Pare and core the apples. Cover with the water and three tablespoons of sugar; simmer until tender. Remove from the syrup and drain. Wash the parings and let simmer with a little water for one-half hour. Beat the white of the egg to a stiff froth and add one tablespoon of sugar. Coat the top of the apples lightly with the meringue and place in a cool oven to dry. Strain the juice from the parings, add two tablespoons of sugar, return to the fire and let boil for five minutes; add a few drops of lemon juice and a little nutmeg, cool and pour around the apples.