A pump for dispensing a liquid from a reservoir comprising: a piston-chamber forming member, a piston forming element received in the piston chamber-forming member axially slidable inwardly and outwardly therein between an inward retracted position and an outward extended position, said piston forming element having a central axially extending hollow stem having a central passageway with an inner end and having an outlet proximate an outer end extending out of the piston-chamber forming member and from which the liquid is dispensed, at least one annular chamber (64, 66) formed annularly about the stem between the piston forming element and the piston-chamber forming member providing for controlled movement of the liquid from the reservoir into the annular chamber (64, 66) and for dispensing of the liquid in the annular chamber (64, 66) to the outlet with reciprocal sliding of the piston forming element between the retracted position and the extended position, characterized by: said piston forming element having a bellows member, the bellows member extending inwardly from the stem to form with the piston-chamber forming-member a bellows chamber open to the inner end of the passageway, the bellows member being collapsible to increase and decrease a volume of the bellows chamber with reciprocal sliding of the piston forming element between the retracted position and the extended position to draw the fluid through the outlet via the passageway into the bellows chamber and to expel the fluid in the bellows chamber via the passageway out the outlet. a piston-chamber forming member, a piston forming element received in the piston chamber-forming member axially slidable inwardly and outwardly therein between an inward retracted position and an outward extended position, said piston forming element having a central axially extending hollow stem having a central passageway with an inner end and having an outlet proximate an outer end extending out of the piston-chamber forming member and from which the liquid is dispensed, at least one annular chamber (64, 66) formed annularly about the stem between the piston forming element and the piston-chamber forming member providing for controlled movement of the liquid from the reservoir into the annular chamber (64, 66) and for dispensing of the liquid in the annular chamber (64, 66) to the outlet with reciprocal sliding of the piston forming element between the retracted position and the extended position, characterized by: said piston forming element having a bellows member, the bellows member extending inwardly from the stem to form with the piston-chamber forming-member a bellows chamber open to the inner end of the passageway, the bellows member being collapsible to increase and decrease a volume of the bellows chamber with reciprocal sliding of the piston forming element between the retracted position and the extended position to draw the fluid through the outlet via the passageway into the bellows chamber and to expel the fluid in the bellows chamber via the passageway out the outlet. said piston forming element having a bellows member, the bellows member extending inwardly from the stem to form with the piston-chamber forming-member a bellows chamber open to the inner end of the passageway, the bellows member being collapsible to increase and decrease a volume of the bellows chamber with reciprocal sliding of the piston forming element between the retracted position and the extended position to draw the fluid through the outlet via the passageway into the bellows chamber and to expel the fluid in the bellows chamber via the passageway out the outlet.