The tight-binding approximation is applied to a study of electronic energy bands in metal borides MeB₆. The 25×25 determinantal secular equation for the energy is reduced by a group-theoretical treatment of the spatial symmetry at certain special values of the wave vector K. The results are that if metal atoms have two valence electrons the valence bands are all filled and the conduction bands are all empty, and in the case of calcium boride CaB₆ the narrowest gap between valence-and conduction-bands is at edges of the first Brillouin zone, the simple cube in the reciprocal space and its width is about 1.5 eV, in good agreement with empirical results that there exist only borides of elements having two valence s electrons in this type of structure.

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The period of out-of-step of ordered alloys with anti-phase domain structure, measured in atomic distance, is generally not an integer, in spite of sharp splits of superlattice reflections. This fractional property of the period has theoretically been examined. The general treatment of this problem has shown that a regular and uniform arrangement of the different periods of anti-phase domains can explain the fractional value of the period, M. The results of numerical calculations in some models of arrangement have suggested, however, that complete regularity in arrangement is not always necessary but only uniformity is essential for the interpretation of the diffraction patterns.

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The simultaneous reflexion by two lattice planes (with indices h and h′) in electron diffraction has been treated by the dynamical theory in order to investigate how it is influenced by the phases of structure amplitudes. For convenience of treatment, a modified formulation of the theory has been developed using particular cross sections of the dispersion surface in reciprocal space. Applying the theory to a lamellar crystal, it was proved that the intensities of transmitted and diffracted waves depend in a relatively simple way on the value of |Φ_hh′|=|\varphi_h−\varphi_h′+\varphi_h′−h|, where \varphi_h, \varphi_h′, and \varphi_h′−h are the phase angles of structure amplitudes for the indices h, h′, and h′−h. It was shown that the phase effect can be most easily demonstrated by observing fine structures of reflexion spectra which are obtained by rotating the crystal in a specified manner. The determination of the value of |Φ_hh′| is most simple when the coupling reflexion h′−h is strong compared with the reflexions h and h′, and the crystal is centrosymmetric.

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The effect of the phases of structure amplitudes appearing in the simultaneous reflexion in electron diffraction as predicted by the dynamical theory has been examined experimentally in convergent-beam electron-diffraction patterns of graphite. Anomalous structures of Kossel-Möllenstedt lines at their cross points have been satisfactorily explained by the theory. Thus, it has been proved that the experimental determination of the phases of structure amplitudes is feasible by the observation of simultaneous reflexion. The phase effects have been found also at the intersecting points of Kikuchi lines.

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The intermolecular potential between spherical polyatomic molecules is calculated, assuming the Lennard-Jones potential between atoms of polyatomic molecules. Owing to the distribution of atoms in polyatomic molecules the degree of infinit of potential is lowered when two polyatomic molecules approach each other. In the case of uniform distribution of atoms in polyatomic molecules, the degree is lowered by 5 orders and the minimum value of the potential is proportional to the radius of polyatomic molecule and to the square of the density of the atoms. At large intermolecular distance, the result of calculation of this case coincides with the results of Atoji and Lipscomb and of Hamaker. Calculation for a parabolic distribution of atoms is also given. The temperature and molecular weight dependence of the second virial coefficient of high polymer solutions are explained by the aid of calculated potential function.

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The microware spectrum of the hyperfine components of the J=1←0 and J=2←1 rotational transitions of ICN molecule has been measured and the dependence of quadrupole coupling constant on the vibrational state was found. The values of (eqQ)_I for each vibrational state are as follows:
(Remark: Graphics omitted.)
The difference in the (eqQ)_I value for the (0, 2, 0) state from that for the (0, 0, 0) state, previously explained by Javan for the (0, 1, 0) state, was confirmed, thuogh the numerical values are slightly different from his. The change of (eqQ)_I due to the excitation of the stretching vibration was also found and was explained in terms of the change of the double bond character of I–C bond.

