new experimental examples that, even in those cases where no significant exciton effect is observable in the singlet—singlet absorption spectrum for the composite molecule (intermediate and weak coupling cases), the enhancement of lowest triplet state excitation may still be conspicuous and significant. The ideas which are summarized in this paper have a curious history. Long ago, Kautsky and Merkel3 demonstrated experimentally that aggregation of dyes facilitated their action as photophysical sensitizers in photochemical reactions, at the same time diminishing their fluorescence efficiency. Kautsky attributed these easily demonstrated effects to enhancement of metastable state excitation in the aggregate dye. There is no doubt today that the metastable state he described is the lowest triplet state of the molecules studied. However, he did not distinguish between intrinsic and enhanced metastable (triplet) state excitation, so his interpretations were largely overlooked. Forster in l946 used the quasi-classical vector model to

The object of the first paper on "Critical Phenomena in Gases" (referred to in this paper as Paper I) was to develop a simple method of dealing with dense gases and to calculate critical temperatures in terms of atomic fields of force. Each atom in a dense gas was pictured as caged for most of its time by a cluster of neighbours, equal in number to those which surround it in the solid (and presumably also in the liquid) phase. The model was intended to provide a general average of the potential field in which any one atom moved by replacing its varying environment by an arrangement of neighbours which could be regarded as typical. This arrangement was taken to be the one in which the neighbours were situated at their mean positions as determined by the density of the gas. The potential energy of any one atom could thus be expressed as a function of the volume of the gas-a step which is probably the crucial one in a theory of critical phenomena. This point of view brings the process of condensation within the category of those described by Fowler (1936) as co-operative phenomena. In passing we may observe that the derivation of van der Waals' equation provides a particular example of this method, for in it the potential energy of each atom is assumed to be inversely proportional to the volume. The present theory goes beyond this simple model, for the potential energy of an atom is considered to be not only a function of volume but also a function of the position of the atom relative to its neighbours. The probability of finding an atom in any assigned position can be calculated by statistical means and its average potential energy and its available free volume easily deduced. The equation of state can then be deduced by thermodynamic methods, as has been pointed out elsewhere (Lennard-Jones 1937). The success of this method in calculating critical temperatures has encouraged an attempt to push the theory a stage further so as to give the boiling points of gases. At the boiling-point the conditions in the gas are very different from those at the critical point. The density is much less and

It is the purpose of this and the following paper to consider the type of broadening of a spectral line, produced by approaches of other atoms to the radiating atom, which we shall call throughout “transits". The aspect with which we are particularly concerned is the transits of single atoms producing the wing of the broadened line. The intensity distribution in spectra of this type, which are intermediate between ordinary pressure broadening and continuous molecular spectra, can be interpreted in a simple way, yielding results on the van der Waals forces. The first paper gives an account of intensity measurements in the single transit region of the mercury line 2537 A. broadened by the admixture of argon.

J. E. Mayer (1937) has published, together with some collaborators, several papers under the same title as the present one. We consider these papers as a most important contribution to statistical mechanics, and this opinion was shared by the International Conference held in Amsterdam, 26 November 1937, in commemoration of Van der Waals’ birth. One of the present authors gave to this meeting a report on Mayer’s work (published in Physica, 1937) which was followed by a vigorous dis­cussion on the question as to whether Mayer’s explanation of the pheno­mena of condensation is correct. Doubts about this point were raised by the referee, because it is difficult to comprehend how a method of approxi­mation such as that of Mayer, starting from the gaseous state, can lead to the discontinuity of the density on an isothermal curve which corresponds to condensation. The usual methods for treating the equilibrium of two phases introduce the equation of state of both phases and derive the con­dition for their co-existence. Mayer’s theory does nothing of this kind, but treats all possible molecular arrangements with their proper weight, as if there were only one phase. How can the gas molecules “know” when they have to coagulate to form a liquid or solid? Mayer’s mathematical method is too involved to make this point quite clear.

