Careful here, My full battens are inserted from the luff, so you put the thick end in first. The general principle seems to be thick end at the leach, thin end at the luff.
Darn thing is, it's so counter-intuitive I always forget; I need a simple way of remembering, like the thin end of the batten goes towards the thin end of the boat. But we have a cat and the hulls are thin at both ends, Doh!