Now appears the use of the third plate. The two surfaces thus formed are sure to be, one of them convex and the other concave, in some corresponding degree. The workman now numbers the plates, by numbers stamped in the edges, these being marked Nos. 1 and 2, and the third plate No. 3. No. 2 is now set aside, and No. 3 is scraped to fit No. 1. It is thus made a duplicate of No. 2. Next, No. 1 is set aside and Nos. 2 and 3 are brought together. Supposing these to be convex, they will bear together at the middle point, on which the upper plate will rock, and the degree of their convexity will thus be shown. The workman then in the same manner scrapes these plates equally to the best of his judgment, until their entire surfaces are brought together, with equal distribution of the points of contact. These two surfaces will now again be, one convex and the other concave, though in a much less degree. The next step is to apply No. 1, which is concave, to either No. 2 or No. 3, and scrape it to fit. It is then applied to the other, of which it has now been made a duplicate, and the same process is repeated, until the three plates can be interchanged in any way, and will have a uniform general bearing on each other, with equal distribution and distinctness of the points of contact. We have thus, in a general way, produced three demonstrated true planes, but the surfaces are yet far from the desired approximation to absolute truth. Now follows the fine scraping, which is not attempted until general truth has thus been established. The object of this is to multiply the points of contact and perfect their equal distribution and prominence. For this operation no raddle is used, but the surfaces are rubbed together dry. When the plates are separated, the points of contact shine like stars. Here skill and care are pre-eminently required. The scraping takes off only a dust. If too strong depressions may be made deeper than before, and requiring the reduction of the entire surface. The superiority of the modern tool is now especially shown. By lowering the angle of the tool, the workman presents the slightly curved edge to the surface in a position as nearly parallel with it as he desires. Interchanges similar to the former ones are now repeated, until the bright points are brought as close together as is desired, with uniform distribution and distinctness. The tedious operation is now finished, and these bright points remain as witnesses.