930 
then a step force exceeding aFy) would be required to produce additional defor- 
matione 
From another point of view, the question arises as to how amall initial 
deformations should be used in attempts to correct for their existence. 
Equation (I-50) shows that the correction is additive, ieee, the incident step 
force F must be calculated from the sum of the final and initial deformation: 
k + 
Fe oe Tp) (1-52) 
=) 
It is obvious that these results are highly idealized and stem from 
assvmptions implioit in Eqe (I-l)e ‘The latter equation is simply an expression 
of Newton's second law and fails to account for phenomena associated with the 
propagation of the plastic wave through the copper sphere and subsequent reflec- 
tions from the interfaces at piston and anvil, iee., Eqe (I-1) assumes that the 
far end of the copper sphere is instantaneously conscious of events at the near 
end. 
The theory developed in this section must consequently be regarded only 
as a first order treatment reliable only when the corrections are not large. 
lle Gauge Not Rigidly Mounted 
When the gauge is free to move under the influence of the pressure wave 
and is so mounted that the rear end of the gauge is not exposed to the pressure, 
the following force diagrams are applicable. 
Pa Pa + k(x, = x,) 
HX, MX, 
k(x, - x,) 
Fig. I-9- Piston and Ball. Fig. I-10. Gauge Body. 
where; 1 8 
P #= applied pressure m # mass of piston + yg mass ball + ry pe 
a = piston area M ©= mass of gauge body 
= area of gauge body x = deformation of copper ball 
x, = piston displacement x, = gauge body displacement 
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