276 
-\4e- 
A few specimen figures from Jones' results are yiven in tne following table. 
TABLE 1. 
The volumes v are in cc., and the pressures p are in units 107 kam/em*. 
For values of v between 145 and 280, the above values are fitted fairly well by the 
equation 
(p + 16.65) (v= 112.3) = 4390 (8) 
and between the limits just quoted the equation is useful for theoretical work. 
Before we go any further we must decide on a value for the initial radius of the charges 
For convenience we take this to be 30 cm., so that the weight is 176 kjm, or 390 1b. By suitable 
scale chanjes, described when we come to consider the experimental results, our results may be 
easily modified to apply to any initial radius. . 
The appropriate modification of the above relation between p and v, valia for 
922 p29.6 is 
(p + 16,65) (v- 0.495) = 19.3 (9) 
where v is the specific volume, i.e. the volume per gm. or i/p, where — is the density. 
From this equation it is easy to find the velocity of sound V. 
VY = / dp/gp = (1950 + 35.2p) metres per second, 
valld for p 2 10, 
For lower values of p, the simplest way to yet V is probably by numerical differentiation. 
We find values shown in Table 2 
The function f(0) may also be obtained in the nigher pressure regions immediately from 
the use of (9), and we find 
(eo) = 1380 Joy, { 1+ p/16.65 ] m./sec. 
For the lower pressure regions direct numerical differentiation and then Integration 
must be made. The values we find are shown in Table 2. 
AS we have already mentioned, absolute values of f(g) are of no consequence; all that 
matters is\differences. The zero which we choose for f(o) corresponds with p = © in (9), and 
therefore has no physical significance, but is nevertheless convenient. 
Table 2 sccce 
