The beta-ray spectra of Co⁶⁰ and Sc⁴⁶ were studied by a semicircular beta-ray spectrometer with the radius of 10 cm. The spectrum of Co⁶⁰ agrees with that of the allowed transition of the Fermi theory from the maximum energy down to about 60 keV. The spectrum of Sc⁴⁶ also agrees with that of the allowed transition from the maximum energy down to 120 keV. For Co⁶⁰ the upward deviation which occurs at the energy less than 60 keV may be due to the effect of the source thickness, but for Sc⁴⁶ the upward deviation at the energy less than 120 keV could not be decisively explained. The maximum energies of Co⁶⁰ and Sc⁴⁶ beta-rays are 316±3 keV and 357±3 keV, respectively.

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A spherical condenser-type electrostatic spectrometer was constructed, and the spectrum of radioactive decay of RaD was studied with it. For the well-known internal conversion lines due to the 46.7 kev gamma-ray, we obtained the intensity ratios L₁:M:N=1:0.23±0.02:0.06±0.01. In the energy region between 16 and 50 kev, no internal conversion line could be found except those due to the 46.7 kev gamma-ray. Many lines were observed below 16 kev, and most of them were identified as L Auger lines of bismuth. Some of them, i.e., lines at 6.6 or 7.0, 11.0, 15∼16 kev may be internal conversion lines. The primary beta-ray seems to have its maximum energy at 16∼18 kev. A tentative decay scheme was proposed to explain the result.

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Assuming a film of pure superfluid on the wall and introducing a mutual friction somewhat different from that suggested by Gorter, the heat conductivity is calculated on the basis of the two fluid model and internal convection. Our formula of the heat conductivity shows a fairly good agreement with the experiments including the case of very narrow slits. The London-Zilsel’s formula is also included as a special case.
In very narrow slits, the heat conductivity approximates to ⟨K⟩=s_λ²T^r+1d⁄2BT_λ. Here T: absolute temperature, d: slit width, T_λ: transition temperature, s_λ: entropy per gram at T_λ, r: numerical constant 5.5∼5.6, B is the quantity concerning with the film and the mutual friction. At the temperature near T_λ, ⟨K⟩ is approximately s_λ²⁄A₁T_λ^2r·(T_λ^r−T^r)T^r+1. A₁ is the quantity concerning with the mutual friction. At the intermediate slit width and temperature, ⟨K⟩ approximates to the London-Zilsel’s formula. B, A₁, and critical velocity are discussed and the numerical values are calculated.

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The investigation of the actions of aqueous heavy metal salts on mineral surfaces was extended to mercuric sulfate-galena system. Fresh cleavage face of galena was soaked in acidic aqueous mercuric sulfate of low concentrations for 30 min. at room temperatures. The reaction products revealed by electron diffraction were: metacinnabarite (cubic HgS) in random and definite orientation with respect to the substrate, and cinnabar (hexagonal HgS) in a certain epitaxial orientation. Besides, the pattern due to a roughened state of galena cleavage face was observed.

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The temperature dependence of the additional resistivity of binary alloys due to the presence of the short-range order is calculated by means of the pair distribution functions of atoms over crystal lattices, whose analytical expressions are given in the previous parts of this series. The present method used in deriving the expression for the resistivity in alloys is almost similar to the one which has already been developed by Nordheim, who has, however, ignored contribution of the short-range order to the resistance of alloys, and therefore obtained the additional resistivity independent of the temperature. The actual calculation is performed only for simple cubic alloys to avoid computational difficulties. According to the result of calculation, the decrease in the resistivity due to the short-range order becomes appreciable at temperatures immediately above the order-disorder transition point, and, indeed, this contribution decreases the additional resistivity by about 20% compared with the one obtained in the completely random case, even at the temperature 30°C above the critical temperature, if the present theory is applied to the case of Cu₃Au alloy.

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Coulomb, exchange, ionic integrals and one-electron integrals which involve 2s and 2p orbitals have been calculated for homopolar diatomic molecules. Slater type orbitals have been used, with equal values for the exponent δ. Two-center integrals are tabulated as functions of α=δR (R: internuclear distance). This work completes the project of tabulation of molecular integrals of which Parts I and II were published in Proc. Phys.-Math. Soe. Japan 20 (1938), 22 (1940), Extra Nos.

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On the assumption that the barrier layer of the selenium rectifier has a construction composed of n-type semiconductor, insulating film and p-type semiconductor, the author has offered a new rectification theory. In this theory, the author contrived a structure with which the direction of rectification due to insulating film does not come out to be inverse to the result of experiment, as Wilson’s theory.

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This report describes a general and concrete method of calculating the capacity in a noisy channel having one state which Dr. Shannon did not solve analytically. In order to express H_x(y) concisely, the author introduces H_x(y) characteristic equations, the solution of which characterizes the channel capacity, and the capacity problem is solved, considering whether the calculated probabilities of symbols are real or not. Then an analogy between capacity and rank is discussed and the capacity when H_x(y) characteristic equations have no solution is also discussed. Numerical examples and a geometrical representation of capacity are described.

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In the previous paper it was pointed out by the writer that the space charge may be formed up in the oxide cathode layer and the Schottky type behavior of the oxide cathode can be well understood as an effect of this space charge. In this paper the theory was extended to the retarding field region and the complete static character of a planar diode was calculated, with some amendment of the theory.
In an accelerating field the static character of the diode depends decisively on the space charge effect in the cathode layer. In a retarding field, however, the space charge has little effect on the static character but the amount of the space charge varies considerably with plate voltages.