A simple model of the low temperature phases of the diatomic molecular solids is examined. The model consists of molecules, interacting via a Lennard-Jones atom-atom potential and quadrupole-quadrupole interactions. The internal energy of any crystallographic structure (excluding thermal effects) can then be given in terms of two dimensionless parameters, which describe the deviation of the molecular shape from a sphere and the relative importance of the quadrupole energy. The minimum energies and optimum molecular configurations in several structures are computed, for values of these dimensionless variables which span the values appropriate to the actual homonuclear diatomic molecular solids, H2, N2, O2, F2, Cl2, Br2and I2. Despite its great simplicity, the model is able to explain several features of these structures. These are (i)o-H2and N2have the optimum quadrupole structure, Pa3; (ii) β-O2is one of the optimum van der Waals’ structures, R3¯m; (iii) the monoclinic α-F2structure is the most stable structure for parameter values very close to those appropriate to F2; (iv) the ortho-rhombic Cmca structure (observed for Cl2, Br2and I2) is the most stable structure for a large range of quadrupole moments which may be appropriate to these molecules. The model, is, of course, unable to take into account intermolecular bonding or spin-dependent interatomic forces. The former is important for the halogens and the latter for the (magnetic) oxygen molecule. The case of α-O2is treated in the following paper.

An examination has been made of the hypothesis that the rate of the para-hydrogen conversion on tungsten is determined by the rate of condensation of hydrogen molecules into an almost full monolayer of chemisorbed atoms. Using the Peierls equation, and employing parameters consistent with the adsorption isotherm and heat data (in particular an interatomic repulsion energy of NV=4800 cal/mole), it is shown that the calculated values of absolute rate, activation energy, and pressure dependency are in disagreement with those observed experimentally. This paper is concerned with one of the postulated mechanisms by which parahydrogen conversion and surface deuterium exchange may occur on aclean tungsten surface. The arguments may also have relevance for other transition metals. At temperatures below 0? C and in the presence of low pressures of hydrogen, e.g. up to 1 mmHg, the surface of tungsten is largely covered by chemisorbed hydrogen (Roberts 1935). The conversion mechanisms that have been suggested are: (1) p-H + HW - WH +o-H2. This involves an exchange of atoms between a molecule in the van der Waals layer or on a gap in the chemisorbed layer, with a chemisorbed hydrogen atom, and was supported by the result of low pressure deuterium exchange experiments (Eley & Rideal 1940; Eley 1941).

The following work was undertaken with a view to obtaining data for the tentative application of Van der Waals’ equation to concentrated solutions. It is evidently probable that if the ordinary gas equation be applicable to dilute solutions, then that of Van der Waals’, or one of an analogous form, should apply to concentrated solutions—that is, to solutions having large osmotic pressures. Saturated solutions were taken for investigation because they presumably have the greatest osmotic pressures, and also because there is reason to believe that, in concentrated solutions at a given temperature, the greater the concentration the less the relative dissociation. For the purpose in view, measurements of volume, pressure and temperature are required.

This paper aims at a simple treatment of van der Waals dispersion forces by applying classical electrostatics of two basic quantum-mechanical equations. Expressions are derived for the forces between macroscopic bodies, and the effects of adsorbed surface layers is considered both quantitatively and qualitatively. Approximate expressions are given for non-retarded dispersion forces in terms of the refractive indices and absorption frequencies of the materials. The results should prove particularly useful in calculating the van der Waals forces in colloidal and biological systems.

