446 



MR. B. HOPKINSON ON MEASURING THE PRESSURE PRODUCED IN THE 



negligible when the wave is long compared with the diameter, the velocity diminishes 

 with the wave-length. If the wave-length be -- , and if the radius of the cylinder 



/E 7 



be a, the velocity is A/ (1 <r 2 y 2 a 2 ) correct to the square of ya* In a wave of 



P 



any form, the simple harmonic components move with different velocities, and the 

 wave accordingly changes its form as it progresses. 



Rough calculation of this effect on waves generally similar in form to that produced 

 by the blow of the bullet, but of periodic character, showed that the change should 

 not be very serious with rods of the lengths and diameters used in these experiments. 

 It was, however, thought advisable to check this inference by direct experiment, and 

 trials were therefore made with a rod 15 inches long and 1 inch diameter. The 

 small mass of this rod precluded its use as a ballistic pendulum suspended in the 

 ordinary way, it was therefore arranged to slide in bearings and to compress a spring 

 buffer. Difficult questions arose as to the precise allowance which should be made 

 for the kinetic energy given to the spring (which was of considerable mass) by the 

 rod, and no attempt was therefore made to get an accurate measure of the total 

 momentum. Instead of taking the fraction of this total which was trapped in the 

 piece, the absolute values of the momenta so trapped were taken in a series of shots, 

 in each of which, from the accuracy of the aiming and the absence of cupping in the 

 end, it might be assumed that the total momentum was approximately equal to the 

 average. The results are shown in the following table and are compared with the 

 corresponding figures obtained with the long rod : 



ROD, 1 inch diameter. 2000 feet per second. 



It is clear from these figures that there is no systematic difference between the 

 results obtained with the two rods. The change, if any, between the forms of the 

 wave when at 15 inches and at 45 inches from the end consists in a shearing of the 



* LOVE, ' Mathematical Theory of Elasticity,' 2nd edition, p. 277. 



