Photo-thermal transformations among various centres in coloured alkali-halide crystals are studied here collectively.

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In obtaining the current voltage relation of a junction transistor, one solves continuity equations for minority carriers with appropriate boundary conditions. There are two kinds of boundary condition which have been extended so as to apply to the high injection level operation of a junction transistor. One is in terms of the electrostatic potential and the other is in terms of the quasi-Fermi levels. Taking into account the effect of the base spreading resistance, it is shown that they can be equivalently used in describing the dc and the low frequency performances of a junction transistor but at medium frequencies the quasi-Fermi level approach is preferable. The small signal ac conductances and capacitances which are related to the emitter junction have another correction factor that saturates to 1/2 at high injection levels. Conductances and capacitances are calculated as functions of the emitter current by using the latter boundary condition.

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Rotation patterns of electron diffraction from oriented silver films prepared by condensation in vacuo onto heated NaCl crystal surface, were obtained by rotating the films about the [100] axis lying in the films. The intensity distribution along the hyperbolae appearing in the patterns was measured. The observed intensity was in good agreement with the intensity calculated on the assumption that the silver film is composed of parts of the parallel-growth structures, the twin structures, and the structures having defects proposed by Göttsche (Z. Phys. 134 (1953) 517). It was found by electronmicroscopy that the twin structures occur here and there on a submicroscopic scale, but the displacement of diffraction spots due to the twin faults was not detected.

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The anomalous effect reported by Fukushima (E. Fukushima; Acta Cryst. 459 (1954) 7), i.e. a large enhancement of X-ray reflection intensity at the boundary of etched and ground regions in quartz crystal slab, is studied by a double crystal spectrometer. The difference can not be found in line width of reflection curves at the ground region and at the boundary region. Lattice bending is not detected at the boundary. It is not larger than 10″, if it exists. The anomalous enhancement is erased by etching the crystal surface for several seconds. This anomalous effect can be observed also in NaClO₃ crystal and calcite but the enhancement is very small in the latter crystal. It is concluded that the anomalous enhancement is due to a reduction of primary extinction caused by elastic distortion accumulated at the boundary region.

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Proton magnetic resonance absorption from long chain normal primary alcohol of probable carbon number 32 was observed between 120°K and its melting point 355°K. Its absorption line width and second moment were constant below 260°K, being 15.5 gauss and 26.5 gauss², respectively. From 260°K to the transition point, the line width decreases gradually with increasing temperature and, at the transition point, abruptly decreases to 4.6 gauss. The narrowing of the absorption line below the transition point is considered to be due to the torsional vibration of the molecules around the carbon chain axis. The relation between the dielectric anomaly below the transition point observed by Takamatsu and the molecular motion revealed from nuclear resonance studies is discussed.

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The specific heat of cobalt ammonium sulfate Co(NH₄)₂(SO₄)₂·6H₂O in the liquid helium temperature region is investigated theoretically. The possible contributions to it are the dipole-dipole and the exchange interactions between Co²⁺ ions and the hyperfine interactions within each ion. Our investigation is to obtain the first two contributions. The dipole-dipole interactions are given by use of the anisotropic g-factors determined from the paramagnetic resonance. And the exchange interactions are determined by modifying the isotropic exchange interactions by the wave functions of the lowest Kramers doublet, where we took into account only the interactions with the first and second neighbouring ions. The result obtained from the moment expansion method gives C_vT²⁄R=30.2×10⁻⁴ which is in good agreement with the experimental value 27×10⁻⁴. Here C_v is the interionic (dipole-dipole and exchange) part of the specific heat at moderately high temperatures, T the absolute temperature and R the gas constant.

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Magnetic anisotropy of cobalt ammonium Tutton salt in the temperature region from about 10°K to 300°K is studied, where we used the wave functions obtained by Abragam and Pryce. The temperature dependence of the effective Bohr magneton is also studied. The agreements of the present theoretical results with the experimental ones are excellent.

