This section is from the book "The Carpenters, Joiners, Cabinet Makers, And Gilders' Companion", by F. Reinnel. Also available from Amazon: The carpenters, joiners, cabinet makers, and gilders' companion.
As Dove-tailing is of great use in the art of joinery, I have represented in Plate I. several sorts; now as much depends on the proper proportioning the parts which fit into each other, so that the pin or socket (that is, the part represented in fig. 1, called the pin of the dove-tail, and that in fig. 2, called the socket,) shall be as nearly as can be of equal strength. I shall lay down some rules for the guidance of the workman, and shall here refer to the pin only at fig. 1, (for the socket is made to correspond to it); let A B C D be a scantling, which is required to be joined to another by means of a single dove-tail; now as much depends on the form of the dove-tail, as well as the proportion it bears to the parts cut away, I shall endeavour to lay down the principle on which the greatest strength is maintained; having squared the end of the scantling, and gauged it to the required thickness A I K L M, divide I M into three equal parts at K L; let K L be the small end of the dove-tail, and make the angles I K G and MLH equal about 75 or 80 degrees, and make G E and F H parallel to A N and B 0, where enter the saw, and cut away the pieces A I K G E N and B M L H F 0, and having cut fig. 2 to correspond by marking the form of the dove-tail on the top of the piece A B C D, it will fit together as shown in fig. 3. We may here observe, that according to the texture of the wood, we may make the bevil of the dove-tail or angle I K G, fig. 1, either more or less than I have mentioned. Hard close-grained wood, and not apt to rive or split, will admit of a greater bevil than that which is soft or subject to chip; thus the dove-tail in deal must be less beviling than that in hard oak, or mahogany. And it is a great fault in many workmen in making their dove-tails too beviling, which instead of holding the joint firmer together, weakens it; for provided the bevil is such that will prevent a possibility of pulling the pieces apart, in general we may observe that the less bevil is given the better, and this may be observed if we compare the dove-tailing of the cabinet-maker and the joiner; the former has very little bevil, while the latter is very much so; and also with regard to the appearance of the work itself, the one looks neat (and is at the same time strong,) while the other appears to aim at great strength, though at the same time looks clumsy and is much the weaker.
Fig. 4 represents the dove-tail in common use for drawer fronts, etc.; where we wish to hide the appearance of the joint in front, the board A B C D is cut with the pin, and AEFB, with the socket; the pins in this sort of dove-tail are in general from about three-quarters of an inch to an inch apart, according to the magnitude of the work in hand. Fig. 5 represents the pin part of a lap dove-tail, which when put together shows only a joint as if the pieces were rebated together as shown at fig. 6; the part A B C D represents the pin, and the part E F G H the socket dove-tail, and when put together only shows the line H G, as a joint; and if the corner A B is rounded to the joint G H, it will appear as if only mitred together; this kind of dove-tail is very useful for many purposes where neatness is required, such as chests, boxes, etc. Fig. 7 is a still neater dove-tail, and as the edges are mitred together, is termed a mitred dove-tail; it is the same nearly as the last figure, only that instead of the square shoulder or rebait in A B, it is cut into a mitre and the other piece is made to correspond.
Dove-Tailing.

Another very neat, as well as expeditious method of joining pieces, and which is somewhat analogous to dovetailing, is shown at fig. 8, where the joint is first formed into a simple mitre, and then keyed together, either by making a saw kerf in a slanting direction, as shown at A B, or by cutting out a piece as at C D, in the form of a dove-tail, and fitting a slip in that, of the required form; the first method, as A B, is amongst workmen called keying together; the second, as C D, is key dove-tailing.
The last method I shall describe is shown at fig. 9, and may be termed mitre dove-tail grooving, the part A B being formed with shoulders cut to the required bevil, and a piece left for the pin dove-tail, which is inserted into the socket dove-tail made to correspond to it in the piece C D, which has been previously formed into a mitre; this method, though not much employed may be used with great advantage in many cases, particularly when we wish to join any pieces together the length way of the grain.
 
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