875 
in e Hillier gauge; it should be incressed by 1/3 the mass of 
the copper pellet, if the pellet is always in contect with ite 
anvil, as in a Grusher gauge. (See Appendix, naregraph 6.) The 
constent, k, is also different in these two cases; it vanishes 
for a freely moving piston. Since the pressure is integrated 
over the mouth of the orifice instead of over the face of the 
piston, the mass, M, must be augmented by that of the water following 
the piston into ite cylinder. This water mass, f Az is zero 
A’ 
for a crusher gauge, since here the piston is elwaye in contact 
with the ball, and the maximum value of z, is negligible. 
A 
14. The equations (9,3) and (13.1) are the two conditions which 
determine the response of the gauge. These do not solve the 
problem completely, because the region of integration in (13.1) 
is A\, while in (9.3) it 16 T,; and, in general, knowledge of 
&p and aC, 4s difficult to obtain. The problem is solved here 
for a gauge designed so that ap ie very small and so that ®¢,, 
makes itself felt only after the gauge has registered. We combine 
the two equations by calculeting the right hand member of (13.1) 
from (9.3). This will be done under two approximations: (a) that 
the velocity of sound is infinite, and (b) that the mean value of 
the presaure over the mouth of the orifice is equel to its value 
et the center of the same. The first approximation is generally 
called the incompressive one, and the second will here be called 
the central approximation. If the time required for sound to 
crose the orifice is small compared to the total time during whish 
