In this paper, the form of the tooth profile and the path of contact are determined mathematically by giving the circular arc for the profile of the toothed wheel gearing, and the pin wheel and Matsumura's tooth profiles are derived as the special cases of the gearing. The specific sliding for the profile is studied and is compared with the other tooth profilees, for instance, cycloidal teeth, involute teeth or Matsumura's teeth by some examples.

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For measuring the cutting force exerted on a drill very accurately, the authors have attempted to apply the piezoelectricity to this problem, and invented a new apparatus. Firstly, by means of this apparatus, how the twisting moment undergoes quantitative changes during the whole process of drilling the sample plate of a determinate thickness made of every kind of metals such as mild steel, copper, bronze, brass, aluminium, zinc, tin and lead was observed ; and it was ascertained that the twisting moment suddenly increasing at the instant of the drill tip piercing through the back of the plate is proportional to the twisting moment revealed during the earlier stage. Again, the changes of those two kinds of twisting moments according to the diameter and the feed were also examined for all those specimens above mentioned. Nextly, the changes of the thrust during the drilling process were examined for the said specimens, and the manner of dependence of the thrust upon the diameter and the feed was also tested. Lastly, the changes of the twisting moments according to the magnitude of the drill angle were measured for several kinds of metals. Diminishing 10 degrees each time from 140 degrees to begin with, the twisting moment diminished rather rapidly at first, but the rate of falling gradually decreased. One of the most essential conditions in carrying out the comparative tests of the cutting force of tools is to grind a great number of them to a similar form very accurately. As a round nose tool presents special difficulties for grinding, the authors devised and put into shape, as a trial, a new contrivance for a small grinder to be used in a laboratory.

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First, the features of the strain figure are refered to the stress distribution from the results of optical determination of strees. Secondly it is ascertained that there is close connection between the strain figure and the yielding point, and lastly it is tried to make clear why the strain figures are set in only in certain metals and not in the others. As the conclusion it is stated that the applications of the strain figure to the detection of cause of failure and to the improvement of the design of machine parts must have important bearing in the future.

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The present writer has measured the change of initial stresses in a cold drawn mild steel shaft (0.25% C) under various temperatures & durations of heating, and also aging, by Heyn's method using Zeiss'optimeter (Fig. 3 & 4) ; and obtained the following results. (1) The initial stresses have gradually released by heating up to about 300℃, markedly over 300℃, and completely at about 620℃ (Fig. 11). (2) At each temperature of heating, the release of initial stresses is remarkable during the first 30 min. of heating, and assymptotic beyond this point. At 300〜600℃, especially about 400℃, however, it is progressing even in 8 hr. of heating (Fig. 9.). (3) The release by aging are remarkable during about 20 days after cold working and assymptotic beyond this point (Fig. 9.) (4) Even a 4 years old test piece had have marked initial stresses and the distribution of initial stresses had been some what changed (Fig. 10.). >From these result the followings are considered. (a) The release of initial stresses by heating under 300℃, and over 300℃, is due to the vigorous vibration of atoms, and recrystallization of strained crystals, respectively. (b) The homogeneously distributed internal stresses, as the internal stresses, as the internal stresses produced by pure tension, etc., can not be measured by any direct methods, but the effects of heating temperatures upon these kinds of internal stresses are to be considered just the same to these results. (c) Compared these results with those of the changes of bardness, tensile properties, numbers of bending, specific gravity, magnetic properties, electric resistance, and stretching ratio of the ferrite grains of cold worked mild steel & of casting stress of cast iron by heating (Fig. 11 & 12), which are obtained by various investigaters. In addition to the above mentioned experiments, the writer measured the distribution of internal stresses of a mild steel, air coold from 650℃ after normalizing.

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The following mechanical properties of lead at ordinary temperature were measured by tension test. (I) Elastic properties (II) Plastic properties (i) Relations among stress, strain and speed of strain. (ii) Effect of strain hardening. (iii) Effect of annealing. (iv) Effect of seasoning.

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Test pieces of large grains of aluminium and iron were made and they were subjected to tensile deformation at the o-dinary temperature and at elevated temperatures as high as the melting point of aluminium and the transformation point of alpha iron into gamma iron. Changes of elongation from point to point were obtained by measuring mean values between gauge length of two millimeters. It was found that the hardness in the vicinity of the grain boundary is always different from that within the grain, which varies also with the direction of tension relative to the crystal axis. Possible explanations of the structure of grain boundary are discussed.

