The stress components are found by means of stress functions that must satisfy the differential equation ▽_1^4x=0 and the boundary conditions, when a disk is subjected to many equal radial compressive loads at equal pitches on its periphery. The contents of the paper are divided into the following four cases accordlog to the number of applied loads : -(I) Two loads ; (II) Any even number of loads ; (III) Three loads ; (IV) Any odd number of loads. Let x_0. be the stress function that cancels the surface stress components calculated from stress functions x_1,x_2,x_3,......etc due to applied loads, P, the applied load, d the diameter of the disk, and h, the thickness of the disk. Then we have the required stress function x for the four cases mentioned above as follows. (I)x_0 is [numerical formula]・r^2,and x=x_1+x_2+x_3. (II)In this case the problem is solved by the princple of superpositon using the solution obtained in (In). (III)x_0 is [numerical formula], and x=x_1+x_2+x_3+x_0. (IV)The number of loads is q+1,if q is even.x_0 is [numerical formula]・r^2,and x=x_1+x_2+x_3+......+x_q+x_<q+1>+x_0.

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The present paper deals with theoretical study of the variations of the hydraulic efficiency of a propeller turbine and of a propeller pump with respect to the following coefficients : - (i) coefficient of peripheral velocity of rotation, k_u, (ii) coefficient of axial velocity of flow, k_c, (iii) ratio of outer diameter to inner diameter of the wheel, m, In addition, for a propeller pump the relation between the manornetric efficiency and the specific speed is studied. It is noteworthy that the relation can not be expressed by a single curve, which is different from what has been generally accepted hitherto for centrifugal pumps, but should be expressed by many curves depending upon ku or k_c and m. Graphical representations of the results will serve to give information to select suitable values of the coefficients.

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The paper consists of two parts, The first part is the torsion problems of long solid cylinders, whose sectional forms are represented by β=0 curves of the equation x+iy=e^<i(α+iβ)>+Ae^<in(α+iβ)>+Be^<i(2n-1)(α+iβ)> where A and B are the arbitrary constants to define the forms of the section. Such shafts under consideration are long enough to apply St. Venant's theorv of torsion. In this part, it is also analvtically proved that the shearing stress-intensity is very great under torsion at the bottom of radial crack from the surface and how the radial depth of such a crack influences on the stress distribution of the section. The results are shown in Fig. 2 and 3. Furthermore the author calculates the relation of the maximum shearing stress to the depth of the groove when the radius of curvature at the bottom of groove is constant and that relation of the stress to the radius of curvature at the constant depth (Fig. 6). In the second part, he applies the above theory to the shaft with a keyway. His assumption is that the shearing stress at the corner A or B(Fig. 7) is nearly equal to that stress at the bottom of the groove which is represented by the dotted line, if the radii of curvatures at the both cases are equal. Then, the shearing stress at the corner of the keyway becomes very great when the radius of curvature is less than r/20,and that stress is nearly constant when the radius of curvature greater than r/20,r being the radius of the shaft. And the stress for the case r/20 is as large as the twice of the maximum shearing stress of the perfect circular cylinder. On the other hand, the torsional moment decreases with the keyway for twisting the same angle. Therefore, the resisting moment of the shaft with keyway (w=D/4 and h=D/6,where w and h are breadth and thickness of key) is 1/2 〓32 of that of perfect circular cylinder of the same diameter. Finally the theoretical values have been proved by experiments to be nearly true with mild steel shafts.

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The paper is a report on the experimental study of the mixing proportion of concrete constituents, that is gravel and sand, giving least cavities among them. According to the generally accepted opinion, such a composition will give us the concrete of the maximum strength. The experiments were carried out with the assumption that the mixing proportion giving the least cavity does not change whether it is or is not filled with the cement paste. With this assumption the experimental procedure were simplified, and the following results have been deduced. It is known experimentally that for the particular kind of constituents. there exists a cirtain mixing proportion giving the least cavity, which can be measured by a very simple device originated by the author. If this method be utilized for the practical purpose in actual field work, a great deal of the economy in consumption of the raw materials will be effected.

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The reqired power for driving a volute centrifugal pump may be calculated by means of momentum theory. In calculation, however, an effective diameter of the pump impeller should be used, which somewhat smaller than its out side diameter. Furthermore the outward flow of water through an impeller deflects slightly from the direction of impeller blades. These facts have been found out of the experimental results of fifty pumps, designed and tested by the author at the Hitachi works,

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