Combine the sugar, water, cream of tartar, and salt in a saucepan and set over high heat, gently swirling to mix the ingredients. Let boil, swirling occasionally, until mixture is perfectly clear, about 4 or 5 minutes. Clap the lid on the pan and let cook for 1 minute. Uncover and attach a candy thermometer, not letting the tip touch the bottom of the pan. Let the syrup boil, uncovered over high heat until it reaches 240'F. Meanwhile start beating the egg whites in a large bowl to stiff but moist peaks.
When the syrup is ready, continue beating at moderately high speed, and with your other hand pour the syrup on in a thin, steady stream. Continue beating for 2 or 3 minutes more until the frosting has cooled a little and is stiff enough to stand in tall peaks. Beat in the vanilla. You use this generously and will have enough to fill and frost two 8-inch layer cakes or a 10-inch tube cake.
Lemon Mountain Frosting.
Decrease the water to 1/3 cup and add 2 tablespoons lemon juice and 1 tablespoon grated lemon rind to the syrup before cooking it.