The grinding machine has a workpiece holder (1) which consists of a rotationally symmetric jacket (2) and a rotatable base (4) driven by a shaft (6) through a central aperture in the floor of a liq. container (6) into which the liq. from the workpiece holder can drain through an annular gap (5) around the rotor. A control container (13) is connected (12) into the outlet (10) from the liq. container to a stopcock (11) operated by switches (15, 19) which can be positioned at various levels. At a critical level (14) the stopcock is opened for a predetermined short time. ADVANTAGE - Different liq. levels in workpiece holder and liq. container can be established as easily and quickly as possible.