The relation between temperature, salinity, and pressure in the Atlantic Ocean is examined. Most of the Atlantic resolves itself into three two-dimensional manifolds of three-dimensional thermodynamic space: a northern, more saline, branch, and a southern, fresher, branch, each quite independent of pressure, and between them a bridge, on which density is uniform at constant pressure. The properties of the branches are crucial to the construction of joint potential density surfaces, patched together at 1000 db intervals. By resolving more finely in pressure (illustrated with 200 db spacing), a finer system of patched potential density surfaces can be obtained, and indeed the continuous limit can be taken. This limit gives a form of orthobaric density, regionally differentiated because it is based on the duplicate regional branches. A mapping can be devised, using the properties of the bridge waters, that links the southern and northern forms of orthobaric density across the boundary between their respective regions of validity. The parallel of patched potential density surfaces to orthobaric density surfaces permits the use of measures developed for the latter to estimate quantitative measures of the material nature (or otherwise) of the former. Simply put, within the waters of the respective branches the patched isopycnals, or orthobaric isopycnals, are very nearly material, limited only by inherent irreversible mixing processes. However, where these isopycnals cross the bridge waters, significant, reversible, material exchange across them may occur.A difficulty may be encountered with coarsely resolved, regionally differentiated, patched potential density. This is that there exist ranges of density which cannot be consistently linked across the regional boundary. A solution for the difficulty, suggested by the continuousform (regionally differentiated orthobaric density), is proposed.