When a cell such as the unfertilized egg of the sea urchin Arbacia punctulata is placed in a solution hypotonic with respect to its natural medium, water enters and the cell swells; conversely, it shrinks in hypertonic solutions. This observation at once suggests that the force which causes water to enter is osmotic pressure, that the cell is acting as an osmometer. Earlier measurements of cells in equilibrium with anisotonic solutions indicated that the unfertilized Arbacia egg is an osmometer of a high degree of excellence, although the observed volume of cells at equilibrium fell somewhat short of the calculated value (1). Since the relations between pressure and volume of the cell forms the basis for a kinetic theory of osmosis which will be given in a subsequent paper (2), it was necessary to determine this relation as accurately as possible, by means of further experiments.The present paper therefore attempts to answer the question:how nearly ideal in its osmotic properties is the Arbacia egg?An ideal osmometer should meet the following requirements: (1) One should be able to measure volume accurately at all pressures.(2) The product of pressure and volume should be constant (law of Boyle-Van't Hoff). (3) The membrane should be actually semipermeable, i.e., should allow passage of water, but not of dissolved substances. (4) The transport of water should be due to osmotic force alone. These requirements will be taken up in order.