The development of the concept of a "neutral surface" - an isopycnal surface refined by the introduction of a variable reference pressure - is presented. Problems in approximating such a surface (concerning, for example and inter alia, the reference water parcel to be used in starting a neutral surface; or the reference pressure and parcel to be used and path to be followed in extending a neutral surface from station to station) are examined. These problems arise because oceanographic reality only provides data at discrete depths from given station networks. The effects of compressibility dependence on the thermohaline properties of a water parcel in delineating a neutral surface are also considered. A new method of approximating neutral surfaces is presented. Neutral surface analysis, that is to say a technique to infer qualitatively circulation based on hydrographic data, is discussed. Data from the Atlantic Ocean and the Mediterranean Sea are used to obtain a number of neutral surfaces, on which the spreading of various water masses is examined, elucidating some oceanographic problems and thereby vividly demonstrating the versatility of the technique proposed.