258 
Mr Sears, On the Longitudinal Impact 
In order that the nature of the impact should not be materially 
affected by slight deviations from axial collinearity, the rods were 
made slightly convex at the ends where the impact took place. 
One most important effect of this is to render the duration and 
other circumstances of the impact, directly calculable from known 
data, the indefinite “ Zwischenschicht ” of Voigt’s theory being 
replaced by a region of separation between the two rods, the 
mechanical properties of which depend only on the shape of their 
ends, and on the elastic constants of the metal. The law connect- 
ing stress and strain (or rather, total pressure and compression) 
in this region is, however, no longer linear, so that St Venant’s 
method cannot now be adapted (as in Voigt’s theory) to suit the 
requirements of the case. In the immediate neighbourhood of the 
point of contact, the relation between pressure and compression 
may be determined by the method of Hertz, but Hertz’s theory of 
impact is inapplicable to the case of long rods, since it takes no 
account of any wave-motion which may be set up. But my 
experiments clearly prove that wave-motion is the determining 
factor of the impact, and that the waves are propagated with the 
velocity /— given by St Venant’s theory. This theory, then, 
must evidently form the basis of the required solution. The 
method must, however, be modified by the aid of Hertz’s theory in 
order to deduce the effects of the rounded ends. I have succeeded 
in effecting the required combination of the two theories — with 
good results so far as I have been able to test them ; but the 
solution is not given here as I wish to check it further before 
publication. 
The times of impact were determined by the method first 
introduced by Pouillet*,and afterwards applied to the same problem 
by Schneebeli-f-, HausmaningerJ, and Hamburger§. The experi- 
ments of the latter are particularly interesting as tending to 
confirm, in a general way, the results given in this paper with 
regard to a straight line law ; but (as he himself remarks) the 
differences he obtains are much too small for St Venant’s theory, 
whilst all his times appear to be very large. This does not seem 
easy to explain, but probably much greater accuracy is obtainable 
with modern instruments than was then possible. Hamburger’s 
method of calibration, in particular, seems to offer considerable 
difficulties. 
The method, as ordinarily employed in my experiments, consists 
in allowing an electric circuit to be completed by the contact 
between the two rods, the total quantity of electricity which passes, 
* Pogg. Ann. 64, 1845. + Ibid. 143—145, 1871-2. 
J Wiener Sitzungsberichte, 88, 2 te Abth. 1883. § Wied. Ann. 28, 1886. 
