882 
21. In order to take account.of the rarefaction (19.2) it 
is necessary either to calculate the velocity of the front face 
of the recoiling block, or to make the block so heavy and so 
nearly rigid that this velocity is negligible. The procedure 
here is to suppoge (19.2) decreased to a small value experi- 
mentally and to estimate this small quantity. The pressure 
(19.2) can be made small by choosing a nearly immovable block. 
Consider one which is rigid an@ laterally infinite, i.e., Ry, =. 
Let it be struck normally by an exponential pulse, namely, Pe = 
Be e7t/e, If the block is infinitely thick as well as wide, 
it does not recoil, and the pressure on its front face is always 
2Pe- If its inertia per unit area is finite, it recoils and the 
pressure on its front face is only a certain fraction of 2p,° 
Let it be 2p,r, where r = 1 for an immovable block, and r de- 
creases when the thickness of the block decreases. In paragraph 
10 of the avnendix, r is calculated. There it may be seen that 
r=i1 at t= 0, and that r decreases as t increases. Its value 
is of no interest for values of the time longer than t = Oo» 
the deformation time of the gauge. In order that r (6g) = 0.99, 
the block must be so thick that the following equation is satisfied. 
C201) m= op in (0.02n +-0.98);; 
n-1 
where 
m = 6/8 fg = density of block 
n = 69/206 d = thickness of block 
64 = Pe a/ Pp c 
aay ae 
