An attempt has been made to interpret the superconducting state of the conduction electrons in the metal by the statistical mechanical treatment, introducting the second order effect of the lattice vibration on the electrons which has first been used by Fröhlich for this problem as the source of the attractive force in the momentum space. Using some reasonable simplifications, we can show the existence of a special equilibrium state which is stable below a certain temperature. If we consider this special state as the superconducting state, we can calculate the jump of the specific heat ΔC and the threshold magnetic field curve which represent well the experimental results: ΔC=γT_c (γ is the electronic specific heat coefficient and T_c is the transition temperature), H=2π³Nk²(T_c−T)⁄3_μ0 (μ₀ is the Fermi energy. N is the number of the electrons in 1 cm³ and k is the Boltzman’s constant).

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In the previous paper the discontinuous elongations of magnitude of a few micron were observed for coarse grain polycrystal specimens of commercial aluminium. In this paper the behaviour of slip lines near the grain boundary was observed and it was found that when the slip lines continued across the grain boundary the discontinuous elogation was not observed, while the jumps occured when the slip lines terminated at the grain boundaries. From these results the cause of the discontinuous elongation was discussed.

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The integro-differential equation for the temperature v(x,t) of an infinite cylinder, which is kept at const. temperature initially, and loses heat by the radiation from its surface with variable transfer coefficient h(t) is set up as follows:
V(x,t)=H(t)\sqrtx−\frac∂∂t∫¹₀G^∗(x,s)V(s,t)ds,V(x,t)=\sqrtxv(z,t).
The surface temperature H(t) is determined by the relations
\frac12∫₀^tH(t)dt−∫_t^∞P(t)dt−∫₀^tP(t−s)H(s)ds+\frac132=\frac12t−∫₀^t(t−s)H(s)h(s)ds,
where P(t)=2∑exp(−λ²_nt)⁄λ²_n, from which further relations between H(t) and h(t)
P(t)−∫₀^tP′(t−s)H(s)ds=\frac12−∫₀^tH(s)h(s)ds,
H(t)h(t)=∫₀^tH′(t−s)P′(s)ds
are obtained. It is shown that in the special case where h=const. known. result can be obtained from these relations. The Fourier transforms of H(t)h(t), H(t) and V(x,t) denoted by K^∗(ζ), H^∗(ζ) and V^∗(x,ζ) respectively, are found to satisfy
V^∗(x,ζ)=\frac\sqrtxJ₀(kx)J₀(k)H^∗(ζ)+\frac\sqrtx\sqrt2π\fracJ₀(kx)−J₀(k)k²J₀(k),
K^∗(ζ)=\left(iζH^∗(ζ)+\frac1\sqrt2π\ ight)J₁(k)⁄kJ₀(k),iζ=k².

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Fluorescent gamma-rays from 32 elements excited by Li-D neutrons were observed by aluminium wall Geiger-Müller counter. Effective mean neutron energy was estimated to be about 10 Mev. Observed gamma-ray intensities, after correcting for experimental conditions and divided by the number of atoms in the specimens, increase almost linearly with atomic weight A up to A≅120 and then become almost constant or slightly decrease at heavier elements. Gamma-ray intensity of uranium is strong but would be ascribed to fission.
These results were discussed utilizing statistical theory and it is suggested that the apparent level spacings beyond A≅120 do not decrease with A, or even become greater, possibly due to the partial excitation of nucleus.
Mean energies of gamma-rays for several elements were estimated by the absorption in lead plates and were found to lie between 0.6 and 3 Mev.

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The end effects—namely the diminution of the effective length and the change of counting probability at the end—in Geiger Mueller counters which have considerably thicker rods at both ends of the central wire than the wire itself are experimentally investigated under various conditions of the filling, and some theoretical interpretations for them are tried. The agreement of the experimentally observed results with the theoretically expected ones is fairly good, and we may conclude that the diminution of the effective length depends not only upon the bend of the lines of electric field but also upon the centrifugal force which affects on the primary electrons traversing along the curved line, and that the change of counting probability at the end of the thin wire is caused by the diffusion of the primary electrons in the axial direction.

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The Oxygen atoms are supposed to become the doubly-charged negative ions within oxide crystals. There is, however, no experimental evidence of the existence of such ions in gas phase, which fact suggests us that they are probably very unstable in the free state. We, therefore, may reasonably suppose that they are stable only within oxide crystals due to the effects of the surrounding ions. In order to elucidate the above situation quantitatively, we have here attempted to work the electronic states of the oxygen ions within the oxide crystals by the variational method, which we adopted already for the calculation of the cohesive energy of LiF. Thus, we have confirmed, for MgO, that the doubly-charged negative ion of oxygen may be actually stable in such crystals. Furthermore, we have calculated also the electronic affinity of the ions and diamagnetic susceptibility of MgO crystals, which results seem to show rather good agreements with the experimental observations as far as our computational accuracy does concern.

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We propose a theory of hindered rotation in molecular crystals, whose basis is on the Kirkwood model. Some values characteristic of the phase trasition due to the molecular hindering are calculated. We obtained for the Curie point, Hc, 1.075, 0.615 and 0.434 for the square, simple cubic and body-centred lattices respectively, where we assumed J⁄2cosγ, for the interaction between two neighbouring molecules, whose relative orientation is specified by γ, and we put H=J⁄2kT. The leap values of the specific heat, ΔC_v⁄R, are obtained as 2.280, 2.466 and 2.514 for the square lattice etc. In contrast with the theory of binary alloys, ΔC_v⁄R is not improved with compare to Bragg-Williams’ value 2,500. It is different from Chang’s result, according to which ΔC_v⁄R is larger than Bragg-Williams’ value considerably. However Chang’s point of view is criticized.

