Pour grits into boiling salted water in a heavy pan. Stir constantly until thick and perfectly smooth. Add butter, stir and remove from stove. Add cheese, cayenne and egg yolks. Cool a bit. Beat egg whites until stiff but not dry. Fold into grit mixture, leaving large pieces of egg white showing. Pour into 1 1/2 quart buttered casserole. Bake 375ºF. for 40 to 50 minutes until top is golden brown and firm in middle.