Preheat the oven to 375 degrees F. Make the cake: in a large mixing bowl, whip the egg whites until white and foamy. Add the cream of tartar and salt and continue whipping until soft, droopy peaks form. Still whipping, add 1 cup of the sugar in a thin stream and whip until stiff and glossy. With a sifter, sift the remaining 1/2 cup sugar and cake flour together 3 times to aerate and lighten the mixture. (Or sift through a strainer onto a sheet of waxed paper.) Fold into the egg whites 1/3 at a time. Fold in the vanilla and the tangerine rind. Gently spoon the mixture into an ungreased tube pan and bake 30 to 35 minutes, until golden brown. Turn the pan upside down and hang it around the neck of a wine bottle to cool to room temperature. Slide a butter knife around the sides of the pan and put a serving plate on top. Turn over and knock the cake out onto the plate. ( The browned crust of the cake will stick to the pan). When the cake has cooled thoroughly, make the glaze: Whisk together the tangerine juice and egg whites, then add the powdered sugar and stir until smooth. Drizzle the glaze evenly over the cake. Let set in a cool place. Garnish with the tangerine slices.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.