A method of electroslag refining of metal is taught. The method starts with the introduction of unrefined metal into an electroslag refining process in which the unrefined metal is first melted at the upper surface of the refining slag. The molten metal in the form if droplets is refined as it passes through the molten slag. The refined metal droplets are collected in a cold hearth apparatus having a skull of refined metal formed on the surface of the cold hearth and protecting the cold hearth from the leaching action of the refined molten metal. A cold finger bottom pour spout is formed at the bottom of the cold hearth to permit dispensing of molten refined metal from the cold hearth. The rate of flow of molten metal through the cold finger apparatus is controlled by controlling the rate of melting of the unrefined metal; by controlling the hydrostatic head of molten metal and salt above the bottom pour cold finger orifice; by controlling the rate of induction heat supplied to the metal within the cold finger apparatus; by controlling the rate of heat removal from the metal within the cold finger apparatus through the cold finger apparatus itself and through adjacent gas cooling means; and by applying force to slow down and/or interrupt the flow of metal through the cold finger apparatus.