A centrifuge (18) is used to introduce a fluid, particularly a viscous fluid such as an encapsulating resin, into a cavity in a container (10), particularly a small cavity such as the inside of an electronic component housing. Measured quantities of the fluid are placed in dispensing vessels (28) in the centrifuge opposite the containers to be filled. The dispensing vessels have openings (36) through which the fluid can flow when centrifugal force is applied. On the application of this force, all the fluid flows out of the vessels into the containers.