Thanks, just use Comet or Bon Ami first to get any dirt out of the way, then work on the stains very slowly, gently and carefully using the hydrogen peroxide and rubbing with the pumice stone. Rinse periodically with water and just keep working away at it. Plan on it taking a LOT of time. This is only for porcelain sinks and won't work for sinks with other finishes and can scratch sinks made of other materials. My 1909 sink above is porcelain over cast iron.
This also works very well for minor rust stains around faucets and drains in sinks and tubs!