Beat butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Add eggs, 1 at a time, beating until blended after each addition.
Combine flour, baking soda, and mace; add to butter mixture, beating until blended.
Divide dough into 8 portions; divide each portion into 12 pieces. Roll each piece into a 3-inch log, and gently press ends together to form a circle.
Place 1/3 cup sugar in a saucer. Gently press 1 side of cookies in sugar, and place, sugared side up, on greased baking sheets; flatten cookies slightly.
Bake at 350° for 10 to 12 minutes or until cookies are lightly browned. Transfer to wire racks to cool.