I have a 1927-type porcelain bathtub, and it once looked that old. I tried fruitlessly over the years to remove the dinginess at the bottom with scouring pads and liquid tile cleaners. Then someone gave me a pumice scouring stick and I was able to restore the tub to good-as-new condition (without marring the finish). It took ten or 15 minutes, and required several rinsings and re-scrubbing of spots I’d missed, or hadn’t worked on hard enough. But in the end, it really worked; and annual touch-ups require three to five minutes. I wouldn’t use these sticks on plastic, though. They’re so abrasive they’d scour into anything softer than glass. As such, the sticks are also good for removing paint from concrete and tile, baked-on build-ups from ovens and grills, and rust from garden tools.
I got one recently for $8.50 at True Value. Pumie also makes a less fancy stick without the plastic handle that costs half as much at True Value ($4.50). I recommend spending the extra bucks: the handle makes it less yucky when scouring a toilet bowl ring, and it doesn’t require you to wear gloves to protect your hands when scouring a tub. These sticks last long enough that it’s worth spending more for convenience. Mine wore down about 30% while doing my tub the first time, and about another 7% getting out some nasty persistent stains in my toilet bowl.