The method and device is used when transferring the quantities of milk concerned from a milk container into a reservoir. By such a method, which operates with a smaller stock of milk than the known methods, an improved degree of elimination of air from milk is achieved than in these methods. The device for carrying out the method and its further development permits a further improvement in the degree of elimination of air from milk than with known devices and a more accurate fixing of quantities, in particular in the case of surging milk conveyance. In the method this is ensured, inter alia, by specifically controlled enforcing of the degassing by centrifugal forces in a rotating main flow, which draws its driving energy from itself, and by carrying out 2-stage degassing. This is achieved by the device, inter alia, by the housing shell (1a) having a small diameter in relation to its height in the area of the inlet nozzle (1d), by the outlet nozzle (1e) opening out tangentially from the housing shell (1a), by the float (6) enclosing the displacement body (5) by the central opening (6a) during its switching phase, and by a tubular, self-contained sheet-metal guide (10) being provided in connection with the inlet nozzle (1d) (Figure 6).