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A general formula for the diffuse scattering of X-rays is derived for the crystal which has a local lattice distortion due to any kind of lattice defect. The intensity is expressible in terms of the Fourier transform of the potential energy parameters, similar to that introduced by Begbie and Born in their theory of diffuse scattering by lattice vibrations, and that of external forces causing the distortion. It is shown that our diffuse scattering may be observed in some crystal in which the density of the lattice defect exceeds a certain value.

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In the quartz capillary part (8mm φ, 10cm in length) of this ion source with a coaxial magnetic field of about 800 gauss, an intense ionization is established by a collimated primary electron beam sent from one end of the capillary. No metal part being contained in the capillary, a high relative concentration of atomic hydrogen is obtained, so that the proton percentage of the ion beam extracted from the other end of the capillary is very large (60∼70%). A proton output up to 1mA is obtained from a 1.3mm hole with a small consumption of power (<200 watts) and hydrogen gas (∼3cc per hour N.T.P.). The ratio of protons to consumed gas molecules is 10∼20%.

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We have worked out the electronic state of F⁻ ion in LiF crystals by means of the variational method with the use of the analytical wavefunction of 2p type with three parameters for the outermost electrons of F⁻ ion. We see the charge distribution of negative ion is somewhat contracted within the crystal. The lattice energy, the lattice constant and the compressibility of LiF crystals are found to become of 239 Kcal/mol, 2.00 Å and 1.96×10⁻¹² cm²/dyne respectively, which results are compared with the observed values of 240 Kcal/mol, 1.99 Å and 1.4×10⁻¹² cm²/dyne respectively.

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The spectral distribution of photoelectric yield and its temperature dependency were measured on the barium oxide, in the form of a sprayed coaling on a nickel base. When sample was held at room temperature, the photoelectric emission showed an enhanced effect, that is, the photo-current from the irradiated sample increased with time. The photon energy giving the maximum enhanced effect lies at 2.3ev coincident with the peak of optical absorption by colour centers in barium oxide. This enhanced effect disappeared by warming the sample to 400°K. The results are discussed in terms of an energy level structure of barium oxide.

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The energy distribution, the most probable and the average energy loss of electrons passing through matter were measured with a 180° focusing spectrometer of approximately 0.7% resolution, using K conversion lines of 606, 1414 and 1761 KeV γ-rays of RsC’ as homogeneous electron source and the various thicknesses of Al, Cu, In and Pb as stopping materials.
The observed value of the most probable energy loss was in accord with Landau’s theory within the limits of our experiment. That of the average energy loss, however, was not in accord with his theory but with Bloch’s formula. The width of the energy distribution curve obtained was considerably greater than predicted by Landau. However, on the high energy side of the peak, the shape of the curve predicted by Landau’s theory was surely better than that of White and Millington’s.

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Using a new circuit, a precise measurement of the frequency ratio of nuclear magnetic resonance of fluorine nucleus to that of proton in HF aq. was performed at the magnetic field of about 1800 gauss. The value ν_F⁄ν_H=0.940816 was obtained with the smallest error ±0.000009 compared with the values by other research workers.

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The sorption properties of Ba-O₂ system were studied. Oxygen is mainly adsorbed physically onto the active centres, below −150°C, differing from other kinds of gas. The activation energy for the physical adsorption is 0.3∼0.9 Kcal/g.mol. At temperatures between −150°C and −30°C, it is adsorbed in the activated state and its activation energy is 5.8 Kcal/g.mol. Beyond −30°C oxygen combines with barium to form oxide.

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The aim of writing this paper is to clarify first the transformation property of spherical harmonics directly from its own definition, and the circumstance that the matrix elements of the irreducible unitary representations of three dimensional rotation group are the eigenfunctions of the so-called symmetric rotor.
It is attempted to treat the old results more naturally and clearly from the standpoint of utilizing the generating polynomial and regarding these matrix elements as the generalization of spherical harmonics. Following this line we see some properties of Jacobi’s polynomial are easily deduced.

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The exact analytical expression, correct to M⁴, for the velocity distribution over an elliptic cylinder which is submerged in a uniform, flow of a compressible fluid (cf. J. Phys Soc. Japan, 6 (1951) 168) is expanded in ascending powers of θ, the eccentric angle of the ellipse, in order to reduce the expression into a more tractable form. Numerical values of coefficients of θ and θ³ are given for various values of thickness ratio t ranging from 0 to 1.0, and it is shown that the convergency of the M²-expansion method is very good near the stagnation point.

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It is found that in fused quartz made in reducing condition three absorption bands having peaks at 2.3, 4.1 and 5.6 ev and in fused quartz made in oxidizing condition two absorption bands having peaks at 4.1 and 5.6 ev are produced by exposure to X-rays. The stability of these centers is studied by bleaching with temperature and light. The band having peak at 5.6 ev is found to be composed of two bands having peaks at 5.6 and 5.87 ev. The band at 2.3 ev is studied to be due to electrons trapped by negative-ion vacancy or by an aggregate of negative-ion vacancies. The luminescent center of fused quartz is proposed to be interstitial silicon atom. It is concluded that fused quartz has in fairly extent short range order of crystal.

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Imai’s thin-wing-expansion method is applied to a uniform flow past an elliptic cylinder at zero angle of attack, in order to obtain the analytic expressions correct to the third approximation for the complex velocity potential, and for the velocity distribution over the cylinder. Numerical calculation is made for the case t=0.1 where t is the thickness ratio of the cylinder. The convergence of the result seems to be satisfactory except near the stagnation point, where the anomalous behaviour appears.

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