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 adiabatic. 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 downwards towards the left, and is very much steeper. The maximumdensity 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.