Greenhouse Visitors

This morning during my daily tour of inspection, I discovered a swallowtail butterfly on the geraniums. Luck was with me, for I had my camera, and was able get this picture. He (or she?) was almost upside down, so this shot is of the underbelly. Obviously she had no experience as a model, or maybe she was camera shy.

Does anyone know exactly what type of swallowtail this is? I got out our butterfly book and tried to identify it, but failed miserably.