An effective practical method of solving eigenvalue equations in Hilbert Space, for example, in problems of rectangular plates, is rationally studied by applying the theories of matrices and determinants, through which much labour and time will be saved. If the equations are given as the transcendetal simultaneous equations, we must further solve them, and if they are given as the linear simultaneous equations, we can immediately get their solutions.

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The purpose of this paper is to illustrate a method of analysis of rectangular rigid frames, considering them as systems of spokewise connected members, by the Takabeya's method of slope distribution. It produces very rapid convergencies of approximate slopes in iteration. It is inevitable, however, that the preliminary computations become more complicated and troublesome than by the current method. To save these labours the author established simple and easily memorable rules by observing physical properties of a spoke system, and succeeded to mechanize the whole computation works.
The scope of this paper is confined to the frames without sidesways.

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In this paper, the number of test specimens in order to know reasonably the quality and uniformity of concrete in the field, and degree of confidence to estimate variance of strength of concrete are described. The author's viewpoints for article 92 in Standard Specifications for Reinforced Concrete published by the Japan Society of Civil Engineers, and the method of rejecting data are also presented.

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It is generally considered that, differing from the pipe flow, the flow in open channels has a free surface and waves appearing on water surface relate to some extent with the laws of resistance to turbulent flow in open channels. According to this idea, the instability of flow is connected with the mixing length of turbulence, and then computing the velocity distribution by Prandtl's equation, Froude Number is added to Reynolds Number in the laws of resistance ot turbulent flow in open channels. Applying this theory, experimental results by the author, Dr. Matsuo and R. W. Powell with smooth open channels can be explained all over the regions of subcritical and supercritical flows, and therefore, the difference between the laws of resistance to turbulent flow in pipe and that in open channel can be made clear.

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In the tension test of wire-rope, wire-ropes can not be usually inserted between grips, but fusible alloy is used to cover each wire of the wire-rope, so that the rope may break at its middle portion. Such fusible alloys as Pb-Sb-alloys, Wodd's alloy and Pb- Sb-Zn-alloy are usually used.
The most important properties of the alloys are: (1) low melting point (2) high bond strength between the wire-rope and alloy and (3) small amount of creep. When creep is not small, there occures plastic deformation of anchor portion of suspension bridges in which wire-ropes are connected with anchor bolts by fusible alloy.
Therefore, the writers analyse experimentally the physical properties, i. e. melting point, bond strength and creep. of Pb-Sb-alloy and Pb-Sn-alloy.
Bond strength is measured by steel bar (diameter=15.9mm) instead of wire-ropes. Relation between bond strength and mixing ratio of Pb to Sb or Pb to Sn, relation between bond strength and embedded length, and relation between bond strength and surface conditions of steel bar are tested.
As for amount of creep of alloys used in this experiment, creep test is not done, so it is obliged to estimate only by stress-strain curve obtained in compression, but this estimation is considered to be correct according to the analysis by one of the writers in near future, creep test will be performed by the writers and the above estimation will be checked.

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The writer has proposed a certification method of intensity of resistance of tree against stone fall by reason of fundamental studies on the prevention forest of stone fall.
Namely, he calculated experimental value of impact-absorb-energy by the test piece of several species of tree.
Moreover, the relation between energy of falling stone, impact-absorb-energy of test piece and diameter of tree is expressed by an equation.
Namely, these results will give the fundamental data to the formation of forest, selection of tree kind of tree, determination of age tree years etc. of prevention forest of stone fall.

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Generally, it is not easy to conformally represent the region of which boundary is any curve in xy-plane, on he semi-infinite plane of which boundary is X-axis in XY-plane. The writer explains the method of approximately conformal representation of the former on the latter.

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Investigating the effects of the locomotive smoke in the tunnel upon the human body, relations between the density of smoke, time and its symptoms are solved analytically in order to apply them to the ventilation engineering.

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In this paper, the distribution of the pore water pressure in the foundation of earth dam is treated as the two dimensional problem. Starting from the fundamental theoretical equation of the two dimensional consolidation, the research is performed for the foundation whichh has infinite depth or under which a perfectly rigid and smooth rock base exists at any depth. First, applying Neuber's theory of elasticity, the stress distribution just after loading is obtained, and using it as the initial condition, the solution of the consolidation equation is represented in the form of Fourier's integral or Fourier's series with regard to each boundary condition. Next, performing the numerical calculation for the case of uniformly distributed load, the pore water pressure is computed as to the sudden loading and also as to the gradual loading on the semi-infinite foundation within the allowable error. Comparing these calculations with each other, the change of the distribution of the pore water pressure in respect of station and time has become clear at each loading condition.

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In the presented paper viscous percolations through table-lands are investigated Applying conformal transformations, analytical solutions of typical flows are obtained in the exact forms and are compared with the experiments. A new method of experiments with special considerations to the law of similarity is introduced, giving an excellent result in the comparison with analytical calculation.

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