871 
¢ = density of medium (water) in which gauge is immersed. 
aS = element of area on T,. 
r = distance from dS to point at which wv is evaluated. 
ce = velocity of sound in medium (water). 
ap = acceleration of the fluid at the projection of 48 
on T, the moving surface defined in (9.2). 
The integral in (9.3) 18 to be extended over the infinite vlane, 
T,, but the retarded integrand makes it cut off at a finite distance. 
At the surface of the gauge ap ie the acceleration of A or of B. 
Elsewhere (c.) 4t 18 not directly related to the motion of the gauge; 
but in our applications of (9.3) the surface 8 is usually taken so 
large that the integrand vanishes on C. by retardation. Equation 
(9.3) is, therefore, the desired exoression for the pressure at any 
time on the plane tT in terms of the gauge motion and the incident 
pressure. The possibility of having an instead of aT, in the form- 
ula for p depends upon the very slight compressibility of water 
(appendix, paragraph 5.) 
10. The equation (9.3) is, of course, acoustic and anpvlicable 
only to "weak" shocks. Although the meaning of "weak" is not 
entirely clear at vresent, a shock of 300 atmospheres in water is 
probably well-described by acoustic theory if it impinges on the 
gauge at normal incidence. When a linear shock of 500 atmosnheres 
is reflected from a rigid wall, the acoustic approximation is 3% 
too low on veak pressure and 2% too high on the momentum imparted 
to the wall (reference 10). Since we assume normal incidence, we 
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