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The hyperfine structure (hfs) of the levels 3d⁹4s^{2 2}D_5⁄2 and ²D_3⁄2 was measured and compared with the usual hfs formulas for d-electrons, and a discrepancy between theory and experiment was found. This can be phenomenologically interpreted by assuming that the values of ⟨1⁄r³⟩ are different for 3d_5⁄2- and 3d_3⁄2-electrons, namely ⟨1⁄r³⟩=7.4 and 8.0 for 3d_5⁄2- and 3d_4⁄2-electrons respectively, where r is measured in unit of hydrogen atom radius.

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(I) The isotope shift in the transition 3s–3p in the spectrum of Ne II (Ne²²–Ne²⁰) was observed, using a liquid-air cooled hollow cathode. The shift in the doublet spectrum of the ³P system was found to be of the order of 0.2 cm⁻¹ and larger than that in the quartet spectrum or the ¹D system.
(II) The component due to the rare isotope W¹⁸⁰ was detected in the line λ 4269 of the spectrum of W I, and the ratio of the distances of the neighboring even isotopes was found to be Δ(186–184):Δ(184–182):Δ(182–180)=1:1.206±0.010:0.88±0.07.

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The fine structure of J=1←0 lines in various isotopic species of methyl alcohol has been explained by a combination method of Itoh’s theory for a rigid asymmetric hinded rotor and Kivelson’s theory for a nonrigid symmetric hindered rotor. All lines have been fitted within errors of 2 Mc by this method. From the analysis the height of potential barrier to internal rotation for CH₃OD has been determined to be 371±5 cm⁻¹. The molecular structure of methyl alcohol has also been calculated and discussed.

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The existence of the group of contact transformations, regarded as the so-called continuous Schrödinger group whose elements commute with Hamiltonian,is intimately related not only to the problem of degeneracy, as shown by Jauch and Hill, but also to the problem of quantization. In the present paper, it is shown that on the basis of representations of the Lie ring generated by the operators which have a certain definite correspondence with a set of independent integrals of the equations of motion in Newtonian mechanics, an energy eigenvalue problem can be constructed in terms of a complete set of the Casimir operators. It is further pointed out that this quantization procedure is, in spite of various restrictions, applicable to quantum-mechanical systems having the continuous Schrödinger group, and then the degree of degeneracy in regard to the angular momentum can be obtained simultaneously.

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A theorem is presented which gives the perturbation stream function \ ildeΨ(r,θ) when a sphere (r=a) is introduced into an unlimited viscous fluid in axisymmetric motion obeying the Stokes equation, of which the stream function is Ψ(r,θ), where (r,θ,\varphi) are the polar coordinates.
\ ildeΨ(r,θ) is given by
\ ildeΨ(r,θ)=\ ildeΨ₁(r,θ)+a²\ ildeΨ₂(r,θ),
\ ildeΨ₁(r,θ)=\left(a−\fracr²a\ ight)\frac∂∂Rψ₁(R,θ)−\left(\frac32\fracra−\frac12\fracr³a³\ ight)ψ₁(R,θ),
\ ildeΨ₂(r,θ)=\left(a−\fracr²a\ ight)\frac∂∂Rψ₂(R,θ)−\left(\frac12\fracra+\frac12\fracr³a³\ ight)ψ₂(R,θ),
ψ₂(r,θ)=−\fracsinθ4\sqrtr∫₀^r\sqrtrω(r,θ)dr, ψ₁(r,θ)=Ψ(r,θ)−r²ψ₂(r,θ),
where ω is the vorticity, and R=a²⁄r.
This gives the stream sheets directly without recourse to manipulation of spherical harmonics, and is very simple when Ψ(r,θ) is irrotational, i.e. ω=ψ₂=0.
As examples of the applications of this theorem, the stream functions for uniform flow, source flow and parabolic flow past a sphere are derived.

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The transverse vibration of a uniform thin elliptic plate with clamped edge is solved in an exact manner by the use of Mathieu functions and modified Mathieu functions. The relationship between the frequency of the fundamental mode of vibration and the eccentricity of the elliptic plate is shown graphically. Also, an approximate formula for the said relationship is derived correct to the fourth power of the eccentricity, which may be adequately used in case when the eccentricity is not so large.

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P. 299 r⁄a in Fig. 6, 7, 8 and 9 should be read (r⁄a)².

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Fig. 1   1200 C.P.M. should be read 12000 C.P.M.

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