In a saucepan, over medium heat, combine the sugar, corn syrup, salt and water. Cook, stirring, until sugar is dissolved. Cook, without stirring, until the mixture reaches the hard ball stage, ( 250 to 260 degrees F) **This is when a small amount of the mixture dropped in cold water forms a hard ball. In the bowl of an electric mixer, fitted with a whip attachment, whip egg whites until stiff, but not dry. While the machine is running and in a steady stream, add 1/4 of the syrup to the egg whites, and continue whipping until mixture holds its shape. Place the syrup back over the heat and cook until the hard crack stage is reached, 300 degrees F. **This is when the mixture separates into hard and brittle threads when dropped in cold water. With the machine running and in a steady stream, add the remaining syrup to the egg white mixture and continue whipping until the mixture holds is shape. Add the butter, a tablespoon at a time and whip until very thick and satiny. Fold in the almonds and cherries. Press into a buttered 8 by 8 by 2-inch pan, smoothing top. Let stand until firm. Turn out of pan, and cut in 1 1/2 by 1-inch pieces. Wrap each piece individually in waxed paper.