In a small bowl, combine the sugars, flour and spices; set aside. In a large bowl, toss apples with lemon juice. Add sugar mixture; toss to coat.
Line a 9-in. pie plate with bottom crust; trim pastry even with edge. Fill with apple mixture; dot with butter. Roll out remaining pastry to fit top of pie. Place over filling. Trim, seal and flute edges. Cut slits in pastry.
Beat egg white until foamy; brush over pastry. Sprinkle with sugar. Cover edges loosely with foil.
Bake at 375° for 25 minutes. Remove foil and bake 20-25 minutes longer or until crust is golden brown and filling is bubbly. Cool on a wire rack.Yield: 8 servings.