The question which prompts the present work is: "How can the concept of the plant cell as an osmometer with semi-permeable walls be justified, when solutes may enter the plant cell vacuole?" Textbooks of plant physiology and physical chemistry treat osmosis in detail only for equilibrium conditions and non-diffusible solutes. To extend the quantitative treatment to the case of a diffusible solute we must abandon the equilibrium approach and study the problem dynamically. We introduce the dynamic approach by applying it to the classical cell osmometer; then we proceed to the case of a diffusible solute.DYNAMICS OF THE CLASSICAL CELL OSMOMETER: We use the following symbols:V, cell volume (cm3). VO, cell volume at zero turgor pressure. v = V/Vo -1, relative departure of cell volume from VO. A, external surface area of cell (cm2). AO, value of A at zero turgor pressure. P, osmotic pressure of cell contents (in the sense of Meyer (14), i.e., as a concentration-dependent property of the solution, independent of the hydrostatic system) (atm). T, turgor pressure (atm). [Broyer and others (4,21,22,27) have shown the general equivalence of T and "wall pressure," and that it is a mistaken over-emphasis of an infinitesimal second-order effect to dwell on the distinction between them (6)]. Kw, permeability of cell wall to water (cm sec-1 atm-1). t, time (sec).We suppose that, initially, T = 0, and P = PO, and that the solutes in the system are non-diffusible. If the cell is now placed in free water, water will enter the cell until the (increasing) turgor pressure becomes equal to the (decreasing) osmotic pressure. The dynamics of this process is described exactly by the equation.(1) subject to the initial condition t = 0, V = VOQuite generally, K,, A, P and T are functions of V. We therefore simplify the analysis by taking K,A as constant and equal to K,A0.If we take P proportional to solute concentration (as it is to a first approximation)If we assume that change of cell volume is proportional to change in turgor pressure, we have for theThe elastic modulus, E, corresponds to the "coefficient of enlargement" of Broyer (5). As Broyer states, e is not strictly constant for perfectly elastic cell walls, except for infinitesimal volume changes. Since the assumption that the wall obeys Hooke's law is, in any case, an approximation (9), it seems permissible to adopt e as constant in the present analysis.We recognize that, in real plants, marked deviations from the linear T (v) relation to be used here may occur. In this sense the present work may be considered a first approximation. Essentially similar results would follow from a more precise, though more elaborate analysis along the same lines in which non-linearity in T(v) was taken into account.The existence of a unique T(v) function implies, however, that the cell volume changes are elastic. Obviously, the plastic, irreversible, deformations associated with cell elongation are beyond the scope of the present treatment, though it may prove possible to include these in a sim...