Hydrographic station data, consisting principally of temperature and salinity determinations, have been used by physical oceanographers to develop a climatological picture of the distribution of these quantities in the oceans of the world. Density as determined by Knudsen's formula, taken together with hydrostatic and geostrophic dynamics, also provides a crude picture of oceanic flow. However, the data probably contain substantially more information than has been derived from them in the past.The quantity that is orthogonal to potential-density curves in the θS plane is suggested as a useful variable to complement the information contained in potential density. The derivation of this quantity, denoted by τ in this paper, is straightforward. A polynomial expression for τ that is suitable for computer calculations of τ from hydrographic station data is given. Shown are examples of hydrographic station data from the Atlantic plotted on the τσθ diagram. The information contained in the τσθ diagram shows many of the features exhibited in the TS plane. Vertical sections of τ appear to provide information about mixing in different parts of the Atlantic. The distribution of τ for abyssal waters at selected stations in the oceans of the world resembles the distribution of abyssal density as plotted by Lynn and Reid (1968). From the data presented, it appears that τ may serve as a good tracer for abyssal water movements.Since τ is defined to be orthogonal to σθ, the expectation is that τ is a dynamically passive variable. However, since σθ does not correlate with abyssal densities, it appears to lose dynamical significance at great depth, and τ assumes dynamical significance because of its orthogonality to σθ. This unexpected feature leads to an exploration of the dynamical significance of σθ. A natural starting point is the question of stability of abyssal water. A distinction is made between stability as determined by in situ determinations and as determined by the potential-density (σθ) distribution. Simple examples are presented to show that analysis based on σθ alone can lead to incorrect conclusions about gravitational stability of the water in the abyssal ocean. The reason is that seawater is a multicomponent thermodynamic system, and the thermodynamic coefficients are functions of pressure, salinity, and temperature. This functional dependence leads to adjustments in density as a water particle moves adiabatically in the vertical direction so that a layer of water that appears to be unstable near the surface may be stable (as determined by in situ determination) at great depth. A local potential density, which is simply the vertical integral of the in situ stability, is derived. This quantity gives a precise picture of gravitational stability in the vertical direction. Some distributions of local potential density are shown.