290 
a Ae 
The maximum error in v apparently occurs in the range 3.5 < p < 5 and is less than 2 parts 
in 1000. For pressures in the ranges .001 < p < 3.5 and 5 < p < 12 the error is smaller by a 
factor 3. At very high pressures, say 0 = 50 or more, the error may be several per cent but the 
experimental data are not at present sufficiently complete to state what the values of v are, within 
a few per cent. 
RY waves in water. 
Consider a plane shock wave in water. Suppose that the oressure on the low pressure side 
is atmospheric, Pye that the volume per gramme is vy and the temperature is 20°C. Let D, be the 
pressure and Vp the volume on the high pressure side, 
The shock wave equations are 
v= vy /(p,- oy - vA) (3) 
us J (>, - 0) (Vy, - yD). (4) 
where V, Is to be found for any soecified Po from the Hugoniot equation 
1 
mE 4 
Emerg ely * 22) Wye= %Q) (5) 
No simple exact exoression is avallable for Eo although the data of Bridgeman are complete 
enough to enable values of E, - eg to be constructed numerically for shock wave pressures up to 12. 
We stall require the solution of shock wave equations uo to much higher pressures, and extrapolation 
of his results is necessary, 
Figure 1 shows diagrammatically four polnts 4, 8, C, Don ap-—v diagram; A represents 
the initi al state of the water before it enters the shock wave, and C is the state after it has 
passed through. There are two convenient reversible paths by which the water may be taken from 
AtoC, The first is ABC; this corresponds to ralsing the pressure adiabatically to 05 and then 
supplying heat along BC at constant pressure p,, Tne second is ADC; this corresoonds to supplying 
heat at atmospheric pressure until the water reaches D, and then raising the pressure adiabatically 
till C is reached. 
The coefficient of thermal exoansion at high preesures is appreciably smaller than it is at 
atmosoherlc pressure, and Va-S Vio even at Dae 50, Is not more than two parts in a thousand, 
Consequently, the path BC is unimportant compared with AB, and AB is known from (1). In contrast, 
the route ADC involves a different adlabatic for every value of Poe Thus route ABC Is much more 
convenient for our calculations than ADC, 
From the first and second laws of thermodynamics, it follows that 
Cc 
Eze. Em p dv + Cat - o(v, - vio) (6) 
8 8 
where cy Is the specific heat at constant pressure Poe 
The leading term on R.H.S. of (6) can be evaluated accurately with the aid of (1). 
Performing the integration, and putting p, = 0, it is found that (5) and (6) lead to 
c 
i Ce = Ee 1 a i 
3 o,lv 2 v2) + Cat (v, v DG Pat 324803} — 0. 16009 Ges We 
(7) 
where v, corresponds with P= 0. 
The solution of (5) for v, given p, is most easily found by iteration. The process 
Cannot be carried far because c and the coefficient of expansion at high oressures are not know 
accurately. 
The sevee 
