The best way to eliminate the battery from consideration is to test the cells with a hydrometer to check the specific gravity of each cell.

http://buy1.snapon.com/catalog/item.asp?P65=&tool=all&item_ID=11359&group_ID=1497&store=snapon-store&dir=catalog

I'm not saying you have to purchase that particular one, but a float-type hydrometer is best, in my experience.

If all cells are a) indicating fully charged and b) very close in specific gravity to each other's readings, then the alternator is over-charging. To get the level of action you're describing, I'd reckon that the voltage being fed to the battery is definately over 15 volts. If the over-charging has boiled off the electrolyte from the battery, then the battery is going to be a goner Real Soon Now, unless that electrolyte gets replaced.