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non-central. The required equation of motion of the piston is, 
by (15.3) and (13.1) 
8 2 ee 
+ + = Re tks - 
(15.4) (M* Ap2,* Rp) Zt Ra = cap, 
The additional mase, 8/3 f R°, was calculated by Rayleigh (12) 
for the case of a disk vibrseting with simple hermonic motion, 
The preceding calculation shows that the mass of the piston is 
augmented by the same amount when the motion is not periodic. 
This conclusion can also be deduced from Rayleigh's result by 
making a Fourier enalysie of an arbitrary motion, and noting 
that the increase of mass for esch frequency is independent of 
that frequency: but the above proof is more direct than Rayleigh's 
for our purpose. The equation (15.4) 1s similer to the one given 
in reference (3) for side-on incidence (but of course the pressure 
4s not doubled in that case). We conclude from (15.4) that in the 
incompressive avproximation the effect of the rarefaction emitted 
by a recoiling viston is simply to increase its effective mass. 
16. In the nomenclature of varagraph 14, the equation (15.4) 
4s correct for the incompressive, non-central approximation. In 
the appendix, paragraph 7., this is comnared with the compressive, 
central and with the incompressive, central equationa. There it 
4s made clear that either the incompressive, or the central arpvroxi- 
mation, or both together, may be used without appreciable error. 
Equation (15.4), the incompressive, non-central apvroximation 
should be used, however, since it is as simple as the incompressive, 
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