277 
Me 
TABLE 2. (p< 10 
Bridgeman has made accurate measurements of v for various values of p and T for water, 
but the maximum value of p which he was able to reach was 0 = 12. Now the most important region 
for our calculations is undouktedly covered by nis measurements, but nevertheless we do require 
to know the relation between p and v along an adfabatic for oressures as hiyh as 40,000 kgm/om2, 
The best that we can do is to fit the adiabatic obtained from Bridyeman's figures up top = 12 
with a sultable équation, and then apply this equation up to 0 = 40, 
From his measurements, Briggeman was able to construct curves showing the adiabatic rise 
in temperature caused by a sudden small increase in pressure in water at various temperatures 
and pressurcs. These curves enable onc to construct curves for water at varlous Initial 
temperatures showing the rise in temperature as the pressure in increased adiabatically. Such 
curves are for the most part sma@th, but do exhibit peculiar bumps, assoclated with the anomalous 
maximum density of water at atmospheric pressure at 4°C, We have made no effort to take such 
fine details into consiaeratlon; by assuming that the water was initially at 20°C, however, an 
adiabatic curve sInygularly free from bumps is obtained, From 8ridjeman’s results we find that 
for the adiabatic for water which is at 2°C for pressure one atmosphere, the following equation 
between p and v holds within about 1% over the pressure range 1< p < 12,000 atmospheres. 
(c + 7.82) (V- 0.6807) = 2.493 (10) 
the error being worst at the low oressure end, 
This is the relation which we use over the entire pressure range with whith we have to 
deal. 
For initial temperatures jreater than 20°C, we find the following adiabatic relation 
holds quite well 
(o + 7.82) [ v - 0.6807 - 0,00035 (T,- 20) ] = 2.93 + 0.0006 (T, - 20), 
where To is the temperature at atmospheric pressure. 
Direct ca'culation shows that the velocity of sound is given by 
Veu=sei950rtes t40p metres per second. 
The function f (0) works out at 
f(e) = 496 103, [ 1+ p/7-82] msec. 
For small values of p we may 2xpand 
f(p) = 63.5~ + ov 
Table 3 shows values of V and f(), for comparison with those of Table 2, It will be 
seen that if our calculations sre valid at the very high pressures, the velocity of sound is 
appreciably greater In water than In the exploded jas. 
TABLE 3 seoee 