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The investigation on the relation between stress and strain in the impact test is a very difficult undertaking, so that up to the present, only a few accurate determinations have been published. The author using the same method as that of Korber and Storp with some improvements, obtained the stress-strain curve and investigated some of the problems in the notched-bar impact test. The materials tested were carbon steels containing 0.1,0.3 and 0.5 percent of carbon, and nickelchromium steels. The test-piece used was of the Izod type. The following results were obtained : - (1) A reliable stress-strain curve has been obtained by the present method. (2) In a test-piece of the same material but of different breadths, the energy absorbed is, in general, not proportional to the breadth, but where the thickness is small as compared with the breadth, the proportion between every and breadth nearly holds good. (3) In a case where the shape and the depth of the notch are equal, but the dimensions of the cross section of the test-piece vary in the same ratio, both the energy absorbed and the maximum stress are proportional to the product of the breadth and the square of the effective thickness of the test-piece. (4) The low-temperature brittleness was investigated and it was found that as the temperature falls the maximum stress decreases similary to the energy absorbed. In the case of the static test, the brittleness occurs at a lower temperature than it does in the impact test.

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In the present study, electrical resistance in steel specimens subjected to repeated bending stress was measured for different increasing stresses. Up to a certain value of the stress, the electrical resistance remained constant and afterwards gradually increased ; but the stress, at which resistance began to increase, was quite distinct and far below the proportional limit of the statical tension test. This stress may be considered as the endurance limit. In stresses a little below this limit, specimens were checked to stand 10,000,000 repetitions of bending stress, and hence the stress found in the above way is practically the endurance limit. Further, the relation between the newly obsarved endurance limit and Shore's hardness number was shown to be represented by a straight line passing through the origin, showing that materials having zero hardness have no endurance limit, and also the angle between this straight line and abscissa may Jepend on the characteristics of the material.

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The machine is an appliance for determining the unbalanced forces beared by a shaft in rotation. In the first part of the paper, the appliance itself is described and explained in detail. The main feature is to utilize the piezo-electricity of quartz, and the forces are so arranged as to act on two axes at right angles to each other in a plane perpendicular to the shaft thus enabling to determine the distribution of the unbalanced force in that plane. In the latter half, the methods of experiments for testifying the propriety of the arrangement as well as their results are described. This appliances can be adapted as well to any case of determining the unbalanced forces sustained by a rotating shaft accompanying reciprocation, to say nothing of the case of a simple rotor.

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A new metallic packing for ensuring the tightness of the stuffing box was invented, and some properties of the packing were investigated. Metallic packing alone is not enough to attain the perfect tightness of air at constant high pressure ; but if an oil box, containing some viscous liquid in it, be placed between the packing rings, no leakage of air and only a few drops of the liquid per minute pushed out will be observed. Results of the experiments of our metallic packing without any oil box employed for the 4 stage air compressor were much more satisfactory in comparison with ordinary non metallic packings. Above 40 atms. of the air pressure the frictional resistance of packing becomes considerable and also its wear will not be negligible.

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The circulation of hot water is definite so long as it behaves as solid water, but when associated with ebullition the circulation is generally thrown into unsteady state, owing to the effect of bubbles generated in the various parts of a vessel. It is necessary to locate the generation of bubbles, combined with the use of an effective down-comer so as not to induce any considerable stress against the movement of hot water in order that the direction of circulation may be kept constant. The rational design of water tube boiler should be based on this principle and accordingly water tube in some boiler, for example, may necessarily be of constant length irrespective of its size.

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So far as the writer is aware, no theory of propeller turbines or of propeller pumps has as yet been investigated, which is capable of clarifying fully the effects of such factors as the number of blades, the blade angle, the breadth of blades and the shape of the blade elements upon, (i) the action of these machines, and upon (ii) the occurrence of cavitation on the face of the blade. The writer has deduced here a theory of these machines in the light of the theory of aerofoil, with special reference to the effects above mentioned. The theoretical treatment has been presented in three parts ; each of which may be regarded as isolated by itself. They are : Part I, the preliminary study on the theory of blade interference ; Part II, the theory of propeller turbines ; Part III, the theory of propeller pumps. For practical purposes : In Part I the functions expressing the effects of interference upon (i) the lift and (ii) the pressure at the point of incipient cavitation, in terms of the pitch, the chord and the blade angle, have been calculated numerically and graphed. In Part II the design formulae for the selection of the profile form and the size and the blade angle of a partial turbine, and a formula in order to check for the prevention of the cavitation trouble have been given, by making use of the results obtained in Part I. In Part III the design formulae have been given in like manner, and, in addition, it has been shown theoretically how much more efficient a propeller pump fitted with guide vanes is than one with directing vanes or than one without either of them, and finally a formula for hydraulic efficiency, to be used in designing, has been given.

