The lateral density distribution of the ionizing particles around the core of the extensive air shower has been observed with ten plastic scintillation counters at mountain altitude (2775 meters above sea level). The lateral density distribution, which has seemed so far to be expressed by the unique function of the distance from the central axis of extensive air showers, has been clearized as that it could be expressed by 1⁄rⁿ approximately is a range of 20 meters from the axis and n varies from 0.8 to 2.0 by the character of each shower. The result seems to have a relation to the fluctuation which has been presented in the previous paper or to the fluctuation of nuclear cascade in the development of extensive air showers.
The density spectrum at single counter has been also analysed and the result supports above conclusion.

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Mu-meson component, observed underground, of the extensive air shower is studied, which has come from the nuclear cascade of the shower core in the ground and possibly shows high concentration of mu-mesons below the ground. The total number of them can be estimated independently of energy and multiplicity distributions of secondary particles of the elementary collision each of shower particles undergoes, and also independently of some fluctuations. It is only because they depend upon the whole feature of the nuclear cascade in the shower core.
Experimental data of the multiple penetrating particles (M.P.P.), whose feature is the high concentration of mu-mesons, could not be interpreted in terms of those mu-mesons, i. e., decay products within the nuclear cascades in the ground initiated by impinging nucleons of high energy in the air shower cores, even though the possible contribution of the K-meson and Hyperon production in the high energy collisions within nuclear cascades is taken into consideration.

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A new type of detector called transition chamber was used to study high-energy nuclear-active particles (N-particles) above 10¹¹ ev in extensive air showers (EAS) of size above 10³. The differential energy spectrum of N-particles is shown to be represented by E_N^−2.0±0.1dE_N up to 3.10¹³ ev irrespective of shower size. The lateral distribution of nuclear-active particles is obtained within 10 m from the axis. This distribution is tentatively explained by a phenomenological model assuming the Maxwell-Boltzmann distribution for the transverse momentum of N-particles. Total number of N-particles of energy E_N≥10¹¹ ev, N_N, in an extensive air shower is expressed as a function of size N_e by N_N=(50±5)(N_e⁄10⁵)^1.1±0.1, for N_e ranging from 10³ to more than 10⁶. Then the total energy carried by all N-particles of E_N≥10¹¹ ev is estimated to be as much as that of the electron component in an EAS. On the basis of the observed general relationship between the electron component and N-particles for a wide range of sizes, a model of the development of EAS is suggested. The energy spectrum of N-particles is discussed in relation to that of high-energy γ-rays. In particular the existence of very high-energy N-particles implies that the average inelasticity in high energy interactions η=0.4∼0.5, if they assumed to be survivors of primary particles. Also the possibilities are discussed for the occurrence of N-particles with energies as much as 10% or more of primary particles.

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The trapping of conduction electrons by dislocation lines in alkali halide crystals was investigated by measuring the temperature dependence of photoconductances of deformed and undeformed crystals. Furthermore, the effect was verified by observing the thermally stimulated currents. In both cases, measurements of electric currents were carried out under application of ac in order to avoid undesirable effects due to space charge formation. Special care was exerted to obtain crystals having a high degree of purity. From the first mentioned experiment, the effective width of dislocation lines for electron trapping was estimated to be 9.3×10⁻⁸ cm, by using dislocation densities determined from nuclear magnetic resonance studies. The thermal depth of dislocation lines was estimated to be 0.21 ev for KBr and 0.24 ev for KCl crystals. A current glow peak, which presumable may correspond to trapping by jogs, was also measured. The thermal depth of jogs may be roughly estimated to be 0.48 ev.

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A self-consistent semiclassical theory is given for explaining the characteristics of the interaction of electrons and holes with acoustic waves in intrinsic semiconductors. The ultrasonic absorption coefficient can be written as Λ=Λ_R+Λ_K, where Λ_R is due to the change of the deformation potential energies of electrons and holes caused by their recombination, Λ_K due to the change of the kinetic energy caused by the intraband transition. The formula of Λ_R is identical with that used by Southgate in the analysis of his experiments, if the frequency at which ωτ=1 satisfies the inequality (ql)²<3(τ₀⁄τ), where ω, q are the angular frequency and the wave number of acoustic waves, and l, τ₀, τ are the mean free path, the intraband relaxation time, the lifetime of electrons or holes respectively. Under such condition as the frequency ω=1⁄τ satisfies (ql)²>3(τ₀⁄τ), no absorption peak can be expected contrary to the simple phenomenological treatment: Λ_R become smaller than the value of Southgate’s formula and is obscured by Λ_K. As a whole, the characteristics of interaction is very similar with those in many-valley semiconductors. The acousto-electromotive force is too small to be detectable in experiments.

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Growing process of GASH crystal was observed. If a droplet of saturated GASH solution on a slide glass is heated from upper side, platelets obtained afloat on the drop show six-rayed-star-shaped terraces. The mechanism of terrace formation is ascribed to bunching of progressing atomic steps. On the other hand, if heated from lower side, some platelets obtained at the bottom of the droplet are large and thick, which show dislocation etch pits on etching, while some remain small and thin showing no pits on etching. It appears that the growing process is not diffusion. controlled but follows the screw dislocation mechanism.
Dissolution process of GASH crystal was observed. Dissolution takes place by progression of macroscopic steps, which are nucleated book at crystal edges and at dislocation emergence points. The kinetics is controlled by diffusion and macroscopic steps are understood as bunching of atomic steps.

