934 
Proceedings of the Royal Society 
For the liquid condition outside this region 
^ is positive. 
Hence, 
from the third thermodynamical relation, we find that in this 
triangular region the adiabatics slope downwards towards the left 
for increased pressure ; while in the other region they slope 
downwards towards the right. So if we take a portion of the 
substance in a state corresponding to a point in the region where 
^ is negative, and allow it to expand adiabatically, its temperature 
rises. From calculations based upon the first and third thermo- 
dynamical relations, it seems that the slope of the adiabatics in this 
region is not so steep as the slope of the maximum-density curve. 
Hence we * have adiabatics meeting this curve. But no such 
adiabatic can pass into the region where ^ has a positive value, 
since the maximum-density curve slopes upwards toward the right. 
It must be determined by experiment then, whether the adiabatic 
coincides with this curve after meeting it, or if it re-enters the 
original region, its slope having become steeper. In either case we 
can have two adiabatics intersecting ; that is, at a given tempera- 
ture, volume, and pressure, we may have water near the maximum- 
density point, in at least two states differing in the amount of 
intrinsic energy possessed. If the adiabatics coincide with the 
maximum-density curve, we may have an infinite number of such 
states. 
Flow consider a portion of the substance in a state represented 
by a point in the region when ^ is positive. On adiabatic 
ctz 
expansion the temperature falls until the maximum-density curve 
is reached. After this, the temperature rises. Hence there is a 
point of minimum temperature upon the adiabatic. This point 
must be looked upon as one in which two adiabatics meet. 
Probably the course of each adiabatic meeting in one point on the 
curve {i.e., the adiabatics whose previous courses have been in the 
region of negative and positive values for ^ respectively), is 
dv 
different on further expansion. The amount of intrinsic energy 
possessed, determines which region the course will pass into on 
adiabatic compression from such a point. This is equivalent to 
