878 
central solution and slightly more accurate. 
17. %&It is also possible to give an upper bound to the error 
sssociated with the use of the incompressive equation (15.4). 
The calculation is made in the appendix, paragraph 8., where it 
is shown that this apvroximation may be regarded as introducing 
an error in the effective mass of the piston. For a crusher gauge 
the relative error in effective mass is of the order of 
(17.1) a, x 107° per cent 
where R,M, and Og are radius of piston, effective mass of piston, 
end deformation time, all in cgs units. For a typical gauge 
this relative error is 0.5%. (Here R = 0.6 cm, M = 15g, and 
Og = 200 x 107§ sec). For a Hilliar piston the relative error 
is even less, namely, 
(17.2) 4R4 x 107° ver cent, 
where @, the eesanmestt of the incident pulse, is generally 
much longer than the time-constant of a crusher gseuge. 
18. In the Hilliar tyve of gauge there are several pistone, 
ell set in the same face of the gauge. There is thus the pnossi- 
bility, suggested by Hartmann, that the recoil of each piston 
will relieve the pressure on every other piston. A simple calcu- 
lation of the effect may be made as follows: The force Fy, which 
piston 1 exerts on piston O is by (9.3) 
(ie1) FL = j J a(t - £) a8, a3, 
CAT.) et Rene ee aries 2a 
where a, is the acceleration of piston 1, r is the distance between 
LS oye 