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The object of this experiment is to investigate the following effects on the efficiency of large centrifugal pumps for low lifts, for which few experimental results are known, and is to offer some date for designer ; (i) angle of inlet and exit of vane. (ii) dimensions of casing. (iii) length of vane. The author verified serious results of those effects on the efficiency of pumps from our experimental date. Test results are as following ; (i) change of angles of inlet and exit of vane, 3 degrees, affects by 9% for its efficiency when dimensions of casing and impeller are kept unchanged. (ii) change of diameter of impeller from 710 mm to 730 mm affects by 18%, when dimension of casing is kept unchanged. (iii) gain of 25% for its efficiency is obtained when angles of vanes and diameter of impeller are suitably changed.

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The clearance space is a wide open space lying between the guide vanes and the runner, and the flow in it being a potential one, the form of the casing and that of the hub of the runner as well as the stream lines in it should obey ordinary hydrodynamic laws of irrotationality. Taking this into consideration, the forms of the casing and the hub are first given, and the stream-line forms in the clearance space are determined by making use of cylindrical co-ordinates. The inflow velocities into the runner are then calculated from the stream lines, and the entrance and exit forms of the runner vanes, to satisfy the condition of minimum hydraulic losses, are determined. The expressions for the developing moment and the power are deduced, and finally a graphical solution, in order to simplify the above calculations relating to the vanes, is introduced.

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The authors tried to ascertain experimentally, how the moving speed will influence the deflection of the beam and the reaction on the supports in case of a load travelling on a continuous beam. To determine the deflection of the beam, a special optical bending indicator was devised, with which the deflection could be most accurately measured by being magnified 4000 times at the scale distance of one meter. To determine the reaction on the supports, the phenomenon of piezoelectricity was utilized ; i.e., the force sustained by the support was conveyed to a pair of quartz-blocks placed at its central part, and the piezo-electricity thus set up was measured. For the latter measurement the string electrometer constructed at our Institute was empoyed. Lastly, the results as obtained by the experiments were compared with calculated values and discussed in detail.

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The present study is the application of spherical coordinates to the solution of the problems of elastic sphere. The investigations hitherto made on such problems have been chiefly in Cartesian coordinates due to Lord Kelvin. In this paper a purely analytical method in polar coordinates introduced by the authors is employed. The paper consists of three sections : the first is on the general solutions, the second is an example for the case of a spherical cavity in elastic solid body under uniform tension and the third that for the case of an imbedded sphere. A noteworthy result is that the stresses in the imbedded sphere are independent of the radial distance from the centre.

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In this paper, strain problems in a general deformation are treated with methods and observations different from the usual theory of general strain, and elasticity in the consideration of general strain is investigated. In the first part of the paper, the obscurity in the usual definitions for strains is made clear, and it is shown that the usual measure of shear strain is not strictly proper. Then, it is shown that almost all the strain problems, in finite or infinitesimal strain, can be simply treated and expressed by the use of vector quantities, which represent, in amount and direction, a material straight line, the normal between a pair of parallel material planes and the relative displacement of a particle. Among the results thus obtained, these results are most noticeable, that the strain of a material plane and its tangential component, i.e. shear strain, bocome the maximum in a general case at pairs of material planes, the normals of which are perpendicular to the axis of the middle principal strain and have inclinations to the axis of the greatest principal strain, in the unstrained state, shown by cos^<-1>±[{(1+e_1)^2-(1+e_1)^<2/3>(1+e_3)^<2/3>}/{(1+e_1)^2-(1+e_3)^2}]^<1/2> for the maximum strain of a material plane, and by cos^<-1>±((1+e_1)/(2+e_1+e_3))^<1/2> for the maximum shear strain, e_1 and e_2 being the greatest and the least principal strains, while the value of the maximum shear strain is the same as stated in the usual theory. In addition to the analytical treatment, strain problems are illustrated graphically by means of strain ellipsoid (or by reciprocal strain ellipsoid) in a general case and by a plane diagram in a case of small strain, the diagram being drawn after, but with a correction to, Mohr's method. Lastly, it is stated from mathematical reasoning that Hooke's law can not strictly be true, that is to say, stress and strain can not strictly be proportional, and that the law has to be modified to be such that the principal strains are in linear relations to the forces on the principal planes, which have unit areas in the unstrained state.

