In a large bowl, cream butter and 1 cup sugar until light and fluffy. Beat in egg and vanilla. Combine the flour, baking soda and cream of tartar; gradually add to the creamed mixture and mix well. In a small bowl, combine cinnamon and remaining sugar. Shape dough into 1-inch balls; roll in cinnamon-sugar. Place 2 inches apart on ungreased baking sheets. Bake at 375° for 10-12 minutes or until lightly browned. Remove to wire racks to cool. Yield: 2 1/2 dozen.