Mix sugar, cream of tartar, and water in a saucepan. Boil slowly, without stirring, until mixture spins a 6-inch to 8-inch thread when a little is dropped from a spoon held over the saucepan. Keep the pan covered for the first 3 minutes to prevent crystals from forming on the sides of the pan. While syrup is cooking, beat egg whites until stiff enough to hold a peak. Pour the hot syrup very slowly in a thin stream into the egg whites, beating constantly. Add vanilla and continue beating until mixture is fluffy and will hold its shape.