In a large bowl, combine the sugars, flour, cinnamon, nutmeg and salt.
Toss the apple slices with the sugar mixture and fill the pie crust.
Dot with butter.
Cover with top crust, seal edges, and cut away excess dough. Make several small slits in the top to allow steam to escape.
Bake 15 minutes in the preheated oven. Reduce the temperature to 350 degrees F (175 degrees C). Continue baking for 35 to 45 minutes, until apples are soft.