Mr Sears, On the Longitudinal Impact of Metal Rods, etc. 257 
On the Longitudinal Impact of Metal Rods with rounded ends. 
By J. E. Sears, B.A., St John’s College. (Communicated by 
Professor Hopkinson.) 
The object of the present paper is to compare the velocities of 
propagation of elastic waves in metal rods, as determined by a 
certain dynamical method, with those obtained by the ordinary 
Experiments by Prof. Hopkinson*' on the momentary extension 
produced in a long wire by a blow at one end proved that the 
observed and calculated velocities were the same within 2 or 3°/ 0 
in a steel or iron wire, but in a copper wire the observed velocity 
came out about 5°/ 0 too high. It appeared probable that the latter 
difference was more than experimental errors could account for 
and it was suggested that it might be due to a time-lag between 
the strain and the stress producing it, which would cause the 
elasticity for stresses applied for a very short time to exceed 
that determined statically in a testing machine. In such a case 
the velocity of wave propagation would be higher than that 
calculated from the formula. The experiments here described 
prove, however, that the two velocities agree within one-half per 
cent, not only in steel and iron but also in copper and aluminium. 
This result is in remarkable contrast with that of Wertheimf, who, 
attacking the same problem in a somewhat different manner, 
almost always found discrepancies between the two methods, far 
too great to be accounted for by any heat effects in the metal. 
The velocities of propagation in my experiments were deter- 
mined by means of observations on the duration of longitudinal 
impact between pairs of equal rods of the metal. According to 
St Venant’s theory, this should be equal to the time taken by a 
wave to travel twice the length of either rod. It was known, 
however, from the experiments of Voigt! an d others, that the 
observed times would be longer than this by an amount depending 
on the nature of the surfaces at the point of impact ; but it was 
hoped that this “ end-effect ” would prove independent of the 
length of the rods, provided the velocity and other conditions of 
the impact were kept unchanged. This was found to be the case, 
so that, by plotting duration of impact against length of rods, a 
straight line was obtained, whose slope gave the required value of 
the wave-velocity. 
* “ On the Effects of Momentary Stresses in Metals,” Proc. Roy. Soc. Vol. 74. 
t Ann. de Chim. et de Pliys. 3 C S6r., Tome 12. 
X Wied. Ann. 19, 1883. 
\Read 6 May 1907.] 
static method, using the formula v = 