The principle of corresponding states is a sound but limited principle from which to predict the thermodynamic properties of pure fluids. We describe formal extensions of the principle to cover wide classes of fluids and their mixtures. These extensions are made in a general form, from which most previous schemes can be obtained as special cases. One of these, which we call van der Waals's approximation, is discussed in detail both for the usual one-fluid model of a mixture, and for a new two-fluid model. Application of these methods, and the testing of the two-fluid model, are to be made in later papers.

where c is the concentration of ortho-hydrogen molecules, T the absolute temperature, and R the gas constant. It is an aim of this paper to inquire into the origin of these two terms. Through calculations by the method of moment expansion, the magnitude of fJ can be explained from the quadrupolar interactions among ortho-molecules, while the anisotropic nature of the valence and van der Waals forces is shown to be effective only as corrective terms. On the other hand, the appearance of a shows that the molecular rotation of an ortho-molecule surrounded by para-molecules should also be quenched. A possible mechanism of this phenomenon may be the rotation-vibration coupling, for which the valence and van der Waals forces should be exclusively responsible. However, we are not yet able to get a complete understanding of this quenching process. Deviation from the above formula, i. e. the linear dependence on c of the the quantity CvT2fR at temperatures not high enough is also derived and compared with experiment. Further, a more exact treatment than the moment expansion method is given for the case of low ortho-concentrations and is applied to the case of 7% ortho.

We examine the limiting free energy density $$a(\varrho ,0 + ) \equiv \mathop {\lim }\limits_{\gamma \to 0} a(\varrho ,\gamma )$$ of a classical system of particles with the two-body potentialq(r)+γ v K (γr), at density ϱ inv dimensions. Starting from a variational formula fora(ϱ, 0 + ), obtained in Part I of these papers, we obtain a new upper bound ona(ϱ, 0 + ) given by $$a(\varrho ,0 + ) \mathbin{\lower.3ex\hbox{$\buildrel

The partial molal volumes of urea, N-monomethylurea, N, N-dimethylurea and N, N′-dimethylurea at infinite dilution were determined from density measurements at ten-degree intervals from 15°C at 45°C. The partial molal expansibility (at infinite dilution) _??_° was calculated from the partial molal volume data at various temperatures. The _??_° value of urea was high compared with N-alkylureas, and that of N-alkylureas decreased with increasing the number of the methyl groups in the molecule. The _??_° value of N-alkylureas increased by raising the temperature, but that of urea showed no temperature dependency over the range of temperature used in this paper. The low _??_° values of N-alkylureas were attributed to the ability of the methyl group to form an icelike species in solution. The thermal expansion of the structured species in water is low, like that of ice. The positive temperature dependency of _??_° of N-alkylureas would be expected, if the extent of the structurally perturbed layer of water molecules decreased with an increase in temperature. The high _??_° value of urea was interpreted as being due to the structure-breaking ability of urea. The thermal expansion of the destructured species in water is higher than that of the structured species. The packing densities, defined as the ratio of van der Waals volume to the partial molal volume of a solute species, of urea and N-alkylureas have been calculated and discussed.

In this paper the Author has shown that by use of a special variable exact expressions may be found with van der Waals' characteristic for the specific heats s, s' of saturated liquid and vapour and for all other magnitudes connected with the state of saturation; and it is deduced that, if k denotes the isometric specific heat, which is constant or a function of the temperature only, (i) s - k is always positive, increasing from R to infinity as the reduced temperature τ rises from 0 to 1; (ii) k - s' is always positive, having a minimum value 4.96 R when τ = 0.72 and being infinity when τ is either 0 or 1; (iii) inversion in the sign of s' can thus occur when k/R > 4.96 or κ = 1 + R/k 11.36 or κ < 1.081, or, on the above assumption, if there are at least eleven atoms in the molecule; (iv) the latent heat of vaporization increases continuously from 0 to infinity as τ falls from 1 to 0; (v) the work of vaporization has a maximum value 0.69 RT when τ = 0.77. The contrast between these results is especially marked for s - k and the latent heat; it subsists further in the neighbourhood of the critical point where dδ/dτ is 4 (v. d. W.) and 7 (Cl.), λ/RT √(1-τ) is 6 (v. d. W.) and 14.8 (Cl), (s-k) √(1 - τ)/R is 1.5 (v. d. W.) and 7.4 (Cl.).