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The distribution in energy and angle of 20–25 kv electrons scattered by Al, Ag and Au evaporated films was measured with an electron velocity analyser of Möllenstedt type. The energy resolution is about 5×10⁻⁵, and the angular resolution better than 5×10⁻⁴ radian. The angular distribution of the characteristic energy loss was compared with Ferrell’s calculation. (Phys. Rev. 101 (’56) 554). The comparison shows that the experimental result is consistent with a simple Bohm-Pines’ approach provided that a correction is made for finite resolution of both energy and angle.

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The 180° domains along the b direction in NaNO₂ single crystals were observed by the etching method at room temperature. The domain boundaries lie parallel to (100). The virgin crystal prepared from the aqueous solution is almost of single-domain, but, after having once been heated above the Curie temperature, it has nearly the same domain structure as the crystal prepared from the melt. These domains were ascertained to be the ferroelectric ones from experiments with dc field. By the alkali etchant the positive end of the domain was more rapidly etched than the negative one, and nearly the contrary result was obtained for the acid etchant. The fact that the domain boundaries lie parallel to (100) would be intimately related with the thermal motion of NO₂⁻ radicals.

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Statistico-thermodynamical investigation is made on the size and density of reversely-polarized microdomains contained within a unidomain c-plate (or a macrodomain of a multidomain c-plate) of BaTiO₃ in thermal equilibrium at room temperature, with or without constant electric field applied. Microdomains treated here are confined to ones running through the crystal plate from the surface on the one side to the surface on the other side. It is found that a thinner crystal plate contains more reversely-polarized microdomains, and a plate thicker than about 2×10⁻⁶ cm contains practically no reversely-polarized microdomains. Reversely-polarized microdomains tend to disperse rather than coalesce, and can hardly be depressed by electric field. Just below the Curie temperature, it is expected that the critical thickness is considerably larger than the above value, since the domain-wall energy per unit area is fairly small.

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The boundary effect, i.e. the anomalous enhancement of transmitted reflection from the boundary of the etched and ground regions of a quartz plate (E. Fukushima. Acta Cryst. 7 (1954) 459) is studied by an X-ray photographic method. By this method it is found that at the boundary a fairly large strain is produced and the strained layer extends to a deeper layer in the crystal than at the ground region. The influence of annealing on the boundary effect is also studied by a Bragg spectrometer. The anomalous enhancement is reduced by the annealing at the temperature of about 400°C.
From the above results and some supplemental experiments on the ground surface, a model of the zone of strain at the boundary region is proposed and the mechanism of zone formation is considered.

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The 222-reflection of electron diffraction from CuCl is theoretically and experimentally studied. Ratio of the integrated intensity of the 222-reflection to that of the 111-reflection is calculated by expansion of the scattering matrix and by the solution of Mathieu equation. Calculated results by the both methods agree sufficiently with each other up to the grain size 140 A for 41.3 kV electrons.
The CdS detector and, in addition, the CdS monitor are used in the intensity measurement. The experimental values of the integrated intensity are found to be smaller than the theoretical values at small grain sizes of crystallites. It is, however, confirmed that the ratio of integrated intensity of the 222-reflection to that of the 111-reflection is nearly proportional to the square of grain size and the wave-length, in qualitative accordance with theory.
The 420-reflection is also measured. Dependence of the integrated intensity on wave-length is the same as that of the 222-reflection.

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The theory of dipole moment and end-to-end length of isotactic polymer is described. The problem of convergence of the infinite series in the matrix, which expresses a transformation of the bond vector, is studied in detail, a skeletal chain of linear polymer being regarded as a vector sum of many C–C bond vectors. The method of classifying the chain configurations is given on the basis of the convergence property of the series, which is an extension of the Neumann series. The polymer chain must be Gaussian, if the segments of polymer can rotate independently of each other. The hindrance potential for the internal rotation is assumed to be of the square-well type.

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The chemical kinetics of radiation-induced polymerization is mathematically investigated. The implication of the “stationary state” hypothesis, currently employed in kinetic treatments, is carefully examined. It is shown that the hypothesis is valid only in a certain time interval. Qualitative behaviors of the total number of polymer radicals as well as of polymer molecules as a function of time are derived without resorting to the stationary state hypothesis. In particular, the asymptotic behavior of the total number of radicals proves to be sensitive to the mode of termination reaction. It is also confirmed that the molecular size distribution approaches to the Poisson type asymptotically.

