Oil a large baking sheet. Bring the water to a boil in a saucepan. Add the sugar and cream of tartar and stir over moderate heat until the sugar is dissolved. Wipe the side of the pan down with a wet pastry brush. Stir in the corn syrup and cook over moderately high heat until the syrup is a light honey color and reaches 350° on a candy thermometer. Stir in the peanuts, butter and salt. Off the heat, stir in the baking soda. Immediately spread the mixture on the baking sheet with a wooden spoon. Let cool completely, then break into pieces. Store in an airtight container for up to 1 week.