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The equations for the field strength of the diffracted electromagnetic wave by mountains are derived for any polarization of the wave and any positions of the transmitter and receiver, without making important assumption except that the change of the mountain characteristics within the distance of a wave length is sufficiently small. Also, the general equation for the contribution of the field strength of any given picture of wave path which consists of the free space propagation parts and the diffraction or reflection parts by mountains is obtain.

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The permittivity of ferroelectric substance was measured in a microwave region by two methods, namely, by observing the resonances of a sample inserted either in a water-filled cavity resonator or in a wave guide window. By the two methods its temperature dependence of (Ba:80%, Sr:20%)TiO₃, its frequency dependence in a region between 2,200 Mc/s and 3,500 Mc/s, and the permittivities for several constitutions of barium and strontium, were measured. The results indicate the existence of a dispersion in this frequency region.

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As a supplement to the previous work on the anomalous hfs. of the spectrum of Al II, the structure of the multiplet λ3587.4−λ3586.5 (3³D–4³F) was studied. The calculated structure of this multiplet was found to be in harmony with that observed by means of interferometers. The triplet separations α=3³D₃–3³D₁ and β=3³D₂–3³D₁ were found to be −2.20 cm⁻¹ and −1.02 cm⁻¹ respectively (the 3³D term being inverted). The hyperfine energy levels of the n³D (n=3,4,5) series are represented diagramatically (in Fig. 4) in order to show how they depart from the ordinary coupling {(L·S)J·I} progressively towards the coupling {(S·I)U·L} as n increases.

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The hyperfine structure of the spectrum of Ru I was studied, and a displacement effect of the order of 0.015 cm⁻¹ between even isotopes having the difference of two neutron numbers was found in the lines corresponding to the transition 5s–5p. The spins of the odd isotopes were found to be 9⁄2≥I⁄≥5⁄2, the nuclear magnetic moments being negative.

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In this paper the method of thin-wing-expansion which has been developed by the author is applied to the case of a uniform flow of a compressible fluid past an arbitrary cylinder in the case of the absence of sources, sinks and circulation. The asymptotic expressions for the velocity potential and the stream function at a great distance, r, from the cylinder are determined correctly to the order of 1/r⁴. Hence the velocity can be found exactly to the order of 1/r⁵. This should be compared with Gröbner’s result which is correct to the order of 1/r⁴ and is restricted to the case of a cylinder symmetrical with respect to the x-axis. Moreover, the present analysis is far simpler than Gröbner’s one in view of the fact that the former requires only some elementary quadratures while the latter the integration of a system of differential equations.
Finally, it is shown that the general expression for the velocity potential is in accord with the author’s previous result for flow past a circular cylinder, which is correct to the order of M⁶, M being the Mach number.

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The relation between the extent of mirror surface appearing at the starting point of crack produced in glass rod by bending and the applied stress is studied. Two series of experiments are carried out: (a) the load is increased linearly with time, (b) the load is kept constant. There is a tendency that the greater the stress at the moment of rupture, the smaller the mean extent of mirror surface. Under the same condition of stress, however, the marked fluctuations are observed on the extent of mirror as well as on the mode of successive ramifications. For the problems of these fluctuations, statistical theory of fracture is applied. If the probability of the first occurrence of ramification which determines the boundary of the mirror after the crack develops for the distance l from the starting point is denoted by μ(l), the following relations are proved to hold good.
μ(l)=A(l−l₀)exp(αf) when l>l₀,
=0 when l≤l₀,
\barl−l₀=Cexp(−α⁄2·f),
where, f being the tensile stress at the starting point of crack, l₀ the minimum extent of the mirror produced under stress f, \barl the mean value of l, and A, C, α, some constants.

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The influence of humidity on the strength of glass strip is studied experimentally. The marked fluctuations are observed on the strength as well as on the extent of mirror surface appearing at the starting point of fracture. By means of statistical analysis, it is found that the probability of breakdown when the load attains the value between f and f+df is expressed by
μ(f)df=aexp[−(E₀−βf)⁄kT]·df.
Here, E₀ is the activation energy of glass, βf the energy applied by external loading, T the absolute temperature and k the Boltzmann’s constant. For the variation of humidity, β is kept constant, while E₀ decreases with increasing humidity. The effect of humidity is negligible to the extent of mirror, for which the following relation is proved to hold good.
\barl−l₀=Cexp(−α⁄2·f)
Here, \barl is the mean extents of mirrors produced by the load f, l₀ the minimum extent of mirror and C, α some constants.

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The molecular sound velocity of Rao R=M⁄ρ·V^1⁄3 and the molecular compressibility introduced by Wada B=M⁄ρ·β^−1⁄7 (=M⁄ρ^6⁄7·V^2⁄7), where M means the molecular weight, ρ the density, V the sound velocity and β the adiabatic compressibility, have been computed for 37 mixtures of mutually soluble liquids employing existing ultrasonic velocity data and the number average molecular weights. Although the sound velocity in and the adiabatic compressibility of liquid mixtures are known to be not necessarily monotonous functions of the concentration, exhibiting maxima or minima in some cases, the molecular compressibilities were found to be linear functions of concentration (molar fraction) in most of the liquids examined. The molecular sound velocities were found to be linear functions of the molar fraction in many of the mixtures, but they deviated from straight lines and became concave upwards in mixtures consisting of one heavy component (such as carbon tetrachloride and chloroform) and one light component. Both R and B, however, failed to be linear functions of molar fraction in water-alcohol mixtures, slightly deviating upwards from the straight lines with maxima of deviation in the neighbourhood of the concentrations corresponding to the velocity maxima. A few mixtures showed irregular R- and B-curves. This is presumably attributable to the inaccuracy of velocity data employed.

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