Cream butter, confectioners sugar, and vanilla. Beat in egg. Sift together flour, soda, cream of tartar, and salt; gradually stir into creamed mixture. Mix well. Shape dough into roll 2 inches in diameter and 12 inches long. Wrap in waxed paper. Chill several hours or overnight. Cut into slices 1/4-inch thick. Place on ungreased cookie sheet. Decorate tops with gumdrop slices. Bake in a 375 degree oven about 12 minutes or until lightly browned. Cool slightly before removing from pan.