Abstract: Spherical workpiece contact elements on a gaging finger of a linear measurement interferometer are positioned and supported by the establishment of four points of contact therewith. The spherical contact elements are located in a V-shaped groove, which defines two of the contact points, and are accessible for replacement by removal of a cap which establishes a third contact point with each spherical contact element. The fourth point of contact defines the position along the length of the V-groove of the contact elements and thus defines the degree of protrusion of the contact elements beyond the periphery of the supporting portion of the gaging finger.