The line shape of the proton absorption in cetyl alcohol was studied with an autodyne receiver between room temperature and the melting point. The second moment was calculated from recorded derivative curves. The obtained second moment had a hysteresis effect. When the temperature was raised from room temperature, the second moment was almost constant of about 18.5 gauss² and it decreased abruptly to the value of 8 gauss² near the melting point. When the temperature was lowered from the melting point the second moment kept a small value till the transition point and then increased. The large second moment seems to be arisen from the monoclinic state and the small second moment from the hexagonal state. It was observed that the resonance line had a fine structure at its center.

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Proton magnetic resonances of water molecules in the single crystals of K₂HgCl₄H₂O and K₂SnCl₄H₂O were observed, and the distance and the direction of proton-proton line in each of water molecules in the unit cell were determined. The absorption lines are generally composed of four component lines, of which the separation varies with the direction of the externally applied magnetic field. These results are fairly well explained with the Pake’s formula for two-proton system and by the fact that there are two different p-p directions in these crystals. The p-p distance in a water molecule determined in this experiment is 1.607 Å, and the angles between the a-axis and p-p lines which lie on the plane parallel to the c-plane are ±21.4° for Hg-salt, and 1.62 Å and ±39.5° respectively for Sn-salt.
Each component line has further fine structures when the external field is applied to some particular directions. This cannot be explained by the assumption of two-spin system only, but understood by introducing the assumption of four-spin system.

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The energy levels and the transition probabilities are calculated for four proton interaction. The result of calculation is applied to the case of the single crystals of K₂HgCl₄·H₂O and K₂SnCl₄·H₂O. Ten absorption lines are expected from the theoretical calculation, of which each five form a group. Since in general cases the separations between the lines belonging to one of these groups are small compared to the separation between these groups as a whole, the expected resonance figure roughly coincides with the case of two proton resonance. But the shapes of resonance peaks have further fine structures. The observed fine structures were analysed by the theoretical consideration, and it is shown that the agreement between the theory and the experiment is satisfactory, if we take the distance of main protons to be 1.607 Å and the distance between the proton-proton lines for adjacent water molecules which are parallel with each other to be 3.60 Å in the case of Hg-salt and 1.62 Å and 3.90 Å respectively in the case of Sn-salt. From these results, the positions of the oxygen atoms in the crystal lattice may be determined with a few assumptions, and the probable space group of K₂SnCl₄·H₂O will be V_h⁹–Pbam which is identical to that of K₂HgCl₄·H₂O contrary to the previous X-ray determination.

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Fractional parentage coefficients defined by G. Racah for nuclear j-j-coupling wave functions ((j)²,j:(j)³), ((j)³,j:(j)⁴) and ((j)⁴,j:(j)⁵) (maximum T only) for j=3⁄2 and j=5⁄2 are calculated by group theoretical method. Using these coefficients formulae are derived for the matrix elements of operators generally defined such as T₀^(p)(S^(k)·L^(k)) or T₀^(p)S₀⁽⁰⁾L₀^(k) in a nuclear configuration consisted of several closed shells and one unfilled shell, in terms of the basic two body integrals.

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Using carbon monoxide as working gas, the concentration of C¹³ by thermal diffusion method was tried. The separation column was a hot wire type and had the length of 5 meters. The separation factor of the column was measured under various pressures and temperatures. The maximum separation factor obtained at the pressure of 53.7 cmHg and the temperature of the hot wire of 1050°K was 5.85. Under these conditions the relaxation time of the column whose both ends closed was about 4.7 hours. The comparison of the results with the theory suggested the existence of the parastic remixing. The measured value of R_T of CO gas was 0.427.

