This section is from the book "Spons' Mechanics' Own Book: A Manual For Handicraftsmen And Amateurs", by Edward Spon. Also available from Amazon: Spons' Mechanics' Own Book.
The mitre-box is an arrangement for guiding a saw-cut at an angle of 45° exactly, or half the dimensions of a right angle. It is mostly required for cutting mouldings, where the end of one piece of wood meeting the end of another has to form with it a true corner of 90° (a right angle). The best illustration of a mitre is to be seen in either of the 4 corners of a picture frame. In its simplest form the mitre-box may be made out of any piece of good sound plank 1 1/2 ft. long and say 6 in. by 3 in. A rebate is cut lengthwise in this. i.e. half its width and half its thickness is cut away. leaving the slab in the form of 2 steps, thus constituting a rest for any work to be operated upon. Next 2 saw-cuts, one facing each way, are carried down through the top step and about 1/4 in. into the lower step, these saw-cuts being exactly at an angle of 45° with the front edge of the "box." When a mitre has to be cut. the wood to be operated on is laid on the lower step and held firmly into the angle, while a saw is passed down in the old cuts in the bos and so through the wood to be mitred.
For cutting other angles than 45°, other saw-cuts might be made in the same box; but the most convenient instrument for cutting a wide series of angles is the Langdon mitre-box, sold by Churchills. and illustrated in Pig. 259. 'Whilst ordinary mitre-boxes range only from right angles (90°) to 45°. this cuts from right angles to 73° on 21/2in. wood. and is the only form adjustable for mitreing circular work in patterns and segments of various kinds. Prices range between 24s. and 70s. without the saw, according to depth and width of cut.
The ordinary mitre-box may also be made in the form of a wide shallow trough, the saw-cuts at an angle of 45 being carried down through the sides to the floor, while the Bides and floor combined form the rest for the work in hand.
All the forms of mitre-box described above are intended for use with a saw, the edges of the mitre being left rough from the saw in order to take glue better.
Another form, admitting of the sawed work being planed up. is called a "shooting-board," and is shown in Fig. 260. It consists of 2 slabs. a b, of good sound mahogany. about 30 in. long, 18 in. wide, and 1 in. thick, screwed together so as to form a step c; on the topmost are screwed 2 strips d of hard wood 1 1/2-2 in. wide, at right angles. The piece of moulding e to be mitred is laid against one guide bar. and sawn off on the line c, or laid on the other side against the second guide bar. and similarly cut off. It will be necessary to use both sides in this way, because, although the piece cut off has also an angle of 45°, it would need to be turned over and applied to the other, which could not be done without reversing the moulding. In a plain unmoulded strip, this would not signify. The strip lying close to the step or rebate of the board, can be trimmed by the plane by laying it on its side, but care must be taken not to plane the edge of the step itself. The plane must be set very fine, and must cut keenly. To saw off a piece at right angles, and not with a mitre, lay it against the bar, and saw it off in a line with the other, when it cannot fail to be cut correctly, d d forming 2 sides of a square.