This paper describes recent studies of the forces between surfaces for separations of the order of tens to hundreds of angstroms. The first part deals with the direct measurement of forces between molecularly smooth mica sheets and shows that normal van der Waals' forces operate for separations less than 100 A, retarded van der Waals' forces for separations greater than 200 A. The second part describes a direct study of the repulsive forces exerted by charged double layers residing on solid surfaces. By using the contact between a soft optically smooth rubber hemisphere and a flat glass surface repulsive forces of the order of 10 5 dyne/cm −2 have been measured for film thicknesses of about 150 A. The equilibrium film thickness decreases with increasing ion concentration and the results are in broad agreement with measurements by Mysels and others on black soap films.

In a recent communication to the Royal Society by Mr. Hartley and myself, the results are given of some measurements of the osmotic pressures of strong aqueous solutions of cane sugar, dextrose, galactose, and mannite. It may be of interest to inquire how far these results can be represented by an equation on the plan of that introduced by Van der Waals to express the relation between the pressures, volumes, and temperatures of gases and vapours.

It is known that in addition to the van der Waals force the hydrophobic bond plays an important role in the aggregation of basic dye.In this paper the effect of electrolytes on the dye aggregation is treated spectrophotometrically to investigate in more detail the role of hydrophobic bond in the aggregation of C. I. Basic Blue 9 and C. I. Basic Violet 10. Thermodynamic consideration indicated that the aggregation is mainly enthalpic for the former dye and is mainly entropic for the latter. Thus it is assumed that the hydrophobic bond is more responsible for the aggregation of C. I. Basic Violet 10. Following results were obtained on the aggregation of these dyes in presence of electrolytes.These dyes in presence of electrolytes.1) The effect of electrolytes on the aggregation of C. I. Basic Violet 10 increases in the order: The effect of these anions is greater than that of the cations.2) The aggregation of C. I. Basic Violet 10 in presence of the electrolyte decreases with rise in temperature.3) The amount of the dimer of C. I. Basic Violet 10, assumed to aggregate mainly by the hydrophobic bond, increases in presence of the electrolyte.The aggregation is explained by two factors; one is the electrostatic neutralization of the charge of the dye cation by the ionic atmosphere and the other is the decrease in the hydration of the polar groups in the dye by the hydration of electrolyte ions. Since there is no change in the spectrum, the ion pair is not formed even when the amount of the counter ion is increased. This indicates that the hydrophobic bond causes the aggregation in presence of the electrolyte.On the contraly, C. I. Basic Blue 9, assumed to aggregate mainly by van der Waals force, forms dimer and higher aggregates in presence of electrolytes, and the ion pair is formed at higher concentration of electrolyte. In short, spectral change of the dye indicates that dimerization takes place in dilute solution of electrolyte, as in the case of C. I. Basic Violet 10, and that the higher aggregates are formed and the interaction occures between the dye ion and the counter ion in concentrated solution.

In a communication* to the Royal Society by one of us it was stated that an attempt would be made to determine directly the osmotic pressures of strong solutions. The purpose for which these determinations were required was to obtain data for the tentative application of VAN DER WAALS’ equation of state to solutions, but we propose, in this communication, to restrict ourselves to the actual results obtained, reserving for a future occasion the theory of the subject. Some time ago, in the proceedings of the Royal Society,! we gave an account of some preliminary experiments. We there described the method and apparatus we used, and at the same time stated that we hoped to get more accurate results by modifying the apparatus. This hope has been fulfilled, and we trust that a somewhat full description of the methods used both in the actual determinations and in the preparation of the membranes will, therefore, not be out of place.

