of Edinburgh, Session 1883-84. 
933 
8. On the Isothermals and Adiabatics of Water near the 
Maximum Density Point. By Mr W. Peddie. Com- 
municated by Professor Crum Brown. 
The state of water, as regards pressure, volume, temperature, 
entropy, and energy, may be represented by surfaces in 'a number 
of ways, depending upon which of the properties we choose to have 
their numerical values measured off along the*axes to which the surface 
is referred. The surface most suited for the consideration of the 
forms of the isothermals and adiabatics is that one the co-ordinates 
of each point of which represent pressure, volume, and temperature. 
The nature of this surface as constructed for water, and some of 
its peculiar features, were first studied by Professor James Thomson, 
and described by him in a communication made to this Society. 
Designating pressure, volume, and temperature by the letters p, v, t, 
the isothermals are the projections upon the plane {p, v) of the 
lines of intersection of planes of constant temperature with the 
surface. The adiabatics are the projections, upon the same plane 
of curves laid down upon the surface, such that, as the substance 
passes from one state to another as represented by points on the 
curve, it does so without absorption or emission of heat. The 
actual curve upon the surface may be termed the complete adia- 
batic. The chief features of the projection of the surface upon the 
plane (p, t) are three curves, which separate the regions representing 
the liquid, solid, and gaseous states. These three curves meet in 
a point, which Professor J. Thomson terms the triple point. If we 
measure pressure downwards and temperature to the right, the 
curve separating the liquid and gaseous regions slopes downwards 
from this point towards the right. The curve separating the solid 
and gaseous regions slopes upwards towards the left, making a 
greater angle with the t axis ; while the other curve slopes down- 
wards towards the left, and is very much steeper. The maximum- 
density curve slopes downwards to the left, but is not nearly so 
steep as the liquid solid curve which it meets at a point corresponding 
to a pressure of nearly three tons weight per square inch. It also meets 
the liquid-gaseous curve. Inside the triangular region so bounded 
the substance is liquid, and the quantity ^ has a negative value. 
ctz 