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The microwave spectrum of vinylindene chloride has been observed and analyzed. The molecular parameters have been determined to be d_CCl=1.727A and ∠Cl C C=123°10′ on the assumption of d_CC=1.32A, d_CH=1.07A and ∠H C C=120°. The quadrupole coupling constant along the bond direction has been found to be −78.7 Mc together with the asymmetry parameter η=0.12, for Cl³⁵. The five percent double bond character of C Cl bond estimated from the quadrupole data is consistent with the value of six percent estimated from the bond length.

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Using a regenerative spectrometer the line widths of the two bromine isotopes in NaBrO₃ were measured at melting ice and liquid oxygen temperatures. The full width at half-maximum intensity of Br⁷⁹ is 3.85±0.1 kc and that of Br⁸¹ is 4.09±1 kc. No observable dependence of the line width on temperature was found. From the ratio of the line widths it is concluded that the main cause of the line width in NaBrO₃ is the magnetic dipole interaction, and the contribution from the relaxation is of the order of 0.1 kc.

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The flux I₀ reflected at specular angles 45°–45° from the surface of glossy paper and the assumed value of its diffuse component I₂ defined experimentally are measured with a goniophotometer. The ratio of I₀ to I₂ is taken as a measure of gloss, and denoted by G_NF according to an earlier paper of E. Fukushima.
For a series of machine glazed papers differing considerably in colour, the values of C_NF are compared with the visual gradings of 36 Japanese observers, and a linear correlation of the logarithm of G_NF with the visual gloss is found with a correlation coefficient +0.986 except for two papers. The method of determining the value of I₂ is also introduced and the voting distributions of the observers for the gloss of the papers are discussed.

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In this paper two-dimensional compressible flow past an arbitrary aerofoil in unlimited fluid or past a straight lattice of aerofoils is considered on the basis of the M²-expansion method, which consists in expanding various quantities in powers of M², M being the Mach number.
The general expressions for the velocity components at any point in the field of flow are obtained, which are correct to M⁴ for an isolated aerofoil and to M² for a wing lattice respectively. In particular, the formulae giving the velocity distribution on the surface of the aerofoil are of such a simple form that the numerical calculation for any arbitrary aerofoil or lattice of aerofoils is no longer a prohibitive work as generally believed.
As an interesting special case, the flow past a symmetrical aerofoil placed symmetrically in a channel is also considered, which was previously dealt with by Goldstein and Lighthill by means of a different method.

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Exact solutions of the Navier-Stokes equations are obtained for the boundary layer growth on an infinite flat plate with uniform suction or injection (with velocity V normal to its plane) which is started at time t=0 (with velocity U along its plane), for the two cases: i) U=arbitrary, V=const and ii) U∞t^α, V∞t^−1⁄2.
i) gives simple relations between the cases of suction and injection and ii) gives similar velocity profiles.
Rayleigh’s problem (U=const) is investigated in detail, and the resulting solutions show the same qualitative natures as the corresponding steady flow solutions for an semi-infinite flat plate so far obtained.

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Both the complete and transonic thin-wing-expansion methods are utilized to obtain the steady irrotational flow of a compressible fluid past an elliptic cylinder. The velocity distribution over the surface is calculated up to the fourth powers in thickness ratio t. Then it is found that the fourth order perturbations include not only terms of O(t⁴) but also those of O(t⁴logt), and that the latter group becomes negatively predominant over the former in the transonic range. In calculating the fluid velocity near the stagnation point there still remains insurmountable difficulty even for moderate subsonic flow. The resulting expressions for an elliptic cylinder prove to be transformed into those for an parabolic cylinder.

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Molecular absorption and dispersion formulas applicable for both liquids and gases have been derived in a phenomenological manner. It was pointed out that the relaxation time of the molecular internal energy τ must be distinguished from the relaxation time of the internal specific heat β and the relation between these two quantities was discussed in detail. The relaxation time τ has the advantage of making the dispersion formula simpler and directly comparable with the dispersion formulas in other cases, such as the relaxation of shear viscosity. The relaxation time β on the other hand, is more closely related with the collision excitation probability of the molecules than τ.

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