Usually the dynamics of star type engines are approximately treated assuming that they have single obliquity, that is to say, their all connecting rods are directly attached to one common crank pin. In these engines, however, a connecting rod containing the crank pin bearings acts as a main rod and the remaining rods, being jointed to it act as the auxiliaries, i.e., they have the construction of double obliquity. The object of the present paper is taking its double obliquity into account to study the dynamics of rotary engine. The dynamics of radial engine that has double obliquity was studied by the writer and the investigation was presented to the Society last spring.

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The flow of water in the draught tube of a water turbine is quite different from that of the ordinary pipe flow. In the draught tube the water whirls round the axis tracing a helical course down to the tail race, and the more the quantity of discharge differs from that of the ideal normal the more this action is augmented. This action depends also on the radius. Hydrodynamical calculations are made with three kinds of draught tubes, cylindrical, conical and hyperboloidal, and it is proved that the pressure just in contact with the inner surface of the draught tube is unchanged by varied discharge, but the pressure inside it is very much influenced by the quantity of dischrge and also by its form. The distribution of pressure on any cross-section of the tube is parabolic, the pressure at the axis being sometimes minimum or sometimes maximum. Uniform pressure is realized only when the dischage is equal to a certain fixed amount, and when the discharge is much less than this amount a cavity is produced inside the tube forming a vacuum space which is not detected from the outside by means of pressure gauges usually attached on the tube wall. This is destructive of the effective action of the tube. In order, therefore, to avoid producing the cavity the turbine should be set so low that the pressure parabola formed on the uppermost cross-section of the tube in the case of the least available discharge lies entirely above the possible vacuum line.

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SEMI-FLUID HONING. When honing a razor or wood working tools, if one use water or oil sparingly, there is produced a gray colored paste like semi-fluid, consisting of water or oil with microscopic stool chips and stone powder detached from the stone face. Experienced men continue their honing, as the finishing time is approached, several minutes on this semi-fluid paste and get excellent finish. The writer points out that this result is due to the abrasive action of the stone powder present in the paste, which scratches the face of steel in a very much milder way than when the powder was fixed on the stone face, the action being comparable with that of a very much finer grained stone. CUTTING QUALITY TESTING MACHINE. During the time of the writer's work on a method of sharpening microtome knives, he dosignod an instrument, which was capable of measuring the cutting quality of the above named knives, razors and the likes. The instrument was so designed that the cutter to be tested cut a standard silk thread which was stretched to make constant angles with the plane bisecting the cutting angle, while the cutter being set at a constant prescribed position relative to the thread. The thread tension was gradually increased until it was cut, and a number reciprocally proportional to the final thread tension was called "the cutting quality" of the test cutter. With this instrument one could foretell how much thickness a microtome knife would cut a cut of, and also could graduate into several degrees the cutting quality of razors honed by experts. CUTTING ANGLE MEASURING INSTRUMENT. All leather sharpened keen cutters such as microtome knives and all stropped razors have their cutting edges not closed by flat faces but by rounded faces and have their cutting angles very much increased from original honed angles. The writer designed an instrument for measuring the roal cutting angles of these cutters. A bundle of woman's hair was stretched hy a light bow. To-and-fro stroke motion was given to this string, the string itself being constantly touching to a point of the cutting edge, just as a violin bow with the strings of the instrument. At the same time angular movement was also given to the bow which sweeped the plane perpendicular to the edge. By so doing, the direction of the hair string at which the edge begins to scrape the hair was noted. Then, the other direction of the hair string at which the edge begins to scrape the hair from the other side of the cutter was also noted. The angle between these two directions was taken as the true cutting angle of the edge. With this instrument, the writer could find that a certain razor had had its cutting angle increased by ordinary stropping from 18° original honed angle to as much as 30°, and yet its cutting quality was good enough for shaving.

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