Measurements of the quenching rate of orthopositronium in helium determine the parameter 1Zeff, the effective number of electrons per atom in a singlet state relative to the positron. This number may be calculated from the wave function for the orthopositronium-helium atom system. In this paper, this wave function is computed in the static-exchange approximation and in an approximation that allows for the long-range van der Waal's forces acting between the neutral atoms; the calculated values of 1Zeff at thermal energies are 1Zeff = 0.037 and 1Zeff = 0.048 respectively. These results are considerably smaller than the most recent measured values 1Zeff = 0.1-0.25 and the possible reasons for the discrepancy are discussed.

von Stackelberg & Muller (1951) and Muller & von Stackelberg (1952) have shown that two structural types of water lattice exist in which various species are intercalated to give solid hydrates. In the present paper a statistical thermodynamic interpretation is given of the properties of these clathrate phases of water. This method is a development of a procedure applied by van der Waals (1956) to clathrate compounds of quinol, and shows that these hydrates should be non-stoicheiometric. It is possible to give a satisfactory explanation of the stabilizing action of ‘hilfsgase’ (von Stackelberg & Meinhold 1954); to interpret various thermochemical quantities and indicate limitations in some of these quantities as previously determined; and to clarify the conditions under which the clathrate phases form. Calculations of heats of intercalation for several inert gases give values close to those derived from thermochemical data. Calculations of equilibrium constants for intercalation of these inert gases lead to reasonable estimates of dissociation pressures of the corresponding clathrates. On the basis of the dissociation pressures the fractionation of mixtures to be expected by formation of clathrate phases may be estimated.

The apparent stability and freedom from settling shown in practice by many colloidal suspensions has in recent years prompted renewed study of the distribution of the particles of colloidal systems under the influence of gravity, and results greatly at variance with earlier work have been obtained. The object of the present communication is (1) to show that the later conclusions are not justified by the experiments on which they are based, and (2) to describe experiments which favour a considerable extension of the applicability to colloidal solutions of a law similar to that which defines the behaviour of ordinary dilute solutions. Perrin, in 1909, showed that there was, within a depth of 0·01 cm. from the surface, a logarithmic decrease of concentration with height for suspensions of gamboge or mastic in gravitational equilibrium. In 1914 Costantin, working at lower depths than Perrin, and with a higher volume concentration of gamboge and correspondingly higher numerical concentration, obtained evidence of a repelling force between the particles at concentrations greater than 8 X 10 10 particles per cubic centimetre. Perrin showed how his equation could be modified to take this into account by assuming a law of the van der Waals’ type, which was found to agree with the observations up to the highest concentration investigated (6 X 10 11 particles per cubic centimetre). In the following year Westgren published the results of a series of measurements on selenium and gold sols with coarse particles, which were in complete harmony with Perrin’s law over a distance of 0·05 cm. and at concentrations up to 5 X 10 10 per cubic centimetre. These investigators were precluded from studying the distribution over greater ranges of depth solely by the restrictions of their experimental method, which demanded that for accurate counting the number of particles in the field of view should not be too large. For this reason also they were limited to moderately dilute sols and to rather large particles, that is, to specially prepared sols.

Broadly speaking, three types of crystal structure may be recognised: ( a ) interpenetrating arrangements of atomic and electric lattices, the electrons being symmetrically disposed with reference to the atoms; ( b ) neutral lattices, of which sulphur and phosphorus among the elements are examples; ( c ) ionic lattices, to which class most salts belong, in which the electrons are unsymmetrically arranged so as to be in close relationship with particular atoms. Sir J. J. Thomson pointed out that by a decrease of the closeness of this association between atoms and the linkage electrons, this type merges into the first. Franck similarly distinguishes between three kinds of linkage: (i) where the electrons remain in unchanged quantum orbits, i. e . homopolar linkage due to van der Waal’s forces owing to mutual polarisation of the atoms; (ii) where the linkage electrons occupy new quantum orbits which may be binuclear, i. e ., homopolar linkage such as occurs in molecules of many gases; and (iii) true heteropolar linking where electrons have been bodily transferred from one atom to the other, and occupy new quantum orbits around a single nucleus. Linkages of type (i) clearly produce crystal lattices of class ( a ), usually possessing electric conductivity, while those of class (ii) are concerned in the formation of insulators having neutral lattices of type ( b ). True homopolar linkage should give no active frequencies of vibration, or, if any exist, they should be, according to Schaefer, of extremely weak resonant amplitude, and should lie in the region where the wave-length of the radiation is comparable to the atomic spacing. Nernst suggests that all crystals are built up by homopolar linkages, but this would appear to be contrary to experience, crystals generally showing sharply defined absorption maxima in the infra-red. Kossel is quoted by Bragg as supposing the CO 3 group in carbonates to be held together by heteropolar attraction between the ionised atoms of the group. De, however, considers the binding to be homopolar, while Bragg and Chapman, Chapman, Topping and Morral, Chapman and Ludlam, Kornfeld, and Lennard-Jones all agree in supposing the group to consist of ions having effective charges modified by deformation of the electronic shells. Fajans and Joos, on the other hand, state that, contrary to Kossel’s assumption, there seems to be little reason for supposing the internal binding of the CO 3 ion to be by heteropolar linkages, they themselves being inclined to think that the setting up of an induced electric moment in the oxygen atoms, by reason of the deformability, provides a sufficient explanation of the stability of the group.

