Filing is performed upon all surface-plates, whether they have been prepared with a planing-machine, chipping, or turning. Small plates are filed while in a vice, and those that are too large for a vice are put flat upon a vice-bench or other bench, and the broad sides filed while the work is fixed with its own weight. To file the narrow sides termed edges, the plate is gripped in a vice, or stood on the floor edgeways and held with packing-blocks if the work is not heavy enough to stand alone. The first step after the planing or turning of a surface-plate is the filing with rough and smooth files having cranked holders, until the machine-tool marks are only just erased; the plate's surface is then put upon the surface of another table, which is a secondary standard of reference; while on this surface, the plate in progress is moved to and fro a few times to be marked with a black oily mixture which is thinly spread over the entire face of the standard. The marks thus made indicate the prominent portions which are to be filed off with short smooth files, in order that the hollow places may not be touched. At this first trial of a plate, only the marks in the middle of the surface should be filed off; and although marks may be seen around the edges, no attention need be given them at the first few trials, because any plate which is convex will exhibit marks of contact on its entire surface merely through the rocking motion given to the work while rubbing it on the standard. In order, therefore, to destroy all convexity on the surface in hand, it must be filed only in the middle after each trial, if any marks are seen in the middle, whether or not they appear near the edges; but as soon as the middle is sufficiently reduced to prevent the marking matter or tange adhering to it, the surrounding parts are reduced, and the reduction of these portions may be safely continued until the middle again exhibits the marks of contact, at which time it must be reduced to produce a hollow form rather than a convex one. While a slight concavity exists at the middle, the surface is favourably progressing; but if only a small degree of convexity exists, the evil will probably increase after each trial, if the entire surface is reduced merely because the marks seem to indicate such a course. By thus duly recognising the possible existence of a convexity, the surface is gradually and surely filed; and, after filing, the scraping is conducted by observing the same order of reducing, first the middle, next the surrounding portions, and lastly the edges.

The secondary standard surface on which the trials are made is that which sustains the greater portion of the rubbing, and therefore also the small amount of wear that results from the attendant friction ; all secondary or tertiary standards are therefore more or less liable to defect, and near the conclusion of a scraping process the work is put upon a sort of primary standard, on which only about three rubs is allowed for fear of injuring its surface.

The processes just mentioned are effectual for producing good surfaces whenever the necessary standards are accessible; if not, straight-edges must be used as standards, and the work itself is also made a standard; this is effected by making three or four plates, and finishing them at one operation, so that all the surfaces are scraped at one time, rubbed together and finished about the same time. When two or three plates are being tried by thus referring them to each other instead of to a finished standard, it is necessary to frequently apply the straight-edge, because one surface which is convex will fit another which is concave, and cause both to appear flat. The management of such surfaces therefore consists in making them as much like planes as possible by means of the straight-edge and referring them to each other. After the surfaces are thus adjusted with smooth filing, the next step is to grind three or four of them together successively with emery and oil until all coincide with each other when put together and appear to be flat. Grinding any two of the surfaces together generally makes the upper one convex and the lower one concave, through the lower one sustaining the weight of the upper one ; consequently, if four surfaces are in progress, all of similar metal, and all equally flattened to the straight-edge at the commencement of the grinding, two pairs of convex and concave surfaces will be produced, the two hollow ones differing from a plane just as much as the two convex ones. At this stage the two hollow ones are selected and rubbed together with the marking matter on one of them instead of emery, and the marks thus made indicate the surrounding portions which are to be filed off with smooth files, or rough ones'if necessary. Another grinding with emery and oil is next given, with emery which is smaller than that first used, in order to indicate distinctly the hollow places, and distinguish them from the prominent edges that are being taken off with grinding.

By means of such grinding and filing, very tolerable surfaces are produced without the aid of a standard plate, but not without a standard straight-edge; therefore, if it happens that the straight-edge in use is defective, an opportunity occurs for improving the tool. This is effected by referring it to both the surfaces which were made by grinding the two hollow ones together ; and, to do this effectually, the straight-edge is rubbed on the plate in various directions. To avoid being deceived with any slight rocking that may arise through a small convexity that may exist on the surface, the straight-edge should be held by holding it at the middle with one hand, and with the other hand at one end, instead of with one hand at each end. By being thus held, it is put into contact and made to touch at least two places in both the straight-edge and the surface-plate; these two places are easily discovered by the light being obstructed at the points of contact. If the work is high enough for convenient observation, the operator will discover which of the two surfaces is convex, and whether the straight-edge is convex. If the tool is held in the mode directed, and no light is seen along the entire length of the straight-edge, the two surfaces in contact are either both straight, or one happens to be as much concave as the other is convex. To ascertain if both are straight, put the straight-edge upon the other surface which was ground with its companion, and if no light is seen at this trial, all the three implements are straight, including the straight-edge and both the plates. When the implements do not thus coincide, the faulty ones are distinguished by the situation of the points of contact. If the straight-edge is held in the proper manner, and each end of it touches each end of the plate, but not at the middle, one of the two tools is hollow; and to discover which one, the straight-edge is put upon the other companion plate, and if the light appears at the middle as before, the straight-edge is hollow, because the two plates which were ground together cannot both be hollow, through having been in close contact with grinding. If one plate is hollow, light will be seen under the middle of the straight-edge while it is on the hollow plate ; but while on the convex-plate, light will be seen only at one end, and will be obstructed at the middle and the other end of the straight-edge. The next test is to find the convexity of the straight-edge, if it possesses any, and this is detected by its rocking on both the surface-plates; it is also detected by holding the straight-edge with one hand at one end, as directed, and observing the light; if the light appears under that end of the straight-edge which is not held, while it is situated on either plate, the straight-edge is convex, and can, therefore, be adjusted with filing and scraping until it is nearer to straightness than either of the plates, at which time it is a better standard than before; consequently the two plates can be further improved, if necessary.