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The surface products of copper-beryllium (0.5, 1.5 and 3.0%) alloys treated under various oxygen pressures and temperatures and their secondary electron emission characteristics are discussed in detail. The results are summarized as follows;
(1) Rapid diffusion of beryllium atoms through copper-beryllium alloy begins at 400°C.
(2) In order to activate copper-beryllium alloys, they must contain beryllium atoms more than 1.5%.
(3) At the activation process temperature must be raised to a desired point at pressure lower than 10⁻⁴mm mercury in order to prevent copper from oxidizing, and then oxygen must be added into the tubes to the treatment pressure.
(4) The formation mechanisms of beryllium oxide layers treated at 800°C and below 700°C are different with each other. This difference of treatment temperature is responsible for two different secondary emission characteristics respectively.

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It has been found experimentally that the change in contact potential difference ΔV_D during the forming process can be determined by observing the variation of a saturation current in the reverse direction with time required for the forming, the values of ΔV_D obtained for three kinds of surfaces ranging from 0.16 V. for a etched surface, from 0.06 V. to 0.07 V. for a cleaved surface, and from 0.04₂ V. to 0.04₆ V. for a surface exposed to nascent hydrogen. The theoretical treatments have been investigated to explain the experimental results, using the idea of Bardeen’s surface levels and assuming that the variations in concentration of donor impurities present in the barrier, which had been caused by the thermal diffusion of acceptor impurities from the surface of the semiconductor, would affect the contact potential difference. The qualitative predictions appear to agree with results satisfactorily.

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The relationship between the thermionic emission and the electrical conductivity of both “sintered” and normal oxide-coated cathodes has been investigated.
The “χ” values which obtained from the difference between the work functions and the activation energies of conductivity were much inconsistent between both cathodes. Moreover, in the low temperature range the activation energey of conductivity, smaller than 0.1 ev, was observed.
These results are attributed to the existence of numerous conduction mechanisms in oxide-coating and to the surface formation of barium layer on the oxide-coating particles.

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The transport phenomena in metals, such as the electrical and the thermal conductivity, are treated as a kind of the diffusion of electrons on the Fermi-surface. Grüneisen’s well-known formula is gained for the electrical conductivity σ, and as for the thermal conductivity κ the expression
κ=σT\fracπ²3\left(\fracke\ ight)²\bigg⁄\left{1+\left(\fracθT\ ight)²\left(\fracKq₀\ ight)²∫₀^θ⁄T\fracx³dxe^x−e^−x\bigg⁄∫₀^θ⁄T\fracx⁵dx(e^x−1)(1−e^−x)\ ight}
is obtained. In this equation θ denotes the Debye temperature, K and q₀ are the maximum wave numbers of electrons and phonons respectively.

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It is shown that we can derive by a comparatively simple procedure the formula of surface tension in terms of distribution functions from purely statistical considerations. Surface tension is derived as the increase of free energy which accompanies the increase of unit area of the interface between the liquid and the vapor phases.
The expression obtained is the same as MacLellan’s:
γ=\frac12∫∫∫∫\fracdφ₁₂dR₁₂\fracx₁₂²−z₁₂²R₁₂ρ_s⁽²⁾(z,R₁₂)dz₁dv₁₂,
where γ is the surface tension, φ₁₂ is the intermolecular potential and ρ_s⁽²⁾(z,R₁₂) is the excess pair density reckoned relative to an arbitrary Gibbs dividing surface. The above expression can be transformed into the form given by Bakker,
γ=∫(p_N−p_T)dz₁,
where
p_N(z₁)=kTρ⁽¹⁾(z₁)−\frac12∫∫∫dv₁₂∫_z1−z12^z₁\fracdφ₁₂dR₁₂\fracz₁₂R₁₂ρ⁽²⁾(ζ,R₁₂)dζ,
p_T(z₁)=kTρ⁽¹⁾(z₁)−\frac12∫∫∫dv₁₂\fracdφ₁₂dR₁₂\fracx₁₂²R₁₂ρ⁽²⁾(z₁,R₁₂).
This result coincides with that of Kirkwood and Buff which was derived by calculating stressed directly. The assumption of density discontinuity, which is often made in the theory of surface tension, is examined closely.