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The fatty plastic body such as butter or margarine possesses the remarkable non-Newtonian character in its rheological properties. The quantitative study of the viscosity, elasticity and yield value of butter has been performed under various conditions of temperature and shearing stress. The apparatus employed in the measurements involve an oscillating plate viscometer, a cone-plate viscometer and a parallel plate plastometer.
The viscosity, elasticity and yield value decrease remarkably when the specimen is subjected to the kneading on the roll mill, but they recover gradually to their original values after setting the specimen for a long time. The phenomenon can be called as a kind of thixotropy.
The volume dilatometry of the specimen has been also carried out continuously for a setting period of two months. From the comparison of results, the magnitude of viscosity or yield value of butter could be successfully connected to the degree of crystallization of fat in butter which had been evaluated from the specific volume of the specimen. The origin of the thixotropic softening and hardening of butter should be sought for, therefore, in the mechanism of rupture and formation of the three dimensional network of fat crystal in the specimen.

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The scattering of a plane microwave incident upon a cylindrically symmetric non-uniform plasma is treated in the Born approximation. When the electric vector is parallel to the axis of the cylinder, the angular distribution function of the cylindrical wave scattered from a cylindrical collisionless plasma is given by
f(θ)=\sqrt\fracπ2e^(3⁄4)πj∫₀^∞k²η(ρ′)J₀\left(2kρ′sin\fracθ2\ ight)ρ′dρ′.
Here θ is the scattering angle, η=(ω_p⁄ω)² with the plasma frequency ω_p, and the incident wave is assumed to be proportional to e^j(ωt−kx). The angular distributions for other cases, e.g. waves with the electric vector perpendicular to the axis and/or plasmas with collision loss in a magnetic field, are simply related to f(θ). For some special density distributions such as that of J₀-type, the integration in f(θ) can be performed analytically. Finally the same formulas are rederived by summing the radiations from electrons which are forced to oscillate by the incident wave.

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A.C. method was employed to investigate the mobility of the conduction electron in KBr under space charge free condition at temperatures between 80°K and room temperature. In this experiment white light was used to illuminate the specimen to enhance the conductivity. The mobility which depends on temperature was found to be inversely proportional to the mean density of phonons excited in the crystal. This fact suggests that the mobility is determined mainly by the scattering of the optical mode of lattice vibration. Using the Low and Pines formula, the following values were obtained:
Effective mass of the bare conduction electron, m^*=0.23 m
Effective mass of the polaron, m_p=0.33 m
Strength of interaction between the electron and the polarization,
α=2.56,
where m is the free electron mass.

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The photoconductivity structures of CdS single crystals near the adsorption edge were investigated using polarized light at about 81°K. Field dependence of wavelengths of peaks and spectral dependence of decay time of the response were measured as well. From these experimental results, the structures are classified into two groups, one is attributed to the photoconductivity due to excitons which occurs in the shorter wavelength range (λ<4870Å) and the other to that from some imperfections involved in the crystal, which appears on the longer wavelength side.

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Observations were made in the boundary layer along a flat plate in a wind tunnel. A sphere of various diameters was placed on the plate as an isolated roughness element and the resulting flow patterns were examined by the smoke emitted from various heights and positions relative to the sphere. The patterns were stereographically photographed from upper and lateral sides, in order to make clear the mechanism of the change of patterns with varying velocities, namely Reynolds numbers. At low velocities, peculiar vortex filaments are formed. With increasing velocity, they begin to be deformed periodically and a characteristic row of arch-shaped vortices is formed. As the velocity is further increased, the wedge-shaped turbulent region appears downstream and gradually approaches the sphere, encroaching upon the laminer part. Vortex filaments parallel to the direction of the main stream appear with a constant spacing with their heads along the sides of the wedge. These observations were compared with measurements by hot-wire and with the results of visualization reported by hot-wire and with the results of visualization reported by other investigators.

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Measurements were made on the vibrational acceleration of a point on a plate and the sound pressure near the plate surface. Attention was given to the initial values of the above quantities, together with coincidence frequency and the waveform of impulsive force, and the following results were obtained.
1) There is a close relation between the hammer momentum (mv) and the initial value (A₀) of the acceleration or the sound pressure, as expressed by the empirical formula; A₀=K₂(mv)^K₁. The physical meaning of these coefficients is considered.
2) The correspondence between vibrational acceleration and sound pressure is fairly complex and depends upon the mechanical properties and thickness of the plate. The coincidence effect was observed.
3) The waveform of the impulsive force was observed with different stiffnesses and with various velocities of the hammer. The frequency spectrum of the vibration depends on this waveform.

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Pole figures for the brass specimens which had been used for the measurement of the change in modulus of rigidity in the previous investigation¹⁾ and had received 90 per cent reduction in cross-sectional area by cold-rolling were obtained. In the pole figure of copper, the most intense rolling texture was {112} ⟨111⟩. In the pole figure of brass containing 10.14 per cent zinc, the most intense texture was {110} ⟨112⟩ and the {110} ⟨001⟩ texture also appeared in the figure in considerable degree. The intensity of the {110} ⟨001⟩ texture increases with the increase of zinc content. The existense of the β-phase in the brass wire containing 40.24 per cent zinc was ascertained, which had been predicted in the previous paper¹⁾. On the basis of these results the variation in the modulus of rigidity of the specimens, 57.5 per cent cold-rolled, with various, with various zinc contents was investigated.

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