Can you post more photos of the chair, including underside and any marks? It looks like it might be a JH-504, with the hand-woven seat caning replaced by a press-in cane. If so, then someone unfortunately would have routed out a channel around the top of the seat rails for the reed spline.
That chair does not pop up very often. Are you restoring it for a client?
http://photagram.net/tag/jh504
There are some photos there that are big enough to show clearly that the cane goes through the slots in the seat rails---none of the underside, though. I think the ends of the cane are wound around the top section of the split rail and tucked under the cane at the top---maybe. That's usually how the cane ends are dealt with on Danish chairs. You might also need to tack them down with very small wire nails or brads, like 5/8" or 1/2" even. I've done other Danish cane seats but not this one.
Filling in the routed spline channel on the tops of the legs so that it looks good will be a challenge.
What sort of jerk routes a spline channel in a chair like this for premade cane?
You can probably fill the channel underneath the cane with spline and sand it smooth. On the corners where the cane does not cover you are going to have to inset some new teak showing the end grain. The chair will always bear this scar. What a jerk to have done that!
Well, in defense of the jerk who did it---most of the world would see this as a chair to sit on and nothing more. And it's way, way easier to redo a seat in pre-woven cane than it is to weave one by hand. It was probably just an unfortunate lack of knowledge rather than willful disregard.
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