The density distribution and the zenith angle distribution of extensive air showers were measured at 2,760 meters elevation, geomagnetic latitude 25°N, by a cloud chamber in connection with a hodoscope consisted of Geiger counter trays shielded by lead absorbers.
Results obtained were as follows: (1) The integral density spectrum of the extensive air showers followed the power law distribution and its exponent was 1.70±0.13, (2) The projected angle distribution of the extensive air showers followed the empirical law of cosⁿθ, where n=6.9±1.3.

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Observations were carried out at a depth of 17 m.w.e. underground by nuclear plates made from Ilford G5 emulsions in gel form. The frequencies of μ-mesons and protons coming to rest in the emulsions were found to be 0.262±0.008 cm⁻³day⁻¹ and 0.049±0.004 cm⁻³day⁻¹, respectively. The angular distribution of these slow protons was found to be isotropic and so they are regarded as being of secondary origin from fast μ-mesons underground. In addition to the stars of the types of N_h+1_p with N_h≥3, several stars of the types of 1+1_p and 2+1_p were found with a cross section for production of a few times 10⁻³⁰ cm² per nucleon. Some of the stars of the type of 1+1_p may possibly be explained by photoproton production through the giant resonance absorption by emulsion nuclei of virtual photons associated with high energy μ-mesons.

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A general theory of the dielectric constant of simple ionic crystals is proposed. The energy change due to the electric field is expressed by a quadratic form of quantities p_x, p₁ and p₂, which represent the dipole moments due to the displacement of ions, the deformation of the negative ion and the deformation of the positive ion in the electric field respectively. Using this formalism it is possible to derive several important relations concerning the dielectric properties of ionic crystals. When the polarizability of the positive ion is much smaller than that of the negative ion, we may be allowed to put p₂=0. In this case our quadratic formalism has only three unknown constants, which are determined by using three observed quantities. For NaCl we determine them by using κ₀, κ and β (the optical dielectric constant, the static dielectric constant and the compressibility). Then we discuss the pressure effect of dielectric constants from our standpoints, and then we have computed the Reststrahlenfrequenz of NaCl considering the ionic polarization. The result agrees well with observation. Finally we propose a method of determining the phenomenological repulsive potential between ions of ionic crystals, which may be more accurate than the previous one.

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The cause of the abnormally high value of the dielectric constant of n-higher alcohols was investigated on the basis of some experimental results. To begin with, the discrepancies between D.C. conductivity and A.C. conductivity were examined in order to clarify the behaviour of the net conduction-current and the absorption-current due to dipole rotation.
Next, the frequency dependency of the dielectric constant in the low frequency region (30 c/sec∼5 kc/sec) was observed and the results were discussed in connexion with Maxwell-Wagner’s formula on the composite dielectric and with Cole’s theory on the conductive dielectric.
Thus, it seems to be reasonable to think that the high value of the dielectric constant of n-higher alcohols is an apparent value due to the higher electrical conductivity of its molecular rotating phase. An idea on the mechanism of the proton transfer in the solid alcohol is presented.

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Evaporated metal crystallites (gold, silver and aluminium) were studied by means of electron diffraction. As was previously reported by E. C. Williams (Research, 5, 1952, 392), measured spacings deviated from the cubic formula by the order of 0.1 percent for gold and silver while no deviation was detected for aluminium. We attributed the deviation to stacking faults in crystallites while Williams attributed it to a dislocation line penetrating through a crystallite.

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With a bent crystal X-ray spectrograph of the Cauchois type, the nondiagram line Kβ_η was resolved into two components and the longer wave-length one was designated as Kβ_l line. The intensity ratios of the Kβ_η and Kβ_l to the Kα₁ line were both estimated approximately to be the order of 10⁻⁴ or less.
On the basis of the wave-length positions, we could ascribe the origin of these lines to the two-electron jump between the double-hole levels (1s2p) and (2s3s). The hypothesis of such a two-electron jump which obeys the Heisenberg selection rule was first proposed by one of the present authors.
The Kβ_η originates from the transition KL_II–L_IM_I, and Kβ_l from KL_III–L_IM_I.

