Apparatus for measuring displacements of a displaceable member (10, 30, 40) along a predetermined displacement path by counting periods of displacement thereof along said predetermined displacement path, said apparatus comprising: a first machine-sensible element (12, 32a, 42a) carried by said displaceable member and occupying a length thereof defining only a portion of a period of displacement of the displaceable member; a first sensor (13a, 33a, 43a) located at a sensing station proximate to said displacement path so as to be capable of sensing the presence or absence of said first machine-sensible element in the sensing station, and thereby of determining the status of the displaceable member at any particular instant during the displacement of said displaceable member; a pulse generator (14, 34, 44) located at a pulse-generation station proximate to said displacement path; a plurality of second machine-sensible elements (15a-d, 35a-h, 45a-n) carried by said displaceable member at spaced intervals along each displacement period of the displacement member, each of said second machine-sensible elements being effective to actuate said pulse generator when moving through said pulse-generation station; an electrical counter (19, 39) for counting the displacement periods of the displaceable member; and an electrical circuit (18,38) configured to be activated by said pulse generator, for a short period of time during which the electrical circuit enables the first sensor to sense the status of the displaceable member at the particular instant one of said second machine-sensible elements passes through said pulse-generation station, and to increment the counter in accordance with said status determination, wherein the said pulse generator is configured to generate a pulse upon movement of each of said plurality of second machine-sensible elements one of toward and away from said pulse generator. a first machine-sensible element (12, 32a, 42a) carried by said displaceable member and occupying a length thereof defining only a portion of a period of displacement of the displaceable member; a first sensor (13a, 33a, 43a) located at a sensing station proximate to said displacement path so as to be capable of sensing the presence or absence of said first machine-sensible element in the sensing station, and thereby of determining the status of the displaceable member at any particular instant during the displacement of said displaceable member; a pulse generator (14, 34, 44) located at a pulse-generation station proximate to said displacement path; a plurality of second machine-sensible elements (15a-d, 35a-h, 45a-n) carried by said displaceable member at spaced intervals along each displacement period of the displacement member, each of said second machine-sensible elements being effective to actuate said pulse generator when moving through said pulse-generation station; an electrical counter (19, 39) for counting the displacement periods of the displaceable member; and an electrical circuit (18,38) configured to be activated by said pulse generator, for a short period of time during which the electrical circuit enables the first sensor to sense the status of the displaceable member at the particular instant one of said second machine-sensible elements passes through said pulse-generation station, and to increment the counter in accordance with said status determination, wherein the said pulse generator is configured to generate a pulse upon movement of each of said plurality of second machine-sensible elements one of toward and away from said pulse generator.