Referring to the quick return motions obtained by slider crank chain such as crank and slotted lever or Whitworth quick-return motion mechanism, the displacement χ of the body to which a quick return motion is to be given can be expressed conveniently in terms of the angle θ over which the driving pin has turned round. If the angular velocity of the driving pin be known the expression of the velocity and of the acceleration of the said body can be derived from that of χ by successive differentiations. These expressions remain the same so far as the ratio m of the radius of the driving pin circle to the length of the fixed link is constant. The length of stroke, the mean velocity, the maximum velocity, the ratio of cutting to return speed etc. of the reciprocating body can be plotted as curves on a base of m. These curves show the characteristics of the quick return motions. When m is greater than unity the expression of χ and accordingly those of the velocity and the acceleration, apply to the crank and slotted lever mechanism and if m is less than unity the same expressions apply to the Whitworth quick-return motion mechanism. The angular velocity of the driving pin of a crank and slotted lever mechanism may be made variable throughout one complete revolution of the pin, by means of the Whitworth mechanism as in the shaping machine of Mammutwerke in Nuernberg. The same expressions serve readily to show the advantages of the motion obtained by this combination of mechanisms.

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(1) Compression tests were made on seven pure metals. "Real stress-strain curves" were found and the "plastic deformation" was defined. (2) In the plastic deformation, the following relations hold : P/α′=Constant. Pl′=Constant. (3) The variation due to the dimension of specimen or the process of londing was examined. The "stress of the plastic deformation" is almost constant and the "range of the plastic deformation" is larger as the shape of specimen is shortor or the rate of loading is slower. (4) As a rule, the stress of the plastic deformation is small but the range is large for a metal whose melting point is low. (5) The effect of temperature was investigated, the temperature ranged between 0° to 560℃. The stress decreases with the rise of temperature and the range increases, but slightly. (6) For each metal, the stress vanishes at melting point and the relation between the stress and temperature can be expressed as follows : (P/α′)=A(M-t)^m or (P/α′)/(P/α)_2=(M-t_1/M-t_2)^m. (7) There exists a definite relation between the constants A or m and melting points, and in general the value of A is larger or m is smaller as the melting point is lower. (8) Each relation makes two series according as metals are hot short or not, or according as their molecular structures are hexagonal or cubic form.

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In the usual design, the entrance angle of vanes of the impeller is selected so that the flow at entrance will be radial. But there will be a whirling motion sot up in the suction pipe as the water approaches the impeller, and the absolute velocity of the water at ontrance to the impeller, even at the normal-condition, will have a component in the direction of the rotation of the impeller. In order to investigate the influence of the entrance angle of vanes on the characteristics of the pump, the six impellers were constructed assuming the several conditions of the flow at entrance. This is the report of the experiments upon the above six impeller. The results of the experiments are given in the attached tables and shown in graphical form.

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