Given a good pair of discs the first step towards fashioning them into an objective is roughing to the approximate form desired. As a guide to the shaping of the necessary curves, templets must be made from the designed curves of the objective as precisely as possible. These are laid out by striking the necessary radii with beam compass or pivoted wire and scribing the curve on thin steel, brass, zinc or glass. The two last are the easier to work since they break closely to form. From these templets the roughing tools are turned up, commonly from cast iron, and with these, supplied with carborundum or even sand, and water, the discs, bearing against the revolving tool, are ground to the general shape required. They are then secured to a slowly revolving table, bearing edgewise against a revolving grindstone, and ground truly circular and of the proper final diameter. At this point begins the really careful work of fine grinding, which must bring the lens very close to its exact final shape. Here again tools of cast iron, or sometimes brass, are used, very precisely brought to shape according to the templets. They are grooved on the face to facilitate the even distribution of the abrasive, emery or fine carborundum, and the work is generally done on a special grinding machine, which moves the tool over the firmly supported disc in a complicated series of strokes imitating more or less closely the strokes found to be most effective in hand polishing. In general terms the operator in handwork at this task supports the disc on a firm vertical post, by cementing it to a suitable holder, and then moves the tool over it in a series of straight or oval strokes, meanwhile walking around the post. A skilful operator watches the progress of his work, varies the length and position of his strokes accordingly, and, despite the unavoidable wear on the tool, can both keep its figure true and impart a true figure to the glass. [Illustration: FIG. 44.—Dr. Draper’s Polishing Machine.]