Abstract: A machine for grinding the cavity in a mold for optical lenses has a spherical grinding tool which is precisely positioned with respect to a predetermined reference by air slides which move the tool in orthogonal directions. The carriages of the air slides move relative to center rails. A film of air between the top plate of each air slide and the center rail is supplied from a first source at a pressure which supports the weight of the carriage. When precise alignment is obtained, the first air supply is cut off to lock the air slides in the position of alignment. A recess in end portions of the top plate has air holes communicating therewith which are supplied from air from a second source. The flow of air from this second source is continuous and is sufficient to prevent foreign material from entering the air slide.