The natural vibration of clamped-free bars is investigated, assuming the cross section to vary as a certain power of the distance from the free end, and further simplifying the calculation by taking the radius of gyration to be constant. The frequency of the gravest mode of vibration is expressed in a simple formula ready for use. Next the vibration of flexible bars attached to the periphery of a rotating disk is dealt with under the same assumption regarding the form of bars as in the preceding case. The frequency is again expressed in a formula. These two kinds of the frequencies may be combined by Lamb-Southwell's method to give the approximate value of the frequency in rotation under the restoring forces, both elastic and centrifugal. The calculation is applied to a turbine blade, and the calculated frequencies of the blade at rest are compared with the values observed in the experiments, which were performed by recording the vibration on a smoked paper in one series, and on a sensitive film in another series. The article consists of four sections, of which the first gives the outlines of the calculation, while the details of the calculation, the methods of the experiments, etc., are shown in the subsequent three sections.

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At exit from the impeller the absolute velocity of the water is suddenly decreased, which naturally is accompanied by shock losses. It is therefore advisable to diminish the shock losses by sharpening the vane tips at exit and having sufficient clearance space between the impeller and guide vanes. The object of the experiments is to study if any variation in the efficiency or characteristics of the pump occured, when the vane tips at exit are sharpened and are not. This variation is also further studied by increaing the clearance space between the impeller and guide vanes. The results of the experiments are given in the attached tables and shown in graphical form.

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Snow flakes which are floating in a scattered condition in the water in the forebay, freely pass through the screen arranged in front of the entrance to the penstock or the conducting pipe to the water turbine. In an ordinary working state of the turbine the velocity of water in the pipe is so large that they are carried off and pass through the runner and draught tube to the tail race with out any risk of derangement to the whole system. But, owing to the less dersity, if the velocity of water in the pipe is very small, the snow flakes mixed in it rise opposite to the flow due to its buoyancy. This is the case when the turbine is going to set to stop in a snowy day. In this case the sluice gate at the entrance to the pipe is first closed, and the water in the pipe is slowly blown off through the turbine and draught tube. If the process of blowing off the water is too slow, the snow flakes rise opposite to the flow, and all of them accumulate on the surface of the water forming amassive block of snow there. This depresses slowly down the pipe with the surface in it, and when it comes to the part of the pipe set nearly horizontal it is liable to be left there. If the pipe is very long, the total quantity of snow flakes contained in it may be so large that the block of snow thus formed is sufficient to clog the pipe, and in a cold weather it then freezes in the form of a solid plug which is so tight that no water can pass through. This is the cause of destruction of a hydroelectric power plant of Fukushima Eleotrie Lighting Co. at Fukushima, which happened at about 3 P. M., on the 4th. day of March, 1923, A massive block of snow choked the conducting pipe at the section about its mid-way in the morning when the turbine was set to stop for cleaning. It was so tight and strong that in the afternoon, when water is admitted from the auxiliary gate made at the entrance to the pipe, for the purpose of starting the turbine, it supported the column of water piled up about one-third of the total length of the pipe. It was then suddenly set in motion due to the weight of the column of water. This sudden motion and consequent acceleration of the snow piston followed by the long column of water made the destruction of the plant. The result of the accident was the collapse of the conducting pipe due to the drop of pressure caused by the sudden motion of the column of water in contact with it, the explesion of the expansion joint, that of the gate valve at the entrance to the turbine casing, the crushing of the spiral casing of the turbine, and the destruction of the roof of the building.

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