I can't tell if this pump was from 1910 or 1916, but nevertheless, we need to be thankful the pump companies have innovated since then! This "bicycle horn" pump would require the mother to squeeze the rubbery ball on the end to create suction, which would (ideally) pool in the dip in the glass. If it got back into the rubbery ball, it would be very difficult to clean (this is definitely an open vs. closed system!). Imagine how long it must have taken to fully pump—the dip in the glass only seems to hold about half of a tablespoon (or 7 ml) before you'd have to empty it and reattach to the breast. I measured the diameter of the opening to be about 25 mm. We've come a long way, baby.
