In the first half of the paper, the role played by various factors of the lagging of hot pipes to lose heat energy was investigated theoretically, and it was found that the conductivity and the thickness of the material are the most important ones. In the seconed half, the experiment conducted by authors is described. The thermal conductivity of various lagging materials in our marcket was estimated by an electrical method, and the effect of the thickness of the lagging was measured at the same time. Some useful formula and conclusions were obtained.

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The distribution of shearing stresses in a beam is mathematically investigated for two forms of cross-sections, namely, (1) a section bounded by two confocal ellipses. and (2) a sector of a circle. From Saint-Venant's flexure functions for these sections, the solutions of which are given in Appendix I, the shearing stress components are obtained. To illustrate the distribution of shearing stresses, those on the neutral axes and on certain boundaries are worked out, and their distributions are shown in diagrams. It is pointed out that, at a sharp corner projecting outwards in the cross-section of a beam, the shearing stress is zero, and, at the end of a crack and near the corner of a sharp re-entrant in the cross-section, the shearing stresses become very great. But, if the sharp corner is on the vertical symmetrical axis of the section, the shearing stress at the corner of such a re-entrant is zero, and, if the crack is along the vertical symmetrical axis, the distribution of the shearing stresses on the section is not influenced by the presence of such a crack. It is also noticed that, for a thin hollow elliptic cylindrical beam, the resultant shearing stress at any point on the cross-section is in the direction of the tangent at that point to the wall of the beam and can be obtained by the usual practical formula given by the equation, q=Wm/2tI, where W is the vertical load at the free end, t the normal thickness of the wall of the beam, and, m and I have their usual significance. The shearing stress components for a circular section and for a hollow circular section are given in Appendix II, and it is shown that the shearing stress on the neutral axis at the side of a very small circular cavity at the centre of a circular cross-section is twice the shearing stress at the corresponding point in a solid circular section of the same diameter.

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The shape of most indicator diagrams taken from high speed Diesel engines is quite different from that of Diesel cycle ; i.e. in the latter, the fuel burns at constant pressure at a time, while in the former, the combustion takes place in two phases. A part of the fuel burns first at nearly constant volume at the end of compression, next the remaining part of it burns at nearly constant pressure at the pressure attained by the former combustion, thus approximating the so-called Sabathe cycle. It is attempted in this paper, first to deduce the formulae for the thermal efficiency of the said cycle, next to compare the thermal efficiency of the said cycle with that of Diesel cycle.

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The endurance test of the steel cantilever beam with a sudden change in cross-section is performed by exciting its free vibration of the first or second order by an A. C. electromagnet. It is found that the fatigue occurs very rapidly when the ratio of two portions of the beam approaches to a definite value, and the fracture occurs always at the point of the discontinuity of the section.

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Hydraulic ram is a simple, ingenious and useful machine for raising water where favourable condition are found. While engineers are all familiar with the principle and working of hydraulic ram, it does not often appear to be regarded as a competitor of other forms of pump. Few reliable experimental data or theoretical investigations have yet been given ever since its invention. In this paper some particulars are given concerning a series of tests on a given hydraulic ram. They seem to show some characteristics of hydraulic ram and I hope that they will serve to be a guide for its pract cal application.

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