H and E: Assuming a traditional stuffing box, some
drip is expected. It's not only expected, but it's necessary
. Water moving thru the packing material keeps it lubricated and cools it. No drip and you'll end up with the packing material abrading the shaft, which is a Very Bad Thing.
But a drip while she's at rest indicates the packing nut is too loose or your packing has reached the end of its useful service life.
If you do choose to try to tighten the nut a bit, do so only in a tiny little increment--until the drip at rest just
stops, then get under way, under motor, to make sure you're still getting a drip every ten seconds or so. Stop the prop and feel the stuffing box to make sure it's not getting hot.
Search the forum. There's been all kinds of discussions about stuffing boxes in here. There's also this: Re-Packing A Traditional Stuffing Box
, which should tell you everything you need to know.