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The simultaneous measurements of electrical resistivity and thermionic emission of silicon over the intrinsic temperature range from 1100°C to 1350°C have been carried out by means of heating a small silicon piece directly. The results indicate that the depth of the conduction band, the energy gap between filled and conduction bands and the work function are 3.47 eV, 1.10 eV and 4.02 eV, respectively, and also Richardson’s constant 5.6 amp. cm.⁻² deg.⁻²

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Following the first paper of the same title (J. Phys. Soc. Jap. 7 1952) 397), in which Bethe’s dynamical theory of electron diffraction (Ann. d. Phys. Lpz. 87 (1928) 55) was extended to the case of finite polyhedral crystal and the general expressions of wave functions for transmitted and interfracted (=reflected by crystal net plane) wave were obtained, they have been rewritten in a form of the so-called Fresnel diffraction with the purpose that we might have better understanding of electron microscope images of crystallites. From these formulae, it is concluded that the striations due to “Pendellösung” are observed in the just-focused images of crystallites in which Bragg reflection occurs while in defocused image they are disturbed in the neighbourhood of a crystal edge by the Fresnel diffraction effect. In a special case where the parameter indicating the deviation from the Bragg condition is very large, the present formulation applies to the phase contrast fringes due to the edge of transparent wedge-shaped substances. The fringes on the vacuum side are expected to be more prominent in the virtual, than in the real, image in accordance with experiment. Some numerical examples of intensity distributions are given for the bright field images of a wedge-shaped crystallite which is out of focus.

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By means of the Lidiard distribution function for free electron gas, the Thomas-Fermi-Dirac (TFD) equations for non-zero temperatures are derived and integrated numerically for Fe. On the basis of the TFD functions there are given also the equations of state of metals under extremely high pressures.

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For the study of dynamical properties of high polymers by low frequency oscillations, a simple torsional coupled oscillator was constructed in which two pendulums of the same type having equal frequency (about 1/2 c.p.s.) were coupled to each other through a test material of cylindrical shape. Two modes of oscillations appear in the motion of the oscillator resulting in generating beats under suitable conditions. By observing the beats, it is possible to obtain the shear modulus and the elastic loss of the material through a simple course of calculation. Polymethyl methacrylate was investigated from about −20°C to about 150°C and anomalous absorption ranges were found at about 130°C and at about 20°C, the latter was considered worthy of mention.

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Secondary absorption region of polymethyl methacrylate was studied dynamically. In addition to the absorption region, which corresponds to so-called second order transition or softening temperature, a secondary absorption region was found at lower temperature, its peak being lower and broader. By means of bending and torsional vibrations, frequencies for the maximum absorption were measured at several temperatures. The activation energy of 29 kcal/mol was obtained. The results of the experiment were compared with those obtained electrically by Mead and Fuoss.

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Wave guide lens is a part of reflex electromagnetic horn invented by me which has very sharp directivity over astonishingly wide band of frequencies and posesses excellent properties for microwave repeater uses. The convex wave guide lens is a curved flat wave guide which transforms entering spherical wave into plane wave over infinitely wide band of frequencies. The determination of the form of the curved flat wall of the lens is theoretically discussed and deduced. Formulas, tables, and the designs fitted to production are given for standard type of convex wave guide lens.

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The hyperfine structures of 32 lines of Gd I and 2 lines of Gd II in the visible region were measured. They could be interpreted as due to the isotope displacement effect of the even isotopes (156, 158 and 160) and the splittings due to the nuclear magnetic moments of the odd isotopes (155 and 157). The ratio of the isotope displacements Δ(158−156)⁄Δ(160−158)=0.97±0.06 was determined. The relative isotope displacement Δ(160−158) in some 30 terms of Gd I is tabulated.

