872 
may use (9.3) end expect it to be error by not more than 2%. 
ll. With the help of (9.3) one may discuss the way in which the 
pressure changes at the mouth of the orifice left by a retreating 
piston. Consider a gauge which has a single, perfectly rigid 
piston end e completely immovable, infinite baffle, i.e., 
(22.2) zm (b,@ , t) 
z(t) b<R 
0) bap an 
zp (b,@ , t) 
wheres Zp, 4s the coordinate of a voint on the surface T, and where 
(b, , z) 48 a cylindricsel coordinate system whose origin is at 
the initial pnosition of the center of the piston. R is the radius 
of the piston. By (9.3) and (11.1) 
2 - Ff ‘ #, (t - <) ar 
ap, * pe Leg(t - &) - 2 (t)] 
uy 
or (11.2) P 
where P is the value of the pressure at center of the orifice 
(r = 0, z = 0), and Z, 16 the coordinate of the piston. Assume 
thet e11 parts of the gauge ere st rest before the shock wave strikes 
it. When the piston first begins to move, z,(t - R/c) is zero, and 
4t remseins zero until t = R/e. During this veriod 
(11.3) P=2P,- pe z(t) 
For large values of the time, on the other hand, P may be exnanded 
in the following form. 
eo Ct) Bea ee 
(a2). eho? = BP." pP 6 [eaves a : | 
ja Nard 
2 ee 
It will be shown later that second and higher order terms in R/e 
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