The remarks hitherto offered on producing a flat surface were based upon the supposition that the operator is in possession of a good straight-edge, and a good surface or planometer, and which is usual under ordinary circumstances; but it may be considered necessary that the more difficult case should be placed before the reader, of originating the planometer itself, by which alone can he render himself independent of external assistance; the previous observations will greatly abridge the description.

* In a Paper read before the British Association for the Advancement of Science. Glasgow, 1810.

first, to originate a straight-edge. - In originating a straightedge, it is judicious to prepare the ground, so far as possible, with the means possessed by every joiner; and accordingly, three pieces of hard straight-grained mahogany should be: planed as straight as possible with the joiner's plane. Calling the three pieces. for distinction. A B and C, when they are compared, A and B may appear to agree everywhere, even when one of them is changed end fur end: this shows A and B be either both straight, or else the one concave, the other convex; but C may be unlike either of them. C is then adjusted also to A, and will therefore become a duplicate of B; but when the duplicates B and C are compared, it may be found that they touch In the middle, and admit light between them at the ends, shewing each to be convex. The central parts both of B and C, which are erroneous in the same direction, arc then each reduced in a nearly equal degree, until in fact, the transmission of light is prevented throughout their length, even when they arc reversed, and by which the condition of each will be somewhat improved.

Next, to ascertain whether B and C, when thus improved, are each pretty near to the truth. The third, or A, is fitted to B, making A and B as nearly as may be, counterparts of one another; and if A, when thus altered, should also agree with the third or C, all are true: but this can scarcely yet be strictly the case. And the routine is therefore continually repeated of Being in an equal degree the two which may show evidence of being nearly alike, (either both convex or both concave,) and then by fitting the third to one of the corrected two,as a test by which to try, if they not alone agree with each other but likewise agree with the third, or the test; as the work can only be perfect when all three admit of being compared without any want of contact being observable in any of the three comparisons.

If the trying-plane is carefully manipulated, the three pieces will, in three or four repetitions of the series of operations, become as nearly accurate as the nature of the tools and of the method will admit; and then, cither the best of the three wooden straight-edges, or all three of them, may be used as the preliminary test in making the steel straight-edges.*

* The more common practice of the joiner is to operate upon only two pieces, each of which is first planed until they agree together when placed edge to edge in the ordinary manner, or in one plane. The two pieces are now placed tide by side,

Sometimes the metal straight-edges are wide strips cut off from a sheet of steel of hard quality; if forged from a bar of steel, the hammering should be continued until the metal is quite cold, to render it hard and elastic; and in some instances, the straight-edge, when partly finished, is hardened and tempered before its edges are completed. In all cases, if the one edge is to be chamfered, this should be done in an early stage, as it is very apt to throw the work crooked; and the sides are always filed, or otherwise finished, before any great progress is made in correcting the edges. When three straight-edges are made at one time, the three are generally united by temporary pins through their ends, to make one thick bar, and are then corrected in the mass as the first stage.

The work having been thus far prepared, the wooden straightedge is rubbed with a dry lump of red chalk, that it may leave evidence of the points of contact. A coarse file is first used, and it may for a time be assisted by the hand-plane; the size and length of the file are gradually decreased, and after a time, it will be found that the wooden straight-edge is no longer sufficiently delicate to afford the required test. When all three of the steel straight-edges have been brought collectively to a state of approximate truth, they are separated, and wrought the one from the other, precisely in the same order that was described in reference to the wooden straight-edges; but as on the steel a very small and smooth file may be used, the process of correction may be carried with the file much higher upon steel straightedges, than upon metallic surfaces. In addition to the mode of examining straight-edges by the transmission of light, they are also compared by laying them two at a time upon a true bench or surface, and rubbing them together without colouring matter; the high places will then mutually rub each other sufficiently to and their edges are placed in agreement at the extremities, so that the fingers, passed transversely across their ends, cannot feel any want of continuity of surface; in other words, cannot feel the joint. If, whilst thus placed, the joint is also inappreciable to the sense of touch at various intermediate parts of the length of both pieces, the work is correct, and the two are straight.

From the very precise action of the trying-plane, the wooden straight-edge may perhaps be equally well produced by the methods requiring either two or three to be made; but the method of making three at once is given in the text, because it is always followed in metal works, in consequence of the different nature of the working tools, and of the abstract superiority of the method leave a small degree of brightness, that may be easily observed on a careful scrutiny; and as both edges of every straight-edge are commonly wrought, the investigation becomes amplified and improved, from there being six comparisons instead of three.