Because cerium oxide is remarkably insoluble in water and in dilute acid. It is commonly used as an abrasive; the powder is used in the grinding/polishing of glass, gems, marble.

 1.Clean the area you're going to work on thoroughly. Be sure there is no dirt or grime on the glass, as this may result in additional scratches once you start buffing.
2.Have two small plastic tubs ready; small containers work well. Fill one halfway with water.
3.Place your polishing wheel into the water; let it become thoroughly damp, but not dripping wet.
4.Put some of Cerium Oxide into the empty tub, and add enough water to create a slurry (a thin, paste-like mixture).
5.Attach the dampened polishing wheel to your electric drill and dip it into the slurry.
6.Place the polishing wheel on your work area, use small size felt wheel if scratch is near corner of windows ; keep the wheel moving in an up and down and circular motion. Be sure that the slurry does not dry up, as this could cause your glass to overheat and crack. If your slurry is becoming dry, you can spritz it with a spray bottle full of water.

For bigger sratches

1. Place a  pad with 100-140 grit polishing compound. You will buff the glass in circular motions, overlapping each circle you have made. Add more compound as the other areas dry. You need to set your speed between 1000-5000 rpm
2.Every couple minutes, stop buffing and place it in glass of water and remove excess compound.
3. Clean the glass surface with warm water and a cotton towel
4. Change the buffing pad to 270-300 grit compound. Using a speed between 1000-5000 rpm, this is last step of grinding down the glass
5.Change your buffing pad and apply 300-400 grit diamond glass polishing compound and remove scratches left on the glass. Use a speed between 1000-5000 rpm. You buff the glass until you see no more scratches
6. Change your buffing pad. Apply cerium oxide compound to your buffing pad and repeat step one. Buff the surface until you are happy with the clarity on the window.