In a large bowl, cream together the butter, oil, confectioners' sugar, and 1 cup white sugar until light and fluffy. Beat in eggs one at a time, and stir in the vanilla. Combine the flour, baking soda, and cream of tartar; stir into the creamed mixture. Roll dough into 1 inch balls, and then roll the balls in remaining white sugar. Place onto ungreased cookie sheets, and flatten with a fork.
Bake for 8 to 10 minutes in the preheated oven, or until the edges begin to brown. Cool on wire racks.