Rung Replacement

Here is a sequence of replacing a broken oak rung prior to reweaving the seat with fiber rush. After removing the broken rung, assisted in this case by a loose rung below(otherwise loosen with steam of denatured alcohol), the procedure is:
Buy an oak dowel of the proper diameter or fabricate a piece of oak to match, then as pictured:

1-Cut the replacement piece to length.
2-hand chisel the tenons and split the ends with a fine saw cut
3-Dry fit(re-measure against the other side just in case)
4-Glue up and clamp both rungs

After 24 hrs., re-weave.