500 Prof. B. Hopkinson. [Jan. 31, 



result is that the total increase of length, caused by the blow, of a 

 piece x' at the top end of the wire is 



where T is the initial tension. In my experiments 2//.3//M is small, and 

 its square may be neglected. The expression then becomes 



The second term is a small correction, but cannot in all cases be 

 neglected. The piece of wire lengthens continuously as the wave 

 passes over it, and begins to contract when the reflected wave arrives 

 at its lower end. The extension then has the value given by expression 

 (1). These results are all to be found in Dr. Hopkinson's papers cited 

 above, or follow at once from the results there given ; and so it does not 

 seem necessary to repeat the proofs here. 



In the same paper Dr. Hopkinson gave the result of some rough 

 experiments which went to confirm the principal conclusion from this 

 analysis, namely, that the power of a blow to rupture a wire should be 

 measured rather by the velocity with which it is delivered than by its 

 energy or its momentum. It also appeared, as might be expected, from 

 the mathematics, that the wire was most likely to break at the upper 

 end. 



In these experiments, made over 30 years ago, the only available 

 means of estimating the momentary stresses produced by the blow was 

 the effect they left upon the wire, e.g., rupture. As the mathematical 

 treatment proceeds upon the assumption that the stress and strain are 

 everywhere and always proportional, it was not to be expected that it 

 could give more than a very general indication of the impulse necessary 

 to rupture the wire. With the appliances now available, however, I 

 think that experiments on these lines are capable of yielding a good 

 deal of information about the effect of stresses applied for a very short 

 time, such as are met with in most cases of shock. The practical 

 importance of such information need not be insisted upon. 



I have, therefore, made some experiments of the same kind, but 

 instead of rupturing the wire I have used blows which leave but little 

 permanent extension. I have measured the momentary extension of 

 a few inches at the top of the wire, and compared this with the 

 extension as calculated from theory and given in expression (1) above. 

 If the two agree, and if not much permanent extension is left, it is 

 clear that the theory is correctly applied, and that the stresses in the 

 material may be calculated from it. Moreover, we know that the 

 material must be substantially elastic up to the maximum stress so 

 calculated if applied for the time given by the theory. 



