Dip the rim of tall glasses into the egg whites, and then the sugar. Put the rum, Triple Sec, and juices into a cocktail shaker. Shake to mix. Fill the glasses with the ice and pour the cocktail over it. Decorate with cherries, pineapple, and/or orange slices, and drink with a straw.
Contains Raw Eggs: The Food Network Kitchen suggest caution in consuming raw and lightly cooked eggs due to the slight risk of salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly refrigerated, clean grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell. For recipes that call for eggs that are raw or undercooked when the dish is served, use shell eggs that have been treated to destroy salmonella, by pasteurization or another approved method.