Tredgold gave the following practical rules for proportioning the different parts of a scarf, according to the strength possessed by the kind of timber in which it is formed, to resist tensional, compressile, or shearing forces, respectively.

1 By Colonel Beaufoy. See Barlow's Strength of Materials, Art. 68.

In Fig. 152, cd must be to c b in the ratio that the force to resist sliding or shearing bears to the direct cohesion of the material - that is,

In Oak, Ash, and Elm, cd must be equal to from 8 to 10 times cb.

In Fir and other straight-grained woods cd must be equal to from 16 to 20 times cb. The sum of the depth of the indents should equal 1/3 the depth of the beam. The length of scarf should bear the following proportions to the depth of the beam.

Without Bolts.

With Bolts.

with Bolts and Indents.

Hard Wood ,(Oak, Ash, Elm)

6 times.

3 times.

2 times.

Fir and other straight-grained woods

12 „

6 „

4 .

Halving of the simplest kind is shown in Fig. 162. Half the thickness of each piece is checked out, and the remaining portion of one just fits into the check in the other - the upper and under surfaces of the pieces being flush. This is a common way of joining wall plates or other timbers, at an angle where there is not room to let the ends project so as to cross one another.