1905.] The Effects of Momentary Stresses in Metals. 499 



In Fig. 1 the abscissae are distances measured from 0, the free end 

 of the wire; the ordinates are the strains, and any one of them, say 

 P'N', is equal to v/a, where v is the velocity which the weight had 

 when the bit of wave at P left it. If t be the time, reckoned from 

 the moment of striking, ON = at, and it is easy to show that 



= a 6 M 



where //. is the mass of the wire per unit length, and M the mass of the 

 weight. The wave of extension represented by the curve and its 

 dotted continuation travels up the wire without change of type to the 

 upper end, where it is reflected, and a similar wave travels down the 

 wire, the effect of which is added to that of the original wave. The 

 strain at any point of the wire, such as N', is zero till the wave reaches 

 it. The strain then becomes V/a, and gradually diminishes according 

 to the exponential law g-***/M un til the reflected wave reaches N', 

 when the strain increases by V/a again. Further reflection will occur 



FIG. 1. 



at the moving weight, but in my experiments this is not considerable, 

 and the maximum strain experienced at any point of the wire, at any 

 rate in the upper half, occurs when the reflected wave reaches it. If 

 x' be the distance of the point from the upper end, the total strain due 



to the up-going and down-coming waves then is (1 + e ) . The 



movement in space of any point N' before the reflected wave reaches 

 it is equal to the area of the curve PNNT'. For the point in question 



this is ^Y (1 - e -^ x>lm }. The strain caused by the blow is added to 



pa 



any initial strain in the wire. When, as is usually the case, the wire 

 is under tension at the moment of the blow, and the tension is released 

 by the blow, the initial strain in the wire is somewhat diminished by 

 the time the wave reaches the top end ; superposed upon the extension 

 caused by the blow there is a slight contraction due to the release of 

 the tension at the lower end at the moment of striking. The ultimate 



