The Parker 51 and its successor the 61 were equipped with an unprecedently effective and capacious capillary ink trap (called a "collector" by Parker) surrounding the feed. Emptying these pens is thus a little tricky, especially for Vacumatic-filling 51s and capillary-filling 61s.
For the average user, the easiest technique is simply to shake out the ink over a sink, using a motion similar to that used in shaking down a thermometer. Be careful not to lose your grip on the pen, and watch that the pen does not strike the sink's sides or bottom!
Parker dealers were originally issued a specially-designed centrifuge that accomplished this same task. There was also a rubber bulb that could be attached to the 61's capillary unit so water could be forced through. Rubber bulbs that can be adapted for this purpose are readily available from photo and electronic stores and pharmacies.