There are several ways in which to do a scarf weld, but the method shown in post 15 is not one of them, this is an inserted weld.
Scarf welding involves upsetting the ends of the two pieces of material to be joined in order to make them thicker, in the most common method you then forge a taper on these two thickened pieces of material, take the weld, and forge down to size.
The weld is taken by heating both pieces of material separately, then placing the tapered faces together on the anvil. It makes life easier if you have your striker hold one piece of material and you hold the other piece.
The result is a longish tapered weld joint in the finished job when viewed side on.
Some methods use a sort of cup and ball overlap, or some other way of assisting the precise location of the pieces to be welded when you take them out of the fire.
A properly executed scarf weld is a very strong joint.
The axe shown in post 25 does not use a scarf weld, this method of axe construction was quite common in 19th century and earlier axes across the world.
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