i 869 
two conditions. First, the motion of any piston denends on the 
preesure over its exvosed face. Second, and inversely, the pressure 
4e a function of the motion of the piston itself, as well as of the 
motions of all other "nearby" parts of the gauge which recoil. 
(A moving element is to be regarded as "nearby" if sound has time 
to come from it before the geuge hss completely registered.) We 
have to express the motion as a function of the total vressure, 
and the total pressure as a function of the motion, as well as 
of the incident vressure. These two conditions, taken together, 
lead to an integro-differential equation which is characteristic 
of this kind of problem, and which is sufficient to determine the 
motion of the viaton (pistona). 
TI, THE PRESSURE FIELD NEAR A GAUGE 
8. We firet excress the total pressure as a function of the 
motion of the moving parts of the gauge and of the incident 
pressure, unverturbed by the gauge. The analytical method of 
doing this 18 provided by Kirchhoff's theorem. This theorem e- 
valuates a solution of the wave equation at any point in an arbi- 
trary, closed region in terms of retarded values of the function 
iteelf, and of ite space-and time-derivatives on the boundary of 
this region. The data required in Kirchhoff's theorem are redundant. 
For example, in our problem, knowledge of only the retarded accele- 
ration of the fluid over an infinite plane is sufficient to determine 
the pressure at any point in a certain region on one side of the 
plane. In paragravhs].-5. of the appendix the explicit exnression 
Hae vies 
