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



described, and others of similar nature. The word wave-meter may 

 probably be preferred in practice, but, if a special term is desired, the 

 author suggests, with diffidence, the name Cymometer or Kymometer 

 (from Ku/i,a, a wave) as applicable to it.* 



"The Effects of Momentary Stresses in Metals." By BERTRAM 

 HOPKINSON, M.A., Professor of Mechanism and Applied 

 Mechanics in the University of Cambridge. Communicated 

 by Professor EWING, F.K.S. Eeceived January 31, Eead 

 February 16, 1905. 



In 1872 the late Dr. John Hopkinson published an investigation 

 into the effect of a blow delivered by a falling weight on the lower 

 and free end of a wire, the upper end of which is fixed, f It is 

 unnecessary to repeat the mathematical analysis in full, but its main 

 features appear in the following argument : As soon as the weight 

 strikes the stop at the lower end a wave of extension starts up the wire, 

 and the velocity with which it is propagated is N/E//O = a, where E is 

 Young's modulus, and p the density of the wire. At a time t after the 

 weight has struck, so short that its velocity is not appreciably 

 diminished, the lower end of the wire has moved through a distance 

 Vtf, where V is the velocity of the weight immediately after striking. 

 That is to say, the wire as a whole is lengthened by an amount Vtf. 

 This extension is felt over a distance at from the lower end, that being 

 the distance through which the wave of extension initiated by the blow 

 has travelled. The mean strain in this portion of the wire is there- 

 fore V/a, and the remainder of the wire is not extended. The wave 

 now travels up the wire to the fixed end, and when it reaches there a 

 reflected wave of equal amplitude starts down the wire. There results 

 momentarily at the top end of the wire a strain equal to 2V/ with a 

 corresponding tension 2EV/a. This is the maximum tension experienced 

 by any part of the wire until the reflected wave again reaches the lower 

 end. 



Each bit of the motion of the weight after striking contributes an 

 element to the wave of extension, which is proportional to the then 

 velocity of the weight. The weight is continually being retarded, and 

 the amplitude of the wave therefore continually diminishes as you go 

 back from its front. 



* The writer is indebted to his colleague, Professor A. Platt, for advice on 

 the correct form of these words. 



t ' Original Papers,' Hopkinson, vol. 2, p. 316. 



