873 
may be dropped. Then 
(11.4) Pisveree—rie 7k: z(t) 
By (11.3) the relief pressure (the decrease in pressure due to 
recoil) is at first pronortional to the velocity of the piston 
and by (11.4) 1t leter becomes proportional to its acceleration. 
At t = 0, the total pressure 1s 2P,. It then falls because of 
the recoil of the piston according to (11.3). This situation 
continues until t = R/e, at which time the pressure-increase vrova- 
gated in from the edge of the orifice has reached its center. From 
then on (11.4) holds if R/c, or the third and higher derivatives of 
ZA are sufficiently small. The neglect of these terms igs tested 
in the avpendix, paragravh 2. Although (11.3), on the other hand, 
is verfectly correct, it holds only for a short time. For example, 
in all Bureau of Ordnance piston gauges R = 1/4", R/e = 4 x00 
sec, The corresvonding deformation time of a crusher gauge with 
e 5/32" ball is, however, of the order of 200 x 1076 sec. \ref- 
erence 3). Hence the initial motion, as described by (11.3), is 
short (4 microsec) compared to the total motion (200 microsec). 
The situation 18 even more exaggerated for Hilliar and for momentum 
gauges where the total motion may require 100-2000 microsec (de- 
pending on the piston) and ebout 4000 microsec, resvectively. For 
dianhragms R/c has been called the "diffraction" time by Kirkwood. 
It is spvproximately the time at which (11.3) ceases to avply and 
at which (11.4) begins to be correct. The fact thet the motion 
changes type in this way is an illustration of Kennard's "reduction 
