My suspicions have been confirmed.
The stave that was showing signs of not being fully seasoned was left with one limb strapped up to a length of 2x2 on my long warm radiator.
I could hardly believe my eyes this morning, the strapped limb hasn't moved any further, but overall the bow has taken on a lot of bend. With the tips placed on the floor there is a 3" gap between floor and the belly measured at the centre. The good news is the bend is pretty much in line with the desired direction of bend of the bow (E.G In line rather than sideways) I could claim that's due to my skill in selecting where to cut the log, but it's probably more luck than judgement!
Note:- There is a pic of the stave on the shave horse in this post, you can see how it was straight:-
Now, had this just been made into a bow it would have been seen as a poor bow with a load of "set". It just goes to show how tricky wood is.
I believe the stave has been cut for several years but has been in an old garage partially open to the elements.
I've had this sort of problem before where wood has been just left in a pile with a tarpaulin over it.
To season wood properly it must be off the ground, protected from rain and with plenty of air circulation around it. Ideally it should be split or sawn into halves or quarters as appropriate, and the end sealed. In the UK I leave the bark on but in some countries it may be best removed and the wood treated to prevent insects laying eggs in it and the grubs feeding on it.
Hopefully the longbow stave has dried considerably now. I'll strap it up and heat bend/heat treat the belly. This should get it back to a sensible shape ensure it's dried through and toughen up the belly a bit. The bark has all popped off now, so hopefully in a few days it will be ready to start tillering again.