A work entitled “Le Point Critique des Corps Purs” has recently been published by E. Mathias, whose opinion on matters relating to the critical state must always carry weight. In this he discusses at length the various theories which have been put forward to explain certain irregularities observed in the behaviour of substances, which were supposed to be pure, at their critical temperatures. These irregularities are not accounted for by the simpler theories of Andrews and Van der Waals. He calls attention to the experiments of certain investigators, which appear to suggest that the currently-accepted values of the critical constants of many common substances may be vitiated, either owing to the time allowed for the establishment of equilibrium between the coexisting phases near the critical point being insufficient, or the temperature at which the dividing surface vanishes not being independent of the relative masses of the two phases at the temperature at which this takes place. According to I. Traube, substances contain different kinds of aggregates, which he calls “gasogenic” and “liquidogenic” molecules. It follows that if equilibrium demands that there shall be a certain concentration of these molecules in the vapour and liquid phases respectively, then unless dissociation and association take place instantaneously, there must elapse a time, following any change of condition, before equilibrium can be established between the two phases.

Interaction forces at very small distances have mainly been investigated by extrapolation from larger distances, and by wetting and contact angle studies. The main result is a satisfactory understanding of the contribution of Van der Waals forces. Other types of forces, in particular those that may arise at distances of atomic dimensions, are not understood. The paper attempts to investigate the “other” forces by combining evidence from contact angle studies with results of direct measurements of the force of adhesion between a small, spherical particle and a flat substrate.

The mechanical strength of unsaturated soil in the water system depends on its capillary attraction force, while its adhesive force is said to be almost equal to the force of chemical potential in its capillary attraction. According to the centrifugal method, the chemical potential of water in soil is calculated by setting the sample subject to centrifugal force. This paper concerns the relation between the strength of cohesive clay and its interstitial force.The change in volume of a sample is found to be equal to that of water drainage by centrifuging. Therefore almost no capillary attraction is observable in centrifuged cohesive sample. The yield strength of the sample qθ, which is drained by the centrifugal force, is recognized to relate to the chemical potential of water Δμ in the sample which is given in the following equation.Δμ=K·qθwhere K is a fluctuation coefficient, ranging from 1 to 8.Consequently, it is suggested that the cohesive strength of clay does not depend exclusively on capillary potential, but on various other potentials including electric potential and van der Waals potential. The total potential of water in soil may be balanced with centrifugal force in process of irreversible drainage of water, and the yield strength of clay would be built by the total potential.