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This paper is relate to an experiment to determine the coefficient of discharge of gas through a nozzle and orifice etc. by the method of measuring the time of efflux of air from a vessel. Notwithstanding that the correct measurement of the temperature change of the air in the vessel is the atmost important thing in this mothod, because it affects the coefficient very severely yet the radiation effect fails the measurement almost to nonsense. In this research the author has made an attempt to measure the correct temperature by the following method : the air which is filled in the vessel with certain pressure and temperature is discharged by opening the cock until it reaches to a certain pressure and the cock is then rapidly closed. After the cock is closed, the pressure and temperature of the air rise gradually and reach finally to a steady condition. The pressure and temperature are then read, and the temperature at the instant when the cock was closed is calculated from the perfect gas law by using these values. The vessel is then filled with the compressed air at the original pressure and temperature. Discharge is made again until another pressure is reached and the temperature at that instant is calculated by the same method as above described. The temperature change thus obtained is shown in the Fig. 7 comparing with that obserbed by the oscillograph. Experiments were repeated changing the initial pressure ; and the coefficients calculated both from the observed and calculated temperatures are compared in the Fig. 11 showing the defect of the value calculated from the former. The coefficients of discharge of the nozzle, sharp orifice and flat edged orifice are compared in the Fig. 12. The coefficient of discharge decreases with the pressure, as shown in the Fig. 12,and especially those of the sharp orifices decrease rapidly at about the critical pressure while the decreasing of those of the nozzles and flat edged orifices are not so remarkable.

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It is proved that Eq. (14) gives the frictional head in a transmisson piping of liquid which is pre-heated at the inlet of the piping. (14) is verified experimentally. It is also shown that there exists always a positive amount of temperature by which the liquid should be pre-heated in order to give the minimum value of the sum of energies-1,consumed for the transmission power and 2,consumed for the process of pre-heating. Eq. (17) gives the transmitting capacity of the piping increased by the process of pre-heating when the maximum allowable fluid pressure in the piping is assumed to be given.

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The velocity of detonation flame is several times that of sound. The reason why such a high velocity is attained by the combustion of strong fuel mixtures is explained. And this velocity of detonation flame and the impulsive pressure due to detonation are calculated.

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The new carburettor consists of a choke tube of the Venturi type and a fuel diffuser, diamond-shaped in section, which is a substitute for the fuel-spray nozzle of the simplest jet-in-tube carburettor. The choke tube is made to slide axially and thereby the passage area of gas is regulated ; a throttle valve, as usually adopted in other carburettors, may be entirely dispensed with. Analytical investigation on air flow through this carburettor was worked and it was found that this construction, when suitably designed, could comple with the fundamental requirement of carburation. A model, based on the result of the analysis, supported experimentally the expectation. A method to compensate the temperature effect on carburation has been also studied, which, however, will be touched upon on another occasion.

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In the course of the experiment on the flow of a fluid, there is a phenomena, often met, that a vortex occupied itself in neighbourhood of a stagnation point of flow. If the fluid be considered as nonviscous, the flow be potential one and the vortex be an irrotational one, the state in which the vortex occupies its position in the flow can be treated as a combined state of the each existency which will fulfil the field independently. Thus, in this paper, a. the movements of vortices are disccussed, b. the potential functions of vortices and flows are deduced by the method of conformal representation with several numerical examples and c. the combined states of the vortex and flow are also disccussed and are accompanied by several examples concerning to the fluid motion in the cylinder of a two cycle internal combustion engine of port scavenging type.

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The present paper describes the mathematical investigation of two dimensional flows of non-viscous fluid bounded wholly or partly by curved wall surfaces. The analytical solutions of the problems are obtained by assuming velocity distributions along walls and problems in more than twenty particular cases are worked out numerically among which those of flows past Venturi meter, Pitot tube, nozzle, knee etc. are discussed as two dimensional problems. The authors point out that the pressures measured along the walls of Venturi meter differ from the mean pressures due to the corresponding sections of the flow as shown in Fig. 4,and that in order to make the coefficient approach unity, the corners at the both ends of the conical tube should be rounded off, and the pressures along the walls should be measured at positions as far from the said corners as possible. With regard to Pitot tube, problems in three particular cases are worked out and the influence of the sectional shapes of the tubes on both dynamic and static pressures discussed.

