Instead of the siliceous sand formerly used, the powder of pounded freestone is employed, as it is found to wear the tools less, and to form a better preparation for the subsequent grinding operations. It is easy to conceive that the action of the fixed rubbers necessarily produces ruts or inequalities in the circular direction. The operation of rough dressing, therefore, is not finished until, when those first rubbers are removed, the surfaces of the segments have been subject, for the required time, to the action of moveable rubbers, attached to arms working as radii of curvature, in a plane at right angles to the horizontal movement of the lathe, which carries the zones. _The Emery Grinding._ The form of the segment should be nearly perfect, after the rough grinding is finished. The lathe and the zone are then subjected to an extremely careful washing. Every place where the stone-powder might adhere is dusted. The radius of curvature is verified afresh, agreeably to the co-ordinates (Appendix, No. IV.); and emery is used instead of powdered stone; beginning with that called No. 1, which is drawn after suspension in water for one minute. Brushes are used for spreading the emery on the surface of the glass. The quantity ought always to be sufficient to prevent the direct contact of the cast-iron rubber with the glass. Splintering or scratching, which cannot be easily effaced, may result from the neglect of this precaution. Practice alone, and an eye duly trained by continual experience, can determine the point of time at which each kind of emery must be discontinued. The celerity of the work depends on circumstances very difficult to appreciate, such as the amount of the pressure of the rubbers, or the degree of accuracy with which the radius of curvature has been adjusted, during the rough grinding. Each kind of emery in succession thus corrects the form of the zone and refines the grain of the surface of the glass; and each change to a fresh material requires the same attention to cleanliness, so as to remove every trace of the substance last used in grinding, and thus to give each successive process its full and legitimate effect. The _douci_ is the _fifth_ and _last_ kind of emery which precedes the _polish_. It is drawn off after ten minutes’ suspension in water, and is extremely fine. Before applying it, the greatest care is necessary to insure cleanliness, as a single grain of any of the preceding kinds of emery might cause scratches, which the polish cannot remove. _The Polish._