Mike is correct......again.

I worked in the glass field years back. If the scratch is deep enough that your fingernail "hangs" up on it, it's probably too deep to polish, for multiple reasons.

We used a high-speed polisher and Cerium Oxide (used with water) to polish scratches......it still took a very long time to do it correctly. Don't try to go too fast or push too hard or you'll end up either breaking the window or causing dull spots. This is especially true with automotive windshields......remember, it's not a full plate of glass, it's safety glass. If you heat the window too much you'll "haze" the plastic laminate and you'll have worse problems than just the scratches. Another problem is thinning out the glass and surrounding area to the point that it looses it's structural rigidity. Go too thin and hitting a bug at high speed will break the glass in that area. One final thing to think about is distortion. When you start taking a lot of glass off there you'll more than likely have distorted view through that spot......... think circus mirrors (made by using thick and thin glass in front of a silver nitrate backing) The actual glass thickness is what's manipulated to cause the distorted view in them.