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The present paper, being the continuation of the auther's earlier reports on the Koku Kenkyusho Zasturoku, consists of two parts. The former is the experiments of the air flow characteristics through an ordinary inlet valve and seat. Generally the air flow through an inlet valve has four different flow configurations I, II, III and IV with the increase of its lift as shown in Fig. 7,and at their tranferences there appear discontinuous points in the lift flow quantity curve, which are called as singular points. The latter is the experiments of variations of the flow configurations and the flow quantities, according to the changes or reformations of the shapes of the inlet valve and seat. There are five changeable points in the shapes as shown in Fig. 3. By these reformations the flow configuration and the flow quantity vary considerably, and often disappear the flow configurations II & III. The most efficient reformation is the rounding of the sharp edges of the valve and seat, and by this reformation Hispano Suiza 300 〓 engine increased 10〜15 〓 at 1800-1900 r.p.m.

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The present report relates to the third experiments made on disc valves with water. The arrangement of the apparatus was nearly the same as those discribed in the second report. The water from a supply tank, Fig. 42,A, flowed, through a 6-inch cast iron pipe of about 20 feet long, into a valve chamber of 4 inches diameter, Fig. 42,B, in which the valves to be tested were fitted. The difference of the level between the two overflow surfaces of the supply tank and the funnel above the valve chamber was nearly 4・85 feet. The pressure heads at several points on the valve chamber wall were measured by mercury manometers. The effective head or the loss of head due to the valve was found in the case of the smaller valves to be about from 4・85 to 4・75 feet. The lifting forces of water acting on the valve were determined by loading the valve with dead weight until it was brought into equilibrium states. The discharges of water through the valve were determined by means of a smaller tank mounted on a steel yard balance, and two larger calibrated measuring tanks. i. Tests have been made to determine the effect of width of the seat face. For this purpose three flat-seated valves were taken which have the diameters of 1 1/4,1 1/2 and 1 3/4 inches respectively, Fig. 1. The diameter of the port was 1 1/4 inches and the space around the valve could be altered by inserting cylindrical bushes of several diameters of from 1 7/8 to 3 inches into the chamber, Fig. 44. The results of the experiments are given in Tables 1,2,3 and Figs. 2,3,4,5. From these we learn that in the case of valve No. 9 (1 3/4 inches in diameter) the pressure drop due to the contraction of stream in the narrow passage on the seat face caused the greatest effect on the lifting force. (see the first and second reports) ii. In valve No. 8 (1 1/4 inch in diameter) the width of the valve seat was naught ; therefore, it might be expected that its characteristics would be of the simplest one. But it was not the case. The behaviors of the curves for lifting force much depend on the space left between the valve and the wall of the cylindrical bushes. Then with this valve the author attempted to determine the pure water pressure on the front face of the valve, and designed, as shown in Fig. 6,a special cylinder fitted with a long piston of 1 1/4 inches in diameter. To the bottom of the latter the valve was attached by means of small screws. The water pressure in the cylinder was measured by a manometer connected to the cylinder by means of a rubber tube. The curves plotted from the results of experiments, Fig. 7 and 8,show that the water pressure on the front face of valve No. 8 diminishes gradually as the valve opening increases. Next the piston was detached from the valve and was fixed to the cylinder by means of a set screw, so as a space of 0・6 inch was left between its bottom face and the back face of the valve resting on the seat. In this case the lifting force increases very rapidly as the valve lifts. We see from the results that the eddy current in the back space of the valve has considerable bearing on the characteristics of disc valve. Figs. 9 (b) and (c) show the arrangements for determining the total pressure on the front face of valves Nos. 6 and 7,one with flat seat and the other with conical seat, both having the diameters of 1 1/2 inches. The results of the experiments are shown in Figs. 10-13. We see in this case also the stream behaves in very complicated manners while flowing through the space between the cylinder and chamber wall. iii. With the object of studying the state of pressure distribution on the valve faces, valve No. 4 was prepared which was made hollow and had several piezometer holes bored on the faces, Fig. 17. A. A rubber tube was connected at one end to the top of the hollow spindle of the valve, and at the other end to a mercury manometer. The diameter of the valve was 2 1/2 inches and of the port 1 1/2 inches and of the chamber 4 inches. The

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