874 
principle" (11), namely, that any motion approaches its incom- 
pressive avvroximation after a sufficiently long time (see para- 
gravh 14.). 
12. Only at the center of the orifice does the pressure vary 
exactly as just described. Near an edge waves coming from the 
direction of that edge spoil the proportionality of the relief 
pressure to the velocity in a shorter time than R/c; but, on 
the other hand, waves coming from the opposite edge take a longer 
time than R/e to arrive. The net effect is probably to make the 
pressure variation nearly the same for central. and eccentric points. 
III, THE RESPONSE OF THE PISTONS 
13. In (9.3) the total pressure is written in terms of the 
motidn and the incident pressure. The second condition, giving 
the motion as a function of the pressure, may now be stated. The 
reeponee of any piston obeye the following equation 
(13.1) (M* paz) 2 * kz, = J p 4s 
(A,) 
where 
M 
effective mass of piston and copper ball or pellet 
face of piston, also its area, 
aN = forward travel of piston, 
k = force constant of pellet corrected for dynamic 
strain-rate, 
p = pressure at mouth of orifice, 
A, = mouth of orifice. 
Here M ie the masse of the piston only if it is moving freely, ae 
Sneigt vs 
