A little grinding is sometimes resorted to in completing steel straight-edges: it is less objectionable with steel, than with cast iron and other metals which are softer and also more porous than steel, but the process of grinding being very difficult of control is not desirable; and as very small files may be used, and with nice discrimination, in correcting straight-edges, the scraper although useful here likewise, does not present the same importance as in correcting wide surfaces or planometers.
Secondly, to originate a surface-plate or planometer. - This process requires that the operator should be in possession of at least one very good straight-edge; one of a series of three that have been accurately tested in the manner just described. The present case also demands, like the last, that three pieces should be operated upon, in order that the same correctional method may be brought into effect.
The planometer should be a plate of hard cast-iron, having ribs at the back to prevent its bending, either from its own weight, or from taking an unequal bearing on the bench or other support. Generally a deep rib extends around the four margins of the planometer, and one, two, or more intermediate and shallower ribs are added, which divide the back into rectangular compartments, as in fig. 865; this planometer would rest upon the bench around its edges, or on four prominent points at the corners represented black. It has been recently proposed by Mr. Whitworth, that the ribs should be placed obliquely and made to converge to three points of bearing, as in fig. 866, which is a much better plan, as the planometer is then at all times supported on precisely the same points, notwithstanding the inequality of the bench, which can scarcely be the case when four feet are used.
The handles are added at the ends, that the planometer may be readily inverted; in order that it may be applied upon such heavy works as it would be inconvenient to lift, and then imme-diately replaced on its feet when returned to the work-bench.
In the absence of the planing-machine, the three castings for the planometers would be chipped all over and roughly filed, and in this case the smith's plane for metal would render most important service for a considerable period. A good wooden straight-edge is now convenient, as when rubbed with red chalk it denotes the high places very effectively, and should be applied at various parts of the length and width, and also obliquely; and indeed a small thick block of beech-wood or mahogany, planed very flat as a surface and rubbed with chalk, will serve to hasten the process of obliterating the coarser errors.
In due time, the plane, the coarse file, and the wooden straight-edge, would all be laid aside, and the work would be prosecuted with a smoother file, under the direction of a metal straight-edge, and which if coloured must be also greased to make the red matter adhere. This part of the work may be carried to no mean degree of perfection, as a very correct judgment of a plane surface can be obtained from a good straightedge applied in all directions, as the eye readily measures the comparative width of the line of light transmitted, and the fingers also appreciate, when the straight-edge is slightly rotated or rubbed sideways, which points of the work are the highest, and give rise to most friction.
One surface, which may be called A, having been corrected very carefully with the file and straight-edge, may be now smeared with red stuff and oil, and employed to hasten the correction of the second piece, or B, and the third, or C, until these two are about as near to truth as the first, or A; the three are afterwards mutually operated upon under the guidance of colouring matter. At this stage of the work it will soon become necessary to discard the file in favour of the scraping-tool, in using which it will be found very convenient to remove by a paper screen, the glare of the bright metallic surface, so as to enable the little patches of colour to be more readily observed. The screen, fig. 867, consists of a small frame of wood, eight to ten inches square, covered with writing-paper, and attached to a small board; the paper is inclined some ten degrees towards the operator, and at night a short piece of candle is placed in the center of the hoard or pedestal as shown.
The three plates having been, as before observed, brought into nearly same preparatory state, it is to be now judged of by the straight-edge, whether all three are nearly alike, or lean to the tame kind of error. Thus, supposing the pieces A and l'» to have a tolerably equal disposition to convexity, or that when placed in contact they rest in the center, but fail to touch around the margin, then A and B are each a little reduced in the middle until the tendency to rotate in the center is gone; A and B will be then each a shade nearer to truth than before. The third piece, or C, is fitted to A, after which, supposing for a moment A and B to be each a true, or a plane surface, C would become also a plane surface, and the task would be then completed. Perfection is not, however, nearly so easy of attainment, and it is almost certain that although A and B may be counterparts, they will not be planes; presuming therefore that C has been fitted to A, it is almost certain that C will not fit B. (This may be called routine One.)
Considering, therefore, that now A and C are the two most nearly alike, or that both are proved to be convex, these are the two upon which an equal amount of correction is this time attempted, until they become counterparts, or fit well together; and the third piece, or B, becomes the arbiter in this stage of the work. (This may be called routine Two.)
We will lastly assume that B, when altered until it fits C, does not quite fit to A, but that B and C present an equal departure from truth, and are still both convex; then B and C are altered in an equal degree until they appear to be perfect counterparts, and this time A, when fitted to one of them, shows whether the whole three are planes, or that two of the pieces are convex and one concave. (This may be called routine Three.)
The method of comparison will probably be rendered somewhat more evident, by the following tabular view of the processes.
A. B. Counterparts.
A. C Counterparts. R Arbiter.
B. C Counterparts. A. Arbiter.
The inspection of the letters in three routines will farther show, that every one of the three surfaces admits of comparison with the two others, and that the abstract method is to fit together those two which appear to have the same error, by altering those two in an equal degree, after which, the third piece, when fitted to one of the other two pieces, incontestably proves whether all three are planes; as this cannot be the case until all three agree together in every comparison. The attainment of true planes will be found to require several repetitions of the three routines, but towards the conclusion increasing care will be continually required, in order that no degeneration may insidiously occur, to disappoint the hope of the progress towards perfection being steadily on the increase.
This correctional process, which is precisely analogous to the mutual correction of three straight-edges, is somewhat familiar to mechanicians, but the process is obviously very much more tedious than the origination of straight-edges, on account of the great increase of the surface to be operated upon, and the circumstance that the quantity taken in excess from any part, must be amended by reducing every other part of that surface in an equal degree.
For the sake of simplicity it has been supposed throughout the description that the two convex pieces were in each case selected for correction; but this is immaterial, as the result would be the same if the two concave pieces were wrought, or the one and other pair alternately, as circumstances may accidentally suggest.
The three planometers having been made as perfect as the skill and patience of the operator will admit, one of them should be carefully laid aside, and only used in the most guarded manner in the reproduction of other planometers, or the correction of those in general use; which latter process will be found occasionally requisite, but the less frequently so, if the instrument is equally worn by rubbing the work to be examined, at all parts of the planometer, instead of upon the central part alone. And a true surface or standard having been once obtained, it should be most scrupulously preserved, as it will be found very considerably less troublesome to copy a good standard, than to originate the three standards themselves from which the one is to be reserved.