Preheat oven to 350°F. Peel and slice the sweet potatoes into 1/4 inch thick rounds. Boil in water until just soft. Drain. Core, peel, and slice apples into rings. Arrange alternate layers of sweet potatoes and apples in a greased baking dish. Mix the brown sugar, cinnamon, and nutmeg together and sprinkle over the sweet potatoes and apples. Dot with butter. Cover and bake for 30 minutes.