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The hyperfine structures of the Pb I lines λλ 5201, 5005, 7228, 4168, 4062, 4020, 3740, 3672, 3573, 4058, 2873, 3683, 3640, 2833 and Pb II lines λλ 6660, 4386.4, 5042.5, 4153 and Pb III line λ 4182.5 were measured, and the ratio of the distances of the adjacent even isotope components Δν(206−204)⁄Δν(208−206) was determined to be 0.905±0.010. The ratio Δν(207−206)⁄Δν(208−207) was found to be constant for all lines (except λ 4062) within experimental error and was found to be 0.615±0.008. The anomaly found in the case of λ 4062 is interpreted to be due to a perturbation.

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A new proof of Lagrange’s theorem about the persistence of curl vector is given in the light of recent theories of linear partial differential equations. Velocity potential for an arbitrary pressure distribution can be constructed as the Extremal field.

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When a plane jet of gas issues steadily from a symmetrical nozzle as a parallel supersonic stream into an external medium at rest, its behaviour is governed by the exist velocity as well as by the ratio of exit pressure to pressure in the external medium. As will be seen from Prandtl’s photographs, when this pressure ratio is nearly equal to unity, the jet has a periodic character to the first approximation, and its structure can be accounted for by the use of the linear theory due originally to Prandtl. When the pressure ratio departs from unity, however, the quantitative behaviours, such as the wave-length of the jet, cannot be fully explained unless the nonlinear character of the fundamental equation is taken into account.
In the present paper, the fundamental equation for the stream function is considered in the hodograph plane, and the true adiabatic relation is replaced by an approximate adiabatic one so that simple exact solutions may be obtained. Thus, it is shown that, if the exit velocity is not so close to the sonic velocity and the external pressure is not so lower than that at the exit, the jet has, to the present approximation, still a completely periodic structure in the downstream as in the case of the linear theory. An expression is obtained for the wave-length of jet and it is found that the agreement between our theoretical result and Prandtl’s experiments is very satisfactory.

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The asymptotic behaviour of the viscous flow past an obstacle for vanishingly small viscosity is discussed on the basis of Prandtl’s boundary layer theory together with Kirchhoff’s dead water theory. If the pressure distribution around the obstacle is such that the separation of the boundary layer on the obstacle takes place, then the flow pattern should involve free stream-lines extending from the separation points. From such considerations it is concluded that the asymptotic flow pattern around a smooth obstacle is a discontinuous flow with dead water region of the Kirchhoff type such that the free stream-lines leave the obstacle with a finite curvature equal to that of the obstacle at the separation point.

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The discontinuous flow past a circular cylinder is studied making use of the theory of discontinuous flow and the boundary-layer theory. The determination of the separation points is carried out by means of an iterative method. It is found that the separation angle which is measured from a forward stagnation point, is approximately equal to 58°. This angle is very close to the smallest one 55° among the angles of separation which can be allowed from the discontinuous flow theory. Thus the flow with separation angles of 55° seems to be the limiting case of the viscous flow past a circular cylinder when the Reynolds number increases indefinitely.

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Surface structures of galena cleavage face heated at reduced air pressures 10⁻²–10⁻³ mm. Hg and at temperatures 100°–600°C. were studied by electron diffraction. Surface roughening commences at 350°C. with the release of sulphur in combination with oxygen. The roughened surface is bounded by the {100}_PbS facets. Extra structure due presumably to some effect of the enriched lead atoms was also observed. As to the oxidation product, epitaxially oriented lead sulphate (PbSO₄) or the suboxide (Pb₂O) crystallites were obtained at temperatures below 400°C. For the latter, the needle like external shape was deduced from the analysis of the diffraction spot. Above 400°C. randomly oriented suboxide or the yellow oxide (PbO) crystallites were observed. With the complete evaporation of the crystal at 600°C. silver powder remained as the residue.

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Diffusion pump oil is analysed by the mass spectrometer, especially for the purpose of obtaining some knowledge about the residual gases at the final vacuum when we use oil diffusion pumps. As a sample, we take alkyl-naphtalene and its spectrum is given graphically. The results of our analyses of residual gases confirm the conclusions obtained by Hickman and Blears.

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