I inherited a tumbler from my grandfather, who made jewelry as
a hobby. I'm wondering if i should put my silver jump rings into
the tumbler; will it make them shinier or anything?
Yes. Brilliantly shiny, particularly if you use steel shot. It
will also probably work harden them, though. Use just enough water
to cover the mix, and a drop of dish detergent. You needn't tumble
for more than a couple hours in my opinion - not having the cash to
throw at a tumbler and shot just now, I've been burnishing my
finished pieces by stuffing them into a small jar and shaking them
up with some Copperhead BB's with very acceptable results after just
a few minutes.