In this paper the author introduced the differential equation of deflection of cast iron beam which subjected to the bending action and solved this equation on the beam having rectangular cross-section. Further from these results the author has indicated the certain approximate method to obtain the relational equation of load and deflection.

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The higher carbon content of nitriding steel becomes the more difficult nitriding. That is, carbon has effect Principally on hardness of nitrided layer in short time nitriding but produces much difference in depth in long time nitriding.
Thus the present auther has come to the conclusion, That carbon prolongs the saturation with nitrogen, and retards the diffusion velocity of nitrogen in inner part of steel during nitriding.

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Fractures of metals and alloys are technically very important. They differ from each other according both to kinds of materials and applied forces. I have classified all these fractures into 4 types according to the path and mechanism of rupture. The types for poly-phase alloys may be considered as combinations of those for mono-phase ones.
Type 1. Transgranular. Separation occurs along cleavage planes or "Spältflache". Fineness of fracture coincides with grain size. Very rough fracture.
Type 2. Transgranular. Slipping occurs along slip planes. Fracture is generally very much finer than grain size, fineness is equal with slip band size. Very fine fracture.
Type 3. Transgranular. Breaking occurs along dendrite boundaries. Fineness is quite indifferent with grain size and coincides with dendrite size. Very fine fracture.
Type 4. Intergranular. An abnormal fracture breaking along grain boundaries. Fineness coincides with grain size. Very rough fracture.
Type 3 was discovered by my experiments. Many common metals and alloys belong to this type, other three types being met with rather in rare cases. The reasons for proposing the new type are described in this paper. Test pieces were always broken by bending with shock force. Fractures, when viewed by naked eyes, give a feeling of fineness or roughness which of course is due to the zigzags on the surface. The characteristic features of type 3 are as following:
(a) The width of zigzags which determines the fineness is far smaller than grains but of equal size with dendrites. The fineness of fracture in natural size of α brass is smaller than 1 1/10mm. The grains are 1mm. or so wide and 10mm. or more long while the dendrites are about 1/30mm. thick and corespond just to the zigzags of the fracture.
(b) The path of fracture runs mostly along the trunks and big branches of dendrites, and even when the force acts so as to cross them they project (or sink) a little resulting in both cases the unevennesses of their sizes on the fracture.
(c) Dendrites are revealed in most fractured surfaces and contribute directly to the feeling of fineness. They are of equal size with the dendrites shown in the photomicrographs of the polished and etched surfaces.
(d) Is the grain size proportional to the dendrite size and consequently proportional also to fineness? That the answer is negative and the fineness is quite independent of grain size was proved by photomicrographs of gun metal ingots cast at various temperatures. Even the specimens of the same grain size give quite different finenesses when the dendrite sizes are different. Besides, specimens of larger grains have finer fracture than specimens of smaller grains when the dendrites of the former are smaller. That the fracture is exceedingly fine as compared with grain size was clearly proved by many photographs. Fracture of large dendrites is coarse and that of small ones is fine. Even different alloys are of the same fineness when their dendrite sizes are equal. These results were confirmed on fractures of steels, various copper alloys, light alloys and pure metals.
Examples of the fractures belonging to the other three types were also given on steels, non-ferrous alloys and pure metals.

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