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The concept of a piled-up group of dislocations is discussed, and its relation to ductile fracture, to brittle fracture and to fatigue. It is suggested that a large enough stress induces fracture at a piled-up group, and a large number of such small cracks can join together to produce a ductile or fatigue fracture.

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An examination of etch patterns obtained with Lacombe’s etchant on polycrystals of “super-purity” aluminium suggests that an etch pit is produced only where there is a precipitate of impurity present in the surface, and that these are located on dislocations which can therefore be regarded as an indirect cause of etching. It is tentatively estimated that, at best, only about 60 or 70 per cent of the dislocations in super purity Al produce etch pits.

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Experimental study on the plastic deformation and the recovery process from strain hardening is described on the single crystals of silver bromide.
The various sorts of defects created during deformation are separated in each stage of recovery process, because of the difference of mobility energies. The difference of the mobility energies is also revealed in the change of the temperature dependence of excess ionic conductivity during the recovery process.
From the measurements of the change of excess ionic conductivity and the release of energy in the recovery process, the number of defects produced by deformation at room temperature was determined to be 10⁻⁷ per atom of anti-Schottky defects and 10⁻⁴ per atom of Schottky defects.
Some discussions are given on the mechanism of recovery from hardening and on the life time of defects in the recovery from strain hardening and in that from thermal quenching.

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The theory of Mott and of Fisher, Hart, and Pry for the production of slip bands is considered. This theory suggests that the kinetic energy of dislocations is what keeps glide on a slip band going; it also asserts that the process is stopped by the back stress resulting from dislocation loops previously generated at the Frank-Read source. Experimental observations giving the damping experienced by a dislocation and giving the velocity of glide are used to show that the potential energy of a dislocation is in general more than a hundred times the kinetic energy. Present evidence indicates that the rate of glide decreases by a factor of about fifty during the production of a single slip band in aluminum. Present data also indicates that twinning requires rapid dislocations whereas slip seems to demand slow dislocations. A way of reconciling these observations is suggested.

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The dislocation theory of strain ageing, as previously given for an isolated dislocation, is applied to the ageing of the dislocation array representing a small angle tilt boundary, and a change in the time law of ageing is predicted. The ageing of the array, and of isolated dislocations, is also considered using a model which allows for diffusion, and for competition for the solute atoms between arrays, or between isolated dislocations. The results are compared with available data for the initial stages of ageing and further experiments are suggested.

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The problem of determining the nature of the lattice defects which are responsible for transport of atoms in metals is discussed. The value of the Kirkendall effect in deciding that most of the transport is associated with migrating vacancies or interstitial atoms is restated. It is emphasized that we do not yet possess a satisfactory experimental method for deciding which of the two types of imperfection most important in typical metals.

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The steady slow motion of a circular cylinder in a viscous liquid bounded by two parallel plane walls is discussed on the basis of Oseen’s linearized equations of motion, confining ourselves to the case when the cylinder is moving midway between the bounding walls. The drag experienced by the cylinder is then calculated to Lamb’s approximation. It is shown that at sufficiently small Reynolds numbers, the drag on the cylinder is independent of the Reynolds number, namely, it is of the so-called Stokes type, as was shown by White’s experiments on wires falling in viscous liquids between two vertical plates. When the ratio of the distance between the walls to the diameter of the cylinder is greater than 20, our theoretical results coincide fairly well with White’s experiments, allowing for some experimental errors.

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The stability of the flow past a sphere which has been calculated previously by use of the Galerkin method was investigated by the method of small perturbation and the Galerkin method. Thus, the ciritical Reynolds number for the flow past a sphere was determined as 51 which should be compared with the experimental value of about 100.

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We obtained the rigorous solutions of Maxwell’s equations in an in homogeneous medium, which led to descriptions of the electromagnetic waves from a dipole source in the medium, where the inductive capacity is an arbitrary function of the distance from the center of the earth sphere. The first approximation of these descriptions give more abundant and complete results than those which have as yet been obtained by Fermat’s principle of geometrical optics and lead to a satisfactory theory for the so-called superrefracted propagation in a layer called the duct.

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