It was prevlously reported by us2), 3), 4) thatα-CH…X-Dye type hydrogen bonding made an important contribution to the interaction between disperse dyes and ester type fibres.In oraer to obtain other suggestions, the interaction between alcohols and disperse dyes is discussed in this paper, using paperchromatography, and noted with the results as follows:1) In similar manner to esters and amines, there exists the correlation between Rf value and alcohol concentration [A].Change of free energy (-ΔF) of interaction may be calculated from the estimated K.2) There is a certain correlation between (-ΔF) and carbon number (C) of alcohol, when the data are plotted on the ordinate and abscisa, respectively, therefor (-ΔF)=α•C+b ………(1)where a; apositive constant and b; a constant.3) The slope a of (1) is related to the molecular weight of dye (Dw) by the equation a=A•Dw+B ………(2)where A; a positive constant and B; a constant.4) The results 2) and 3) can not be explained by proton donating or accepting mechanism alone and suggest that an important contribution can be ascribed to van der Waals force as the interaction force between alcohol and dyes.But, this does not contradict the co-existence of other forces.5) Hence, it is supposed that van der Waals force makes a good part of contribution to disperse dyeing, too.

We have used the quantum theory of radiation, within the time-dependent Hartree approximation, to study exciton states of a van der Waals molecular crystal. The radiation variables are eliminated to give a semi-classical picture of molecular dipoles interacting through a retarded potential, and the solutions of the Hartree equations are closely connected with the quasi-particle excited states in Agranovich’s theory. In the Lorentz-Lorenz approximation the crystal has excited states which correspond to both longitudinal and transverse exciton weaves, and the refractive index behaves classically. The paper concludes with a brief discussion of metallic reflexion by dye crystals.

It is one of the most fundamental problems not only in the enzymological but also in the pharmacological researches to consider quantum-chemically the interaction between an enzyme and its inhibitor on the molecular basis. The author has recently extensively studied on the relation between electronic structure of phenylacetate derivatives and their rates to be hydrolyzed by the cholinesterase (1); though this paper deals partially with those results, it is confined at present to the problem on the relationship between the electronic structure and inhibiting force of cholinesterase inhibitors. A competitive inhibition seems to be of a simpler reaction type and such a secondary effect as the molecular deformation to be derived from the drug absorption may be also easily excluded, so it would be the most favorable object for the present experimentation. Wilson et al. (2) showed the development of competitive inhibition between cholinesterase and various phenyltrimethylammonium derivatives assuming it as derived from the hydrogen-bonding of the esteratic site of cholinesterase to phenylhydroxyl group of those derivatives, and they also emphasized that in order to determine the inhibiting force in those reaction systems the spacial arrangement of molecules or molecular complimentariness was more important factor than the chemical change thereby exerted. They added, however, that the significance of chemical change as a cause of the inhibiting force could not be entirely avoided, and they attributed the weakness in the inhibiting force of 2-hydroxybenzyl.trime thylammoniurn bromide (compound No. 8 in Table 1) to the larger value of pKa than that of 3 hydroxypheny.ltrimethylammonium salts, all of which, however, were the same in spacial distance from the quaternary ammonium radical to the hydroxyl group and from the esteratic site to the anionic site of cholinesterase. But if it might be true, there is a discrepancy for the fact that the pKa value of the compound No. 8 is 8.7 which is weaker in the inhibiting force than the compound No. 5, that is 6-methoxy-3-hydroxyphenyltriniethylammonium chloride, the pKa value (8.6) of the latter being, however, almost as large as that of the compound No. 8. Thus, it is clear that there is at least no intimate connection between the pKa value and inhibiting force in the case of 3-hydroxyphenylmethylammonium derivatives. According to Wilson et al. (2) the fact that 2.9 kcal of free energy change resulted from the KI ratio of the compound No. 1 vs. the compound No. 6 was just coincided to what was brought about by the hydrogen-bonding in this reaction appeared to give some support to their hydrogen-bonding hypothesis. But neither this energy change would necessarily brought about by the hydrogen-bonding nor this phenomenon would be characteristic of the hydrogen-bonding. In the author's opinion there should be three possibilities to be taken into consideration in order to interpret this phenomenon quantum-chemically which are as follows : (i) There would be the formation of charge transfer complex or some substitution reaction, instead of the hydrogen-bonding. (ii) There would be surely the hydrogen-bonding, the pKa value being, however, no appropriate decisive index. (iii) Apart from the hydrogen-bonding, there would be some other forces, e.g., van der Waals', contributable to the reaction.