gary, in the motorcycle world we deal with this all the time for face shields and windshields. you need to know if it's a poly or an acrylic shield and use the product that's right for it. if your compass and mine are the same, it's a polycarbonate cover, and i'd use a plastic polish, with maybe a little chrome polish and/or some crest-type toothpaste mixed in, depending on the 'cut' you get. use the least abrasive first, then move to the next until you get the cloudiness out, use a little water in the mix also. after you've got the bulk cleaned and are looking at some finer scratches, start using the 'lesser' cutting paste until you get the scratches out. then you're done.
remember though that it's your elbow grease that really does the work as it's what generates the heat needed for polishing. the 'grit' of the polish helps, but it can't do it alone. you can probably google motorcycle windshield scratch removal or something similar to find the process listed in more detail.
it's really not rocket science and can be a bit of fun with a small enough chore.
jack b
